Comparative Predicted Probabilities Based on Retrospective Data with Binary Links

• Activity Number: 644
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Di Fang*+ and Jeffrey Wilson
• Companies: Arizona State University and Arizona State University
• Keywords: Logit link ; inclusion probability ; generalized linear model ; log-log ; probit

Abstract

Predictive probabilities based on the fitted model is a common request in data analysis. However, it is often overlooked that prediction of probabilities will differ if the data on which the model was formed is retrospective versus to prospective. The difference will depend to a large extent on the inclusion probabilities. This paper examines some common binary models (logistic model, complimentary log-log model or probit model) and show that the differences in predicted probabilities are the same regardless of the link used. This paper shows if the inclusion probabilities for the non-event group in the sample are smaller (larger) than that of the treatment group, then the corresponding predictive probabilities for retrospective data are not larger (smaller) than those for prospective data. Hospital discharge data in the study of re-admissions within 30 days are presented as an example.