A logistic PH regression model for interval censored survival data

The survival function of the logistic proportional hazards (PH) regression model, MacKenzie (1996), is obtained. A general likelihood for interval censored survival data which depends only on various closed forms of the survival function of a continuous underlying failure time distribution is introduced. The use of the logistic PH survival distribution is proposed for the analysis of interval censored data following a PH distribution. The corresponding interval censored likelihood is developed and compared with a mis-specified likelihood which treats the interval censored data as if they were exact. A simulation study is used to compare the two likelihoods.