class: center, middle, inverse, title-slide # The mathematics of overdiagnosis ### Claus Thorn Ekstrøm<br>UCPH Biostatistics<br>.small[<a href="mailto:ekstrom@sund.ku.dk">ekstrom@sund.ku.dk</a> ] ### November 26th, 2018<br><svg style="height:0.8em;top:.04em;position:relative;fill:steelblue;" viewBox="0 0 512 512"><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg> <span class="citation">@ClausEkstrom</span> <br> .small[Slides: <a href="www.biostatistics.dk/talks/">biostatistics.dk/talks/</a>] --- class: middle # The impact of screening on patients *"If screening positive do I have the disease?"* *"If screening positive do I have a disease that can be treated?"* *"If screening positive do I have a disease that will give me problems?"* --- background-image: url('pics/graph.png') background-size: 90% class: top --- # Shiny ```r shiny::runGitHub("ekstroem/overdiagnosis") ``` --- # More precise diagnoses *"If screening positive do I have the disease?"* Positive predictive value: `$$\begin{split}PPV &= P(\text{disease} | \text{screen positive}) \\ &= \frac{P(\text{screen positive}|\text{disease}) \cdot P(\text{disease})}{P(\text{screen positive})} \\ &= \frac{\text{sensitivity} \cdot P(\text{disease})}{\text{sens.} \cdot P(\text{disease}) + (1-\text{spec.}) \cdot P(\text{no disease})} \end{split}$$` --- # Honest PPV *"If screening positive do I have a disease that will give me problems?"* `$$\begin{split} hPPV &= P(\text{problematic disease} | \text{screen pos.}) \\ & = \underbrace{P(\text{prob. dis.} | \text{scr pos., disease})}_{(1-OD)}\cdot \underbrace{P(\text{dis.}|\text{scr pos.})}_{PPV} \\ & + \underbrace{P(\text{prob. dis.} | \text{scr pos., no dis.})}_{0}\cdot \underbrace{P(\text{no dis.}|\text{scr pos.})}_{} \\ &= (1-OD)\cdot PPV \end{split}$$` -