Failure Time Outcome Research Articles

Marshall Joffe's Contributions to Causal Inference, Biostatistics, and Epidemiology.

We pay tribute to Marshall Joffe, PhD, and his substantial contributions to the field of causal inference with focus in biostatistics and epidemiology. By compiling narratives written by us, his colleagues, we not only present highlights of Marshall's research and their significance for causal inference but also offer a portrayal of Marshall's personal accomplishments and character. Our discussion of Marshall's research notably includes (but is not limited to) handling of posttreatment variables such as noncompliance, employing G-estimation for treatment effects on failure-time outcomes, estimating effects of time-varying exposures subject to time-dependent confounding, and developing a causal framework for case-control studies. We also provide a description of some of Marshall's unpublished work, which is accompanied by a bonus anecdote. We discuss future research directions related to Marshall's research. While Marshall's impact in causal inference and the world outside of it cannot be wholly captured by our words, we hope nonetheless to present some of what he has done for our field and what he has meant to us and to his loved ones.

Instrumental variable estimation of the causal hazard ratio.

Cox's proportional hazards model is one of the most popular statistical models to evaluate associations of exposure with a censored failure time outcome. When confounding factors are not fully observed, the exposure hazard ratio estimated using a Cox model is subject to unmeasured confounding bias. To address this, we propose a novel approach for the identification and estimation of the causal hazard ratio in the presence of unmeasured confounding factors. Our approach is based on a binary instrumental variable, and an additional no-interaction assumption in a first-stage regression of the treatment on the IV and unmeasured confounders. We propose, to the best of our knowledge, the first consistent estimator of the (population) causal hazard ratio within an instrumental variable framework. A version of our estimator admits a closed-form representation. We derive the asymptotic distribution of our estimator and provide a consistent estimator for its asymptotic variance. Our approach is illustrated via simulation studies and a dataapplication.

Trial emulation and survival analysis for disease incidence registers: A case study on the causal effect of pre-emptive kidney transplantation.

When drawing causal inference from observed data, failure time outcomes present additional challenges of censoring often combined with other missing data patterns. In this article, we follow incident cases of end‐stage renal disease to examine the effect on all‐cause mortality of starting treatment with transplant, so‐called pre‐emptive kidney transplantation, vs starting with dialysis possibly followed by delayed transplantation. The question is relatively simple: which start‐off treatment is expected to bring the best survival for a target population? To address it, we emulate a target trial drawing on the long term Swedish Renal Registry, where a growing common set of baseline covariates was measured nationwide. Several lessons are learned which pertain to long term disease registers more generally. With characteristics of cases and versions of treatment evolving over time, informative censoring is already introduced in unadjusted Kaplan‐Meier curves. This leads to misrepresented survival chances in observed treatment groups. The resulting biased treatment association may be aggravated upon implementing IPW for treatment. Aware of additional challenges, we further recall how similar studies to date have selected patients into treatment groups based on events occurring post treatment initiation. Our study reveals the dramatic impact of resulting immortal time bias combined with other typical features of long‐term incident disease registers, including missing covariates during the early phases of the register. We discuss feasible ways of accommodating these features when targeting relevant estimands, and demonstrate how more than one causal question can be answered relying on the no unmeasured baseline confounders assumption.

On the targets of inference with multivariate failure time data.

There are several different topics that can be addressed with multivariate failure time regression data. Data analysis methods are needed that are suited to each such topic. Specifically, marginal hazard rate models are well suited to the analysis of exposures or treatments in relation to individual failure time outcomes, when failure time dependencies are themselves of little or no interest. On the other hand semiparametric copula models are well suited to analyses where interest focuses primarily on the magnitude of dependencies between failure times. These models overlap with frailty models, that seem best suited to exploring the details of failure time clustering. Recently proposed multivariate marginal hazard methods, on the other hand, are well suited to the exploration of exposures or treatments in relation to single, pairwise, and higher dimensional hazard rates. Here these methods will be briefly described, and the final method will be illustrated using the Women's Health Initiative hormone therapy trial data.

Extending prediction models for use in a new target population with failure time outcomes.

Prediction models are often built and evaluated using data from a population that differs from the target population where model-derived predictions are intended to be used in. In this article, we present methods for evaluating model performance in the target population when some observations are right censored. The methods assume that outcome and covariate data are available from a source population used for model development and covariates, but no outcome data, are available from the target population. We evaluate the finite sample performance of the proposed estimators using simulations and apply the methods to transport a prediction model built using data from a lung cancer screening trial to a nationally representative population of participants eligible for lung cancer screening.

Optimal cut points of N-terminal of the prohormone brain natriuretic peptide (NT-proBNP) in patients with COVID-19

BackgroundCOVID19 patients may suffer from multiple cardiovascular complications. Recently, N-terminal of the prohormone brain natriuretic peptide (NT-proBNP) was a potentially independent risk factor for COVID-19 in-hospital death. The present study aimed to find new optimal cut points for NT-proBNP across censored survival failure time outcomes in hospitalized COVID-19 patients.ResultsThis cohort study was conducted on 272 patients with COVID-19 whose initial records were recorded from March 2020 to July 2020. Demographic characteristics, clinical examinations, and laboratory measurements were collected at the beginning of the admission registered in the patient record system located in the hospital. We used the maximally selected rank statistics to determine the optimal cut points for NT-proBNP (the most significant split based on the standardized log-rank test). Survival time was defined as the days from hospital admission to discharge day. In this cohort study, two optimal cut points for NT-proBNP were 331 (pg/mL) and 11,126 (pg/mL) based on a survival model. The adjusted HR of NT-proBNP for in-hospital death was 3.41 (95% CI: 1.22–9.51, P = 0.02) for medium against low category, and 3.84 (95% CI: 1.30–11.57, P = 0.01) for high in comparison with low group.ConclusionsWe reported a dramatically increased concentration of NT-proBNP among COVID-19 patients without heart failure in both severe and non-severe cases. Moreover, our study showed that a high level of NT-proBNP was highly associated with the prolonged survival time of patients with COVID-19. NT-proBNP is a strong prognostic indicator of in-hospital death in the second week of admission.

Instrumental variable estimation of the marginal structural Cox model for time-varying treatments.

Robins (1998) introduced marginal structural models, a general class of counterfactual models for the joint effects of time-varying treatments in complex longitudinal studies subject to time-varying confounding. Robins (1998) established the identification of marginal structural model parameters under a sequential randomization assumption, which rules out unmeasured confounding of treatment assignment over time. The marginal structural Cox model is one of the most popular marginal structural models for evaluating the causal effect of time-varying treatments on a censored failure time outcome. In this paper, we establish sufficient conditions for identification of marginal structural Cox model parameters with the aid of a time-varying instrumental variable, in the case where sequential randomization fails to hold due to unmeasured confounding. Our instrumental variable identification condition rules out any interaction between an unmeasured confounder and the instrumental variable in its additive effects on the treatment process, the longitudinal generalization of the identifying condition of Wang & Tchetgen Tchetgen (2018). We describe a large class of weighted estimating equations that give rise to consistent and asymptotically normal estimators of the marginal structural Cox model, thereby extending the standard inverse probability of treatment weighted estimation of marginal structural models to the instrumental variable setting. Our approach is illustrated via extensive simulation studies and an application to estimating the effect of community antiretroviral therapy coverage on HIV incidence.

Instrumental variable estimation for a time-varying treatment and a time-to-event outcome via structural nested cumulative failure time models

BackgroundIn many applications of instrumental variable (IV) methods, the treatments of interest are intrinsically time-varying and outcomes of interest are failure time outcomes. A common example is Mendelian randomization (MR), which uses genetic variants as proposed IVs. In this article, we present a novel application of g-estimation of structural nested cumulative failure models (SNCFTMs), which can accommodate multiple measures of a time-varying treatment when modelling a failure time outcome in an IV analysis.MethodsA SNCFTM models the ratio of two conditional mean counterfactual outcomes at time k under two treatment strategies which differ only at an earlier time m. These models can be extended to accommodate inverse probability of censoring weights, and can be applied to case-control data. We also describe how the g-estimates of the SNCFTM parameters can be used to calculate marginal cumulative risks under nondynamic treatment strategies. We examine the performance of this method using simulated data, and present an application of these models by conducting an MR study of alcohol intake and endometrial cancer using longitudinal observational data from the Nurses’ Health Study.ResultsOur simulations found that estimates from SNCFTMs which used an IV approach were similar to those obtained from SNCFTMs which adjusted for confounders, and similar to those obtained from the g-formula approach when the outcome was rare. In our data application, the cumulative risk of endometrial cancer from age 45 to age 72 under the “never drink” strategy (4.0%) was similar to that under the “always ½ drink per day” strategy (4.3%).ConclusionsSNCFTMs can be used to conduct MR and other IV analyses with time-varying treatments and failure time outcomes.

Predicting the onset of breast cancer using mammogram imaging data with irregular boundary.

With mammography being the primary breast cancer screening strategy, it is essential to make full use of the mammogram imaging data to better identify women who are at higher and lower than average risk. Our primary goal in this study is to extract mammogram-based features that augment the well-established breast cancer risk factors to improve prediction accuracy. In this article, we propose a supervised functional principal component analysis (sFPCA) over triangulations method for extracting features that are ordered by the magnitude of association with the failure time outcome. The proposed method accommodates the irregular boundary issue posed by the breast area within the mammogram imaging data with flexible bivariate splines over triangulations. We also provide an eigenvalue decomposition algorithm that is computationally efficient. Compared to the conventional unsupervised FPCA method, the proposed method results in a lower Brier Score and higher area under the ROC curve (AUC) in simulation studies. We apply our method to data from the Joanne Knight Breast Health Cohort at Siteman Cancer Center. Our approach not only obtains the best prediction performance comparing to unsupervised FPCA and benchmark models but also reveals important risk patterns within the mammogram images. This demonstrates the importance of utilizing additional supervised image-based features to clarify breast cancer risk.

An approximate quasi-likelihood approach for error-prone failure time outcomes and exposures.

Measurement error arises commonly in clinical research settings that rely on data from electronic health records or large observational cohorts. In particular, self-reported outcomes are typical in cohort studies for chronic diseases such as diabetes in order to avoid the burden of expensive diagnostic tests. Dietary intake, which is also commonly collected by self-report and subject to measurement error, is a major factor linked to diabetes and other chronic diseases. These errors can bias exposure-disease associations that ultimately can mislead clinical decision-making. We have extended an existing semiparametric likelihood-based method for handling error-prone, discrete failure time outcomes to also address covariate error. We conduct an extensive numerical study to compare the proposed method to the naive approach that ignores measurement error in terms of bias and efficiency in the estimation of the regression parameter of interest. In all settings considered, the proposed method showed minimal bias and maintained coverage probability, thus outperforming the naive analysis which showed extreme bias and low coverage. This method is applied to data from the Women's Health Initiative to assess the association between energy and protein intake and the risk of incident diabetes mellitus. Our results show that correcting for errors in both the self-reported outcome and dietary exposures leads to considerably different hazard ratio estimates than those from analyses that ignore measurement error, which demonstrates the importance of correcting for both outcome and covariate error.

Improved generalized raking estimators to address dependent covariate and failure-time outcome error.

Biomedical studies that use electronic health records (EHR) data for inference are often subject to bias due to measurement error. The measurement error present in EHR data is typically complex, consisting of errors of unknown functional form in covariates and the outcome, which can be dependent. To address the bias resulting from such errors, generalized raking has recently been proposed as a robust method that yields consistent estimates without the need to model the error structure. We provide rationale for why these previously proposed raking estimators can be expected to be inefficient in failure-time outcome settings involving misclassification of the event indicator. We propose raking estimators that utilize multiple imputation, to impute either the target variables or auxiliary variables, to improve the efficiency. We also consider outcome-dependent sampling designs and investigate their impact on the efficiency of the raking estimators, either with or without multiple imputation. We present an extensive numerical study to examine the performance of the proposed estimators across various measurement error settings. We then apply the proposed methods to our motivating setting, in which we seek to analyze HIV outcomes in an observational cohort with EHR data from the Vanderbilt Comprehensive CareClinic.

Semiparametric analysis of interval‐censored failure time data with outcome‐dependent observation schemes

AbstractDisease progression is often monitored by intermittent follow‐up “visits” in longitudinal cohort studies, resulting in interval‐censored failure time outcomes. Furthermore, the timing and frequency of visits is often found related to a person's history of disease‐related variables in practice. This article develops a semiparametric estimation approach using weighted binomial regression and a kernel smoother to analyze interval‐censored failure time data. Visit times are allowed to be subject‐specific and outcome‐dependent. We consider a collection of widely used semiparametric regression models, including additive hazards and linear transformation models. For additive hazards models, the nonparametric component has a closed‐form estimator and the estimators of regression coefficients are shown to be asymptotically multivariate normal with sandwich‐type covariance matrices. Simulations are conducted to examine the finite sample performance of the proposed estimators. A data set from the Toronto Psoriatic Arthritis (PsA) Cohort Study is used to illustrate the proposed methodology.

Feature screening for case-cohort studies with failure time outcome.

Case-cohort design has been demonstrated to be an economical and efficient approach in large cohort studies when the measurement of some covariates on all individuals is expensive. Various methods have been proposed for case-cohort data when the dimension of covariates is smaller than sample size. However, limited work has been done for high-dimensional case-cohort data which are frequently collected in large epidemiological studies. In this paper, we propose a variable screening method for ultrahigh-dimensional case-cohort data under the framework of proportional model, which allows the covariate dimension increases with sample size at exponential rate. Our procedure enjoys the sure screening property and the ranking consistency under some mild regularity conditions. We further extend this method to an iterative version to handle the scenarios where some covariates are jointly important but are marginally unrelated or weakly correlated to the response. The finite sample performance of the proposed procedure is evaluated via both simulation studies and an application to a real data from the breast cancer study.

G-estimation of structural nested restricted mean time lost models to estimate effects of time-varying treatments on a failure time outcome.

G-estimation of structural nested models (SNMs) plays an important role in estimating the effects of time-varying treatments with appropriate adjustment for time-dependent confounding. As SNMs for a failure time outcome, structural nested accelerated failure time models (SNAFTMs) and structural nested cumulative failure time models have been developed. The latter models are included in the class of structural nested mean models (SNMMs) and are not involved in artificial censoring, which induces several difficulties in g-estimation of SNAFTMs. Recently, restricted mean time lost (RMTL), which corresponds to the area under a distribution function up to a restriction time, is attracting attention in clinical trial communities as an appropriate summary measure of a failure time outcome. In this study, we propose another SNMM for a failure time outcome, which is called structural nested RMTL model (SNRMTLM) and describe randomized and observational g-estimation procedures that use different assumptions for the treatment mechanism in a randomized trial setting. We also provide methods to estimate marginal RMTLs under static treatment regimes using estimated SNRMTLMs. A simulation study evaluates finite-sample performances of the proposed methods compared with the conventional intention-to-treat and per-protocol analyses. We illustrate the proposed methods using data from a randomized controlled trial for cardiovascular disease with treatment changes. G-estimation of SNRMTLMs is a useful tool to estimate the effects of time-varying treatments on a failure time outcome.

Randomization inference with general interference and censoring.

Interference occurs between individuals when the treatment (or exposure) of one individual affects the outcome of another individual. Previous work on causal inference methods in the presence of interference has focused on the setting where it is a priori assumed that there is "partial interference," in the sense that individuals can be partitioned into groups wherein there is no interference between individuals in different groups. Bowers et al. (2012, Political Anal, 21, 97-124) and Bowers et al. (2016, Political Anal, 24, 395-403) consider randomization-based inferential methods that allow for more general interference structures in the context of randomized experiments. In this paper, extensions of Bowers et al. that allow for failure time outcomes subject to right censoring are proposed. Permitting right-censored outcomes is challenging because standard randomization-based tests of the null hypothesis of no treatment effect assume that whether an individual is censored does not depend on treatment. The proposed extension of Bowers et al. to allow for censoring entails adapting the method of Wang et al. (2010, Biostatistics, 11, 676-692) for two-sample survival comparisons in the presence of unequal censoring. The methods are examined via simulation studies and utilized to assess the effects of cholera vaccination in an individually randomized trial of 73 000 children and women in Matlab, Bangladesh.

Semiparametric inference for a two-stage outcome-dependent sampling design with interval-censored failure time data.

We propose a two-stage outcome-dependent sampling design and inference procedure for studies that concern interval-censored failure time outcomes. This design enhances the study efficiency by allowing the selection probabilities of the second-stage sample, for which the expensive exposure variable is ascertained, to depend on the first-stage observed interval-censored failure time outcomes. In particular, the second-stage sample is enriched by selectively including subjects who are known or observed to experience the failure at an early or late time. We develop a sieve semiparametric maximum pseudo likelihood procedure that makes use of all available data from the proposed two-stage design. The resulting regression parameter estimator is shown to be consistent and asymptotically normal, and a consistent estimator for its asymptotic variance is derived. Simulation results demonstrate that the proposed design and inference procedure performs well in practical situations and is more efficient than the existing designs and methods. An application to a phase 3 HIV vaccine trial is provided.

Informatively clustering longitudinal microarrays using binary or survival outcome data

ABSTRACTThe goal of this research is to discover what groups of genes are associated with the disease process. We use binary and failure time outcomes to inform the clustering of longitudinally-collected microarray data. We propose a linear model with normally distributed cluster-specific random effects for the longitudinal gene expression trajectory. The random effects are linearly related to a latent continuous representation of the outcome, where the probability or hazard of the outcome depends on these latent variables. We apply our method to microarray data collected from trauma patients in the inflammation and host response to Injury project.

Estimation of parametric failure time distributions based on interval-censored data with irregular dependent follow-up.

Event history studies based on disease clinic data often face several complications. Specifically, patients may visit the clinic irregularly, and the intermittent observation times could depend on disease-related variables; this can cause a failure time outcome to be dependently interval-censored. We propose a weighted estimating function approach so that dependently interval-censored failure times can be analysed consistently. A so-called inverse-intensity-of-visit weight is employed to adjust for the informative inspection times. Left truncation of failure times can also be easily handled. Additionally, in observational studies, treatment assignments are typically non-randomized and may depend on disease-related variables. An inverse-probability-of-treatment weight is applied to estimating functions to further adjust for measured confounders. Simulation studies are conducted to examine the finite sample performances of the proposed estimators. Finally, the Toronto Psoriatic Arthritis Cohort Study is used for illustration. Copyright © 2017 John Wiley & Sons, Ltd.

Variable selection for case-cohort studies with failure time outcome.

Case-cohort designs are widely used in large cohort studies to reduce the cost associated with covariate measurement. In many such studies the number of covariates is very large, so an efficient variable selection method is necessary. In this paper, we study the properties of a variable selection procedure using the smoothly clipped absolute deviation penalty in a case-cohort design with a diverging number of parameters. We establish the consistency and asymptotic normality of the maximum penalized pseudo-partial-likelihood estimator, and show that the proposed variable selection method is consistent and has an asymptotic oracle property. Simulation studies compare the finite-sample performance of the procedure with tuning parameter selection methods based on the Akaike information criterion and the Bayesian information criterion. We make recommendations for use of the proposed procedures in case-cohort studies, and apply them to the Busselton Health Study.

Causal mediation analysis on failure time outcome without sequential ignorability.

Mediation analysis is an important topic as it helps researchers to understand why an intervention works. Most previous mediation analyses define effects in the mean scale and require a binary or continuous outcome. Recently, possible ways to define direct and indirect effects for causal mediation analysis with survival outcome were proposed. However, these methods mainly rely on the assumption of sequential ignorability, which implies no unmeasured confounding. To handle the potential confounding between the mediator and the outcome, in this article, we proposed a structural additive hazard model for mediation analysis with failure time outcome and derived estimators for controlled direct effects and controlled mediator effects. Our methods allow time-varying effects. Simulations showed that our proposed estimator is consistent in the presence of unmeasured confounding while the traditional additive hazard regression ignoring unmeasured confounding produces biased results. We applied our method to the Women's Health Initiative data to study whether the dietary intervention affects breast cancer risk through changing body weight.