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I have data that is normally distributed related to risk of a particular disease. At the median of the distribution, you would expect to observe the population prevalence level of disease P0=0.01. For each threshold of the ROC curve I want to calculate post test probability P1.

However, for all points on the ROC curve the likelihood ratio (LR+) is >1 which means for every threshold P1>P0. Reasoning that the sens=spec line represents an LR=1 across all thresholds I have used LR-1 instead in all calculations. My distribution now looks correct with P0 falling at the median of the distribution, lower probability below the median approaching P1=0 and greater probability above the median.

Is this statistically valid or is there a more valid method of calibrating the probabilities?

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  • $\begingroup$ Please elaborate on your problem and provide definitions. What is your model for this test? It's unclear how normally distributed data is converted to binary classification, and hence ends up computing a probability. $\endgroup$
    – Daeyoung
    Commented Mar 16, 2022 at 20:16
  • $\begingroup$ My model is genetic risk for a disease which is normally distributed in a population. At each threshold of the distribution, using the sensitivity and specificity I want to know how the prior probability (prevalence) is altered. We should expect that the prior probability falls below the median and increases above the median. But for a ROC curve the LR is always > 1 which is not helpful in this case. $\endgroup$
    – sethsh7
    Commented Mar 16, 2022 at 20:52
  • $\begingroup$ What is the model for classification? How did you calculate sensitivity and specificity (there must be a classification rule to compute them)? $\endgroup$
    – Daeyoung
    Commented Mar 16, 2022 at 20:54
  • $\begingroup$ Logistic regression which we have then calculated sensitivity, specificity and LR+/- at every threshold $\endgroup$
    – sethsh7
    Commented Mar 16, 2022 at 22:54

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