Clustered Survival Data with Left-truncation

Left‐truncation occurs frequently in survival studies, and it is well known how to deal with this for univariate survival times. However, there are few results on how to estimate dependence parameters and regression effects in semiparametric models for clustered survival data with delayed entry. Surprisingly, existing methods only deal with special cases. In this paper, we clarify different kinds of left‐truncation and suggest estimators for semiparametric survival models under specific truncation schemes. The large‐sample properties of the estimators are established. Small‐sample properties are investigated via simulation studies, and the suggested estimators are used in a study of prostate cancer based on the Finnish twin cohort where a twin pair is included only if both twins were alive in 1974.