THE UNIVERSITY OF BRITISH COLUMBIA

Faculty of Pharmaceutical Sciences & UBC Division of Respiratory Medicine
Respiratory Evaluation Sciences Program

Research Methodology Methods

Identification of distributions for risks based on the first moment and c-statistic

AUTHORS:

We show that for any family of distributions with support on [0,1] with strictly monotonic cumulative distribution function that has no jumps and is quantile-identifiable (i.e., any two distinct quantiles identify the distribution), knowing the first moment and c-statistic is enough to identify the distribution. The derivations motivate numerical algorithms for mapping a given pair of expected value and c-statistic to the parameters of specified two-parameter distributions for probabilities. We implemented these algorithms in R and in a simulation study evaluated their numerical accuracy for common families of distributions for risks (beta, logit-normal, and probit-normal). An area of application for these developments is in risk prediction modeling (e.g., sample size calculations and Value of Information analysis), where one might need to estimate the parameters of the distribution of predicted risks from the reported summary statistics.

RELATED RESEARCH:

Methodology : Methods

Emergency Procedures   |   Terms of Use   |   UBC Copyright   |   Accessibility