Shiny

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?"

$$\begin{split} hPPV &= P(\text{problematic disease} | \text{screen pos.}) \\ & = \underbrace{P(\text{prob. dis.} | \text{scr pos., disease})}_{(1-OD)}\cdot \underbrace{P(\text{dis.}|\text{scr pos.})}_{PPV} \\ & + \underbrace{P(\text{prob. dis.} | \text{scr pos., no dis.})}_{0}\cdot \underbrace{P(\text{no dis.}|\text{scr pos.})}_{} \\ &= (1-OD)\cdot PPV \end{split}$$

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