Event History Regression with Pseudo-Observations: Computational Approaches and an Implementation in R

Due to tradition and ease of estimation, the vast majority of clinical and epidemiological papers with time-to-event data report hazard ratios from Cox proportional hazards regression models. Although hazard ratios are well known, they can be difficult to interpret, particularly as causal contrasts, in many settings. Nonparametric or fully parametric estimators allow for the direct estimation of more easily causally interpretable estimands such as the cumulative incidence and restricted mean survival. However, modeling these quantities as functions of covariates is limited to a few categorical covariates with nonparametric estimators, and often requires simulation or numeric integration with parametric estimators. Combining pseudo-observations based on non-parametric estimands with parametric regression on the pseudo-observations allows for the best of these two approaches and has many nice properties. In this paper, we develop a user friendly, easy to understand way of doing event history regression for the cumulative incidence and the restricted mean survival, using the pseudo-observation framework for estimation. The interface uses the well known formulation of a generalized linear model and allows for features including plotting of residuals, the use of sampling weights, and correct variance estimation

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

Methods for Clustered Competing Risks Data and Causal Inference using Instrumental Variables for Censored Time-to-event Data

In this dissertation, we propose new methods for analysis of clustered competing risks data (Chapters 1 and 2) and for instrumental variable (IV) analysis of univariate censored time-to-event data and competing risks data (Chapters 3 and 4). In Chapter 1, we propose estimating center effects through cause-specific proportional hazards frailty models that allow correlation among a center’s cause-specific effects. To evaluate center performance, we propose a directly standardized excess cumulative incidence (ECI) measure. We apply our methods to evaluate Organ Procurement Organizations with respect to (i) receipt of a kidney transplant and (ii) death on the wait-list. In Chapter 2, we propose to model the effects of cluster and individual-level covariates directly on the cumulative incidence functions of each risk through a semiparametric mixture component model with cluster-specific random effects. Our model permits joint inference on all competing events and provides estimates of the effects of clustering. We apply our method to multicenter competing risks data. In Chapter 3, we turn our focus to causal inference in the censored time-to-event setting in the presence of unmeasured confounders. We develop weighted IV estimators of the complier average causal effect on the restricted mean survival time. Our method accommodates instrument-outcome confounding and covariate dependent censoring. We establish the asymptotic properties, derive easily implementable variance estimators, and apply our method to compare modalities for end stage renal disease (ESRD) patients using national registry data. In Chapter 4, we develop IV analysis methods for competing risks data. Our method permits simultaneous inference of exposure effects on the absolute risk of all competing events and accommodates exposure dependent censoring. We apply the methods to compare dialytic modalities for ESRD patients with respect to risk of death from (i) cardiovascular diseases and (ii) other causes.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144110/1/shdharma_1.pd

The Liability Threshold Model for Censored Twin Data

Family studies provide an important tool for understanding etiology of diseases, with the key aim of discovering evidence of family aggregation and to determine if such aggregation can be attributed to genetic components. Heritability and concordance estimates are routinely calculated in twin studies of diseases, as a way of quantifying such genetic contribution. The endpoint in these studies are typically defined as occurrence of a disease versus death without the disease. However, a large fraction of the subjects may still be alive at the time of follow-up without having experienced the disease thus still being at risk. Ignoring this right-censoring can lead to severely biased estimates. We propose to extend the classical liability threshold model with inverse probability of censoring weighting of complete observations. This leads to a flexible way of modeling twin concordance and obtaining consistent estimates of heritability. We apply the method in simulations and to data from the population based Danish twin cohort where we describe the dependence in prostate cancer occurrence in twins

Crude incidence in two-phase designs in the presence of competing risks.

BackgroundIn many studies, some information might not be available for the whole cohort, some covariates, or even the outcome, might be ascertained in selected subsamples. These studies are part of a broad category termed two-phase studies. Common examples include the nested case-control and the case-cohort designs. For two-phase studies, appropriate weighted survival estimates have been derived; however, no estimator of cumulative incidence accounting for competing events has been proposed. This is relevant in the presence of multiple types of events, where estimation of event type specific quantities are needed for evaluating outcome.MethodsWe develop a non parametric estimator of the cumulative incidence function of events accounting for possible competing events. It handles a general sampling design by weights derived from the sampling probabilities. The variance is derived from the influence function of the subdistribution hazard.ResultsThe proposed method shows good performance in simulations. It is applied to estimate the crude incidence of relapse in childhood acute lymphoblastic leukemia in groups defined by a genotype not available for everyone in a cohort of nearly 2000 patients, where death due to toxicity acted as a competing event. In a second example the aim was to estimate engagement in care of a cohort of HIV patients in resource limited setting, where for some patients the outcome itself was missing due to lost to follow-up. A sampling based approach was used to identify outcome in a subsample of lost patients and to obtain a valid estimate of connection to care.ConclusionsA valid estimator for cumulative incidence of events accounting for competing risks under a general sampling design from an infinite target population is derived

Methodological biases in observational hospital studies of COVID-19 treatment effectiveness: pitfalls and potential

Introduction This study aims to discuss and assess the impact of three prevalent methodological biases: competing risks, immortal-time bias, and confounding bias in real-world observational studies evaluating treatment effectiveness. We use a demonstrative observational data example of COVID-19 patients to assess the impact of these biases and propose potential solutions.Methods We describe competing risks, immortal-time bias, and time-fixed confounding bias by evaluating treatment effectiveness in hospitalized patients with COVID-19. For our demonstrative analysis, we use observational data from the registry of patients with COVID-19 who were admitted to the Bellvitge University Hospital in Spain from March 2020 to February 2021 and met our predefined inclusion criteria. We compare estimates of a single-dose, time-dependent treatment with the standard of care. We analyze the treatment effectiveness using common statistical approaches, either by ignoring or only partially accounting for the methodological biases. To address these challenges, we emulate a target trial through the clone-censor-weight approach.Results Overlooking competing risk bias and employing the naive Kaplan-Meier estimator led to increased in-hospital death probabilities in patients with COVID-19. Specifically, in the treatment effectiveness analysis, the Kaplan-Meier estimator resulted in an in-hospital mortality of 45.6% for treated patients and 59.0% for untreated patients. In contrast, employing an emulated trial framework with the weighted Aalen-Johansen estimator, we observed that in-hospital death probabilities were reduced to 27.9% in the X-treated arm and 40.1% in the non-X-treated arm. Immortal-time bias led to an underestimated hazard ratio of treatment.Conclusion Overlooking competing risks, immortal-time bias, and confounding bias leads to shifted estimates of treatment effects. Applying the naive Kaplan-Meier method resulted in the most biased results and overestimated probabilities for the primary outcome in analyses of hospital data from COVID-19 patients. This overestimation could mislead clinical decision-making. Both immortal-time bias and confounding bias must be addressed in assessments of treatment effectiveness. The trial emulation framework offers a potential solution to address all three methodological biases