Non-inferiority trials with time-to-event data: clarifying the impact of censoring

In non-inferiority (NI) trials with time-to-event data, different types and patterns of censoring may occur, but their impact on trial results is not entirely clear. We investigated the influence of informative and non-informative censoring by conducting extensive simulation studies under the assumption that the NI margin is defined as a maximum acceptable hazard ratio and scenarios typically observed in recent NI trials. We found that while non-informative censoring tends to only affect the power, informative censoring can impact the treatment effect estimates, type I error rate, and power. The magnitude of these effects depends on the between-group differences in the failure and informative censoring risks, as well as the correlation between censoring and failure times, among other factors. The adverse impact of informative censoring was generally decreased with larger NI margins.

Clayton copula for survival data with dependent censoring: An application to a tuberculosis treatment adherence data

Ignoring the presence of dependent censoring in data analysis can lead to biased estimates, for example, not considering the effect of abandonment of the tuberculosis treatment may influence inferences about the cure probability. In order to assess the relationship between cure and abandonment outcomes, we propose a copula Bayesian approach. Therefore, the main objective of this work is to introduce a Bayesian survival regression model, capable of taking into account the dependent censoring in the adjustment. So, this proposed approach is based on Clayton's copula, to provide the relation between survival and dependent censoring times. In addition, the Weibull and the piecewise exponential marginal distributions are considered in order to fit the times. A simulation study is carried out to perform comparisons between different scenarios of dependence, different specifications of prior distributions, and comparisons with the maximum likelihood inference. Finally, we apply the proposed approach to a tuberculosis treatment adherence dataset of an HIV cohort from Alvorada-RS, Brazil. Results show that cure and abandonment outcomes are negatively correlated, that is, as long as the chance of abandoning the treatment increases, the chance of tuberculosis cure decreases.

An Expectation-Maximization Algorithm for Including Oncological COVID-19 Deaths in Survival Analysis

We address the problem of how COVID-19 deaths observed in an oncology clinical trial can be consistently taken into account in typical survival estimates. We refer to oncological patients since there is empirical evidence of strong correlation between COVID-19 and cancer deaths, which implies that COVID-19 deaths cannot be treated simply as non-informative censoring, a property usually required by the classical survival estimators. We consider the problem in the framework of the widely used Kaplan-Meier (KM) estimator. Through a counterfactual approach, an algorithmic method is developed allowing to include COVID-19 deaths in the observed data by mean-imputation. The procedure can be seen in the class of the Expectation-Maximization (EM) algorithms and will be referred to as Covid-Death Mean-Imputation (CoDMI) algorithm. We discuss the CoDMI underlying assumptions and the convergence issue. The algorithm provides a completed lifetime data set, where each Covid-death time is replaced by a point estimate of the corresponding virtual lifetime. This complete data set is naturally equipped with the corresponding KM survival function estimate and all available statistical tools can be applied to these data. However, mean-imputation requires an increased variance of the estimates. We then propose a natural extension of the classical Greenwood's formula, thus obtaining expanded confidence intervals for the survival function estimate. To illustrate how the algorithm works, CoDMI is applied to real medical data extended by the addition of artificial Covid-death observations. The results are compared with the estimates provided by the two naïve approaches which count COVID-19 deaths as censoring or as deaths by the disease under study. In order to evaluate the predictive performances of CoDMI an extensive simulation study is carried out. The results indicate that in the simulated scenarios CoDMI is roughly unbiased and outperforms the estimates obtained by the naïve approaches. A user-friendly version of CoDMI programmed in R is freely available.

Evidence of the Different Associations of Prognostic Factors With Censoring Across Treatment Groups and Impact on Censoring Weight Model Specification: The Example of Anticoagulation in Atrial Fibrillation

Inverse probability of censoring weights (IPCWs) may reduce selection bias due to informative censoring in longitudinal studies. However, in studies with an active comparator, the associations between predictors and censoring may differ across treatment groups. We used the clinical example of anticoagulation treatment with warfarin or a direct oral anticoagulant (DOAC) in atrial fibrillation to illustrate this. The cohort of individuals initiating an oral anticoagulant during 2010-2016 was identified from the Régie de l'assurance maladie du Québec (RAMQ) databases. The parameter of interest was the hazard ratio (HR) of the composite of stroke, major bleeding, myocardial infarction, or death associated with continuous use of warfarin versus DOACs. Two strategies for the specification of the model for estimation of censoring weights were explored: exposure-unstratified and exposure-stratified. The HR associated with continuous treatment with warfarin versus DOACs adjusted with exposure-stratified IPCWs was 1.26 (95% confidence interval: 1.20, 1.33). Using exposure-unstratified IPCWs, the HR differed by 15% in favor of DOACs (1.41, 95% confidence interval: 1.34, 1.48). Not accounting for the different associations between the predictors and informative censoring across exposure groups may lead to misspecification of censoring weights and biased estimate on comparative effectiveness and safety.

Weighted least-squares regression with competing risks data

The semiparametric accelerated failure time (AFT) model linearly relates the logarithm of the failure time to a set of covariates, while leaving the error distribution unspecified. This model has been widely investigated in survival literature due to its simple interpretation and relationship with linear models. However, there has been much less focus on developing AFT-type linear regression methods for analyzing competing risks data, in which patients can potentially experience one of multiple failure causes. In this article, we propose a simple least-squares (LS) linear regression model for a cause-specific subdistribution function, where the conventional LS equation is modified to account for data incompleteness under competing risks. The proposed estimators are shown to be consistent and asymptotically normal with consistent estimation of the variance-covariance matrix. We further extend the proposed methodology to risk prediction and analysis under clustered competing risks scenario. Simulation studies suggest that the proposed method provides rapid and valid statistical inferences and predictions. Application of our method to two oncology datasets demonstrate its utility in routine clinical data analysis.

A unified approach to variable selection for Cox's proportional hazards model with interval-censored failure time data

Cox's proportional hazards model is the most commonly used model for regression analysis of failure time data and some methods have been developed for its variable selection under different situations. In this paper, we consider a general type of failure time data, case K interval-censored data, that include all of other types discussed as special cases, and propose a unified penalized variable selection procedure. In addition to its generality, another significant feature of the proposed approach is that unlike all of the existing variable selection methods for failure time data, the proposed approach allows dependent censoring, which can occur quite often and could lead to biased or misleading conclusions if not taken into account. For the implementation, a coordinate descent algorithm is developed and the oracle property of the proposed method is established. The numerical studies indicate that the proposed approach works well for practical situations and it is applied to a set of real data arising from Alzheimer's Disease Neuroimaging Initiative study that motivated this study.

New methods for the additive hazards model with the informatively interval-censored failure time data

The additive hazards model is one of the most commonly used models for regression analysis of failure time data and many inference procedures have been developed for it under various situations. In particular, Wang et al. (2018a, Computational Statistics and Data Analysis, 125, 1-9) discussed the situation where one observes informatively interval-censored data and proposed a likelihood estimation approach. However , it involves estimation of the unknown baseline cumulative hazard function and thus may be time-consuming . Corresponding to this, we propose two new procedures, an estimating equation-based one and an empirical likelihood-based one, and both do not need estimation of the cumulative hazard function and can be easily implemented. The asymptotic properties of the proposed methods are established and an extensive simulation study suggests that they work well in practical situations. An application is also provided.

Comparing New-User Cohort Designs: The Example of Proton Pump Inhibitor Effectiveness in Idiopathic Pulmonary Fibrosis

The prevalent new-user cohort design is useful for assessing the effectiveness of a medication in the absence of an active comparator. Alternative approaches, particularly in the presence of informative censoring, include a variant of this design based on never users of the study drug and the marginal structural Cox model approach. We compared these approaches in assessing the effectiveness of proton pump inhibitors (PPIs) in reducing mortality among patients with idiopathic pulmonary fibrosis (IPF) using a cohort of IPF patients identified in the United Kingdom's Clinical Practice Research Datalink and diagnosed between 2003 and 2016. The cohort included 2,944 IPF patients, 1,916 of whom initiated use of PPIs during follow-up. There were 2,136 deaths (mortality rate = 25.8 per 100 person-years). Using the conventional prevalent new-user design, we found a hazard ratio for death associated with PPI use compared with nonuse of 1.07 (95% confidence interval (CI): 0.94, 1.22). The variant of the prevalent new-user design comparing PPI users with never users found a hazard ratio of 0.82 (95% CI: 0.73, 0.91), while the marginal structural Cox model found a hazard ratio of 1.08 (95% CI: 0.85, 1.38). The marginal structural model and the conventional prevalent new-user design, both accounting for informative censoring, produced similar results. However, the prevalent new-user design variant based on never users introduced selection bias and should be avoided.

Robust Wald-type tests under random censoring

Randomly censored survival data are frequently encountered in biomedical or reliability applications and clinical trial analyses. Testing the significance of statistical hypotheses is crucial in such analyses to get conclusive inference but the existing likelihood-based tests, under a fully parametric model, are extremely nonrobust against outliers in the data. Although there exists a few robust estimators given randomly censored data, there is hardly any robust testing procedure available in the literature in this context. One of the major difficulties here is the construction of a suitable consistent estimator of the asymptotic variance of robust estimators, since the latter is a function of the unknown censoring distribution. In this article, we take the first step in this direction by proposing a consistent estimator of asymptotic variance of the M-estimators based on randomly censored data without any assumption on the censoring scheme. We then describe and study a class of robust Wald-type tests for parametric statistical hypothesis, both simple as well as composite, under such a set-up. Robust tests for comparing two independent randomly censored samples and robust tests against one sided alternatives are also discussed. Their advantages and usefulness are demonstrated for the tests based on the minimum density power divergence estimators and illustrated with clinical trials and other medical data.

Construction of a survival tree for dependent censoring

In this study, we examined the problem of constructing a model for time-to-event data considering dependent censoring. Our goal was to construct a set of subgroups of covariate space, wherein each element had the same failure model considering the dependency of failure and censoring times. As such, a model was constructed based on the parametric form from the identifiability problem of censoring. We used the copula to represent the dependency between failure and censoring times. Under the assumption of parametric models for failure and censoring times and a copula function, which have unknown parameters, we proposed a method for constructing the tree-structured model through the test statistics. We subsequently evaluated the performance of the splitting rule and tree obtained using the proposed method and compared it with the general method that assumes independent censoring through simulation studies. We also present the analysis results for AIDS clinical trial research to show the utility of the method.

An introduction to joint models-applications in nephrology

In nephrology, a great deal of information is measured repeatedly in patients over time, often alongside data on events of clinical interest. In this introductory article we discuss how these two types of data can be simultaneously analysed using the joint model (JM) framework, illustrated by clinical examples from nephrology. As classical survival analysis and linear mixed models form the two main components of the JM framework, we will also briefly revisit these techniques.

Variable selection in joint frailty models of recurrent and terminal events

Recurrent event data are commonly encountered in biomedical studies. In many situations, they are subject to an informative terminal event, for example, death. Joint modeling of recurrent and terminal events has attracted substantial recent research interests. On the other hand, there may exist a large number of covariates in such data. How to conduct variable selection for joint frailty proportional hazards models has become a challenge in practical data analysis. We tackle this issue on the basis of the "minimum approximated information criterion" method. The proposed method can be conveniently implemented in SAS Proc NLMIXED for commonly used frailty distributions. Its finite-sample behavior is evaluated through simulation studies. We apply the proposed method to model recurrent opportunistic diseases in the presence of death in an AIDS study.

Assessing predictive accuracy of survival regressions subject to nonindependent censoring

Survival regression is commonly applied in biomedical studies or clinical trials, and evaluating their predictive performance plays an essential role for model diagnosis and selection. The presence of censored data, particularly if informative, may pose more challenges for the assessment of predictive accuracy. Existing literature mainly focuses on prediction for survival probabilities with limitation work for survival time. In this work, we focus on accuracy measures of predicted survival times adjusted for a potentially informative censoring mechanism (ie, coarsening at random (CAR); non-CAR) by adopting the technique of inverse probability of censoring weighting. Our proposed predictive metric can be adaptive to various survival regression frameworks including but not limited to accelerated failure time models and proportional hazards models. Moreover, we provide the asymptotic properties of the inverse probability of censoring weighting estimators under CAR. We consider the settings of high-dimensional data under CAR or non-CAR for extensions. The performance of the proposed method is evaluated through extensive simulation studies and analysis of real data from the Critical Assessment of Microarray Data Analysis.

A bivariate joint frailty model with mixture framework for survival analysis of recurrent events with dependent censoring and cure fraction

In the study of multiple failure time data with recurrent clinical endpoints, the classical independent censoring assumption in survival analysis can be violated when the evolution of the recurrent events is correlated with a censoring mechanism such as death. Moreover, in some situations, a cure fraction appears in the data because a tangible proportion of the study population benefits from treatment and becomes recurrence free and insusceptible to death related to the disease. A bivariate joint frailty mixture cure model is proposed to allow for dependent censoring and cure fraction in recurrent event data. The latency part of the model consists of two intensity functions for the hazard rates of recurrent events and death, wherein a bivariate frailty is introduced by means of the generalized linear mixed model methodology to adjust for dependent censoring. The model allows covariates and frailties in both the incidence and the latency parts, and it further accounts for the possibility of cure after each recurrence. It includes the joint frailty model and other related models as special cases. An expectation-maximization (EM)-type algorithm is developed to provide residual maximum likelihood estimation of model parameters. Through simulation studies, the performance of the model is investigated under different magnitudes of dependent censoring and cure rate. The model is applied to data sets from two colorectal cancer studies to illustrate its practical value.

Diagnosing Covariate Balance Across Levels of Right-Censoring Before and After Application of Inverse-Probability-of-Censoring Weights

Covariate balance is a central concept in the potential outcomes literature. With selected populations or missing data, balance across treatment groups can be insufficient for estimating marginal treatment effects. Recently, a framework for using covariate balance to describe measured confounding and selection bias for time-varying and other multivariate exposures in the presence of right-censoring has been proposed. Here, we revisit this framework to consider balance across levels of right-censoring over time in more depth. Specifically, we develop measures of covariate balance that can describe what is known as "dependent censoring" in the literature, along with its associated selection bias, under multiple mechanisms for right censoring. Such measures are interesting because they substantively describe the evolution of dependent censoring mechanisms. Furthermore, we provide weighted versions that can depict how well such dependent censoring has been eliminated when inverse-probability-of-censoring weights are applied. These results provide a conceptually grounded way to inspect covariate balance across levels of right-censoring as a validity check. As a motivating example, we applied these measures to a study of hypothetical "static" and "dynamic" treatment protocols in a sequential multiple-assignment randomized trial of antipsychotics with high dropout rates.

Regression analysis of longitudinal data with outcome-dependent sampling and informative censoring

We consider regression analysis of longitudinal data in the presence of outcome-dependent observation times and informative censoring. Existing approaches commonly require correct specification of the joint distribution of the longitudinal measurements, observation time process and informative censoring time under the joint modeling framework, and can be computationally cumbersome due to the complex form of the likelihood function. In view of these issues, we propose a semi-parametric joint regression model and construct a composite likelihood function based on a conditional order statistics argument. As a major feature of our proposed methods, the aforementioned joint distribution is not required to be specified and the random effect in the proposed joint model is treated as a nuisance parameter. Consequently, the derived composite likelihood bypasses the need to integrate over the random effect and offers the advantage of easy computation. We show that the resulting estimators are consistent and asymptotically normal. We use simulation studies to evaluate the finite-sample performance of the proposed method, and apply it to a study of weight loss data that motivated our investigation.

Mixed-effects models for slope-based endpoints in clinical trials of chronic kidney disease

In March of 2018, the National Kidney Foundation, in collaboration with the US Food and Drug Administration and the European Medicines Agency, sponsored a workshop in which surrogate endpoints other than currently established event-time endpoints for clinical trials in chronic kidney disease (CKD) were presented and discussed. One such endpoint is a slope-based parameter describing the rate of decline in the estimated glomerular filtration rate (eGFR) over time. There are a number of challenges that can complicate such slope-based analyses in CKD trials. These include the possibility of an early but short-term acute treatment effect on the slope, both within-subject and between-subject heteroscedasticity, and informative censoring resulting from patient dropout due to death or onset of end-stage kidney disease. To address these issues, we first consider a class of mixed-effects models for eGFR that are linear in the parameters describing the mean eGFR trajectory but which are intrinsically nonlinear when a power-of-mean variance structure is used to model within-subject heteroscedasticity. We then combine the model for eGFR with a model for time to dropout to form a class of shared parameter models which, under the right specification of shared random effects, can minimize bias due to informative censoring. The models and methods of analysis are described and illustrated using data from two CKD studies one of which was one of 56 studies made available to the workshop analytical team. Lastly, methodology and accompanying software for prospectively determining sample size/power estimates are presented.

Factor analysis for survival time prediction with informative censoring and diverse covariates

Fulfilling the promise of precision medicine requires accurately and precisely classifying disease states. For cancer, this includes prediction of survival time from a surfeit of covariates. Such data presents an opportunity for improved prediction, but also a challenge due to high dimensionality. Furthermore, disease populations can be heterogeneous. Integrative modeling is sensible, as the underlying hypothesis is that joint analysis of multiple covariates provides greater explanatory power than separate analyses. We propose an integrative latent variable model that combines factor analysis for various data types and an exponential proportional hazards (EPH) model for continuous survival time with informative censoring. The factor and EPH models are connected through low-dimensional latent variables that can be interpreted and visualized to identify subpopulations. We use this model to predict survival time. We demonstrate this model's utility in simulation and on four Cancer Genome Atlas datasets: diffuse lower-grade glioma, glioblastoma multiforme, lung adenocarcinoma, and lung squamous cell carcinoma. These datasets have small sample sizes, high-dimensional diverse covariates, and high censorship rates. We compare the predictions from our model to three alternative models. Our model outperforms in simulation and is competitive on real datasets. Furthermore, the low-dimensional visualization for diffuse lower-grade glioma displays known subpopulations.

Informative censoring by health plan disenrollment among commercially insured adults

PURPOSE

Health plan disenrollment occurs frequently in commercial insurance claims databases. If individuals who disenroll are different from those who remain enrolled, informative censoring may bias descriptive statistics as well as estimates of causal effect. We explored whether patterns of disenrollment varied by patient or health plan characteristics.

METHODS

In a large cohort of commercially insured adults (2007-2013), we examined two primary outcomes: (a) within-year disenrollment between January 1 and December 30, which was considered to occur due to patient disenrollment from the health plan, and (b) end-of-year disenrollment on December 31, which was considered to occur due to either patient disenrollment from the health plan or withdrawal of the entire health plan from the commercial insurance database. In yearly cohorts, we identified factors independently associated with disenrollment by using log-binomial regression models to estimate risk ratios (RR) and 95% confidence intervals (CI).

RESULTS

Among 2 053 100 unique patient years, the annual proportion of within-year disenrollment remained steady across years (range, 13% to 14%) whereas the annual proportion of end-of-year disenrollment varied widely (range, 8% to 26%). Independent predictors of within-year disenrollment were related to health status, including age, comorbidities, frailty, hospitalization, emergency room visits, use of durable medical equipment, use of preventive care, and use of prescription medications. In contrast, independent predictors of end-of-year disenrollment were related to health plan characteristics including insurance plan type and geographic characteristics.

CONCLUSIONS

Differential risk of disenrollment suggests that analytic approaches to address selection bias should be considered in studies using commercial insurance databases.

Exaggeration of PFS by blinded, independent, central review (BICR)

BACKGROUND

Recent published studies have shown meaningful discrepancies between local investigator and blinded, independent, central review (BICR) assessed median progression-free survival (PFS). When the local review but not BICR shows progression, generally, no further assessments are carried out and patients are censored in the BICR analysis, leading to violation of the statistical assumptions of independence between censoring and outcome used in survival analysis methods.

METHODS

We carried out a simulation study to assess methodological reasons behind these discrepancies and corroborated our findings in a case study of three BRCA-mutated ovarian cancer trials. We briefly outline possible methodological solutions that may lead to improved estimation of the BICR medians.

RESULTS

The Kaplan-Meier (KM) curve for the BICR PFS can often be exaggerated. The degree of bias is largest when there is reasonably strong correlation between BICR and local PFS, especially when PFS is long compared with assessment frequency. This can result in an exaggeration of the medians and their difference; however, the hazard ratio (HR) is much less susceptible to bias. Our simulation shows that when the true BICR median PFS was 19 months, and patients assessed every 12 weeks, the estimated KM curves were materially biased whenever the correlation between BICR and local PFS was 0.4 or greater. This was corroborated by case studies where, in the active arm, the BICR median PFS was between 6 and 11 months greater than the local median PFS. Further research is required to find improved methods for estimating BICR survival curves.

CONCLUSIONS

In general, when there is a difference between local and BICR medians, the true BICR KM curve is likely to be exaggerated and its true median will probably lie somewhere between the observed local and BICR medians. Presentation of data should always include both BICR and local results whenever a BICR is carried out.

Semiparametric probit model for informative current status data

Semiparametric probit models have recently attracted some attention for regression analysis of failure time data partly due to the popularity of the normal distribution and its special features. In this paper, we discuss the fitting of such models to informative current status data, which often occur in many areas such as medical studies and whose analysis has also recently attracted a lot of attention. For inference, a sieve maximum likelihood approach is developed and the methodology is further generalized to a class of generalized semiparametric probit models. A simulation study is conducted to assess the finite sample properties of the presented approach and indicates that it works well in practical situations. An application that motivated this study is provided.

Covariate adjustment using propensity scores for dependent censoring problems in the accelerated failure time model

In many medical studies, estimation of the association between treatment and outcome of interest is often of primary scientific interest. Standard methods for its evaluation in survival analysis typically require the assumption of independent censoring. This assumption might be invalid in many medical studies, where the presence of dependent censoring leads to difficulties in analyzing covariate effects on disease outcomes. This data structure is called "semicompeting risks data," for which many authors have proposed an artificial censoring technique. However, confounders with large variability may lead to excessive artificial censoring, which subsequently results in numerically unstable estimation. In this paper, we propose a strategy for weighted estimation of the associations in the accelerated failure time model. Weights are based on propensity score modeling of the treatment conditional on confounder variables. This novel application of propensity scores avoids excess artificial censoring caused by the confounders and simplifies computation. Monte Carlo simulation studies and application to AIDS and cancer research are used to illustrate the methodology.

How serious is bias in effect estimation in randomised trials with survival data given risk heterogeneity and informative censoring?

It is often assumed that randomisation will prevent bias in estimation of treatment effects from clinical trials, but this is not true of the semiparametric Proportional Hazards model for survival data when there is underlying risk heterogeneity. Here, a new formula is proposed for estimation of this bias, improving on a previous formula through ease of use and clarity regarding the role of the mid-study cumulative hazard rate, shown to be an important factor for the bias magnitude. Informative censoring (IC) is recognised as a source of bias. Here, work on selection effects among survivors due to risk heterogeneity is extended to include IC. A new formula shows that bias in causal effect estimation under IC has two sources: one consequent on heterogeneity and one from the additional impact of IC. The formula provides new insights not previously shown: there may less bias under IC than when there is no IC and even, in principle, zero bias. When tested against simulated data, the new formulae are shown to be very accurate for prediction of bias in Proportional Hazards and accelerated failure time analyses which ignore heterogeneity. These data are also used to investigate the performance of accelerated failure time models which explicitly model risk heterogeneity ('frailty models') and G estimation. These methods remove bias when there is simple censoring but not with informative censoring when they may lead to overestimation of treatment effects. The new formulae may be used to help researchers judge the possible extent of bias in past studies. Copyright © 2017 John Wiley & Sons, Ltd.

A latent class model for competing risks

Survival data analysis becomes complex when the proportional hazards assumption is violated at population level or when crude hazard rates are no longer estimators of marginal ones. We develop a Bayesian survival analysis method to deal with these situations, on the basis of assuming that the complexities are induced by latent cohort or disease heterogeneity that is not captured by covariates and that proportional hazards hold at the level of individuals. This leads to a description from which risk-specific marginal hazard rates and survival functions are fully accessible, 'decontaminated' of the effects of informative censoring, and which includes Cox, random effects and latent class models as special cases. Simulated data confirm that our approach can map a cohort's substructure and remove heterogeneity-induced informative censoring effects. Application to data from the Uppsala Longitudinal Study of Adult Men cohort leads to plausible alternative explanations for previous counter-intuitive inferences on prostate cancer. The importance of managing cardiovascular disease as a comorbidity in women diagnosed with breast cancer is suggested on application to data from the Swedish Apolipoprotein Mortality Risk Study. Copyright © 2017 John Wiley & Sons, Ltd.

Median Analysis of Repeated Measures Associated with Recurrent Events in Presence of Terminal Event

Recurrent events are often encountered in medical follow up studies. In addition, such recurrences have other quantities associated with them that are of considerable interest, for instance medical costs of the repeated hospitalizations and tumor size in cancer recurrences. These processes can be viewed as point processes, i.e. processes with arbitrary positive jump at each recurrence. An analysis of the mean function for such point processes have been proposed in the literature. However, such point processes are often skewed, leading to median as a more appropriate measure than the mean. Furthermore, the analysis of recurrent event data is often complicated by the presence of death. We propose a semiparametric model for assessing the effect of covariates on the quantiles of the point processes. We investigate both the finite sample as well as the large sample properties of the proposed estimators. We conclude with a real data analysis of the medical cost associated with the treatment of ovarian cancer.

Analyzing semi-competing risks data with missing cause of informative terminal event

Cancer studies frequently yield multiple event times that correspond to landmarks in disease progression, including non-terminal events (i.e., cancer recurrence) and an informative terminal event (i.e., cancer-related death). Hence, we often observe semi-competing risks data. Work on such data has focused on scenarios in which the cause of the terminal event is known. However, in some circumstances, the information on cause for patients who experience the terminal event is missing; consequently, we are not able to differentiate an informative terminal event from a non-informative terminal event. In this article, we propose a method to handle missing data regarding the cause of an informative terminal event when analyzing the semi-competing risks data. We first consider the nonparametric estimation of the survival function for the terminal event time given missing cause-of-failure data via the expectation-maximization algorithm. We then develop an estimation method for semi-competing risks data with missing cause of the terminal event, under a pre-specified semiparametric copula model. We conduct simulation studies to investigate the performance of the proposed method. We illustrate our methodology using data from a study of early-stage breast cancer. Copyright © 2016 John Wiley & Sons, Ltd.

Statistical issues in the design, conduct and analysis of two large safety studies

BACKGROUND/AIMS

The emergence, post approval, of serious medical events, which may be associated with the use of a particular drug or class of drugs, is an important public health and regulatory issue. The best method to address this issue is through a large, rigorously designed safety study. Therefore, it is important to elucidate the statistical issues involved in these large safety studies.

METHODS

Two such studies are PRECISION and EAGLES. PRECISION is the primary focus of this article. PRECISION is a non-inferiority design with a clinically relevant non-inferiority margin. Statistical issues in the design, conduct and analysis of PRECISION are discussed.

RESULTS

Quantitative and clinical aspects of the selection of the composite primary endpoint, the determination and role of the non-inferiority margin in a large safety study and the intent-to-treat and modified intent-to-treat analyses in a non-inferiority safety study are shown. Protocol changes that were necessary during the conduct of PRECISION are discussed from a statistical perspective. Issues regarding the complex analysis and interpretation of the results of PRECISION are outlined. EAGLES is presented as a large, rigorously designed safety study when a non-inferiority margin was not able to be determined by a strong clinical/scientific method. In general, when a non-inferiority margin is not able to be determined, the width of the 95% confidence interval is a way to size the study and to assess the cost-benefit of relative trial size.

CONCLUSION

A non-inferiority margin, when able to be determined by a strong scientific method, should be included in a large safety study. Although these studies could not be called "pragmatic," they are examples of best real-world designs to address safety and regulatory concerns.

Correcting for dependent censoring in routine outcome monitoring data by applying the inverse probability censoring weighted estimator

Censored data make survival analysis more complicated because exact event times are not observed. Statistical methodology developed to account for censored observations assumes that patients' withdrawal from a study is independent of the event of interest. However, in practice, some covariates might be associated to both lifetime and censoring mechanism, inducing dependent censoring. In this case, standard survival techniques, like Kaplan-Meier estimator, give biased results. The inverse probability censoring weighted estimator was developed to correct for bias due to dependent censoring. In this article, we explore the use of inverse probability censoring weighting methodology and describe why it is effective in removing the bias. Since implementing this method is highly time consuming and requires programming and mathematical skills, we propose a user friendly algorithm in R. Applications to a toy example and to a medical data set illustrate how the algorithm works. A simulation study was carried out to investigate the performance of the inverse probability censoring weighted estimators in situations where dependent censoring is present in the data. In the simulation process, different sample sizes, strengths of the censoring model, and percentages of censored individuals were chosen. Results show that in each scenario inverse probability censoring weighting reduces the bias induced in the traditional Kaplan-Meier approach where dependent censoring is ignored.

Semiparametric Random Effects Models for Longitudinal Data with Informative Observation Times

Longitudinal data frequently arise in many fields such as medical follow-up studies focusing on specific longitudinal responses. In such situations, the responses are recorded only at discrete observation times. Most existing approaches for longitudinal data analysis assume that the observation or follow-up times are independent of the underlying response process, either completely or given some known covariates. We present a joint analysis approach in which possible correlations among the responses, observation and follow-up times can be characterized by time-dependent random effects. Estimating equations are developed for parameter estimation and the resulting estimates are shown to be consistent and asymptotically normal. A simulation study is conducted to assess the finite sample performance of the approach and the method is applied to data arising from a skin cancer study.

Semicompeting risks in aging research: methods, issues and needs

A semicompeting risks problem involves two-types of events: a nonterminal and a terminal event (death). Typically, the nonterminal event is the focus of the study, but the terminal event can preclude the occurrence of the nonterminal event. Semicompeting risks are ubiquitous in studies of aging. Examples of semicompeting risk dyads include: dementia and death, frailty syndrome and death, disability and death, and nursing home placement and death. Semicompeting risk models can be divided into two broad classes: models based only on observables quantities (class [Formula: see text]) and those based on potential (latent) failure times (class [Formula: see text]). The classical illness-death model belongs to class [Formula: see text]. This model is a special case of the multistate models, which has been an active area of methodology development. During the past decade and a half, there has also been a flurry of methodological activity on semicompeting risks based on latent failure times ([Formula: see text] models). These advances notwithstanding, the semicompeting risks methodology has not penetrated biomedical research, in general, and gerontological research, in particular. Some possible reasons for this lack of uptake are: the methods are relatively new and sophisticated, conceptual problems associated with potential failure time models are difficult to overcome, paucity of expository articles aimed at educating practitioners, and non-availability of readily usable software. The main goals of this review article are: (i) to describe the major types of semicompeting risks problems arising in aging research, (ii) to provide a brief survey of the semicompeting risks methods, (iii) to suggest appropriate methods for addressing the problems in aging research, (iv) to highlight areas where more work is needed, and (v) to suggest ways to facilitate the uptake of the semicompeting risks methodology by the broader biomedical research community.

Relaxing the independent censoring assumption in the Cox proportional hazards model using multiple imputation

The Cox proportional hazards model is frequently used in medical statistics. The standard methods for fitting this model rely on the assumption of independent censoring. Although this is sometimes plausible, we often wish to explore how robust our inferences are as this untestable assumption is relaxed. We describe how this can be carried out in a way that makes the assumptions accessible to all those involved in a research project. Estimation proceeds via multiple imputation, where censored failure times are imputed under user-specified departures from independent censoring. A novel aspect of our method is the use of bootstrapping to generate proper imputations from the Cox model. We illustrate our approach using data from an HIV-prevention trial and discuss how it can be readily adapted and applied in other settings. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.

Joint model for a diagnostic test without a gold standard in the presence of a dependent terminal event

Breast cancer patients after breast conservation therapy often develop ipsilateral breast tumor relapse (IBTR), whose classification (true local recurrence versus new ipsilateral primary tumor) is subject to error, and there is no available gold standard. Some patients may die because of breast cancer before IBTR develops. Because this terminal event may be related to the individual patient's unobserved disease status and time to IBTR, the terminal mechanism is non-ignorable. This article presents a joint analysis framework to model the binomial regression with misclassified binary outcome and the correlated time to IBTR, subject to a dependent terminal event and in the absence of a gold standard. Shared random effects are used to link together two survival times. The proposed approach is evaluated by a simulation study and is applied to a breast cancer data set consisting of 4477 breast cancer patients. The proposed joint model can be conveniently fit using adaptive Gaussian quadrature tools implemented in SAS 9.3 (SAS Institute Inc., Cary, NC, USA) procedure NLMIXED.

Semiparametric estimation of treatment effect with time-lagged response in the presence of informative censoring

In many randomized clinical trials, the primary response variable, for example, the survival time, is not observed directly after the patients enroll in the study but rather observed after some period of time (lag time). It is often the case that such a response variable is missing for some patients due to censoring that occurs when the study ends before the patient's response is observed or when the patients drop out of the study. It is often assumed that censoring occurs at random which is referred to as noninformative censoring; however, in many cases such an assumption may not be reasonable. If the missing data are not analyzed properly, the estimator or test for the treatment effect may be biased. In this paper, we use semiparametric theory to derive a class of consistent and asymptotically normal estimators for the treatment effect parameter which are applicable when the response variable is right censored. The baseline auxiliary covariates and post-treatment auxiliary covariates, which may be time-dependent, are also considered in our semiparametric model. These auxiliary covariates are used to derive estimators that both account for informative censoring and are more efficient then the estimators which do not consider the auxiliary covariates.

Testing independent censoring for longitudinal data

A common problem associated with longitudinal studies is the dropouts of subjects or censoring before the end of follow-up. In most existing methods, it is assumed that censoring is noninformative about missed responses. This assumption is crucial to the validity of many statistical procedures. We develop some nonparametric hypothesis testing procedures to test for independent censoring in the absence/presence of covariates. The test statistics are constructed by contrasting two estimators of the conditional mean of cumulative responses for each stratum of covariate space from sample subsets with different patterns of censoring. Our method does not require the modelling of longitudinal response processes, therefore is robust to model misspecifications. A diagnostic plot procedure is also developed that can be used to identify dependent censoring to certain covariate strata. The finite sample performances of the tests are investigated through extensive simulation studies. The potential of our methods is demonstrated through the application of the tests to a chronic granulomatous disease study.

REGRESSION ANALYSIS OF CASE II INTERVAL-CENSORED FAILURE TIME DATA WITH THE ADDITIVE HAZARDS MODEL

Interval-censored failure time data often arise in clinical trials and medical follow-up studies, and a few methods have been proposed for their regression analysis using various regression models (Finkelstein (1986); Huang (1996); Lin, Oakes, and Ying (1998); Sun (2006)). This paper proposes an estimating equation-based approach for regression analysis of interval-censored failure time data with the additive hazards model. The proposed approach is robust and applies to both noninformative and informative censoring cases. A major advantage of the proposed method is that it does not involve estimation of any baseline hazard function. The implementation of the propsoed approach is easy and fast. Asymptotic properties of the proposed estimates are established and some simulation results and an application are provided.

Analyzing Length-biased Data with Semiparametric Transformation and Accelerated Failure Time Models

Right-censored time-to-event data are often observed from a cohort of prevalent cases that are subject to length-biased sampling. Informative right censoring of data from the prevalent cohort within the population often makes it difficult to model risk factors on the unbiased failure times for the general population, because the observed failure times are length biased. In this paper, we consider two classes of flexible semiparametric models: the transformation models and the accelerated failure time models, to assess covariate effects on the population failure times by modeling the length-biased times. We develop unbiased estimating equation approaches to obtain the consistent estimators of the regression coefficients. Large sample properties for the estimators are derived. The methods are confirmed through simulations and illustrated by application to data from a study of a prevalent cohort of dementia patients.