Robust analyzes for longitudinal clinical trials with missing and non-normal continuous outcomes.

Missing data is unavoidable in longitudinal clinical trials, and outcomes are not always normally distributed. In the presence of outliers or heavy-tailed distributions, the conventional multiple imputation with the mixed model with repeated measures analysis of the average treatment effect (ATE) based on the multivariate normal assumption may produce bias and power loss. Control-based imputation (CBI) is an approach for evaluating the treatment effect under the assumption that participants in both the test and control groups with missing outcome data have a similar outcome profile as those with an identical history in the control group. We develop a robust framework to handle non-normal outcomes under CBI without imposing any parametric modeling assumptions. Under the proposed framework, sequential weighted robust regressions are applied to protect the constructed imputation model against non-normality in the covariates and the response variables. Accompanied by the subsequent mean imputation and robust model analysis, the resulting ATE estimator has good theoretical properties in terms of consistency and asymptotic normality. Moreover, our proposed method guarantees the analysis model robust-ness of the ATE estimation in the sense that its asymptotic results remain intact even when the analysis model is misspecified. The superiority of the proposed robust method is demonstrated by comprehensive simulation studies and an AIDS clinical trial data application.

Multiply robust estimators in longitudinal studies with missing data under control-based imputation.

Longitudinal studies are often subject to missing data. The recent guidance from regulatory agencies, such as the ICH E9(R1) addendum addresses the importance of defining a treatment effect estimand with the consideration of intercurrent events. Jump-to-reference (J2R) is one classical control-based scenario for the treatment effect evaluation, where the participants in the treatment group after intercurrent events are assumed to have the same disease progress as those with identical covariates in the control group. We establish new estimators to assess the average treatment effect based on a proposed potential outcomes framework under J2R. Various identification formulas are constructed, motivating estimators that rely on different parts of the observed data distribution. Moreover, we obtain a novel estimator inspired by the efficient influence function, with multiple robustness in the sense that it achieves n1/2-consistency if any pairs of multiple nuisance functions are correctly specified, or if the nuisance functions converge at a rate not slower than n-1/4 when using flexible modeling approaches. The finite-sample performance of the proposed estimators is validated in simulation studies and an antidepressant clinical trial.

Safety signal detection with control of latent factors.

Postmarket drug safety database like vaccine adverse event reporting system (VAERS) collect thousands of spontaneous reports annually, with each report recording occurrences of any adverse events (AEs) and use of vaccines. We hope to identify signal vaccine-AE pairs, for which certain vaccines are statistically associated with certain adverse events (AE), using such data. Thus, the outcomes of interest are multiple AEs, which are binary outcomes and could be correlated because they might share certain latent factors; and the primary covariates are vaccines. Appropriately accounting for the complex correlation among AEs could improve the sensitivity and specificity of identifying signal vaccine-AE pairs. We propose a two-step approach in which we first estimate the shared latent factors among AEs using a working multivariate logistic regression model, and then use univariate logistic regression model to examine the vaccine-AE associations after controlling for the latent factors. Our simulation studies show that this approach outperforms current approaches in terms of sensitivity and specificity. We apply our approach in analyzing VAERS data and report our findings.

A novel power prior approach for borrowing historical control data in clinical trials.

There has been an increased interest in borrowing information from historical control data to improve the statistical power for hypothesis testing, therefore reducing the required sample sizes in clinical trials. To account for the heterogeneity between the historical and current trials, power priors are often considered to discount the information borrowed from the historical data. However, it can be challenging to choose a fixed power prior parameter in the application. The modified power prior approach, which defines a random power parameter with initial prior to control the amount of historical information borrowed, may not directly account for heterogeneity between the trials. In this paper, we propose a novel approach to pick a power prior based on some direct measures of distributional differences between historical control data and current control data under normal assumptions. Simulations are conducted to investigate the performance of the proposed approach compared with current approaches (e.g. commensurate prior, meta-analytic-predictive, and modified power prior). The results show that the proposed power prior improves the study power while controlling the type I error within a tolerable limit when the distribution of the historical control data is similar to that of the current control data. The method is developed for both superiority and non-inferiority trials and is illustrated with an example from vaccine clinical trials.

Estimands and estimators of two-level methods using return to baseline strategy for longitudinal clinical trials with incomplete daily patient reported outcomes.

Returning to baseline (RTB) has been a practical method for handling missing data. Here we consider longitudinal clinical trials with daily patient reported outcomes (PROs), where efficacy endpoints are often defined as the average daily values in a cycle (such as a month or a week). The conventional method treats data at cycle level and ignores daily values. In this paper, we build a two-level constrained longitudinal data analysis (cLDA) model on daily values and propose two-level RTB method to impute daily values. Standard multiple imputation (MI) approach and likelihood-based approach are proposed and evaluated by simulations.

SMIM: A unified framework of survival sensitivity analysis using multiple imputation and martingale.

Censored survival data are common in clinical trial studies. We propose a unified framework for sensitivity analysis to censoring at random in survival data using multiple imputation and martingale, called SMIM. The proposed framework adopts the δ-adjusted and control-based models, indexed by the sensitivity parameter, entailing censoring at random and a wide collection of censoring not at random assumptions. Also, it targets a broad class of treatment effect estimands defined as functionals of treatment-specific survival functions, taking into account missing data due to censoring. Multiple imputation facilitates the use of simple full-sample estimation; however, the standard Rubin's combining rule may overestimate the variance for inference in the sensitivity analysis framework. We decompose the multiple imputation estimator into a martingale series based on the sequential construction of the estimator and propose the wild bootstrap inference by resampling the martingale series. The new bootstrap inference has a theoretical guarantee for consistency and is computationally efficient compared to the nonparametric bootstrap counterpart. We evaluate the finite-sample performance of the proposed SMIM through simulation and an application on an HIV clinical trial.

Sensitivity analyses in longitudinal clinical trials via distributional imputation.

Missing data is inevitable in longitudinal clinical trials. Conventionally, the missing at random assumption is assumed to handle missingness, which however is unverifiable empirically. Thus, sensitivity analyses are critically important to assess the robustness of the study conclusions against untestable assumptions. Toward this end, regulatory agencies and the pharmaceutical industry use sensitivity models such as return-to-baseline, control-based, and washout imputation, following the ICH E9(R1) guidance. Multiple imputation is popular in sensitivity analyses; however, it may be inefficient and result in an unsatisfying interval estimation by Rubin's combining rule. We propose distributional imputation in sensitivity analysis, which imputes each missing value by samples from its target imputation model given the observed data. Drawn on the idea of Monte Carlo integration, the distributional imputation estimator solves the mean estimating equations of the imputed dataset. It is fully efficient with theoretical guarantees. Moreover, we propose weighted bootstrap to obtain a consistent variance estimator, taking into account the variabilities due to model parameter estimation and target parameter estimation. The superiority of the distributional imputation framework is validated in the simulation study and an antidepressant longitudinal clinical trial.

Efficient Multiple Imputation for Sensitivity Analysis of Recurrent Events Data with Informative Censoring.

Missing data are commonly encountered in clinical trials due to dropout or nonadherence to study procedures. In trials in which recurrent events are of interest, the observed count can be an undercount of the events if a patient drops out before the end of the study. In many applications, the data are not necessarily missing at random and it is often not possible to test the missing at random assumption. Consequently, it is critical to conduct sensitivity analysis. We develop a control-based multiple imputation method for recurrent events data, where patients who drop out of the study are assumed to have a similar response profile to those in the control group after dropping out. Specifically, we consider the copy reference approach and the jump to reference approach. We model the recurrent event data using a semiparametric proportional intensity frailty model with the baseline hazard function completely unspecified. We develop nonparametric maximum likelihood estimation and inference procedures. We then impute the missing data based on the large sample distribution of the resulting estimators. The variance estimation is corrected by a bootstrap procedure. Simulation studies demonstrate the proposed method performs well in practical settings. We provide applications to two clinical trials.

Mixture survival trees for cancer risk classification.

In oncology studies, it is important to understand and characterize disease heterogeneity among patients so that patients can be classified into different risk groups and one can identify high-risk patients at the right time. This information can then be used to identify a more homogeneous patient population for developing precision medicine. In this paper, we propose a mixture survival tree approach for direct risk classification. We assume that the patients can be classified into a pre-specified number of risk groups, where each group has distinct survival profile. Our proposed tree-based methods are devised to estimate latent group membership using an EM algorithm. The observed data log-likelihood function is used as the splitting criterion in recursive partitioning. The finite sample performance is evaluated by extensive simulation studies and the proposed method is illustrated by a case study in breast cancer.

Inferring latent heterogeneity using many feature variables supervised by survival outcome.

In cancer studies, it is important to understand disease heterogeneity among patients so that precision medicine can particularly target high-risk patients at the right time. Many feature variables such as demographic variables and biomarkers, combined with a patient's survival outcome, can be used to infer such latent heterogeneity. In this work, we propose a mixture model to model each patient's latent survival pattern, where the mixing probabilities for latent groups are modeled through a multinomial distribution. The Bayesian information criterion is used for selecting the number of latent groups. Furthermore, we incorporate variable selection with the adaptive lasso into inference so that only a few feature variables will be selected to characterize the latent heterogeneity. We show that our adaptive lasso estimator has oracle properties when the number of parameters diverges with the sample size. The finite sample performance is evaluated by the simulation study, and the proposed method is illustrated by two datasets.

Estimand framework: Delineating what to be estimated with clinical questions of interest in clinical trials.

ICH (International Council for Harmonization) E9 R1 (2019) proposes a framework to define estimands in clinical trials. Although the concept of estimand was proposed previously when US Food and Drug Administration (FDA) issued the panel report on handling missing data in clinical trials, many details including attributes and different strategies have not been developed until the recent ICH E9 (R1) addendum. A clearly defined estimand should include considerations of five attributes including patient population, treatment regimen of interest, endpoint/variables, handling of intercurrent events (IEs), and summary measures for assessing treatment effect. To evaluate the underlying treatment effects of a new investigational drug or biologic product, it is desirable to consider estimands that are aligned with the objectives of the study and that are meaningful to the stakeholders such as physicians or patients, health authority administration, and payers, etc.. In this paper, the concepts, attributes and strategies of the estimand framework will be reviewed and illustrated with clinical trial examples. Some common estimands and their associated scientific questions are discussed within a causal inference framework for longitudinal clinical trials.

Analysis of time-to-event data using a flexible mixture model under a constraint of proportional hazards.

Cox proportional hazards (PH) model evaluates the effects of interested covariates under PH assumption without specified the baseline hazard. In clinical trial applications, however, the explicitly estimated hazard or cumulative survival function for each treatment group helps to assess and interpret the meaning of treatment difference. In this paper, we propose to use a flexible mixture model under the PH constraint to fit the underline survival functions. Simulations are conducted to evaluate its performance and show that the proposed mixture PH model is very similar to the Cox PH model in terms of estimating the hazard ratio, bias, confidence interval coverage, type-I error and testing power. Application to several real clinical trial examples demonstrates that the results from this approach are almost identical to the results from Cox PH model. The explicitly estimated hazard function for each treatment group provides additional useful information and helps the interpretation of hazard comparisons.

Two-level approaches to missing data in longitudinal trials with daily patient-reported outcomes.

In longitudinal clinical trials with daily patient-reported outcomes, the analysis endpoints are often defined as the averaged daily diary outcomes in a treatment cycle (such as a month or a week). Conventional methods often deal with missing data at the cycle level by imputing the average, and the cycle average is treated as missing if the number of days with available outcomes in the treatment cycle is less than a certain number. This was the method used for a case study of a phase 3 clinical trial evaluating a treatment for insomnia with daily patient-reported outcomes. Such methods may introduce bias. Motivated by this, we propose methods to impute missing daily outcomes in this paper. Specifically, we define a two-level missing pattern for clinical trials with daily patient-reported outcomes, and propose two-level methods to impute missing data at daily base. Other than the standard methods by multiple imputations, we derive analytic formulas for the proposed two-level methods to reduce computational intensity and improve the estimates of variances. The proposed two-level methods provide more powerful approaches to estimate the treatment difference compared to the conventional cycle-level methods, which are evaluated by theoretical development and simulation studies. In addition, the methods are applied to the motivating phase 3 trial evaluating a treatment for insomnia with daily patient-reported outcomes.

Controlling false discovery proportion in identification of drug-related adverse events from multiple system organ classes.

Analyzing safety data from clinical trials to detect safety signals worth further examination involves testing multiple hypotheses, one for each observed adverse event (AE) type. There exists certain hierarchical structure for these hypotheses due to the classification of the AEs into system organ classes, and these AEs are also likely correlated. Many approaches have been proposed to identify safety signals under the multiple testing framework and tried to achieve control of false discovery rate (FDR). The FDR control concerns the expectation of the false discovery proportion (FDP). In practice, the control of the actual random variable FDP could be more relevant and has recently drawn much attention. In this paper, we proposed a two-stage procedure for safety signal detection with direct control of FDP, through a permutation-based approach for screening groups of AEs and a permutation-based approach of constructing simultaneous upper bounds for false discovery proportion. Our simulation studies showed that this new approach has controlled FDP. We demonstrate our approach using data sets derived from a drug clinical trial.

A flexible parametric survival model for fitting time to event data in clinical trials.

Time-to-event data are common in clinical trials to evaluate survival benefit of a new drug, biological product, or device. The commonly used parametric models including exponential, Weibull, Gompertz, log-logistic, log-normal, are simply not flexible enough to capture complex survival curves observed in clinical and medical research studies. On the other hand, the nonparametric Kaplan Meier (KM) method is very flexible and successful on catching the various shapes in the survival curves but lacks ability in predicting the future events such as the time for certain number of events and the number of events at certain time and predicting the risk of events (eg, death) over time beyond the span of the available data from clinical trials. It is obvious that neither the nonparametric KM method nor the current parametric distributions can fulfill the needs in fitting survival curves with the useful characteristics for predicting. In this paper, a full parametric distribution constructed as a mixture of three components of Weibull distribution is explored and recommended to fit the survival data, which is as flexible as KM for the observed data but have the nice features beyond the trial time, such as predicting future events, survival probability, and hazard function.

Efficient methods for signal detection from correlated adverse events in clinical trials.

It is an important and yet challenging task to identify true signals from many adverse events that may be reported during the course of a clinical trial. One unique feature of drug safety data from clinical trials, unlike data from post-marketing spontaneous reporting, is that many types of adverse events are reported by only very few patients leading to rare events. Due to the limited study size, the p-values of testing whether the rate is higher in the treatment group across all types of adverse events are in general not uniformly distributed under the null hypothesis that there is no difference between the treatment group and the placebo group. A consequence is that typically fewer than 100α percent of the hypotheses are rejected under the null at the nominal significance level of α . The other challenge is multiplicity control. Adverse events from the same body system may be correlated. There may also be correlations between adverse events from different body systems. To tackle these challenging issues, we develop Monte-Carlo-based methods for the signal identification from patient-reported adverse events in clinical trials. The proposed methodologies account for the rare events and arbitrary correlation structures among adverse events within and/or between body systems. Extensive simulation studies demonstrate that the proposed method can accurately control the family-wise error rate and is more powerful than existing methods under many practical situations. Application to two real examples is provided.

Control-based imputation for sensitivity analyses in informative censoring for recurrent event data.

In clinical trials, missing data commonly arise through nonadherence to the randomized treatment or to study procedure. For trials in which recurrent event endpoints are of interests, conventional analyses using the proportional intensity model or the count model assume that the data are missing at random, which cannot be tested using the observed data alone. Thus, sensitivity analyses are recommended. We implement the control-based multiple imputation as sensitivity analyses for the recurrent event data. We model the recurrent event using a piecewise exponential proportional intensity model with frailty and sample the parameters from the posterior distribution. We impute the number of events after dropped out and correct the variance estimation using a bootstrap procedure. We apply the method to an application of sitagliptin study.

On inference of control-based imputation for analysis of repeated binary outcomes with missing data.

Missing data are common in longitudinal clinical trials. How to handle missing data is critical for both sponsors and regulatory agencies to assess treatment effect from the trials. Recently, a control-based imputation has been proposed, where the missing data are imputed based on the assumption that patients who discontinued the test drug will have a similar response profile to the patients in the control group. Under control-based imputation, the variance estimation may be biased using Rubin's formula which could produce biased statistical inferences. We evaluate several statistical methods for obtaining appropriate variances under control-based imputation for analysis of repeated binary outcomes with monotone missing data and show that both the analytical method developed by Robins & Wang and the nonparametric bootstrap method provide more appropriate variance estimates under various simulation settings. We use the methods in an application of an antidepressant Phase III clinical trial and give discussion and recommendations on method performance and preference.

Lot-to-lot Consistency, Safety, Tolerability and Immunogenicity of an Investigational Hexavalent Vaccine in US Infants.

BACKGROUND: This multicenter phase III study (NCT01340937) evaluated the consistency of immune responses to 3 separate lots of diphtheria-tetanus toxoids-acellular pertussis 5, inactivated poliovirus vaccine, Haemophilus influenzae type b, and hepatitis B (DTaP5-IPV-Hib-HepB), an investigational hexavalent vaccine (HV). METHODS: Healthy infants were randomized (2:2:2:1) to receive HV or Pentacel (Control). Groups 1, 2 and 3 received HV at 2, 4 and 6 months, and Control at 15 months. Group 4 received Control at 2, 4, 6 and 15 months, plus Recombivax HB (HepB) at 2 and 6 months. Concomitant Prevnar 13 was given to all groups at 2, 4, 6 and 15 months; pentavalent rotavirus vaccine (RV5) was given to all groups at 2, 4 and 6 months. Blood specimens (3-5 mL) were collected immediately before administration of dose 1, postdose 3, immediately before toddler dose, and after toddler dose. Adverse events were recorded after each vaccination. RESULTS: The 3 manufacturing lots of HV induced consistent antibody responses to all antigens. Immunogenicity of HV was noninferior to Control for all antibodies, except for pertussis filamentous hemagglutinin geometric mean concentration postdose 3, and pertussis pertactin (PRN) geometric mean concentration after toddler dose. Postdose 3 immunogenicity of concomitantly administered Prevnar 13 was generally similar (except for serotype 6B) when given with HV or Control. Adverse events of HV were similar to Control, except for a higher rate of fever ≥38.0°C [49.2% vs. 35.4%, estimated difference 13.7% (8.4, 18.8)]. CONCLUSIONS: HV demonstrated lot-to-lot manufacturing consistency; safety and immunogenicity were comparable with the licensed vaccines. HV provides a new combination vaccine option within the US 2-month, 4-month and 6-month vaccine series.