Testing noninferiority in three-armed clinical trials based on likelihood ratio statistics

Optimization the design of fixed and group sequential three-arm non-inferiority trials with dichotomous endpoints of risk difference and odds ratio

Although the risk difference (RD) is the most common and well explored functional form for testing efficacy with dichotomous endpoint, odds ratio (OR) is also suggested and well applied measure for non-inferiority (NI) trials. Since the construction and interpretation of these function forms are quite different, this study aims to provide detailed discussions and comprehensive comparisons on the design and testing approach for RD and OR scales for the fixed and group sequential three-arm NI trials under various of situations. The sample size determinations and testing approaches for assessing NI of a new treatment in three-arm clinical trials for RD and OR scales were reviewed comprehensively. Simulation studies are conducted for hundreds of scenarios with parameter configurations of the response rates, randomized allocations, NI margins and interim analysis. The operating characteristic (OC) of RD and OR scales based on the MLE and RMLE methods were thoroughly investigated. A trial example was designed and analyzed to demonstrate the methodologies. It is found that sample size determination on OR scale gives smaller sample size and robust procedure compared to RD scale in the majority of situations. When evaluating the behaviors of the attained power, the RMLE methods based on OR scale outperforms the MLE method and tend to have more power to reject the null hypothesis especially under the small sample size situations. Compared to the fixed design, the group sequential design has better OC, which provides a comparable power while needing smaller total average sample sizes for all cases. In addition, we suggest a lower significance level with a higher power for the sample size determination in the superiority test stage in the group sequential design, which can significantly reduce the total sample sizes while the number of subjects in the placebo group does not increase much. It can offer some recommendations for the investigators to choose the optimal endpoints and parameter configurations to design a three-arm NI trial under certain situations.

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.

Testing non-inferiority of a new treatment in three-arm clinical trials with binary endpoints

BACKGROUND

A two-arm non-inferiority trial without a placebo is usually adopted to demonstrate that an experimental treatment is not worse than a reference treatment by a small pre-specified non-inferiority margin due to ethical concerns. Selection of the non-inferiority margin and establishment of assay sensitivity are two major issues in the design, analysis and interpretation for two-arm non-inferiority trials. Alternatively, a three-arm non-inferiority clinical trial including a placebo is usually conducted to assess the assay sensitivity and internal validity of a trial. Recently, some large-sample approaches have been developed to assess the non-inferiority of a new treatment based on the three-arm trial design. However, these methods behave badly with small sample sizes in the three arms. This manuscript aims to develop some reliable small-sample methods to test three-arm non-inferiority.

METHODS

Saddlepoint approximation, exact and approximate unconditional, and bootstrap-resampling methods are developed to calculate p-values of the Wald-type, score and likelihood ratio tests. Simulation studies are conducted to evaluate their performance in terms of type I error rate and power.

RESULTS

Our empirical results show that the saddlepoint approximation method generally behaves better than the asymptotic method based on the Wald-type test statistic. For small sample sizes, approximate unconditional and bootstrap-resampling methods based on the score test statistic perform better in the sense that their corresponding type I error rates are generally closer to the prespecified nominal level than those of other test procedures.

CONCLUSIONS

Both approximate unconditional and bootstrap-resampling test procedures based on the score test statistic are generally recommended for three-arm non-inferiority trials with binary outcomes.

The likelihood ratio test for non-standard hypotheses near the boundary of the null – with application to the assessment of non-inferiority

We consider a class of testing problems where the null space is the union of k-1 subgraphs of the form h j (θ j )≤θ k , with j=1,…,k-1, (θ 1,…,θ k ) the unknown parameter, and h j given increasing functions. The data consist of k independent samples, assumed to be drawn from a distribution with parameter θ j , j=1,…,k, respectively. An important class of examples covered by this setting is that of non-inferiority hypotheses, which have recently become important in the evaluation of drugs or therapies. When the true parameter approaches the boundary at a 1/√n rate, we give the explicit form of the asymptotic distribution of the log-likelihood ratio statistic. This extends previous work on the distribution of likelihood ratio statistics to local alternatives. We consider the prominent example of binomial data and illustrate the theory for k=2 and 3 samples. We explain how this can be used for planning a non-inferiority trial. To this end we calculate the optimal sample ratios yielding the maximal power in a binomial non-inferiority trial.