Adverse events in single-arm clinical trials with non-fatal time-to-event efficacy endpoint: from clinical questions to methods for statistical analysis.

BACKGROUND: In any single-arm trial on novel treatments, assessment of toxicity plays an important role as occurrence of adverse events (AEs) is relevant for application in clinical practice. In the presence of a non-fatal time-to-event(s) efficacy endpoint, the analysis should be broadened to consider AEs occurrence in time. The AEs analysis could be tackled with two approaches, depending on the clinical question of interest. Approach 1 focuses on the occurrence of AE as first event. Treatment ability to protect from the efficacy endpoint event(s) has an impact on the chance of observing AEs due to competing risks action. Approach 2 considers how treatment affects the occurrence of AEs in the potential framework where the efficacy endpoint event(s) could not occur. METHODS: In the first part of the work we review the strategy of analysis for these two approaches. We identify theoretical quantities and estimators consistent with the following features: (a) estimators should address for the presence of right censoring; (b) theoretical quantities and estimators should be functions of time. In the second part of the work we propose the use of alternative methods (regression models, stratified Kaplan-Meier curves, inverse probability of censoring weighting) to relax the assumption of independence between the potential times to AE and to event(s) in the efficacy endpoint for addressing Approach 2. RESULTS: We show through simulations that the proposed methods overcome the bias due to the dependence between the two potential times and related to the use of standard estimators. CONCLUSIONS: We demonstrated through simulations that one can handle patients selection in the risk sets due to the competing event, and thus obtain conditional independence between the two potential times, adjusting for all the observed covariates that induce dependence.

Win-loss parameters for right-censored event data, with application to recurrent events.

The win ratio has become a popular method for comparing multiple event data between two groups in clinical cohort studies. The win ratio compares the event data in prioritized order, where the first prioritized event is death and a typical example for the second prioritized event is hospitalization. Literature is sparse on inference for win and loss parameters, including the win ratio, for censored event data. Inference for two prioritized censored event times has been developed for independent right-censoring. Many clinical studies include recurrent event data such as hospitalizations. In this article, we suggest inference for win-loss parameters for death and a recurrent event outcome under independent right-censoring. The small sample properties of the proposed method are studied in a simulation study showing that the variance formula is accurate even for small samples. The method is applied on a data set from a randomized clinical trial.

Win statistics (win ratio, win odds, and net benefit) can complement one another to show the strength of the treatment effect on time-to-event outcomes.

Conventional analyses of a composite of multiple time-to-event outcomes use the time to the first event. However, the first event may not be the most important outcome. To address this limitation, generalized pairwise comparisons and win statistics (win ratio, win odds, and net benefit) have become popular and have been applied to clinical trial practice. However, win ratio, win odds, and net benefit have typically been used separately. In this article, we examine the use of these three win statistics jointly for time-to-event outcomes. First, we explain the relation of point estimates and variances among the three win statistics, and the relation between the net benefit and the Mann-Whitney U statistic. Then we explain that the three win statistics are based on the same win proportions, and they test the same null hypothesis of equal win probabilities in two groups. We show theoretically that the Z-values of the corresponding statistical tests are approximately equal; therefore, the three win statistics provide very similar p-values and statistical powers. Finally, using simulation studies and data from a clinical trial, we demonstrate that, when there is no (or little) censoring, the three win statistics can complement one another to show the strength of the treatment effect. However, when the amount of censoring is not small, and without adjustment for censoring, the win odds and the net benefit may have an advantage for interpreting the treatment effect; with adjustment (e.g., IPCW adjustment) for censoring, the three win statistics can complement one another to show the strength of the treatment effect. For calculations we use the R package WINS, available on the CRAN (Comprehensive R Archive Network).

Two-sample inference procedures under nonproportional hazards.

We introduce a new two-sample inference procedure to assess the relative performance of two groups over time. Our model-free method does not assume proportional hazards, making it suitable for scenarios where nonproportional hazards may exist. Our procedure includes a diagnostic tau plot to identify changes in hazard timing and a formal inference procedure. The tau-based measures we develop are clinically meaningful and provide interpretable estimands to summarize the treatment effect over time. Our proposed statistic is a U-statistic and exhibits a martingale structure, allowing us to construct confidence intervals and perform hypothesis testing. Our approach is robust with respect to the censoring distribution. We also demonstrate how our method can be applied for sensitivity analysis in scenarios with missing tail information due to insufficient follow-up. Without censoring, Kendall's tau estimator we propose reduces to the Wilcoxon-Mann-Whitney statistic. We evaluate our method using simulations to compare its performance with the restricted mean survival time and log-rank statistics. We also apply our approach to data from several published oncology clinical trials where nonproportional hazards may exist.

On logistic regression with right censored data, with or without competing risks, and its use for estimating treatment effects.

Simple logistic regression can be adapted to deal with right-censoring by inverse probability of censoring weighting (IPCW). We here compare two such IPCW approaches, one based on weighting the outcome, the other based on weighting the estimating equations. We study the large sample properties of the two approaches and show that which of the two weighting methods is the most efficient depends on the censoring distribution. We show by theoretical computations that the methods can be surprisingly different in realistic settings. We further show how to use the two weighting approaches for logistic regression to estimate causal treatment effects, for both observational studies and randomized clinical trials (RCT). Several estimators for observational studies are compared and we present an application to registry data. We also revisit interesting robustness properties of logistic regression in the context of RCTs, with a particular focus on the IPCW weighting. We find that these robustness properties still hold when the censoring weights are correctly specified, but not necessarily otherwise.

Adjusting win statistics for dependent censoring.

For composite outcomes whose components can be prioritized on clinical importance, the win ratio, the net benefit and the win odds apply that order in comparing patients pairwise to produce wins and subsequently win proportions. Because these three statistics are derived using the same win proportions and they test the same hypothesis of equal win probabilities in the two treatment groups, we refer to them as win statistics. These methods, particularly the win ratio and the net benefit, have received increasing attention in methodological research and in design and analysis of clinical trials. For time-to-event outcomes, however, censoring may introduce bias. Previous work has shown that inverse-probability-of-censoring weighting (IPCW) can correct the win ratio for bias from independent censoring. The present article uses the IPCW approach to adjust win statistics for dependent censoring that can be predicted by baseline covariates and/or time-dependent covariates (producing the CovIPCW-adjusted win statistics). Theoretically and with examples and simulations, we show that the CovIPCW-adjusted win statistics are unbiased estimators of treatment effect in the presence of dependent censoring.

The inverse-probability-of-censoring weighting (IPCW) adjusted win ratio statistic: an unbiased estimator in the presence of independent censoring.

The win ratio method has received much attention in methodological research, ad hoc analyses, and designs of prospective studies. As the primary analysis, it supported the approval of tafamidis for the treatment of cardiomyopathy to reduce cardiovascular mortality and cardiovascular-related hospitalization. However, its dependence on censoring is a potential shortcoming. In this article, we propose the inverse-probability-of-censoring weighting (IPCW) adjusted win ratio statistic (i.e., the IPCW-adjusted win ratio statistic) to overcome censoring issues. We consider independent censoring, common censoring across endpoints, and right censoring. We develop an asymptotic variance estimator for the logarithm of the IPCW-adjusted win ratio statistic and evaluate it via simulation. Our simulation studies show that, as the amount of censoring increases, the unadjusted win proportions may decrease greatly. Consequently, the bias of the unadjusted win ratio estimate may increase greatly, producing either an overestimate or an underestimate. We demonstrate theoretically and through simulation that the IPCW-adjusted win ratio statistic gives an unbiased estimate of treatment effect.

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.

Review and comparison of ROC curve estimators for a time-dependent outcome with marker-dependent censoring.

To quantify the ability of a marker to predict the onset of a clinical outcome in the future, time-dependent estimators of sensitivity, specificity, and ROC curve have been proposed accounting for censoring of the outcome. In this paper, we review these estimators, recall their assumptions about the censoring mechanism and highlight their relationships and properties. A simulation study shows that marker-dependent censoring can lead to important biases for the ROC estimators not adapted to this case. A slight modification of the inverse probability of censoring weighting estimators proposed by Uno et al. (2007) and Hung and Chiang (2010a) performs as well as the nearest neighbor estimator of Heagerty et al. (2000) in the simulation study and has interesting practical properties. Finally, the estimators were used to evaluate abilities of a marker combining age and a cognitive test to predict dementia in the elderly. Data were obtained from the French PAQUID cohort. The censoring appears clearly marker-dependent leading to appreciable differences between ROC curves estimated with the different methods.

Dynamic Prediction of Near-Term Overall Survival in Patients with Advanced NSCLC Based on Real-World Data.

Patients with terminal cancers commonly receive aggressive and sub-optimal treatment near the end of life, which may not be beneficial in terms of duration or quality of life. To improve end-of-life care, it is essential to develop methods that can accurately predict the short-term risk of death. However, most prediction models for patients with cancer are static in the sense that they only use patient features at a fixed time. We proposed a dynamic prediction model (DPM) that can incorporate time-dependent predictors. We apply this method to patients with advanced non-small-cell lung cancer from a real-world database. Inverse probability of censoring weighted AUC with bootstrap inference was used to compare predictions among models. We found that increasing ECOG performance status and decreasing albumin had negative prognostic associations with overall survival (OS). Moreover, the negative prognostic implications strengthened over the patient disease course. DPMs using both time-independent and time-dependent predictors substantially improved short-term prediction accuracy compared to Cox models using only predictors at a fixed time. The proposed model can be broadly applied for prediction based on longitudinal data, including an estimation of the dynamic effects of time-dependent features on OS and updating predictions at any follow-up time.

A Conditional Probability Model to Predict the Mortality in Patients With Breast Cancer: A Bayesian Network Analysis.

BACKGROUND: The aim of this study was to compute the event rate of patients with breast cancer (BC) using Bayesian network (BN) structure. METHOD: Data for 1,154 patients newly diagnosed with BC were recruited in this study during 2007 and 2016 in Iran. The database was linked to the regional death registration system and active follow-up was performed by referring to hospital information system or calling the patients. BN structure with inverse probability of censoring weighting (IPCW) approach was used to assess the relationship between event rate and underlying risk factors. RESULTS: The median (25th, 75th percentiles) of patients' survival time was 46.8 (32.6, 69.3) months. There were 217 (18.8%) deaths from BC by the end of the study. The optimal BN structure (Akaike Information Criteria = -8743.66 and Bayesian Information Criteria = -8790.80) indicated that being male (conditional probability [CP] = 0.316), age >50 (CP = 0.215), higher grades (CP = 0.301) and lower survival times (CP = 0.566) had higher event rate. Also lobular carcinoma (CP = 0.157) and ductal carcinoma (CP = 0.178) type of morphology had lower event rate while other types (CP = 0.316) had higher. CONCLUSIONS: The BN structure in which time was as a mediator of predictors-event relationship could be presented as the optimal tool to compute the event rate of BC. The findings could be used to identify the high risk patients and recommend for health policy making, prevention and planning for decrease the mortality in patients with BC.

Guidance for a causal comparative effectiveness analysis emulating a target trial based on big real world evidence: when to start statin treatment.

Aim: The aim of this project is to describe a causal (counterfactual) approach for analyzing when to start statin treatment to prevent cardiovascular disease using real-world evidence. Methods: We use directed acyclic graphs to operationalize and visualize the causal research question considering selection bias, potential time-independent and time-dependent confounding. We provide a study protocol following the 'target trial' approach and describe the data structure needed for the causal assessment. Conclusion: The study protocol can be applied to real-world data, in general. However, the structure and quality of the database play an essential role for the validity of the results, and database-specific potential for bias needs to be explicitly considered.

Prediction accuracy for the cure probabilities in mixture cure models.

Prediction accuracy of a cure model when it is used to predict the cure probability of a patient is an important but not well-addressed issue in survival analysis. We propose a method to assess the prediction accuracy of a mixture cure model in predicting cure probability based on inverse probability of censoring weights to incorporate the censoring and latent cure status in the data. The inverse probability of censoring weight-adjusted estimator is shown to be consistent for the true expected prediction error for cure probability. A simulation study shows that the estimator performs well with finite samples when subjects with censored survival times greater than the largest uncensored time are identified as cured, an approach that is often used in mixture cure model literature to increase model identifiability. The simulation study also investigates the performance of the estimator with different thresholds to identify cured subjects and the estimator based on observed (training) data only. The method is applied to bone barrow transplant data for leukemia patients for assessing prediction accuracy for the cure probabilities.

CD4 trajectory adjusting for dropout among HIV-positive patients receiving combination antiretroviral therapy in an East African HIV care centre.

OBJECTIVE: Estimates of CD4 response to antiretroviral therapy (ART) obtained by averaging data from patients in care, overestimate population CD4 response and treatment program effectiveness because they do not consider data from patients who are deceased or not in care. We use mathematical methods to assess and adjust for this bias based on patient characteristics. DESIGN: We examined data from 25,261 HIV-positive patients from the East Africa IeDEA Consortium. METHODS: We used inverse probability of censoring weighting (IPCW) to represent patients not in care by patients in care with similar characteristics. We address two questions: What would the median CD4 be "had everyone starting ART remained on observation?" and "were everyone starting ART maintained on treatment?" RESULTS: Routine CD4 count estimates were higher than adjusted estimates even under the best-case scenario of maintaining all patients on treatment. Two years after starting ART, differences between estimates diverged from 30 cells/µL, assuming similar mortality and treatment access among dropouts as patients in care, to over 100 cells/µL assuming 20% lower survival and 50% lower treatment access among dropouts. When considering only patients in care, the proportion of patients with CD4 above 350 cells/µL was 50% adjusted to below 30% when accounting for patients not in care. One-year mortality diverged 6-14% from the naïve estimates depending on assumptions about access to care among lost patients. CONCLUSIONS: Ignoring mortality and loss to care results in over-estimation of ART response for patients starting treatment and exaggerates the efficacy of treatment programs administering it.