Assessing toxicities in a clinical trial: Bayesian inference for ordinal data nested within categories

Assessing the incidence and severity of drug adverse events: a Bayesian hierarchical cumulative logit model

Detection of safety signals based on multiple comparisons of adverse events (AEs) between two treatments in a clinical trial involves evaluations requiring multiplicity adjustment. A Bayesian hierarchical mixture model is a good solution to this problem as it borrows information across AEs within the same System Organ Class (SOC) and modulates extremes due merely to chance. However, the hierarchical model compares only the incidence rates of AEs, regardless of severity. In this article, we propose a three-level Bayesian hierarchical non-proportional odds cumulative logit model. Our model allows for testing the equality of incidence rate and severity for AEs between the control arm and the treatment arm while addressing multiplicities. We conduct simulation study to investigate the operating characteristics of the proposed hierarchical model. The simulation study demonstrates that the proposed method could be implemented as an extension of the Bayesian hierarchical mixture model in detecting AEs with elevated incidence rate and/or elevated severity. To illustrate, we apply our proposed method using the safety data from a phase III, two-arm randomized trial.

Statistical methods for the analysis of adverse event data in randomised controlled trials: a scoping review and taxonomy

BACKGROUND

Statistical methods for the analysis of harm outcomes in randomised controlled trials (RCTs) are rarely used, and there is a reliance on simple approaches to display information such as in frequency tables. We aimed to identify whether any statistical methods had been specifically developed to analyse prespecified secondary harm outcomes and non-specific emerging adverse events (AEs).

METHODS

A scoping review was undertaken to identify articles that proposed original methods or the original application of existing methods for the analysis of AEs that aimed to detect potential adverse drug reactions (ADRs) in phase II-IV parallel controlled group trials. Methods where harm outcomes were the (co)-primary outcome were excluded. Information was extracted on methodological characteristics such as: whether the method required the event to be prespecified or could be used to screen emerging events; and whether it was applied to individual events or the overall AE profile. Each statistical method was appraised and a taxonomy was developed for classification.

RESULTS

Forty-four eligible articles proposing 73 individual methods were included. A taxonomy was developed and articles were categorised as: visual summary methods (8 articles proposing 20 methods); hypothesis testing methods (11 articles proposing 16 methods); estimation methods (15 articles proposing 24 methods); or methods that provide decision-making probabilities (10 articles proposing 13 methods). Methods were further classified according to whether they required a prespecified event (9 articles proposing 12 methods), or could be applied to emerging events (35 articles proposing 61 methods); and if they were (group) sequential methods (10 articles proposing 12 methods) or methods to perform final/one analyses (34 articles proposing 61 methods).

CONCLUSIONS

This review highlighted that a broad range of methods exist for AE analysis. Immediate implementation of some of these could lead to improved inference for AE data in RCTs. For example, a well-designed graphic can be an effective means to communicate complex AE data and methods appropriate for counts, time-to-event data and that avoid dichotomising continuous outcomes can improve efficiencies in analysis. Previous research has shown that adoption of such methods in the scientific press is limited and that strategies to support change are needed.

TRIAL REGISTRATION

PROSPERO registration: https://www.crd.york.ac.uk/prospero/display_record.php?RecordID=97442.

Response-adaptive treatment allocation for clinical studies with ordinal responses

Ordinal responses are common in clinical studies. Although the proportional odds model is a popular option for analyzing ordered-categorical data, it cannot control the type I error rate when the proportional odds assumption fails to hold. The latent Weibull model was recently shown to be a superior candidate for modeling ordinal data, with remarkably better performance than the latent normal model when the data are highly skewed. In clinical trials with ordinal responses, a balanced design is common, with equal sample allocation for each treatment. However, a more ethical approach is to adopt a response-adaptive allocation scheme in which more patients receive the better treatment. In this paper, we propose the use of the doubly adaptive biased coin design to generate treatment allocations that benefit the trial participants. The proposed treatment allocation scheme not only allows more patients to receive the better treatment, it also maintains compatible test power for the comparison of treatment efficiencies. A clinical example is used to illustrate the proposed procedure.

Nonparametric spatial models for clustered ordered periodontal data

Clinical attachment level (CAL) is regarded as the most popular measure to assess periodontal disease (PD). These probed tooth-site level measures are usually rounded and recorded as whole numbers (in mm) producing clustered (site measures within a mouth) error-prone ordinal responses representing some ordering of the underlying PD progression. In addition, it is hypothesized that PD progression can be spatially-referenced, i.e., proximal tooth-sites share similar PD status in comparison to sites that are distantly located. In this paper, we develop a Bayesian multivariate probit framework for these ordinal responses where the cut-point parameters linking the observed ordinal CAL levels to the latent underlying disease process can be fixed in advance. The latent spatial association characterizing conditional independence under Gaussian graphs is introduced via a nonparametric Bayesian approach motivated by the probit stick-breaking process, where the components of the stick-breaking weights follows a multivariate Gaussian density with the precision matrix distributed as G-Wishart. This yields a computationally simple, yet robust and flexible framework to capture the latent disease status leading to a natural clustering of tooth-sites and subjects with similar PD status (beyond spatial clustering), and improved parameter estimation through sharing of information. Both simulation studies and application to a motivating PD dataset reveal the advantages of considering this flexible nonparametric ordinal framework over other alternatives.

Multiple comparisons with two controls for ordered categorical responses

In clinical studies, ordered categorical responses are common. To compare the efficacy of several treatments with a control for ordinal responses, the normal latent variable model has recently been proposed. This approach conceptualizes the responses as manifestations of an underlying continuous normal variable. In this article, we extend this idea to develop the multiple comparison method for use when there are two controls in the clinical trial. The proposed method is constructed such that the familywise type I error rate is controlled at a prespecified level. In addition, for a given level of test power, the procedure to evaluate the required sample size is provided. The proposed testing procedure is also illustrated by an example from a clinical study.

Mitigating Bias in Generalized Linear Mixed Models: The Case for Bayesian Nonparametrics

Generalized linear mixed models are a common statistical tool for the analysis of clustered or longitudinal data where correlation is accounted for through cluster-specific random effects. In practice, the distribution of the random effects is typically taken to be a Normal distribution, although if this does not hold then the model is misspecified and standard estimation/inference may be invalid. An alternative is to perform a so-called nonparametric Bayesian analyses in which one assigns a Dirichlet process (DP) prior to the unknown distribution of the random effects. In this paper we examine operating characteristics for estimation of fixed effects and random effects based on such an analysis under a range of "true" random effects distributions. As part of this we investigate various approaches for selection of the precision parameter of the DP prior. In addition, we illustrate the use of the methods with an analysis of post-operative complications among n = 18, 643 female Medicare beneficiaries who underwent a hysterectomy procedure at N = 503 hospitals in the US. Overall, we conclude that using the DP priori n modeling the random effect distribution results in large reductions of bias with little loss of efficiency. While no single choice for the precision parameter will be optimal in all settings, certain strategies such as importance sampling or empirical Bayes can be used to obtain reasonable results in a broad range of data scenarios.

Comparison of two treatments with skewed ordinal responses

In clinical studies, the proportional odds model is widely used to compare treatment efficacies when the responses are categorically ordered. However, this model has been shown to be inappropriate when the proportional odds assumption is invalid, mainly because it is unable to control the type I error rate in such circumstances. To remedy this problem, the latent normal model was recently promoted and has been demonstrated to be superior to the proportional odds model. However, the application of the latent normal model is limited to compare treatments with similar underlying distributions except possibly their means and variances. When the underlying distributions are very different in skewness, both of the aforementioned procedures suffer from the undesirable inflation of the type I error rate. To solve the problem for clinical studies with ordinal responses, we provide a viable solution that relies on the use of the latent Weibull distribution, which is a member of the log-location-scale family. The proposed model is able to control the type I error rate regardless of the degree of skewness of the treatment responses. In addition, the power of the test also outperforms that of the latent normal model. The testing procedure draws on newly developed theoretical results related to latent distributions from the location-scale family. The testing procedure is illustrated with two clinical examples.

A unified framework for the comparison of treatments with ordinal responses

Different latent variable models have been used to analyze ordinal categorical data which can be conceptualized as manifestations of an unobserved continuous variable. In this paper, we propose a unified framework based on a general latent variable model for the comparison of treatments with ordinal responses. The latent variable model is built upon the location-scale family and is rich enough to include many important existing models for analyzing ordinal categorical variables, including the proportional odds model, the ordered probit-type model, and the proportional hazards model. A flexible estimation procedure is proposed for the identification and estimation of the general latent variable model, which allows for the location and scale parameters to be freely estimated. The framework advances the existing methods by enabling many other popular models for analyzing continuous variables to be used to analyze ordinal categorical data, thus allowing for important statistical inferences such as location and/or dispersion comparisons among treatments to be conveniently drawn. Analysis on real data sets is used to illustrate the proposed methods.

Step-up testing procedure for multiple comparisons with a control for a latent variable model with ordered categorical responses

In clinical studies, multiple comparisons of several treatments to a control with ordered categorical responses are often encountered. A popular statistical approach to analyzing the data is to use the logistic regression model with the proportional odds assumption. As discussed in several recent research papers, if the proportional odds assumption fails to hold, the undesirable consequence of an inflated familywise type I error rate may affect the validity of the clinical findings. To remedy the problem, a more flexible approach that uses the latent normal model with single-step and stepwise testing procedures has been recently proposed. In this paper, we introduce a step-up procedure that uses the correlation structure of test statistics under the latent normal model. A simulation study demonstrates the superiority of the proposed procedure to all existing testing procedures. Based on the proposed step-up procedure, we derive an algorithm that enables the determination of the total sample size and the sample size allocation scheme with a pre-determined level of test power before the onset of a clinical trial. A clinical example is presented to illustrate our proposed method.

Pairwise comparisons with ordered categorical data

Clinical trials frequently involve pairwise comparisons of different treatments to evaluate their relative efficacy. In this study, we examine methods for conducting pairwise tests of treatments with ordered categorical responses. A modified version of the Wilcoxon-Mann-Whitney test based on a logistic regression model assuming proportional odds is a popular choice for comparing two treatments. This paper discusses the extension of this test to pairwise comparisons involving more than two treatments. However, when the proportional odds assumption is not valid, the Wilcoxon-Mann-Whitney-type test procedure cannot control the overall type I error rate at the prespecified level of significance. We therefore propose a better strategy in which a latent normal model is employed. We presented a simulated comparative study of power and the overall type I error rate to illustrate the superiority of the latent normal model. Examples are also given for illustrative purposes.

Multiple comparisons with a control for a latent variable model with ordered categorical responses

Ordered categorical data are frequently encountered in clinical studies. A popular method for comparing the efficacy of treatments is to use logistic regression with the proportional odds assumption. The test statistic is based on the Wilcoxon-Mann-Whitney test. However, the proportional odds assumption may not be appropriate. In such cases, the probability of rejecting the null hypothesis is much inflated even though the treatments have the same mean efficacy. An alternative approach that does not rely on the proportional odds assumption is to conceptualize the responses as manifestations of some underlying continuous variables. However, statistical procedures were developed only for the comparison of two treatments. In this article, we derive testing procedures that compare several treatments to a control, utilizing a latent normal distribution with the latent variable model. The proposed procedure is useful because multiple comparisons with a control is very frequently an objective of a clinical study. Data from clinical trials are used to illustrate the proposed procedures.