Causal estimation using semiparametric transformation models under prevalent sampling

Nonparametric estimation of the survival distribution under covariate-induced dependent truncation

There is often delayed entry into observational studies, which results in left truncation. In the estimation of the distribution of time-to-event from left-truncated data, standard survival analysis methods require quasi-independence between the truncation time and event time. Incorrectly assuming quasi-independence may lead to biased estimation. We address the problem of estimation of the survival distribution when dependence between the event time and its left truncation time is induced by shared covariates. We introduce propensity scores for truncated data and propose two inverse probability weighting methods that adjust for both truncation and dependence, if all of the shared covariates are measured. The proposed methods additionally allow for right censoring. We evaluate the proposed methods in simulations, conduct sensitivity analyses, and provide guidelines for use in practice. We illustrate our approach in application to data from a central nervous system lymphoma study. The proposed methods are implemented in the R package, depLT.

Estimating time-dependent ROC curves using data under prevalent sampling

Prevalent sampling is frequently a convenient and economical sampling technique for the collection of time-to-event data and thus is commonly used in studies of the natural history of a disease. However, it is biased by design because it tends to recruit individuals with longer survival times. This paper considers estimation of time-dependent receiver operating characteristic curves when data are collected under prevalent sampling. To correct the sampling bias, we develop both nonparametric and semiparametric estimators using extended risk sets and the inverse probability weighting techniques. The proposed estimators are consistent and converge to Gaussian processes, while substantial bias may arise if standard estimators for right-censored data are used. To illustrate our method, we analyze data from an ovarian cancer study and estimate receiver operating characteristic curves that assess the accuracy of the composite markers in distinguishing subjects who died within 3-5 years from subjects who remained alive. Copyright © 2016 John Wiley & Sons, Ltd.

Cox proportional hazards models with left truncation and time-varying coefficient: Application of age at event as outcome in cohort studies

When analyzing time-to-event cohort data, two different ways of choosing a time scale have been discussed in the literature: time-on-study or age at onset of disease. One advantage of choosing the latter is interpretability of the hazard ratio as a function of age. To handle the analysis of age at onset in a principled manner, we present an analysis of the Cox Proportional Hazards model with time-varying coefficient for left-truncated and right-censored data. In the analysis of Northern Manhattan Study (NOMAS) with age at onset of stroke as outcome, we demonstrate that well-established risk factors may be important only around a certain age span and less established risk factors can have a strong effect in a certain age span.