Impact of dependent left truncation in semiparametric competing risks methods: A simulation study

In this study, we investigated the robustness of the methods that account for independent left truncation when applied to competing risks settings with dependent left truncation. We specifically focused on the methods for the proportional cause-specific hazards model and the Fine–Gray model. Simulation experiments showed that these methods are not in general robust against dependent left truncation. The magnitude of the bias was analogous to the strength of the association between left truncation and failure times, the effect of the covariate on the competing cause of failure, and the baseline hazard of left truncation time

Regression Modeling of Complex Survival Data based on Pseudo-Observations

The restricted mean survival time (RMST) is a clinically meaningful summary measure in studies with survival outcomes. Statistical methods have been developed for regression analysis of RMST to investigate impacts of covariates on RMST, which is a useful alternative to the Cox regression analysis. However, existing methods for regression modeling of RMST are not applicable to left-truncated right-censored data that arise frequently in prevalent cohort studies, for which the sampling bias due to left truncation and informative censoring induced by the prevalent sampling scheme must be properly addressed. Meanwhile, statistical methods have been developed for regression modeling of the cumulative incidence function for left-truncated right-censored competing risks data. Nevertheless, existing methods typically involve complicated weighted estimating equations or nonparametric conditional likelihood function and often require a restrictive assumption that censoring and/or truncation times are independent of failure time. Andersen et al. introduced an approach of using pseudo observations (POs) in regression analysis of right-censored data. In this dissertation, we develop statistical methods for regression modeling of complex survival data based on POs. In Chapter 1, we propose to directly model RMST as a function of baseline covariates based on POs for left-truncated right-censored data under general censoring mechanisms. We adjust for the potential covariate-dependent censoring or dependent censoring by the inverse probability of censoring weighting method. We establish large sample properties of the proposed estimators and assess their finite sample performances by simulation studies under various scenarios. We apply the proposed methods to a prevalent cohort of women diagnosed with stage IV breast cancer identified from Surveillance, Epidemiology, and End Results-Medicare linked database. In Chapter 2, we extend the PO approach to left-truncated right-censored competing risks data and propose to directly model the cumulative incidence as a function of baseline covariates based on POs, under general truncation and censoring mechanisms. We adjust for potential covariate-dependent truncation and/or covariate-dependent censoring by incorporating covariate-adjusted weights into the inverse probability weighted estimator of the cumulative incidence function. We derive large sample properties of the proposed estimators under reasonable model assumptions and regularity conditions and assess their finite sample performances by simulation studies under various scenarios. We apply the proposed methods to a cohort study on HIV disease progression and a cohort study on pregnancy exposed to coumarin derivatives for illustration

Flexible Models for Competing Risks and Weighted Analyses of Composite Endpoints

In many clinical studies the occurrence of different types of disease events over time is of interest. For example, in cardiovascular studies, disease events such as death, stroke or myocardial infarction are of interest. As another example, in central nervous system infections such as cryptococcal meningitis, unfavourable events such as death or neurological events and favourable events such as coma or fungal clearance are relevant. In statistical terminology, competing risks refer to data where the time and type of the first disease event are analysed. Such data arise naturally if a nonfatal disease event is of interest but is precluded by death in a substantial proportion of subjects. Competing risks are the topic of the first four chapters of this thesis. An alternative approach used in many randomized controlled clinical trials is to combine different harmful events to a single composite endpoint. The analysis of trials with a composite endpoints is the topic of the fifth chapter. This thesis is organised as follows: Chapters 1 and 2 are introductory chapters and provide an overview of statistical approaches to competing risks and semi-nonparametric (SNP) density estimation. Two concepts that form the basis for the work in Chapters 3 and 4 are introduced here: the cumulative incidence function (CIF) and SNP densities. For competing risks data, the CIF describes the absolute risk of different event types depending on time and is the most important quantity for data description, prognostic modelling, and medical decision making. SNP densities are densities that can be expressed as the product of a squared polynomial (of variable degree) and a base density which is chosen as the standard normal or the exponential density in this work. Chapter 3 presents a novel approach to CIF-estimation. The underlying statistical model is specified via a mixture factorization of the joint distribution of the event type and time and the time to event distributions conditional on the event type are modelled using SNP densities. One key strength of the approach is that it can handle arbitrary censoring and truncation. A stepwise forward algorithm for model estimation and adaptive selection of SNP polynomial degrees is presented, implemented in the statistical software R, evaluated in a sequence of simulation studies, and applied to data sets from clinical trials in central nervous system infections. The simulations demonstrate that the SNP approach frequently outperforms both parametric and nonparametric alternatives. They also support the use of “ad hoc” asymptotic inference to derive confidence intervals despite a lack of a formal mathematical verification for the relevant asymptotic properties. Chapter 4 extends the work of Chapter 3 to regression modelling, i.e. the quantification of cov-ariate effects on the CIF. A careful discussion of interpretational and identifiability issues which are intrinsic to models based on the mixture factorization is provided and the usage of the model is only recommended in settings with sufficient follow-up relative to the timing of the events. A simulation study demonstrates that the proposed approach is competitive compared to common statistical models for competing risks in terms of accuracy of parameter estimates and predictions. However, it also shows that “ad hoc” asymptotic inference is only valid if sample size is large. The chapter also provides a suggestion for model diagnostics of the proposed model, an area that has been somewhat neglected for competing risks data. Chapter 5 discusses the analysis of composite endpoints. A common critique of traditional analyses of composite endpoints is that all disease events are equally weighted whereas their clinical relevance may differ substantially. This chapter addresses this by introducing a framework for the weighted analysis of composite endpoints that handles both binary and time-to-event data. To address the difficulty in selecting an exact set of weights, it proposes a method for constructing simultaneous confidence intervals and tests that protect the familywise type I error in the strong sense across families of weights which satisfy flexible inequality and order constraints based on the theory of χ-2-distributions. It is then demonstrated in several simulation scenarios as well as applications that the proposed method achieves the nominal simultaneous overall coverage rate with lower efficiency loss compared to the standard Scheffe’s procedure. Final remarks are given in Chapter 6 together with an outlook for potential future research directions