Binary Logistic Regression Using Survival Analysis

Survival analysis problems have elsewhere been recast as problems in logistic regression, after the event times were grouped into intervals. Here we discuss the opposite connection: how binary logistic regression can be viewed fruitfully as a special case of accelerated failure time models in survival analysis. In the corresponding survival analysis setting, all data is either left- or right-censored, and all observation times are the same (taken as t=1). Using this connection, researchers modeling binary outcome data can go beyond the routinely used logit and probit models, to conveniently include the distributions routinely available within survival analysis programs, such as gaussian and exponential. Large data sets may be fruitfully analyzed using this approach with a view to choosing the best available distribution. Our ideas are not new, and our aim is simply to be accessible to a broad community of nonspecialist nonstatisticians. We demonstrate our ideas with numerical examples in R