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

Multiple assessments of non-inferiority trials with ordinal endpoints

Non-inferiority (NI) trials are implemented when there is a practical demand to search for alternatives to standard therapies, such as to reduce side effects. An experimental treatment is considered non-inferior to the standard treatment when it exhibits clinically non-significant loss of efficacy. Ordinal categorical responses are frequently observed in clinical trials. It has been reported that responses measured using an ordinal scale produce more informative analysis than when responses collapse into binary outcomes. We study the NI trials using ordinal endpoints. We propose a latent variable model for ordinal categorical responses. Based on the proposed latent variable model, the mean efficacy of the different treatments is denoted by the corresponding mean parameter of the underlying continuous distributions. A two-step procedure is proposed for model identification and parameter estimation. A non-inferiority analysis can then be conducted based on the latent variable model and the corresponding estimation procedure. We also develop a method and an algorithm to produce an optimal sample size configuration based on the proposed testing procedure. Two clinical examples are provided for demonstrative purposes.

Comparison of treatments with ordinal responses in trials with sequential monitoring and response-adaptive randomization

In clinical trials, comparisons of treatments with ordinal responses are frequently conducted using the proportional odds model. However, the use of this model necessitates the adoption of the proportional odds assumption, which may not be appropriate. In particular, when responses are skewed, the use of the proportional odds model may result in a markedly inflated type I error rate. The latent Weibull distribution has recently been proposed to remedy this problem, and it has been demonstrated to be superior to the proportional odds model, especially when response-adaptive randomization is incorporated. However, there are several drawbacks associated with the latent Weibull model and the previously suggested response-adaptive treatment randomization scheme. In this paper, we propose the modified latent Weibull model to address these issues. Based on the modified latent Weibull model, the original response-adaptive design was also revised. In addition, the group sequential monitoring mechanism was included to enable interim analyses to be performed to determine, during a trial, whether a specific treatment is significantly more effective than another. If so, this will enable the trial to be terminated at a much earlier stage than a trial based on a fixed sample size. We performed a simulation study that clearly demonstrated the merits of our proposed framework. Furthermore, we redesigned a clinical study to further illustrate the advantages of our response-adaptive approach.

Noninferiority testing for matched-pair ordinal data with misclassification

New treatments that are noninferior or equivalent to-but not necessarily superior to-the reference treatment may still be beneficial to patients because they have fewer side effects, are more convenient, take less time, or cost less. The noninferiority test is widely used in medical research to provide guidance in such situation. In addition, categorical variables are frequently encountered in medical research, such as in studies involving patient-reported outcomes. In this paper, we develop a noninferiority testing procedure for correlated ordinal categorical variables based on a paired design with a latent normal distribution approach. Misclassification is frequently encountered in the collection of ordinal categorical data; therefore, we further extend the procedure to account for misclassification using information in the partially validated data. Simulation studies are conducted to investigate the accuracy of the estimates, the type I error rates, and the power of the proposed procedure. Finally, we analyze one substantive example to demonstrate the utility of the proposed approach.

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.

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.