General single‐index survival regression models for incident and prevalent covariate data and prevalent data without follow‐up

Summary This article mainly focuses on analyzing covariate data from incident and prevalent cohort studies and a prevalent sample with only baseline covariates of interest and truncation times. Our major task in both research streams is to identify the effects of covariates on a failure time through very general single‐index survival regression models without observing survival outcomes. With a strict increase of the survival function in the linear predictor, the ratio of incident and prevalent covariate densities is shown to be a non‐degenerate and monotonic function of the linear predictor under covariate‐independent truncation. Without such a structural assumption, the conditional density of a truncation time in a prevalent cohort is ensured to be a non‐degenerate function of the linear predictor. In light of these features, some innovative approaches, which are based on the maximum rank correlation estimation or the pseudo least integrated squares estimation, are developed to estimate the coefficients of covariates up to a scale factor. Existing theoretical results are further used to establish the n ‐consistency and asymptotic normality of the proposed estimators. Moreover, extensive simulations are conducted to assess and compare the finite‐sample performance of various estimators. To illustrate the methodological ideas, we also analyze data from the Worcester Heart Attack Study and the National Comorbidity Survey Replication.