Two-stage optimal designs with survival endpoint when the follow-up time is restricted

Response adaptive randomization design for a two-stage study with binary response

Response adaptive randomization has the potential to treat more participants in better treatments in a trial to benefit participants. We propose optimal response adaptive randomization designs for a two-stage study with binary response, having the smallest expected sample size or the fewest expected number of failures. Equal randomization is used in the first stage, and data from the first stage is used to determine the adaptive sample size ratio in the second stage. In the proposed optimal designs, the type I error rate and the statistical power are calculated from the asymptotic normal distributions. The new designs that minimize the expected number of failures have the advantage over the existing optimal randomized designs to substantially reduce the number of failures.

Effects of dose change on the success of clinical trials

The search for disease modifying therapies in Alzheimers disease (AD) has recently led to promising results but also revealed design issues in clinical trials themselves. Of particular importance is the potential statistical challenges that can arise when dosages change after an interim analysis, which is not uncommon in contemporary AD trials. Following the recent Aducanumab trials, we sought to study the implications of dose changes on the statistical power of an AD trial. We conducted extensive simulations to calculate statistical power when the relationship between treatment effect size and time is linear or non-linear, and the investigated drug has delayed treatment effect or not. Statistical power depends on many design factors including the dose change time, correlation, population homogeneity, and treatment effect time. We recommend that researchers conduct simulation studies at the interim analysis to justify the modified sample size and/or follow-up time modification meanwhile the type I and II error rates are controlled.

Monte Carlo cross-validation for a study with binary outcome and limited sample size

Cross-validation (CV) is a resampling approach to evaluate machine learning models when sample size is limited. The number of all possible combinations of folds for the training data, known as CV rounds, are often very small in leave-one-out CV. Alternatively, Monte Carlo cross-validation (MCCV) can be performed with a flexible number of simulations when computational resources are feasible for a study with limited sample size. We conduct extensive simulation studies to compare accuracy between MCCV and CV with the same number of simulations for a study with binary outcome (e.g., disease progression or not). Accuracy of MCCV is generally higher than CV although the gain is small. They have similar performance when sample size is large. Meanwhile, MCCV is going to provide reliable performance metrics as the number of simulations increases. Two real examples are used to illustrate the comparison between MCCV and CV.

Continuity corrected score confidence interval for the difference in proportions in paired data

For paired binary data, the hybrid method and the score method are often recommended for use to calculate the confidence interval for risk difference. These asymptotic intervals do not control the coverage probability. We propose to develop a new score interval with continuity correction to further improve the performance of the existing intervals. The traditional correction value may be too large which leads to a wide interval. For that reason, we propose three different correction values to identify the optimal correction interval with balanced coverage probability and interval width. From simulation studies, we find that a small correction value for the score interval has good performance. In addition, we derive the non-iterative solutions for the developed continuity correction score intervals.

Optimal two-stage designs based on restricted mean survival time for a single-arm study

Restricted mean survival time is an alternative measure of treatment effect to hazard ratio in clinical trials with time-to-event outcome. The current methods have been focused on one-stage designs. In this article, we propose optimal two-stage designs for a single-arm study with the smallest expected sample size. We compare the performance of the new optimal two-stage designs with the existing one-stage design with regards to the expected sample size and the expected total study length. The simulation results indicate that the new two-stage designs can save the expected sample size substantially as compared to the one-stage design. We use a non-small cell lung cancer trial to illustrate the application of the proposed designs. The proposed optimal two-stage designs are recommended for use when time for patient accrual is longer than the pre-specified follow-up time.

Optimal two-stage design of single arm Phase II clinical trials based on median event time test

The Phase II clinical trials aim to assess the therapeutic efficacy of a new drug. The therapeutic efficacy has been often quantified by response rate such as overall response rate or survival probability in the Phase II setting. However, there is a strong desire to use survival time, which is the gold standard endpoint for the confirmatory Phase III study, when investigators set the primary objective of the Phase II study and test hypotheses based on the median survivals. We propose a method for median event time test to provide the sample size calculation and decision rule of testing. The decision rule is simple and straightforward in that it compares the observed median event time to the identified threshold. Moreover, it is extended to optimal two-stage design for practice, which extends the idea of Simon’s optimal two-stage design for survival endpoint. We investigate the performance of the proposed methods through simulation studies. The proposed methods are applied to redesign a trial based on median event time for trial illustration, and practical strategies are given for application of proposed methods.

Two-stage optimal designs based on exact variance for a single-arm trial with survival endpoints

Sample size calculation based on normal approximations is often associated with the loss of statistical power for a single-arm trial with a time-to-event endpoint. Recently, Wu (2015) derived the exact variance for the one-sample log-rank test under the alternative and showed that a single-arm one-stage study based on exact variance often has power above the nominal level while the type I error rate is controlled. We extend this approach to a single-arm two-stage design by using exact variances of the one-sample log-rank test for the first stage and the two stages combined. The empirical power of the proposed two-stage optimal designs is often not guaranteed under a two-stage design setting, which could be due to the asymptotic bi-variate normal distribution used to estimate the joint distribution of the test statistics. We adjust the nominal power level in the design search to guarantee the simulated power of the identified optimal design being above the nominal level. The sample size and the study time savings of the proposed two-stage designs are substantial as compared to the one-stage design.

Efficient statistical inference for a parallel study with missing data by using an exact method

In a parallel group study comparing a new treatment with a standard of care, missing data often occur for various reasons. When the outcome is binary, the data from such studies can be summarized into a 2 × 3 contingency table, with the missing observations in the last column. When the missingness is neither related to the outcome of interest nor related to other outcomes from the study but it is covariate dependent with the sole covariate being treatment, this type of missing data mechanism is considered as missing at random. In 2016, Tian et al.  proposed three statistics to test the hypothesis that the response rate is equivalent for a parallel group study with missing data. The asymptotic limiting distributions of these test statistics were used for statistical inference. However, asymptotic approaches for testing proportions generally do not have satisfactory performance with regard to type I error rate control for a clinical trial with the sample size from small to medium. For this reason, we consider an exact approach based on maximization to provide valid and efficient statistical inference for a parallel group study with missing data. Exact approaches can guarantee the type I error rate and they are computationally feasible in this setting. We conduct extensive numerical studies to compare the performance of the exact approach based on the three statistics for a one-sided hypothesis testing problem. We conclude that the exact approach based on the likelihood ratio statistic is more powerful than the exact approach based on the other two statistics. Two real clinical trial data sets are used to illustrate the application of the proposed exact approach.