Study design for non‐recurring,time‐to‐event outcomes in the presence of error‐prone diagnostic tests or self‐reports

Sequentially administered, laboratory‐based diagnostic tests or self‐reported questionnaires are often used to determine the occurrence of a silent event. In this paper, we consider issues relevant in design of studies aimed at estimating the association of one or more covariates with a non‐recurring, time‐to‐event outcome that is observed using a repeatedly administered, error‐prone diagnostic procedure. The problem is motivated by the Women's Health Initiative, in which diabetes incidence among the approximately 160,000 women is obtained from annually collected self‐reported data. For settings of imperfect diagnostic tests or self‐reports with known sensitivity and specificity, we evaluate the effects of various factors on resulting power and sample size calculations and compare the relative efficiency of different study designs. The methods illustrated in this paper are readily implemented using our freely available R software package icensmis, which is available at the Comprehensive R Archive Network website. An important special case is that when diagnostic procedures are perfect, they result in interval‐censored, time‐to‐event outcomes. The proposed methods are applicable for the design of studies in which a time‐to‐event outcome is interval censored. Copyright © 2016 John Wiley & Sons, Ltd.     

Martingale residual‐based method to control for confounders measured only in a validation sample in time‐to‐event analysis

Unmeasured confounding remains an important problem in observational studies, including pharmacoepidemiological studies of large administrative databases. Several recently developed methods utilize smaller validation samples, with information on additional confounders, to control for confounders unmeasured in the main, larger database. However, up‐to‐date applications of these methods to survival analyses seem to be limited to propensity score calibration, which relies on a strong surrogacy assumption. We propose a new method, specifically designed for time‐to‐event analyses, which uses martingale residuals, in addition to measured covariates, to enhance imputation of the unmeasured confounders in the main database. The method is applicable for analyses with both time‐invariant data and time‐varying exposure/confounders. In simulations, our method consistently eliminated bias because of unmeasured confounding, regardless of surrogacy violation and other relevant design parameters, and almost always yielded lower mean squared errors than other methods applicable for survival analyses, outperforming propensity score calibration in several scenarios. We apply the method to a real‐life pharmacoepidemiological database study of the association between glucocorticoid therapy and risk of type II diabetes mellitus in patients with rheumatoid arthritis, with additional potential confounders available in an external validation sample. Compared with conventional analyses, which adjust only for confounders measured in the main database, our estimates suggest a considerably weaker association. Copyright © 2016 John Wiley & Sons, Ltd.     

Time‐varying effect moderation using the structural nested mean model: estimation using inverse‐weighted regression with residuals

This article considers the problem of examining time‐varying causal effect moderation using observational, longitudinal data in which treatment, candidate moderators, and possible confounders are time varying. The structural nested mean model (SNMM) is used to specify the moderated time‐varying causal effects of interest in a conditional mean model for a continuous response given time‐varying treatments and moderators. We present an easy‐to‐use estimator of the SNMM that combines an existing regression‐with‐residuals (RR) approach with an inverse‐probability‐of‐treatment weighting (IPTW) strategy. The RR approach has been shown to identify the moderated time‐varying causal effects if the time‐varying moderators are also the sole time‐varying confounders. The proposed IPTW+RR approach provides estimators of the moderated time‐varying causal effects in the SNMM in the presence of an additional, auxiliary set of known and measured time‐varying confounders. We use a small simulation experiment to compare IPTW+RR versus the traditional regression approach and to compare small and large sample properties of asymptotic versus bootstrap estimators of the standard errors for the IPTW+RR approach. This article clarifies the distinction between time‐varying moderators and time‐varying confounders. We illustrate the methodology in a case study to assess if time‐varying substance use moderates treatment effects on future substance use. Copyright © 2013 John Wiley & Sons, Ltd.     

Incorporating baseline measurements into the analysis of crossover trials with time‐to‐event endpoints

Two‐period two‐treatment (2×2) crossover designs are commonly used in clinical trials. For continuous endpoints, it has been shown that baseline (pretreatment) measurements collected before the start of each treatment period can be useful in improving the power of the analysis. Methods to achieve a corresponding gain for censored time‐to‐event endpoints have not been adequately studied. We propose a method in which censored values are treated as missing data and multiply imputed using prespecified parametric event time models. The event times in each imputed data set are then log‐transformed and analyzed using a linear model suitable for a 2×2 crossover design with continuous endpoints, with the difference in period‐specific baselines included as a covariate. Results obtained from the imputed data sets are synthesized for point and confidence interval estimation of the treatment ratio of geometric mean event times using model averaging in conjunction with Rubin's combination rule. We use simulations to illustrate the favorable operating characteristics of our method relative to two other methods for crossover trials with censored time‐to‐event data, ie, a hierarchical rank test that ignores the baselines and a stratified Cox model that uses each study subject as a stratum and includes period‐specific baselines as a covariate. Application to a real data example is provided.     

Bayesian quantile regression‐based nonlinear mixed‐effects joint models for time‐to‐event and longitudinal data with multiple features

This article explores Bayesian joint models for a quantile of longitudinal response, mismeasured covariate and event time outcome with an attempt to (i) characterize the entire conditional distribution of the response variable based on quantile regression that may be more robust to outliers and misspecification of error distribution; (ii) tailor accuracy from measurement error, evaluate non‐ignorable missing observations, and adjust departures from normality in covariate; and (iii) overcome shortages of confidence in specifying a time‐to‐event model. When statistical inference is carried out for a longitudinal data set with non‐central location, non‐linearity, non‐normality, measurement error, and missing values as well as event time with being interval censored, it is important to account for the simultaneous treatment of these data features in order to obtain more reliable and robust inferential results. Toward this end, we develop Bayesian joint modeling approach to simultaneously estimating all parameters in the three models: quantile regression‐based nonlinear mixed‐effects model for response using asymmetric Laplace distribution, linear mixed‐effects model with skew‐t distribution for mismeasured covariate in the presence of informative missingness and accelerated failure time model with unspecified nonparametric distribution for event time. We apply the proposed modeling approach to analyzing an AIDS clinical data set and conduct simulation studies to assess the performance of the proposed joint models and method. Copyright © 2016 John Wiley & Sons, Ltd.     

Bayesian adjustment for covariate measurement errors: A flexible parametric approach

In most epidemiological investigations, the study units are people, the outcome variable (or the response) is a health‐related event, and the explanatory variables are usually environmental and/or socio‐demographic factors. The fundamental task in such investigations is to quantify the association between the explanatory variables (covariates/exposures) and the outcome variable through a suitable regression model. The accuracy of such quantification depends on how precisely the relevant covariates are measured. In many instances, we cannot measure some of the covariates accurately. Rather, we can measure noisy (mismeasured) versions of them. In statistical terminology, mismeasurement in continuous covariates is known as measurement errors or errors‐in‐variables. Regression analyses based on mismeasured covariates lead to biased inference about the true underlying response–covariate associations. In this paper, we suggest a flexible parametric approach for avoiding this bias when estimating the response–covariate relationship through a logistic regression model. More specifically, we consider the flexible generalized skew‐normal and the flexible generalized skew‐t distributions for modeling the unobserved true exposure. For inference and computational purposes, we use Bayesian Markov chain Monte Carlo techniques. We investigate the performance of the proposed flexible parametric approach in comparison with a common flexible parametric approach through extensive simulation studies. We also compare the proposed method with the competing flexible parametric method on a real‐life data set. Though emphasis is put on the logistic regression model, the proposed method is unified and is applicable to the other generalized linear models, and to other types of non‐linear regression models as well. Copyright © 2009 John Wiley & Sons, Ltd.     

Considerations for analysis of time‐to‐event outcomes measured with error: Bias and correction with SIMEX

For time‐to‐event outcomes, a rich literature exists on the bias introduced by covariate measurement error in regression models, such as the Cox model, and methods of analysis to address this bias. By comparison, less attention has been given to understanding the impact or addressing errors in the failure time outcome. For many diseases, the timing of an event of interest (such as progression‐free survival or time to AIDS progression) can be difficult to assess or reliant on self‐report and therefore prone to measurement error. For linear models, it is well known that random errors in the outcome variable do not bias regression estimates. With nonlinear models, however, even random error or misclassification can introduce bias into estimated parameters. We compare the performance of 2 common regression models, the Cox and Weibull models, in the setting of measurement error in the failure time outcome. We introduce an extension of the SIMEX method to correct for bias in hazard ratio estimates from the Cox model and discuss other analysis options to address measurement error in the response. A formula to estimate the bias induced into the hazard ratio by classical measurement error in the event time for a log‐linear survival model is presented. Detailed numerical studies are presented to examine the performance of the proposed SIMEX method under varying levels and parametric forms of the error in the outcome. We further illustrate the method with observational data on HIV outcomes from the Vanderbilt Comprehensive Care Clinic.     

A joint logistic regression and covariate‐adjusted continuous‐time Markov chain model

The use of longitudinal measurements to predict a categorical outcome is an increasingly common goal in research studies. Joint models are commonly used to describe two or more models simultaneously by considering the correlated nature of their outcomes and the random error present in the longitudinal measurements. However, there is limited research on joint models with longitudinal predictors and categorical cross‐sectional outcomes. Perhaps the most challenging task is how to model the longitudinal predictor process such that it represents the true biological mechanism that dictates the association with the categorical response. We propose a joint logistic regression and Markov chain model to describe a binary cross‐sectional response, where the unobserved transition rates of a two‐state continuous‐time Markov chain are included as covariates. We use the method of maximum likelihood to estimate the parameters of our model. In a simulation study, coverage probabilities of about 95%, standard deviations close to standard errors, and low biases for the parameter values show that our estimation method is adequate. We apply the proposed joint model to a dataset of patients with traumatic brain injury to describe and predict a 6‐month outcome based on physiological data collected post‐injury and admission characteristics. Our analysis indicates that the information provided by physiological changes over time may help improve prediction of long‐term functional status of these severely ill subjects. Copyright © 2017 John Wiley & Sons, Ltd.     

Survival trees for interval‐censored survival data

Interval‐censored data, in which the event time is only known to lie in some time interval, arise commonly in practice, for example, in a medical study in which patients visit clinics or hospitals at prescheduled times and the events of interest occur between visits. Such data are appropriately analyzed using methods that account for this uncertainty in event time measurement. In this paper, we propose a survival tree method for interval‐censored data based on the conditional inference framework. Using Monte Carlo simulations, we find that the tree is effective in uncovering underlying tree structure, performs similarly to an interval‐censored Cox proportional hazards model fit when the true relationship is linear, and performs at least as well as (and in the presence of right‐censoring outperforms) the Cox model when the true relationship is not linear. Further, the interval‐censored tree outperforms survival trees based on imputing the event time as an endpoint or the midpoint of the censoring interval. We illustrate the application of the method on tooth emergence data.     

A measurement error model with a Poisson distributed surrogate

We study a linear model in which one of the covariates is measured with error. The surrogate for this covariate is the event count in unit time. We model the event count by a Poisson distribution, the rate of which is the unobserved true covariate. We show that ignoring the measurement error leads to inconsistent estimators of the regression coefficients and propose a set of unbiased estimating equations to correct the bias. The method is computationally simple and does not require using supplemental data as is often the case in other measurement error analyses. No distributional assumption is made for the unobserved covariate. The proposed method is illustrated with an example from the Wisconsin Sleep Cohort Study.     

Bayesian semiparametric mixture Tobit models with left censoring,skewness, and covariate measurement errors

Common problems to many longitudinal HIV/AIDS, cancer, vaccine, and environmental exposure studies are the presence of a lower limit of quantification of an outcome with skewness and time‐varying covariates with measurement errors. There has been relatively little work published simultaneously dealing with these features of longitudinal data. In particular, left‐censored data falling below a limit of detection may sometimes have a proportion larger than expected under a usually assumed log‐normal distribution. In such cases, alternative models, which can account for a high proportion of censored data, should be considered. In this article, we present an extension of the Tobit model that incorporates a mixture of true undetectable observations and those values from a skew‐normal distribution for an outcome with possible left censoring and skewness, and covariates with substantial measurement error. To quantify the covariate process, we offer a flexible nonparametric mixed‐effects model within the Tobit framework. A Bayesian modeling approach is used to assess the simultaneous impact of left censoring, skewness, and measurement error in covariates on inference. The proposed methods are illustrated using real data from an AIDS clinical study. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimating the effect of a rare time‐dependent treatment on the recurrent event rate

In many observational studies, the objective is to estimate the effect of treatment or state‐change on the recurrent event rate. If treatment is assigned after the start of follow‐up, traditional methods (eg, adjustment for baseline‐only covariates or fully conditional adjustment for time‐dependent covariates) may give biased results. We propose a two‐stage modeling approach using the method of sequential stratification to accurately estimate the effect of a time‐dependent treatment on the recurrent event rate. At the first stage, we estimate the pretreatment recurrent event trajectory using a proportional rates model censored at the time of treatment. Prognostic scores are estimated from the linear predictor of this model and used to match treated patients to as yet untreated controls based on prognostic score at the time of treatment for the index patient. The final model is stratified on matched sets and compares the posttreatment recurrent event rate to the recurrent event rate of the matched controls. We demonstrate through simulation that bias due to dependent censoring is negligible, provided the treatment frequency is low, and we investigate a threshold at which correction for dependent censoring is needed. The method is applied to liver transplant (LT), where we estimate the effect of development of post‐LT End Stage Renal Disease (ESRD) on rate of days hospitalized.     

Retracted: Bayesian inference on mixed‐effects location scale models with skew‐t distribution and mismeasured covariates for longitudinal data

In AIDS studies, heterogeneous between and within subject variations are often observed on longitudinal endpoints. To accommodate heteroscedasticity in the longitudinal data, statistical methods have been developed to model the mean and variance jointly. Most of these methods assume (conditional) normal distributions for random errors, which is not realistic in practice. In this article, we propose a Bayesian mixed‐effects location scale model with skew‐t distribution and mismeasured covariates for heterogeneous longitudinal data with skewness. The proposed model captures the between‐subject and within‐subject (WS) heterogeneity by modeling the between‐subject and WS variations with covariates as well as a random effect at subject level in the WS variance. Further, the proposed model also takes into account the covariate measurement errors, and commonly assumed normal distributions for model errors are substituted by skew‐t distribution to account for skewness. Parameter estimation is carried out in a Bayesian framework. The proposed method is illustrated with a Multicenter AIDS Cohort Study. Simulation studies are performed to assess the performance of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

Logistic‐AFT location‐scale mixture regression models with nonsusceptibility for left‐truncated and general interval‐censored data

In conventional survival analysis there is an underlying assumption that all study subjects are susceptible to the event. In general, this assumption does not adequately hold when investigating the time to an event other than death. Owing to genetic and/or environmental etiology, study subjects may not be susceptible to the disease. Analyzing nonsusceptibility has become an important topic in biomedical, epidemiological, and sociological research, with recent statistical studies proposing several mixture models for right‐censored data in regression analysis. In longitudinal studies, we often encounter left, interval, and right‐censored data because of incomplete observations of the time endpoint, as well as possibly left‐truncated data arising from the dissimilar entry ages of recruited healthy subjects. To analyze these kinds of incomplete data while accounting for nonsusceptibility and possible crossing hazards in the framework of mixture regression models, we utilize a logistic regression model to specify the probability of susceptibility, and a generalized gamma distribution, or a log‐logistic distribution, in the accelerated failure time location‐scale regression model to formulate the time to the event. Relative times of the conditional event time distribution for susceptible subjects are extended in the accelerated failure time location‐scale submodel. We also construct graphical goodness‐of‐fit procedures on the basis of the Turnbull–Frydman estimator and newly proposed residuals. Simulation studies were conducted to demonstrate the validity of the proposed estimation procedure. The mixture regression models are illustrated with alcohol abuse data from the Taiwan Aboriginal Study Project and hypertriglyceridemia data from the Cardiovascular Disease Risk Factor Two‐township Study in Taiwan. Copyright © 2013 John Wiley & Sons, Ltd.     

Joint mixed‐effects models for causal inference with longitudinal data

Causal inference with observational longitudinal data and time‐varying exposures is complicated due to the potential for time‐dependent confounding and unmeasured confounding. Most causal inference methods that handle time‐dependent confounding rely on either the assumption of no unmeasured confounders or the availability of an unconfounded variable that is associated with the exposure (eg, an instrumental variable). Furthermore, when data are incomplete, validity of many methods often depends on the assumption of missing at random. We propose an approach that combines a parametric joint mixed‐effects model for the study outcome and the exposure with g‐computation to identify and estimate causal effects in the presence of time‐dependent confounding and unmeasured confounding. G‐computation can estimate participant‐specific or population‐average causal effects using parameters of the joint model. The joint model is a type of shared parameter model where the outcome and exposure‐selection models share common random effect(s). We also extend the joint model to handle missing data and truncation by death when missingness is possibly not at random. We evaluate the performance of the proposed method using simulation studies and compare the method to both linear mixed‐ and fixed‐effects models combined with g‐computation as well as to targeted maximum likelihood estimation. We apply the method to an epidemiologic study of vitamin D and depressive symptoms in older adults and include code using SAS PROC NLMIXED software to enhance the accessibility of the method to applied researchers.     

Sparse boosting for high‐dimensional survival data with varying coefficients

Motivated by high‐throughput profiling studies in biomedical research, variable selection methods have been a focus for biostatisticians. In this paper, we consider semiparametric varying‐coefficient accelerated failure time models for right censored survival data with high‐dimensional covariates. Instead of adopting the traditional regularization approaches, we offer a novel sparse boosting (SparseL₂Boosting) algorithm to conduct model‐based prediction and variable selection. One main advantage of this new method is that we do not need to perform the time‐consuming selection of tuning parameters. Extensive simulations are conducted to examine the performance of our sparse boosting feature selection techniques. We further illustrate our methods using a lung cancer data analysis.     

How to control for unmeasured confounding in an observational time‐to‐event study with exposure incidence information: the treatment choice Cox model

In an observational study of the effect of a treatment on a time‐to‐event outcome, a major problem is accounting for confounding because of unknown or unmeasured factors. We propose including covariates in a Cox model that can partially account for an unknown time‐independent frailty that is related to starting or stopping treatment as well as the outcome of interest. These covariates capture the times at which treatment is started or stopped and so are called treatment choice (TC) covariates. Three such models are developed: first, an interval TC model that assumes a very general form for the respective hazard functions of starting treatment, stopping treatment, and the outcome of interest and second, a parametric TC model that assumes that the log hazard functions for starting treatment, stopping treatment, and the outcome event include frailty as an additive term. Finally, a hybrid TC model that combines attributes from the parametric and interval TC models. As compared with an ordinary Cox model, the TC models are shown to substantially reduce the bias of the estimated hazard ratio for treatment when data are simulated from a realistic Cox model with residual confounding due to the unobserved frailty. The simulations also indicate that the bias decreases or levels off as the sample size increases. A TC model is illustrated by analyzing the Women's Health Initiative Observational Study of hormone replacement for post‐menopausal women. Published 2017. This article has been contributed to by US Government employees and their work is in the public domain in the USA.     

Time‐to‐event data with time‐varying biomarkers measured only at study entry,with applications to Alzheimer's disease

Relating time‐varying biomarkers of Alzheimer's disease to time‐to‐event using a Cox model is complicated by the fact that Alzheimer's disease biomarkers are sparsely collected, typically only at study entry; this is problematic since Cox regression with time‐varying covariates requires observation of the covariate process at all failure times. The analysis might be simplified by using study entry as the time origin and treating the time‐varying covariate measured at study entry as a fixed baseline covariate. In this paper, we first derive conditions under which using an incorrect time origin of study entry results in consistent estimation of regression parameters when the time‐varying covariate is continuous and fully observed. We then derive conditions under which treating the time‐varying covariate as fixed at study entry results in consistent estimation. We provide methods for estimating the regression parameter when a functional form can be assumed for the time‐varying biomarker, which is measured only at study entry. We demonstrate our analytical results in a simulation study and apply our methods to data from the Rush Religious Orders Study and Memory and Aging Project and data from the Alzheimer's Disease Neuroimaging Initiative.     

Assessing the impact of selection bias on test decisions in trials with a time‐to‐event outcome

If past treatment assignments are unmasked, selection bias may arise even in randomized controlled trials. The impact of such bias can be measured by considering the type I error probability. In case of a normally distributed outcome, there already exists a model accounting for selection bias that permits calculating the corresponding type I error probabilities. To model selection bias for trials with a time‐to‐event outcome, we introduce a new biasing policy for exponentially distributed data. Using this biasing policy, we derive an exact formula to compute type I error probabilities whenever an F‐test is performed and no observations are censored. Two exemplary settings, with and without random censoring, are considered in order to illustrate how our results can be applied to compare distinct randomization procedures with respect to their performance in the presence of selection bias. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.