In observational studies with time-to-event outcomes subject to
competing risks, the g-formula can be used to estimate a treatment
effect in the presence of confounding factors. The construction of valid
pointwise confidence intervals and time-simultaneous confidence bands
for the causal risk difference, however, is complicated. A convenient
solution is to approximate the asymptotic distribution of the
corresponding stochastic process by means of resampling
approaches.
In this talk, we consider three different resampling
methods, namely the classical nonparametric bootstrap, the influence
function equipped with a resampling approach as well as a
martingale-based bootstrap version, the so-called wild bootstrap. We
compare these approaches with regard to asymptotic properties and based
on simulation studies and demonstrate their usage in a data example.
Causal inference methods have become critical across diverse domains,
such as healthcare, public health, and social sciences, enabling the
dissection of complex systems and guiding pivotal decisions. The recent
integration of machine learning and advanced statistical techniques has
enhanced the power of causal inference, but many of these methods rely
on complex, black-box models. While effective, these models can obscure
the underlying mechanisms of their estimates, raising concerns about
credibility, especially in contexts where lives or significant resources
are at stake. To mitigate these risks, ensuring interpretability in
causal estimation is paramount. n this presentation, I introduce our
interpretable approach to addressing a fundamental challenge in
randomized controlled trials (RCTs): generalizing results to target
populations when certain subgroups are underrepresented. RCTs are
essential for understanding causal effects, but effect heterogeneity and
underrepresentation often limit their generalizability. Our work
proposes a novel framework to identify and characterize these
underrepresented subgroups, refining target populations for improved
inference. Specifically, we present the Rashomon Set of Optimal Trees
(ROOT), an optimization-based method that minimizes the variance of
treatment effect estimates to ensure more precise and interpretable
results. We apply ROOT to the Starting Treatment with Agonist
Replacement Therapies (START) trial, extending inferences to the broader
population represented by the Treatment Episode Dataset: Admissions
(TEDS-A). This method enhances decision-making accuracy and improves
communication of treatment effects, offering a systematic approach for
future trials and applications in healthcare. Our findings demonstrate
that improving the interpretability of causal inference can advance
precision and applicability in real-world scenarios.
NOTE: This
will be a zoom meeting: https://ucph-ku.zoom.us/j/8274562019?pwd=ZEJuZkZUY05WNE02YzNWUGhONWoyUT09
Renal replacement therapy (RRT) is a treatment commonly used for
managing critically ill patients with severe acute kidney injury (AKI),
particularly those experiencing metabolic or fluid-related
complications. RRT may rapidly correct some of the life-threatening
issues associated with AKI, such as fluid overload. However, it is a
very invasive treatment and may therefore be harmful to some patients.
The timing of RRT initiation in critically ill patients with AKI remains
a long-standing dilemma for nephrologists. Multiple randomized trials
have attempted to address this question, but they compare only a limited
number of treatment initiation strategies. In light of this, we use
routinely collected observational data from the Ghent University
Hospital intensive care units to investigate treatment strategies for
starting RRT in critically ill AKI patients. We develop a methodology
for identifying the optimal treatment initiation strategy from several
pre-specified options in the presence of competing risks. We then apply
it to evaluate a total of 81 RRT initiation strategies, expressed in
terms of serum potassium, pH, and urine output, allowing us to identify
the optimal thresholds for these criteria. Furthermore, we develop a
unified framework of weighted Neyman-orthogonal learners for estimating
heterogeneous treatment effects to support clinical decision-making
regarding treatment initiation.
NOTE: This will be a zoom
meeting: https://ucph-ku.zoom.us/j/8274562019?pwd=ZEJuZkZUY05WNE02YzNWUGhONWoyUT09
We propose Deep Longitudinal Targeted Minimum Loss-based Estimation (Deep LTMLE), a novel approach to estimate the mean of counterfactual outcome under dynamic treatment policies in longitudinal problem settings. Our approach utilizes a transformer architecture with heterogeneous type embedding trained using temporal-difference learning. After obtaining an initial estimate using the transformer, following the targeted minimum loss-based likelihood estimation (TMLE) framework, we statistically corrected for the bias commonly associated with machine learning algorithms. Furthermore, our method also facilitates statistical inference by enabling the provision of 95% confidence intervals grounded in asymptotic statistical theory. Simulation results demonstrate our method’s competitive performance with existing approaches for simple settings and superior computational performance, particularly in complex, long time-horizon scenarios. It remains effective in small-sample, short-duration contexts, matching the performance of asymptotically efficient estimators. To demonstrate our method in practice, we applied our method to estimate counterfactual mean outcomes for standard versus intensive blood pressure management strategies in a real-world cardiovascular epidemiology cohort study. I will also present the continuous-time extension of the Deep LTMLE.
Titman and Putter (TP) (2022) proposed the log rank test of the Markov property in multi-state models for event history analysis. Rodriguez-Girondo and Una-Alvarez (2012) developed the test of the Markov property in an illness-death model based on Kendall’s coefficient of concordance (Kendall’s tau). Both papers allowed for right censored observations in their models. However, there has been no work reported in literature on the test of Markov property for interval censored multi-state models. I develop the test of Markov property in a three-state progressive model when all transition times are interval-censored. Such model is called doubly censored and arises when patients are observed intermittently for the progression of a disease. The test is based on extended Kendall’s tau. The developed test is illustrated with Aids data. I also adapt TP’s log-rank test to an interval-censored three-state progressive model through the procedure described in the paper - this is work in progress. Since most of multi-state models considered in the literature are assumed to be Markov, it is important to test Markov assumption as there are alternatives to this assumption, such as independence of durations in states and semi-Markov model, that may lead to different conclusions about the modeling problem at hand.
Accelerated failure time (AFT) models are frequently used for modelling survival data. It is an appealing approach as it asserts a direct relationship between the time to event and covariates, wherein the failure times are either accelerated or decelerated by a multiplicative factor in the presence of these covariates. Several methods exist in the current literature for fitting semiparametric AFT models with time-fixed covariates. However, most of these methods do not easily extend to settings involving both time-varying covariates and partly interval censored data. We propose a maximum penalized likelihood approach to fit a semiparametric AFT model with both time-fixed and time-varying covariates, for survival data with partly interval censored failure times.
Lucia de Berk, a Dutch nurse, was arrested in 2001, and tried and
convicted of serial murder of patients in her care. At a lower court the
only hard evidence against her was the result of a probability
calculation: the chance that she was present at so many suspicious
deaths and collapses in the hospitals where she had worked was 1 in 342
million. During appeal proceedings at a higher court, the prosecution
shifted gears and gave the impression that there was now hard evidence
that she had killed one baby. Having established that she was a killer
and a liar (she claimed innocence) it was not difficult to pin another 9
deaths and collapses on her. No statistics were needed any more. In 2005
the conviction was confirmed by the supreme court. But at the same time,
some whistleblowers started getting attention from the media. A long
fight for the hearts and minds of the public, and a long fight to have
the case reopened (without any new evidence - only new scientific
interpretation of existing evidence) began and ended in 2010 with
Lucia’s complete exoneration. A number of statisticians played a big
role in that fight. The idea that the conviction was purely based on
objective scientific evidence was actually an illusion. This needed to
be explained to journalists and to the public. And the judiciary needed
to be convinced that something had to be done about it.
Lucy
Letby, an English nurse, was arrested in 2020 for murder of a large
number of babies at a hospital in Chester, UK, in Jan 2015-June 2016.
Her trial started in 2022 and took 10 months. She was convicted and
given a whole life sentence in 2023.
In my opinion, the
similarities between the two cases are horrific. Again there is
statistical evidence: a cluster of unexplained bad events, and Lucy was
there every time; there is apparently irrefutable scientific evidence
for two babies; and just like with Lucia de Berk, there are some weird
personal and private writings which can be construed as a confession.
For many reasons, the chances of a fair retrial for Lucy Letby are very
thin indeed, but I am convinced she is innocent and that her trial was
grossly unfair. I will try to convince you, too.
I predict that
it will take between 6 and 12 years before she is exonerated.
Understanding the causal relationships between demographic information
and biomarkers can be extremely useful to get a better understanding of
causal risk factors in healthcare. It can motivate future studies to
search for an intervention that lowers the risk or for possible
treatment alternatives that can improve quality of life expectations.
Using random controlled trials (RCTs), we can try to infer specific
causal relationships. However, it is not always possible to directly
intervene on (proxy) variables due to ethical reasons, or it is just
impossible in practice. Causal discovery algorithms try to address this
problem by searching for the causal structure between variables in an
observational data set instead of using interventions on the
variables.Nonetheless, in medical journals, the currently used methods
to analyze data are usually not based on causal discovery methods due to
the assumptions made which are difficult to test for, and the
non-intuitive definitions that are required for this field. In this
research, we aim to show how to handle these using a specific case study
that exhibits many of these challenges.
This study is motivated
by a data set containing subjects who had aortic surgery at the
St. Antonius Hospital in Nieuwegein. We use this data set to demonstrate
what important steps are needed for the analysis. Challenges of this
aortic surgery data set are (1) small sample size, (2) consisting of a
complex combination of very different variables, both discrete and
continuous, (3) unknown causal structure (there might be unknown
confounders in the causal structure), (4) context variables and
time-dependent variables (variables from the different phases in the
perioperative period), and (5) missing values. We suggest how to combine
the outputs of a causal discovery method with bootstrapping to make it
more robust for small data sets, how to deal with context variables, and
how to deal with mixed data.
Graphs are often used as representations of conditional independence
structures of random vectors. In stochastic processes, one may use
graphs to represent so-called local independence. Local independence is
an asymmetric notion of independence which describes how a system of
stochastic processes (e.g., point processes or diffusions) evolves over
time. Let A, B, and C be three subsets of the coordinate processes of
the stochastic system. Intuitively speaking, B is locally independent of
A given C if at every point in time knowing the past of both A and C is
not more informative about the present of B than knowing the past of C
only. Directed graphs can be used to describe the local independence
structure of the stochastic processes using a separation criterion which
is analogous to d-separation. In such a local independence graph, each
node represents an entire coordinate process rather than a single random
variable.
In this talk, we will describe various properties of
graphical models of local independence and then turn our attention to
the case where the system is only partially observed, i.e., some
coordinate processes are unobserved. In this case, one can use so-called
directed mixed graphs to describe the local independence structure of
the observed coordinate processes. Several directed mixed graphs may
describe the same local independence model, and therefore it is of
interest to characterize such equivalence classes of directed mixed
graphs. It turns out that directed mixed graphs satisfy a certain
maximality property which allows one to construct a simple graphical
representation of an entire Markov equivalence class of marginalized
local independence graphs. This is convenient as the equivalence class
can be learned from data and its graphical representation concisely
describes what underlying structure could have generated the observed
local independencies.
Deciding Markov equivalence of two directed
mixed graphs is computationally hard, and we introduce a class of
equivalence relations that are weaker than Markov equivalence, i.e.,
lead to larger equivalence classes. The weak equivalence classes enjoy
many of the same properties as the Markov equivalence classes, and they
provide a computationally feasible framework while retaining a clear
interpretation. We discuss how this can be used for graphical modeling
and causal structure learning based on local independence.
Effective management of emerging and existing epidemics requires strategic decisions on where, when, and to whom interventions should be applied. However, personalized decision-making in infectious disease applications introduces new and unique statistical challenges. For instance, the individuals at risk of infection are unknown, the true outcome of interest (positive infection status) is often a latent variable, and the presence of complex dependence reduces data to a single observation. In this work, we investigate an adaptive sequential design under latent outcome structures and unspecified dependence through space and time. The statistical problem is addressed within a nonparametric model that respects the unknown dependence structure. I will begin by formalizing a treatment allocation strategy that utilizes up-to-date data to inform who is at risk of infection in real-time, with favorable theoretical properties. The optimal allocation strategy, or optimal policy, maximizes the mean latent outcome under a resource constraint. The proposed estimator learns the optimal policy over time and exploits the double-robust structure of the efficient influence function of the target parameters of interest. In the second part of the talk, I will present the study of data-adaptive inference on the mean under the optimal policy, where the target parameter adapts over time in response to the observed data (state of the epidemic). Lastly, I present a novel paradigm in nonparametric efficient estimation particularly suited for target parameters with complex dependence.
Randomized trials are one of the best ways to establish causal effects without making strong untestable assumptions. Although randomization can ensure that the apparent causal effect is not due a confounding factor that affects both the treatment choice and the response, the interpretation of the causal estimand is sometimes not straightforward. To avoid some common misinterpretations of causal estimands from randomized trials, I discuss two overlapping classes of estimands: individual-level and population-level causal estimands. The individual-level causal estimand first compares potential outcomes on each of the two treatment arms within an individual, then summarizes those comparisons across a population. In contrast, the population-level causal estimand first summarizes the marginal distribution of each of the two potential outcomes, then compares the two summaries. Difference-in-means estimands are members of both classes, but some other common estimands (e.g., the Mann-Whitney parameter or the hazard ratio) are only population-level estimands and are often causally misinterpreted as individual-level estimands. I discuss these issues using a placebo-controlled randomized vaccine trial as an example.
Hazards condition on previous survival, which makes them both identifiable based on censored data and the inferential key quantities of survival analysis. It also makes them subject to critique from a causal point of view. The worry is that after randomization of the intention to treat a more beneficial treatment will help sicker patients to survive longer, rendering treatment intention and markers of sickness dependent after time origin. Called ‘collider bias’, this is interpreted as breaking randomization and therefore complicating detection of a causal treatment effect. The strange part of this argument is that the situation at later times is explained as a causal consequence of treatment. I will try to review this dilemma - identifiability vs. causal concerns - and argue that there is a causal effect of today’s intention to treat on the future hazard function, if interpreted in a functional way. I will also argue that things are the way they should be and ‘collider bias’ really ‘collider effect’, that the latter has little to do with time-to-event, and that piecewise constant hazard ratios carry information on how treatment works. My impression is that the debate is a bit pointed, but that there is general agreement that analyses of hazards - where the causal effect is hidden or perhaps obvious - should routinely be translated onto the probability scale. My worry is that these subtleties are lost in translation and I will illustrate matters with a (typical?) example from benefit-risk assessment in Germany, where a company managed to both claim a better and a worse safety profile of their drug, while only partially acknowledging the need to account for censoring. Time permitting, I will also discuss a multistate approach to g-computation motivated by a phase 3 trial of non-small-cell lung cancer patients where the experimental treatment was put on’(‘clinical’) hold by the FDA for some months shortly before recruitment was completed. The aim of the analysis is to estimate the survival distributions (sic) in the hypothetical scenario where the put-on-hold hazard is equated with zero (sic). The difficulty is that time-to-clinical-hold and time-to-death are not independent.
Causal discovery methods aim to estimate a (causal) graph from data.
These methods have well-known issues: The output in form of an estimated
equivalence class (represented by a so-called CPDAG) can be sensitive to
statistical errors and is often not very informative. Including
background knowledge, if correct, can only improve (and never harm) the
result of causal discovery. This talk will focus on temporal background
knowledge as would be available in longitudinal or cohort studies, but
the results presented here are valid for any kind of data that has a
tiered ordering of the variables. This type of background knowledge is
reliable, straightforward to incorporate, and the resulting estimated
graphs have desirable properties.
First, I will describe how to
incorporate temporal background knowledge in a causal discovery
algorithm, and provide a practical example of how it can be applied to
cohort data. This algorithm outputs restricted equivalence classes
(represented by so-called tiered MPDAGs) that are more informative, and
more robust to statistical errors compared to CPDAGs.
Second, I
will show how tiered MPDAGs can be characterised as distinct from MPDAGs
based on other types of background knowledge, and how this allows us to
determine exactly when temporal knowledge adds new information, and when
it is redundant. Finally, I will show that this class of graphs inherits
key properties of CPDAGs so that they retain the usual interpretation as
well as computational efficiency.
Two important areas in biostatistics are causal inference and statistical methods in diagnostic medicine. In this talk, I give an overview on my research interests in these two areas. Particularly, I discuss some new developments in the statistical methodology for making causal inference, and discuss some future research directions. In addition, I give an overview on some new developments in statistical methods in evaluation of the accuracy of medical devices.
This talk is about the situation where we (in principle) have a
d‐dimensional parameter estimate of interest and the d x d dimensional
(co‐)variance of it and make inference from that. Often, we test a null
hypothesis H0: that the parameter of interest is 0, versus the
alternative H1: that the parameter can be anywhere in the d-dimensional
parameter space.
The testing mindset has many unfortunate
behavioural side effects on what is reported and how in the scientific
literature. Furthermore, traditional significance testing, i.e., using p
values, does not suffice to compare the evidence in favour of H0 and H1,
respectively, as it only makes assumptions about H0. In practise, it is
therefore biased in the direction of favouring H1. Bayesian methodology
takes H1 into consideration, but often in a way that is either
subjective (contradicting scientific ideals) or objective by way of
assuming very little information in the prior, which by itself is
untrustworthy and often clearly favours H0.
Here we develop an
approximation of the so‐called Bayes factor (BF) applicable in the above
setting; BF is the Bayesian equivalent of a likelihood ratio. By design
the approximation is monotone in the p value. It it thus a tool to
transform p values into evidence (probabilities of H0 and H1,
respectively). This BF depends on a parameter that expresses the ratio
of information contained in the likelihood and the prior. We give
suggestions for choosing this parameter. The standard version of our BF
corresponds to a continuous version of the Akaike information criterion
for model (hypothesis) selection.
Posterior odds of H1 and H0,
i.e., Pr(H1|X)/Pr(H0|X) (and hence probabilities and evidence for each),
are obtained by multiplying BF with prior (pre-data) odds of H1 and H0,
i.e., Pr(H1)/Pr(H0). We suggest that for scientific reporting and
discussion prior odds should be set to 1; the reader can modify prior
odds to fit their own a priori beliefs and obtain the corresponding
posterior inferences. BF=1 represents equiprobability of the hypothesis,
H0 and H1. BF is thus centered at the right value, for the purpose of
making immediate judgments about which hypothesis is the more likely and
how strong the evidence is for that based only on the likelihood
function.
Replacing p-values (and implicit tests by confidence
intervals) by BFs should allow for shorter, more informative, and less
biased reporting of many scientific studies.
We exemplify the
calculations and interpretations and illustrate the flexibility of our
approach based on a real-world epidemiologic example where we a priori
believe H0 to be a good approximation of physical reality. H0 is that an
8-dimensional predictor has exactly the same non-trivial effect
(measured by a hazard ratio) on two distinct disease
outcomes.
Finally, we compare these new BF-based inferences with
those based on p values. Although there is a bijection between BF and p
for fixed d it is non-trivial – so you need to calculate BF. Generally,
BF-based inference is more in favour of H0 than p-value inference, i.e.,
less biased in favour of the alternative, H1. The BF is easy to
calculate (only requires d and p or a test statistic), flexible and
objective. It is a Bayesian solution to the Fisherian project of making
statistical inference based exclusively on the likelihood function.
We propose a new Bayesian non-parametric (BNP) method for estimating the causal effects of mediation in the presence of a post-treatment confounder. We specify an enriched Dirichlet process mixture (EDPM) to model the joint distribution of the observed data (outcome, mediator, post-treatment confounder, treatment, and baseline confounders). For identifiability, we use the extended version of the standard sequential ignorability as introduced in Hong et al. (2022, Biometrics). The observed data model and causal identification assumptions enable us to estimate and identify the causal effects of mediation, i.e., the natural direct effects (NDE), and indirect effects (NIE). Our method enables easy computation of NDE and NIE for a subset of confounding variables and addresses missing data through data augmentation under the assumption of ignorable missingness. We conduct simulation studies to assess the performance of our proposed method. Furthermore, we apply this approach to evaluate the causal mediation effect in the Rural LITE trial, demonstrating its practical utility in real-world scenarios.
Aalen–Johansen estimation targets transition probabilities in multi-state Markov models subject to right-censoring. In particular, it belongs to the standard toolkit of statisticians specializing in health and disability. We introduce for the first time the conditional Aalen-Johansen estimator, a kernel-based estimator that allows for the inclusion of covariates and, importantly, is also applicable in non-Markov models. We establish uniform strong consistency and asymptotic normality under lax regularity conditions; here, the theory of empirical processes plays a central role and leads to a transparent treatment. We also illustrate the practical implications and strength of the estimation methodology.
This talk is about local inference in functional data analysis: that is, assessing which part of a domain that is ‘significant’ in terms of a given (pointwise) null hypothesis. Due to the continuous domain, this is an extreme case of the multiple testing problem. A popular approach is the interval-wise testing procedure. We extend this to a general setting where the domain is a Riemannian manifold. This requires new methodology such as how to define adjustment sets on product manifolds and how to handle non-zero curvature. We present data and simulation examples and also relate to another recent local inference procedure
Choosing the most important variables in supervised and unsupervised learning is a difficult task, especially when dealing with high-dimensional data where the number of variables far exceeds the number of observations. In this study, we focus on two popular multivariate statistical methods - principal component analysis (PCA) and partial least squares (PLS) - both of which are linear dimensionality reduction techniques used in a variety of fields such as genomics, biology, environmental science, and engineering. Both PCA and PLS generate new variables, known as principal components, that are combinations of the original variables. However, interpreting these components can be challenging when working with large numbers of variables. To address this issue, we propose a method that incorporates the best subset selection approach into the PCA and PLS frameworks using a continuous optimization algorithm. Our empirical results demonstrate the effectiveness of our method in identifying the most relevant variables. We illustrate the use of our algorithm on two real datasets - one analyzed using PCA and the other using PLS.
In many modern data applications there is a need for an objective framework for the analysis of data that can be represented as shapes (or curves or functions, etc.). While standard analytic techniques could be applied to scalar-valued summary measures of such objects, a more objective approach would involve comparing the data objects in shape space (curve space, function space, etc.). This would require the determination of a measure of ‘distance’ between objects, ideally one that respects the topology of the space. Once such metric has been established, many traditional statistical modeling techniques can be applied to such data. This talk will describe some potential metrics for closed curves and propose some corresponding adaptations of statistical inference procedures. The analysis will be applied to data from an experiment in animal cell biology, in which exercise regimen is thought to have an effect on mitochondrial morphology.
Using analysis of covariance to improve the efficiency of clinical
trials has a long tradition within drug development and is explicitly
recognised as being a valuable thing to do by regulatory guidelines.
Nevertheless it continues to attract criticism and it also raises
various issues. In this talk I shall look at some of them in
particular.
1. What the difference is between stratification and
analysis of covariance.
2. How this relates to type I and type II
sums of squares.
3. Whether propensity score adjustment is a valid
alternative to analysis of covariance.
4. What problems arise in
connection with hierarchical data.
5. What the Rothamsted approach
teaches us and its relevance to Lord’s paradox.
6. What changes when
we move from common two parameter models, such as the Normal model, to
single parameter models such as the Poisson distribution.
7. Whether
marginal or conditional estimates are generally to be preferred or of
there is a role for both.
8. What care must be taken when considering
covariate by treatment interaction.
I shall conclude that using
covariates wisely does require care but it is valuable and that despite
the general regulatory approval, underused and that it would make a much
bigger contribution to design efficiency than the currently fashionable
topic of flexible designs.
Twenty years ago, the late Leo Breiman sent a wake-up call to the
statistical community, thereby criticizing the dominant use of
data models’ (Breiman, 2001). In this talk, I will revisit his critiques in light of the developments on algorithmic modeling, debiased machine learning and targeted learning that have taken place over the past 2 decades, largely within the causal inference literature (Vansteelandt, 2021). I will argue that these developments resolve Breiman's critiques, but are not ready for mainstream use by researchers without in-depth training in causal inference. They focus almost exclusively on evaluating the effects of dichotomous exposures; when even slightly more complex settings are envisaged, then this restrictive focus encourages poor practice (such as dichotomization of a continuous exposure) or makes users revert to the traditional modeling culture. Moreover, while there is enormous value in the ability to quantify the effects of specific interventions, this focus is also artificial in the many scientific studies where no specific interventions are targeted.<br><br>I will accommodate these concerns via a general conceptual framework on assumption-lean regression, which I recently introduced in a discussion paper that was read before the Royal Statistical Society (Vansteelandt and Dukes, 2022). This framework builds heavily on the debiased / targeted machine learning literature, but intends to be as broadly useful as standard regression methods, while continuing to resolve Breiman's concerns and other typical concerns about regression.<br><br>A large part of this talk will be conceptual and is aimed to be widely accessible; parts of the talk will demonstrate in more detail how assumption-lean regression works in the context of generalised linear models and Cox proportional hazard models (Vansteelandt et al., 2022).<br><br>References:<br>Breiman, L. (2001). Statistical modeling: The two cultures (with comments and a rejoinder by the author). Statistical science, 16(3), 199-231.<br>Vansteelandt, S. (2021). Statistical Modelling in the Age of Data Science. Observational Studies, 7(1), 217-228.<br>Vansteelandt, S and Dukes, O. (2022) Assumption-lean inference for generalised linear model parameters (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 84(3), 657– 685. <br>Vansteelandt, S., Dukes, O., Van Lancker, K., & Martinussen, T. (2022). Assumption-lean Cox regression. Journal of the American Statistical Association, 1-10.<br></div></p></div><div class="panel-footer"><h4 class="panel-title">Room: 35.3.13 </h4></div></p></div><div class="panel panel-primary"><div class="panel-heading"><h3 class="panel-title"> Monday, September 26, 2022, 15:15 </h3></div><div class="panel-body"><div class="abstract-name"> Andrew Vickers </div><div class="abstract-affiliation"> Memorial Sloan Kettering Cancer Center, Attending Research Methodologist </div><div class="abstract-title"><a class="abstract-title" data-toggle="collapse" href="#abstract23">If calibration, discrimination, Brier, lift gain, precision recall, F1, Youden, AUC, and 27 other accuracy metrics can’t tell you if a prediction model (or diagnostic test, or marker) is of clinical value, what should you use instead?</a><p class="collapse abstract" align = "left" id="abstract23">A typical paper on a prediction model (or diagnostic test or marker) presents some accuracy metrics - say, an AUC of 0.75 and a calibration plot that doesn’t look too bad – and then recommends that the model (or test or marker) can be used in clinical practice. But how high an AUC (or Brier or F1 score) is high enough? What level of miscalibration would be too much? The problem is redoubled when comparing two different models (or tests or markers). What if one prediction model has better discrimination but the other has better calibration? What if one diagnostic test has better sensitivity but worse specificity? Note that it doesn’t help to state a general preference, such as “if we think sensitivity is more important, we should take the test with the higher sensitivity” because this does not allow to evaluate trade-offs (e.g. test A with sensitivity of 80% and specificity of 70% vs. test B with sensitivity of 81% and specificity of 30%). The talk will start by showing a series of everyday examples of prognostic models, demonstrating that it is difficult to tell which is the better model, or whether to use a model at all, on the basis of routinely reported accuracy metrics such as AUC, Brier or calibration. We then give the background to decision curve analysis, a net benefit approach first introduced about 15 years ago, and show how this methodology gives clear answers about whether to use a model (or test or marker) and which is best. Decision curve analysis has been recommended in editorials in many major journals, including JAMA, JCO and the Annals of Internal Medicine, and is very widely used in the medical literature, with well over 1000 empirical uses a year.</div></p></div><div class="panel-footer"><h4 class="panel-title">Room: 5.2.46 (Biostats library) </h4></div></p></div><div class="panel panel-primary"><div class="panel-heading"><h3 class="panel-title"> Tuesday, June 21, 2022, 15:15 </h3></div><div class="panel-body"><div class="abstract-name"> Benoit Liquet-Weiland </div><div class="abstract-affiliation"> School of Mathematics and physical sciences, Macquarie University and Laboratory of Mathematics and their Applications, University of Pau and Pays de l’Adour </div><div class="abstract-title"><a class="abstract-title" data-toggle="collapse" href="#abstract24">Leveraging pleiotropic association using sparse group variable selection</a><p class="collapse abstract" align = "left" id="abstract24">Genome-wide association studies (GWAS) have identified genetic variants associated with multiple complex diseases. We can leverage this phenomenon, known as pleiotropy, to integrate multiple data sources in a joint analysis. Often integrating additional information such as gene pathway knowledge can improve statistical efficiency and biological interpretation. In this talk, we propose frequentist ad Bayesian statistical methods which incorporate both gene pathway and pleiotropy knowledge to increase statistical power and identify important risk variants affecting multiple traits. Our methods are applied to identify potential pleiotropy in an application considering the joint analysis of thyroid and breast cancers.</div></p></div><div class="panel-footer"><h4 class="panel-title">Room: 5.2.46 (Biostats library) </h4></div></p></div><div class="panel panel-primary"><div class="panel-heading"><h3 class="panel-title"> Wednesday, June 08, 2022, 15:15 </h3></div><div class="panel-body"><div class="abstract-name"> Carolin Herrmann </div><div class="abstract-affiliation"> Institute of Biometry and Clinical Epidemiology, Charité – University Medicine Berlin </div><div class="abstract-title"><a class="abstract-title" data-toggle="collapse" href="#abstract25">Sample size adaptations during ongoing clinical trials – possibilities and challenges</a><p class="collapse abstract" align = "left" id="abstract25">One central design aspect of clinical trials is a valid sample size calculation. The sample size needs to be large enough to detect an existing effect with sufficient power and at the same time it needs to be ethically feasible. Sample size calculations are based on the applied test statistic as well as the significance level and desired power. However, it is not always straightforward to determine the underlying parameter values, such as the expected treatment effect size and variance, during the planning stage of a clinical trial.<br><br>Adaptive designs provide the possibility of adapting the sample size during an ongoing trial. At so called interim analyses, nuisance parameters can be re-estimated. Alternatively, unblinded interim analyses may be performed where the treatment effect can be re-estimated and the trial may also be stopped early for efficacy or futility. In this talk, we will focus on unblinded interim analyses and its different possibilities for recalculating the sample size. We discuss their performance evaluation as well as possibilities for improving existing and optimizing sample size recalculation approaches.</div></p></div><div class="panel-footer"><h4 class="panel-title">Room: 5.2.46 (Biostats library) </h4></div></p></div><div class="panel panel-primary"><div class="panel-heading"><h3 class="panel-title"> Monday, May 30, 2022, 15:15 </h3></div><div class="panel-body"><div class="abstract-name"> Robin Evans </div><div class="abstract-affiliation"> Associate Professor, Department of Statistics at the University of Oxford </div><div class="abstract-title"><a class="abstract-title" data-toggle="collapse" href="#abstract26">Parameterizing and Simulating from Causal Models</a><p class="collapse abstract" align = "left" id="abstract26">Many statistical problems in causal inference involve a probability distribution other than the one from which data are actually observed; as an additional complication, the object of interest is often a marginal quantity of this other probability distribution. This creates many practical complications for statistical inference, even where the problem is non-parametrically identified. In particular, it is difficult to perform likelihood-based inference, or even to simulate from the model in a general way.<br><br>We introduce the frugal parameterization, which places the causal effect of interest at its centre, and then build the rest of the model around it. We do this in a way that provides a recipe for constructing a regular, non-redundant parameterization using causal quantities of interest. In the case of discrete variables we can use odds ratios to complete the parameterization, while in the continuous case copulas are the natural choice; other possibilities are also discussed.<br><br>We introduce thefrugal
parameterization’, which places the causal effect of interest at its
centre, and then build the rest of the model around it. We do this in a
way that provides a recipe for constructing a regular, non-redundant
parameterization using causal quantities of interest. In the case of
discrete variables we can use odds ratios to complete the
parameterization, while in the continuous case copulas are the natural
choice; other possibilities are also discussed.
This is joint
work with Vanessa Didelez (University of Bremen and Leibniz Institute
for Prevention Research and Epidemiology).
Over the last few decades, Bayesian methods have gained momentum also within pharmaceutical drug development. During this talk, I will try to dig into this issue. This first covers how the Bayesian philosophy considers probability, parameters and populations. I will give my personal assessment of whether drug development has obtained a completely new paradigm or just an expansion of the statistical toolbox. This also includes a prioritized list of where Bayesian methods can add value compared to standard frequentist methods.
Joint models are well suited to modelling linked data from laboratories and health registers. However, there are few examples of joint models that allow for (a) multiple markers, (b) multiple survival outcomes, (c) delayed entry and (d) scalability. We propose a full likelihood approach for joint models based on a Gaussian variational approximation to satisfy criteria (a)-(d). Our simulations and applications show that the variational approximation is close to the full likelihood, very fast to optimize, and scalable. Our open source implementation is available with support for general joint models and computation in parallel.
CANCELLED - will be postponed
Due to tradition and ease of estimation, the vast majority of clinical and epidemiological papers with time-to-event data report hazard ratios from Cox proportional hazards regression models. Although hazard ratios are well known, they can be difficult to interpret, particularly as causal contrasts, in many settings. Nonparametric or fully parametric estimators allow for the direct estimation of more easily causally interpretable estimands such as the cumulative incidence and restricted mean survival. However, modeling these quantities as functions of covariates is limited to a few categorical covariates with nonparametric estimators, and often requires simulation or numeric integration with parametric estimators. Combining pseudo-observations based on non-parametric estimands with parametric regression on the pseudo-observations allows for the best of these two approaches and has many nice properties. In this talk, I will describe an implementation of these methods in the eventglm R package, focusing on the computational approach, usage from the average data analyst’s perspective, and features for further development and extension.
In this talk I’ll discuss the renewal equation and its use in epidemic modelling. I will briefly discuss how many popular approaches result in a renewal equation, and highlight a few applications where the renewal equation is used. I will then discuss new work we have recently done to rigorously derive how the renewal equation arises from age dependent branching processes. I will then discuss a few interesting (i think) implications of this derivation - including overdispersion and a link to generalised Fibonacci numbers! Paper is under second review currently and available here https://arxiv.org/abs/2107.05579
Outcome-dependent sampling designs are common in many different scientific fields including epidemiology, ecology, and economics. As with all observational studies, such designs often suffer from unmeasured confounding, which generally precludes the nonparametric identification of causal effects. Nonparametric bounds can provide a way to narrow the range of possible values for a nonidentifiable causal effect without making additional untestable assumptions. The nonparametric bounds literature has almost exclusively focused on settings with random sampling, and the bounds have often been derived with a particular linear programming method. We derive novel bounds for the causal risk difference, often referred to as the average treatment effect, in six settings with outcome-dependent sampling and unmeasured confounding for a binary outcome and exposure. Our derivations of the bounds illustrate two approaches that may be applicable in other settings where the bounding problem cannot be directly stated as a system of linear constraints.
In the first part of the talk, we will give a review of how causal
models of event processes and local independence graphs are linked. In
particular, how local independence graphs can represent partially
observed systems and how local independence testing can be used to infer
local independence graphs.
In the second part of the talk, we
will show how to build flexible models of event intensities using a deep
learning framework, specifically Tensorflow. Combined with double
machine learning techniques, this makes nonparametric local independence
testing feasible. However, the Tensorflow implementation may be of
independent interest for other nonparametric modeling purposes.
The Joint Initiative for Causal Inference Webinar Series is a series of presentations on utilizing causal inference and targeted learning methods to answer pressing health questions in the modern methodological and data ecosystem. Targeted learning methods bring the rigor and power of classical statistics and causal inference together with advances in machine learning to bring robust insight and evidence to the important health challenges. This program is organized by the University of California, Berkeley’s Center for Targeted Machine Learning, University of Copenhagen, and Novo Nordisk, a leading global healthcare company headquartered in Denmark. The talks will range from those targeted at a general audience with an interest in the future of trials and real-world evidence generation to statisticians and data scientists working at or interested in the intersection of causal inference, machine learning, and statistics.
Inspired by the influential paper of Ferretti et al. (2020), many
countries have decided to use a digital contact tracing app as part of
their COVID-19 response. Due to its widespread availability on standard
mobile phones and its privacy preserving decentralized approach, Google
and Apple’s Exposure Notification (GAEN) framework based on Bluetooh Low
Energy proximity tracing, has become the de-facto standard on which such
digital contact tracing apps are based.
In this data-free talk, I
will give a short introduction to the aims of digital contact tracing
and then focus on the mathematical calculations occurring within the
GAEN while determining the risk of being infected. In particular I will
focus on the possibility to perform a more detailed computation of the
so called Transmission Risk Level (TRL), which is an indication of how
infectious a given individual is at the time of the potential exposure
event. This TRL score computation is used as part of the German
Corona-Warn-App (CWA) and consists of deducing infectiousness based on
the day of upload via a stochastic model. I will end the talk with some
remarks about the importance of transparency when using mathematical
risk scoring in applications that heavily depend on widespread voluntary
use in the population. A transparency the Danish smitte|stop app
currently does not have, but appears to have planned for
2021.
Literature:
CWA Team (2020), Epidemiological
Motivation of the Transmission Risk Level, https://github.com/corona-warn-app/cwa-documentation/blob/master/transmission_risk.pdf
Ferretti,
L., Wymant, C., Kendall, M., Zhao, L., Nurtay, A., Abeler-Dörner, L.,
Parker, M., Bonsall, D., & Fraser, C. (2020). Quantifying SARS-CoV-2
transmission suggests epidemic control with digital contact tracing.
Science (New York, N.Y.), 368(6491), eabb6936. https://doi.org/10.1126/science.abb6936
Höhle, M.
(2020), Risk Scoring in Digital Contact Tracing Apps, https://staff.math.su.se/hoehle/blog/2020/09/17/gaen_riskscoring.html
Increasingly, human behavior can be monitored through the collection of data from digital devices revealing information on behaviors and locations. In the context of higher education, a growing number of schools and universities collect data on their students with the purpose of assessing or predicting behaviors and academic performance, and the COVID-19 induced move to online education dramatically increases what can be accumulated in this way, raising concerns about students’ privacy. We focus on academic performance and ask whether predictive performance for a given data set can be achieved with less-privacy invasive, but more task-specific, data. We draw on a unique data set on a large student population containing both highly detailed measures of behavior and personality and high quality third-party reported individual level administrative data. We find that models estimated using the big behavioral data are indeed able to accurately predict academic performance out-of-sample. However, models using only low-dimensional and arguably less privacy-invasive administrative data perform considerably better and, importantly, do not improve when we add the high-resolution, privacy-invasive behavioral data. We argue that combining big behavioral data with `ground truth’ administrative registry data can ideally allow the identification of privacy-preserving task-specific features that can be employed instead of current indiscriminate troves of behavioral data, with better privacy and better prediction resulting.
This thesis develops statistical methodology for causal inference based
on observational longitudinal data. The work is motivated by problems in
pharmacoepidemiology, where hazard ratios routinely are used to assess
the association of time-fixed and time-dependent exposure with
time-to-event outcomes. However, the interpretation of hazard ratios as
the measure of treatment effect is hampered for many reasons. Causal
effect parameters may instead be formulated as intervention-specific
mean outcomes, for instance to target the effect of dynamic treatment
regimes on the absolute risk scale.
Targeted minimum loss-based
estimation (TMLE) provides a general template for efficient estimation
of such causal parameters in semiparametric models. The main part of my
thesis is concerned with a generalization of the TMLE template to a
continuous-time setting. In this setting, the number and schedule of
covariate changes and intervention time-points are allowed to be
subject-specific and to occur in continuous time. I propose a novel
targeting estimation algorithm, where nuisance parameters are handled by
super learning, and derive the asymptotic distribution of the resulting
estimator.
In my thesis I also suggest extensions of generalized
random forests for conditional and marginal causal effect estimation
with time-to-event outcome observed in presence of right-censoring and
competing risks. I apply these methods to Danish registry data to search
through all drugs on the market for repurposing
effects.
Assessment committee:
Associate Professor
Andreas Kryger Jensen, Section of Biostatistics, Department of Public
Health, University of Copenhagen
Assistant Professor Edward H.
Kennedy, Department of Statistics & Data Science, Carnegie Mellon
University
Professor Søren Feodor Nielsen, Center for Statistics,
Department of Finance, Copenhagen Business School
We review targeted minimum loss estimation (TMLE), which provides a general template for the construction of asymptotically efficient plug-in estimators of a target estimand under realistic statistical assumptions. TMLE involves maximizing a parametric likelihood along a so-called least favourable parametric model that uses as off-set an initial estimator (e.g., ensemble super-learner) of the relevant functional of the data distribution. The asymptotic normality and efficiency of the TMLE relies on the asymptotic negligibility of a second-order term. We present a general Highly Adaptive Lasso (HAL) estimator of the data distribution and its functionals that converges at a sufficient n-1/3 regardless of the dimensionality of the data/model, under almost no additional regularity. This allows us to propose a general TMLE that is asymptotically efficient in great generality. We also discuss the appealing properties of HAL, due to HAL being an MLE over a big function class, and present various of its implications for super- learning and TMLE.
The draft ICH E9 (R1) addendum by the International Conference on Harmonisation working group opens for the use of a principal stratum in the analysis of study data for regulatory purpose, if a relevant estimand can be justified. Inspired by the so-called complier average causal effect and work within this framework, I will propose a new estimator – Extrapolation based on propensity to comply – that estimates the treatment effect of an active treatment A relative to a comparator B (active or placebo), in the principal stratum of patients who would comply, if they were treated with treatment A. Sensitivity of the approach to the number of covariates and their ability to predict principal stratum membership will be shown based on data from a placebo-controlled study of brexpiprazole in schizophrenia. The performance of the estimator is compared with another estimator that is also based on principal stratification. A simulation study supports that the proposed estimator has a negligible bias even with a small sample size, except when the covariate predicting compliance is very weak. Not surprisingly, precision of the estimate increases substantially with stronger predictors of compliance.
We’ve all heard that a picture is worth a thousand words, but what if we
don’t understand what we’re looking at?
Charts, infographics, and
diagrams are ubiquitous. They are useful because they can reveal
patterns and trends hidden behind the numbers we encounter in our lives.
Good charts make us smarter—if we know how to read them.
However,
they can also deceive us. Charts lie in a variety of ways—displaying
incomplete or inaccurate data, suggesting misleading patterns, and
concealing uncertainty— or are frequently misunderstood. Many of us are
ill-equipped to interpret the visuals that politicians, journalists,
advertisers, and even our employers present each day. This talk teaches
to not only spot the lies in deceptive visuals, but also to take
advantage of good ones.
Link to the
slides
When designing a data visualization, showing the data comes first. After
all, the main goal of a visualization is letting the reader spot
patterns and trends behind numbers. But what if the visualization we
design is to be presented to a general audience? In that case we may
want to think deeply about visual design elements such as typography,
color, composition, and hierarchy. This talk teaches non-designers such
as scientists and statisticians how to make our charts, graphs,
publications, and conference posters look better.
Link to the
slides
In a general population, a proportional change of mortality results in a
change in life expectancy which, to a close approximation, is
proportional to the logarithm of the change in mortality.
Using
censored follow-up data, this relationship may be used to predict the
difference in average remaining lifetime between two groups of
individuals with approximately proportional mortality. The usefulness of
the methodology in a clinical trial setting is explored using follow-up
data from a clinical trial of breast cancer patients. Two methods are
considered. One approach applies standardized mortality ratios with
special attention to non-proportionality early in the follow-up period,
the second approach uses a hazard ratio estimated in Cox regression
analysis. Advantages and disadvantages of these approaches are
discussed. The results are not discouraging, and the methodology seems
potentially useful in a cost-effectiveness analysis of a new treatment
option.
Estimating the average monthly medical costs from disease diagnosis to a terminal event such as death for an incident cohort of patients is a topic of immense interest to researchers in health policy and health economics because patterns of average monthly costs over time reveal how medical costs vary across phases of care. The statistical challenges to estimating monthly medical costs longitudinally are multifold; the longitudinal cost trajectory (formed by plotting the average monthly costs from diagnosis to the terminal event) is likely to be nonlinear, with its shape depending on the time of the terminal event, which can be subject to right censoring. We tackle this statistically challenging topic by estimating the conditional mean cost at any month given the time of the terminal event. The longitudinal cost trajectories with different terminal event times form a bivariate surface, under some constraint. We propose to estimate this surface using bivariate penalized splines in an Expectation-Maximization algorithm that treats the censored terminal event times as missing data. We evaluate the proposed model and estimation method in simulations and apply the method to the medical cost data of an incident cohort of stage IV breast cancer patients from the Surveillance, Epidemiology and End Results–Medicare Linked Database. This is a joint work of Li, Wu, Ning, Huang, Shih and Shen.
Interval-censored data analysis is important in biomedical statistics for any type of time-to-event response where the time of response is not known exactly, but rather only known to occur between two assessment times. Many clinical trials and longitudinal studies generate interval-censored data; one common example occurs in medical studies that entail periodic follow-up. In this paper, we propose a survival forest method for interval-censored data based on the conditional inference framework. We describe how this framework can be adapted to the situation of interval-censored data. We show that the tuning parameters have a non-negligible effect on the survival forest performance and guidance is provided on how to tune the parameters in a data-dependent way to improve the overall performance of the method. Using Monte Carlo simulations, we show that the proposed survival forest is at least as effective as a survival tree method when the underlying model has a tree structure, performs similarly to an interval-censored Cox proportional hazards model when the true relationship is linear, and outperforms the survival tree method and Cox model when the true relationship is nonlinear. We illustrate the application of the method on a breast cancer data.
Antimicrobial resistance is one of the major burdens for today’s
society. The challenges for researches conducting studies on the effect
of those rare exposures on the hospital stay are manifold.
For
large cohort studies with rare outcomes nested case-control designs are
favorable due to the efficient use of limited resources. In our setting,
nested case-control designs apply but do not lead to truly reduced
sample sizes, because the outcome is not rare. We, therefore, study a
modified nested case-control design, which samples all exposed patients
but not all unexposed ones. Here, the inclusion probability of observed
events evolves over time. This new scheme improves on the classical
nested case-control design where for every observed event controls are
chosen at random.
We will discuss several options on how to
account for past time-dependent exposure status within a nested
case-control design and their related merits. It will be seen that a
smart utilization of the available information at each point in time can
lead to a powerful and simultaneously less expensive design. We will
also sketch alternative designs, e.g. treating exposure as a
left-truncation event that generates matched controls, and
time-simultaneous inference of the baseline hazard using the wild
bootstrap. The methods will be applied to observational data on the
impact of hospital-acquired pneumonia on the length-of-stay in hospital,
which is an outcome commonly used to express both the impact and the
costs of such adverse events.
The work presented in this thesis aims at contributing to the field of
statistical methodology for the analysis of excess risk in matched
cohort studies. The project was initiated by the Danish Cancer Society
Research Center and motivated by the desire to investigate long-term
health consequences of childhood cancer survivors. During the last five
decades, as a consequence of improved survival rates, the major concern
of childhood cancer research shifted from survival to late effects
related to childhood cancer diagnosis and treatment. In 2009, thanks to
dedicated childhood cancer researchers and to the resourceful Nordic
national registries, the Adult Life after Childhood Cancer in
Scandinavia (ALiCCS) was established to improve knowledge about late
effects of childhood cancer. This study has a matched cohort design
where for each childhood cancer survivor, five healthy comparison
subjects of the same sex, age and country were randomly selected. The
statistical models introduced in this thesis exploit the matching
structure of the data to get a representative estimate of the excess
risk of late effects in childhood cancer survivors. Two are the methods
described: the first models the excess risk in terms of excess hazard,
while the second estimates the excess cumulative incidence function.
Both approaches assume that the risk for a childhood cancer survivor is
the sum of a cluster-specific background risk defined on the age time
scale and an excess term defined on the time since exposure time scale.
Estimates of the excess model parameters are obtained by pairwise
comparisons between the cancer survivor and all the other matched
comparison members in the same cluster. The contribution of the models
introduced in this thesis on the public health area is presented by an
application on the 5-year soft-tissue sarcoma survivor data from the
ALiCCS study. By handling different features of registry data, such as
multiple events, different time scales, right censoring and left
truncation, this approach offers an easy tool to study how the excess
risk develops in time and how it is affected by important risk factors,
such as treatment.
Functions estimating the excess risk models
were implemented in R and are publicly available.
Supervisors:
Thomas Scheike, Klaus K. Andersen, Christian Dehlendorff and Jeanette
Falck Winther
Evaluators: Thomas Alexander Gerds, Martin Bøgsted,
Bjørn Møller.
In this presentation, we will introduce the possibility and practice of
using random forests, an ensembled machine learning method, in causal
mediation analysis. We will also discuss the advantages and potential
risks of using RF-based methods in causal inference.
We would
firstly describe the limitations of the traditional regression-based
mediation analysis. We then briefly describe the basic procedure of
random forests. We proposed a residual based method to remove
confounding effects in RF analysis and introduce its applications in
high dimensional genetic analysis[1]. The proposed RF-based mediation
analysis framework includes three steps. First, we build a causal forest
model under the counterfactual framework to model the relationship
between outcome, treatment, mediators and covariates[2]. Next, we
predict the mediators using traditional random forests using predictors
including treatment and covariates. The average effects are then
estimated using weighted methods. Possible candidates for the weights
include the inverses of probabilities and variances. We performed
extensive computer simulations to evaluate the performance of random
forests in mediation analysis. We observed that the proposed methods can
obtain accurate estimates on the direct and in-direct effects.
Meanwhile, The results demonstrated that RF-based methods is more
flexible than traditional regression based methods. As the RF-based
method can handle non-linear relationship and high order interactions,
we do not need to specify whether there is exposure-mediator
interactions and their types as that in traditional regression-based
methods.
Data from phase-II and III clinical trials of a novel
small molecular multi-targeted cancer drug , which is already marketed
in China, is used to illustrate the application of the RF-based
mediation analysis. We evaluated the mediation effects of some
measurements from the blood regular tests, such as platelets, on the
progression and death outcome for non-small cell lung cancer
patients.
Conclusions are that RF-based methods have their
advantages in the mediation analysis.
Many clinical or epidemiological studies aim to estimate the casual
effect of some exposure or intervention on some outcome. The use of
causal inference helps to design statistical analyses that come as close
as possible to answering the causal questions of interest. In this
thesis we focus on the statistical methodology for causal inference in
general and mediation analysis in particular. Specifically, we compare
five existing software solutions for mediation analysis to provide
practical advice for the applied researchers interested in mediation
analysis. We further focus on natural effect models and propose a new
estimation approach that is especially advantageous in settings where
the mediator and the outcome distributions are difficult to model, but
the exposure is a single binary variable. Finally, we propose a
penalized g-computation estimator of marginal structural models with
monotonicity constraints to estimate the counterfactual 30-day survival
probability in cardiac arrest patients receiving/not receiving
cardiopulmonary resuscitation (CPR) as a non-increasing function of
ambulance response time.
Supervisors: Theis Lange, Thomas A.
Gerds
Evaluators: Frank Eriksson, Jacob v. B. Hjelmborg, Ingeborg
Waernbaum.
It is well established that incorporation of prior knowledge on the
structure existing in the data for potential grouping of the covariates
is key to more accurate prediction and improved
interpretability.
In this talk, I will present new multivariate
methods incorporating grouping structure in frequentist methodology for
variable selection and dimension reduction to tackle the analysis of
high dimensional and Big-Data set.
A regression approach based on substituting observed and unobserved
outcome values for pseudo-observations ought to work if the
pseudo-observations have the appropriate conditional expectation. The
pseudo-observations under study are jack-knife pseudo-values of some
estimator and are closely related to the influence function of the
estimator they are based on.
In this talk, we will have a look
at some examples of such influence functions and look at potential
problems and solutions concerning the conditional expectation.
Specifically, influence functions from inverse probability of censoring
weighted estimators where the estimate of the censoring distribution is
allowed to take covariates into account and influence functions of the
Kaplan–Meier estimator in a delayed entry setting will be considered.
Machine learning methods and in particular random forests (RFs) are promising approaches for classification and regression based on omics data sets. I will first give a short introduction to RFs and variable selection, i.e. the identification of variables that are important for prediction. In the second part of my talk I will present some results of our current methodological work on RFs. We performed a simulation based comparison of different variable selection methods where Boruta (Kursa & Rudnicki, 2010, J Stat Softw) and Vita (Janitza et al. 2016 Adv Data Anal Classif) were consistently superior to the other approaches. Furthermore, we developed a novel method called surrogate minimal depth (SMD). It is based on the structure of the decision trees in the forest and additionally takes into account relationships between variables. In simulation studies we showed that correlation patterns can be reconstructed and that SMD is more powerful than existing variable selection methods. We are currently working on an evaluation of extensions of the RF algorithm that integrate pathway membership information into the model building process and I will show the first preliminary results.
Causation and correlation are two fundamentally different concepts, but too often correlation is misunderstood as causation. Based on given data, correlations are straightforward to establish, whereas the underlying causal structures that can explain a given association are hypothetically endless in their variety. The importance of the statistical discipline known as causal inference has been recognized in the past decades, and the field is still expanding. In this thesis we turn our attention to survival outcome, and how to estimate proportional hazards from which we can learn about causation. Our focus is specifically the case where an instrumental variable is present.
A 2012 report commissioned by the US Food and Drug Administration (FDA) on the prevention and analysis of trial results in the presence of missing data, has recently lead to significant changes in the clinical drug development. The report also introduced estimands as a new concept - a concept elaborated on in recently updated statistical guidelines for the pharmaceutical industry (the ICH-E9(R1) still in draft). The focus of the ICH-E9(R1) guideline is to discuss how intercurrent events, such as death or discontinuation of the randomised trial product can be embraced in the estimation of a treatment effect rather than just seen as a source of bias. In this talk we will outline how the estimand concept and the focus on prevention of missing data have changed the way clinical trials for new drug approvals are designed and conducted, how the data is analysed and how the results are communicated.
Gene expression measurement technology has shifted from microarrays to sequencing, producing ever richer high-througput data for transcriptomics studies. As studies using these data grow in size, frequency, and importance, it is becoming urgent to develop and refine the statistical tools available for their analysis. In particular, there is a need for methods that better control the type-I error as clinical RNA-seq studies are including a growing number of subjects (measurements being cheaper) resulting in larger sample sizes. We model RNA-seq counts as continuous variables using nonparametric regression to account for their inherent heteroscedasticity, in a principled, model-free, and efficient manner for detecting differentially expressed genes from RNA-seq data. Our method can identify the genes whose expression is significantly associated with one or several factors of interest in complex experimental designs, including studies with longitudinal measurement of gene expression. We rely on a powerful variance component score test that can account for both adjustement covariates and data heteroscedasticity without assuming any specific parametric distribution for the (transformed) RNA-seq counts. Despite the presence of a nonparametric component, our test statistic has a simple form and limiting distribution, which can be computed quickly. A permutation version of the test is also derived for small sample sizes, but this leads to issues in controlling the False Discovery Rate. Finally we also propose an extension of the method for Gene Set Analysis. Applied to both simulated data and real benchmark datasets, we show that our test has good statistical properties when compared to state-of-the-art methods limma/voom, edgeR, and DESeq2. In particular, we show that those three methods can all fail to control the type I error and the False Discovery Rate under realistic settings, while our method behaves as expected. We apply our proposed method to two candidate vaccine phase-I studies with repeated gene expression measurements: one public dataset investigating a candidate vaccine against EBOLA, and one original dataset investigating a candidate vaccine against HIV.
Many biomedical studies focus on the association between a longitudinal measurement and a time-to-event outcome and quantify this association by means of a longitudinal-survival joint model. In this paper we propose the LLR test, a longitudinal extension of the log-rank test statistic given by Peto and Peto (1972), to provide evidence of a plausible association between a time-to-event outcome (right- or interval-censored) and a longitudinal covariate. As joint model methods are complex and hard to interpret, a preliminar test for the association between both processes, such as LLR, is wise. The statistic LLR can be expressed in the form of a weighted difference of hazards, yielding to a broad class of weighted log-rank test statistics, LWLR, which allow to assess the association between the longitudinal covariate and the survival time stressing earlier, middle or late hazard differences through different weighting functions. The asymptotic distribution of LLR is derived by means of a permutation approach under the assumption that the underlying censoring process is identical for all individuals. A simulation study is conducted to evaluate the performance of the test statistics LLR and LWLR and shows that the empirical size is close to the significance level and that the power of the test depends on the association between the covariates and the survival time. Four data sets together with a toy example are used to illustrate the LLR test. Three of the data sets involve right-censored data and correspond to the European Randomized Screening for Prostate Cancer study (Serrat and others, 2015) and two well-known data sets given in the R package JM. The fourth data set explores the study Epidemiology of Diabetes Interventions and Complications (Sparling and others, 2006) which includes interval-censored data.
In managing bone metastases, estimation of life expectancy is central for individualizing patient care given a range of radiotherapy (RT) treatment options. With access to larger volume and more complex patient data and statistical models, oncologists and statisticians must develop methods for optimal decision support. Approaches incorporating many covariates should identify complex interactions and effects while also managing missing data. In this talk, I discuss how a statistical learning approach, random survival forests (RSF), handles these challenges in building survival prediction models. I show how we applied RSF to develop a clinical model which predicts survival for patients with bone metastases using 26 predictor variables and outperforms two simpler, validated Cox regression models. I will conclude by introducing a simple bootstrap based procedure, which can be used for both simple and complex prediction models, to produce valid confidence interval estimates for model performance metrics using internal validation.
Hougaard, Harvald and Holm (JASA, 1992) used frailty models to consider the survival of same-sex Danish twins born between 1881-1930 with follow-up until 1980 for twins where both were alive at age 15. This presentation gives an update to that analysis. For the birth cohorts 1870-1930, same-sex twins, where both were alive at age 6, are considered. For the birth cohorts 1931-2000, all twins are included. Follow-up is to 2016. Besides presenting the results, I will discuss the appropriateness of shared frailty models for studying this problem.
There has been a growing interest in using genotype data to perform genetic prediction of complex traits. Accurate genetic prediction can facilitate genomic selection in animal and plant breeding programs, and can aid in the development of personalized medicine in humans. Because most complex traits have a polygenic architecture and are each influenced by many genetic variants with small effects, accurate genetic prediction requires the development of polygenic methods that can model all genetic variants jointly. Many recently developed polygenic methods make parametric modeling assumptions on the effect size distribution and different polygenic methods differ in such effect size assumption. However, depending on how well the effect size distribution assumption matches the unknown truth, existing polygenic methods can perform well for some traits but poorly for others. To enable robust phenotype prediction performance across a range of phenotypes, we develop a novel polygenic model with a flexible assumption on the effect size distribution. We refer to our model as the latent Dirichlet Process Regression (DPR). DPR relies on the Dirichlet process to assign a prior on the effect size distribution itself, is non-parametric in nature, and is capable of inferring the effect size distribution from the data at hand. Because of the flexible modeling assumption, DPR is able to adapt to a broad spectrum of genetic architectures and achieves robust predictive performance for a variety of complex traits. We compare the predictive performance of DPR with several commonly used polygenic methods in simulations. We further illustrate the benefits of DPR by applying it to predict gene expressions using cis-SNPs, to conduct PrediXcan based gene set test, to perform genomic selection of four traits in two species, and to predict five complex traits in a human cohort. Our method is implemented in the DPR software, freely available at www.xzlab.org/software.html.
Pseudovalues may provide a way to use ‘standard’ estimation procedures in survival analysis, where ‘standard’ refer to methods not specifically designed for accounting of censoring. In this work a generalized additive linear model is analyzed using pseudo-values to provide a smooth estimate of the survival function by using P-spline basis functions. The performances of the estimator compared to both standard tools of survival analysis and machine learning techniques are presented through simulations and a real example.
Network Meta Analysis (NMA) is a statistical framework that allows for comparison of several pharmacological treatments based on results reported in clinical trials. The value of NMAs lies in that they permit the summary of the overall evidence and ranking of different treatment in terms of efficacy and safety endpoints combining both direct and indirect evidence. The statistical model is itself relatively simple and allows for addressing specific model assumptions such as heterogeneity and consistency (both of which will be defined and discussed). The methodology will be introduced through two examples, one concerning the efficacy and safety of SSRIs/SNRIs in the treatment of Depression, and one that compares the cognitive performance as measured by the digit-symbol-substitution test DSST in patients with Depression
Causal inference methods have been developed for longitudinal observational study designs where confounding is thought to occur over time. In particular, marginal structural models model the expectation of the counterfactual outcome conditional only on past treatment and possibly a set of baseline covariates. In such contexts, model covariates (potential time-varying confounders) are generally identified using domain-specific knowledge. However, this may leave an analyst with a large set of potential confounders that may hinder estimation. Previous approaches to data-adaptive variable selection in causal inference were generally limited to the single time-point setting. We develop a longitudinal extension of collaborative targeted minimum loss-based estimation (C-TMLE) for the estimation of the parameters in a marginal structural model that can be applied to perform variable selection in propensity score models. We demonstrate the properties of this estimator through a simulation study and apply the method to investigate the safety of trimester-specific exposure to inhaled corticosteroids during pregnancy in women with mild asthma.
The sibling comparison design is an important epidemiological tool to control for unmeasured confounding, in studies of the causal effect of an exposure on an outcome. It is routinely argued that within-sibling associations are automatically controlled for all measured and unmeasured covariates that are shared (constant) within sets of siblings, such as early childhood environment and parental genetic make-up. However, an important lesson from modern causal inference theory is that not all types of covariate control are desirable. In particular, it has been argued that collider control always lead to bias, and that mediator control may or may not lead to bias, depending on the research question. In this presentation we use Directed Acyclic Graphs (DAGs) to distinguish between shared confounders, shared mediators and shared colliders, and we examine which of these shared covariates the sibling comparison design really controls for.
Electronic health records (EHR) data provide unique opportunities for public health and medical research. From a methodological perspective, much of the focus in the literature has been on the control of confounding bias. In contrast, selection due to incomplete data is an under-appreciated source of bias in analyzing EHR data. When framed as a missing-data problem, standard methods could be applied to control for selection bias in the EHR context. In such studies, however, the process by which data are complete for any given patient likely involves the interplay of numerous clinical decisions made by patients, health care providers, and the health system. In this sense, standard methods fail to capture the complexity of the data so that residual selection bias may remain. Building on a recently-proposed framework for characterizing how data arise in EHR-based studies, sometimes referred to as the data provenance, we develop and evaluate a statistical framework for regression modeling based on inverse probability weighting that adjusts for selection bias in the complex setting of EHR-based research. We show that the resulting estimator is consistent and asymptotically Normal, and derive the form of the asymptotic variance. Plug-in estimators for the latter are proposed. We use simulations to: (i) highlight the potential for bias in EHR studies when standard approaches are used to account for selection bias, and (ii) evaluate the small-sample operating characteristics of the proposed framework. Finally, the methods are illustrated using data from an on-going, multi-site EHR-based study of bariatric surgery on BMI.
Competing risks frequently occur in medical studies, when individuals
are exposed to several mutually exclusive event types. A common approach
is to model the cause specific hazards. Challenges arise from the fact
that the relation between the cause specific hazard and the
corresponding cumulative incidence function is complex. The product
limit estimator based on the cause specific hazard systematically
overestimates the cumulative incidence function and estimated regression
parameters are not interpretable with regard to the cumulative incidence
function.
Direct regression modeling of the cumulative incidence
function has thus become popular for analyzing such complex time to
event data. The special feature of the Fine-Gray model is that
regression parameters target the subdistribution hazard, which has a
one-to-one correspondence to the cumulative incidence function. This
enables the extension to a general likelihood framework that is proposed
and further developed in this thesis. In particular we establish a
nonparametric maximum likelihood estimation and its extension to the
practical relevant setting of recurrent event data with competing
terminal events and to independently left-truncated and right-censored
competing risks data.
We establish asymptotic properties of the
estimated parameters and propose a sandwich estimator for the variance.
The solid performance of the proposed method is demonstrated in
comprehensive simulation studies. To illustrate its practical utility we
provide applications to a bone marrow transplant dataset, a bladder
cancer dataset and to an HIV dataset from the CASCADE collaboration.
Causal inference has lately had a huge impact on how statistical analyses based on non-experimental data are done. The idea is to use data from a non-experimental scenario that could be subject to several spurious effects and then fit a model that would govern the frequencies we would have seen in a related hypothetical scenario where the spurious effects are eliminated.This opens up for using health registries to answer new and more ambitious questions. However, there has not been so much focus on causal inference based time-to-event data or survival analysis. The now well established theory of causal Bayesian networks is for instance not suitable for handling such processes. Motivated by causal inference event-history data from the health registries, we have introduced causal local independence models. We show that they offer a generalization of causal Bayesian networks that also enables us to carry out causal inference based on non-experimental data when there is continuous-time processes involved. The main purpose of this work in collaboration with Vanessa Didelez, is to provide new tools for determining identifiability of causal effects of event history data that is subject to censoring. It builds on previous work on local independence graphs and delta-separation by Vanessa Didelez and previous work on causal inference for counting processes by Kjetil Røysland. We provide a new result that gives quite general graphical criteria for when causal validity of a local independence model is preserved in sub-models. If the observable variables, or processes, form a causally valid sub-model, then we can identify most relevant causal effects by re-weighting the actual observations. This is used to prove that the continuous time marginal structural models for event history analysis, based on martingale dynamics, are valid in a much more general context than what has been known previously.
For biomarkers there is a consensus definition from 2001. However, there is no similar thing for personalized medicine. This has created some confusion. Actually, I believe that conceptually there are two contrasting viewpoints on what personalized medicine covers. Besides, there are differences on a smaller scale regarding the technical complexity of the individual information to be used in a treatment strategy. Based on a series of scenarios, I will discuss these issues. I will not end up with a formal definition but rather an informal description of the two possibilities; thus allowing for discussion. Finally, I will have some slides on the drug development program needed for progressing a personalized treatment.
We consider different resampling approaches for testing general linear hypothesis with dependent data. We distinguish between a repeated measures model, where subjects are repeatedly observed over time, and multivariate data. Furthermore, we consider semi-parametric approaches for metric data, where we test null hypotheses formulated in terms of means, as well as non-parametric rank-based models for ordinal data. In these settings, current state-of-the-art test statistics include the Wald-type statistic (WTS), which is asymptotically chi-square-distributed, and the ANOVA-type statistic (ATS), which is no asymptotic pivot, but can be approximated by an F-distribution. To improve the small sample behavior of these test statistics in the described settings, we consider different resampling schemes. In each setting, we prove the asymptotic validity of the considered approach(es), analyze the small sample behavior of the tests in simulation studies and apply the resampling approaches to data examples from the life sciences.
The pseudo value approach has been developed for estimating regression models for health indicators like absolute risk to develop a disease or life expectancy without disease when data are right censored. The Penalized likelihood approach allows estimating an Illness-death model taking into account competing risks and interval censoring of the time of illness. In this work, we propose to use a pseudo value with estimators from an illness death model estimated by penalized likelihood. We illustrate this approach with cohort data with the aim to estimate the (remaining) lifetime probabilities to develop dementia.