Multiple spells in the Prentice–Gloeckler–Meyer likelihood with unobserved heterogeneity

Based on previous work by Prentice and Gloeckler (Prentice, R.L., Gloeckler, L.A., 1978. Regression analysis of grouped survival data with application to breast cancer data. Biometrics 34, 57–67), Meyer shows how to estimate, for single-spell data, a proportional hazard with time-varying covariates and unobserved heterogeneity for which the effect of time on the hazard rate is specified non-parametrically. With multiple-spell data, the number of terms in each likelihood contribution grows geometrically with the number of spells. We present a systematic method of ordering the terms in the multiple-spell case and using the binary representation of the order number to construct the likelihood contributions