Master of Science / Department of Statistics / Christopher Vahl / Sample size estimation is generally based on assumptions made during the planning stage of a clinical trial. Often, there is limited information available to estimate the initial sample size. This may result in a poor estimate. For instance, an insufficient sample size may not have the capability to produce statistically significant results, while an over-sized study will lead to a waste of resources or even ethical issues in that too many patients are exposed to potentially ineffective treatments. Therefore, an interim analysis in the middle of a trial may be worthwhile to assure that the significance level is at the nominal level and/or the power is adequate to detect a meaningful treatment difference. In this report, the impact of sample size re-estimation on the type I error rate for the continuous end-point in a clinical trial with two treatments is evaluated through a simulation study. Two sample size estimation methods are taken into consideration: blinded and partially unblinded. For the blinded method, all collected data for two groups are used to estimate the variance, while only data from the control group are used to re-estimate the sample size for the partially unblinded method. The simulation study is designed with different combinations of assumed variance, assumed difference in treatment means, and re-estimation methods. The end-point is assumed to follow normal distribution and the variance for both groups are assumed to be identical. In addition, equal sample size is required for each group. According to the simulation results, the type I error rates are preserved for all settings.

Master of Science / Department of Statistics / Christopher I. Vahl / Estimation of sample size is an important and critical procedure in the design of clinical trials. A trial with inadequate sample size may not produce a statistically significant result. On the other hand, having an unnecessarily large sample size will definitely increase the expenditure of resources and may cause a potential ethical problem due to the exposure of unnecessary number of human subjects to an inferior treatment. A poor estimate of the necessary sample size is often due to the limited information at the planning stage. Hence, the adjustment of the sample size mid-trial has become a popular strategy recently. In this work, we introduce two methods for sample size re-estimation for trials with a binary endpoint utilizing the interim information collected from the trial: a blinded method and a partially unblinded method. The blinded method recalculates the sample size based on the first stage’s overall event proportion, while the partially unblinded method performs the calculation based only on the control event proportion from the first stage. We performed simulation studies with different combinations of expected proportions based on fixed ratios of response rates. In this study, equal sample size per group was considered. The study shows that for both methods, the type I error rates were preserved satisfactorily.

Superiority clinical trials are often designed with a planned interim analysis for the purpose of sample size re-estimation (SSR) when limited information is available at the start of the trial to estimate the required sample size. Typically these trials are designed with a two-arm internal pilot where subjects are enrolled to both treatment arms prior to the interim analysis. Circumstances may sometimes call for a trial with a single-arm internal pilot (enroll only in the control group). For a dichotomous outcome, Herson and Wittes proposed a SSR method (HW-SSR) that can be applied to single-arm internal pilot trials using an unblinded estimate of the control group outcome rate. Previous evaluations of the HW-SSR method reported conflicting results regarding the impact of the method on the two-sided Type I error rate and power of the final hypothesis test. In this research we evaluate the HW-SSR method under the null and alternative hypothesis in various scenarios to investigate the one-sided Type I error rate and power of trials with a two-arm internal pilot. We find that the one-sided Type I error rate is sometimes inflated and that the power is sometimes reduced. We propose a new method, the Critical Value and Power Adjusted Sample Size Re-estimation (CVPA-SSR) algorithm to adjust the critical value cutoff used in the final Z-test and the power critical value used in the interim SSR formula to preserve the nominal Type I error rate and the desired power. We conduct simulations for trials with single-arm and two-arm internal pilots to confirm that the CVPA-SSR algorithm does preserve the nominal Type I error rate and the desired power. We investigate the robustness of the CVPA-SSR algorithm for trials with single-arm and two-arm internal pilots when the assumptions used in designing the trial are incorrect. No Type I error inflation is observed but significant over- or under-powering of the trial occurs when the treatment effect used to design the trial is misspecified.

A common approach to adapt the design of a clinical trial based on interim results is sample size re-estimation (SSR). SSR allows an increase in the trial's sample size in order to maintain, at the desired nominal level, the desired power to reject the null hypothesis conditioned on the interim observed treatment effect and its variance (i.e., the conditional power). There are several established approaches to SSR for clinical studies with independent and identically distributed observations; however, no established methods have been developed for trials where there is more than one observation collected per subject where within-subject correlation exists. Without accurately accounting for the within-subject correlation in SSR, a sponsor may incorrectly estimate the trial's conditional power to obtain statistical significance at the final analysis and hence risk overestimating or underestimating the number of patients required to complete the trial as planned. In this dissertation, we propose an extension of Mehta and Pocock's promising zone approach to SSR that reconciles the within-subject correlation in the data for a variety of superiority clinical trials. We consider trials with continuous and binary primary endpoints, and further we explore cases where patients contribute both the same and varying numbers of observations to the analysis of the primary endpoint. Using a simulation study, we show that in each case, our proposed conditional power formula accurately calculates conditional power and our proposed SSR methodology preserves the nominal type I error rate under the null hypothesis and maintains adequate power under the alternative hypothesis. Additionally, we demonstrate the robustness of our methodology to the mis-specification of a variety of distributional assumptions regarding the underlying population from which the data arise. / 2024-06-21T00:00:00Z

This thesis considers two related problems that has application in the field of experimental design for clinical trials: • fixed sample size determination for parallel arm, double-blind survival data analysis to test the hypothesis of no difference in survival functions, and • blinded sample size re-estimation for the same. For the first problem of fixed sample size determination, a method is developed generally for testing of hypothesis, then applied particularly to survival analysis; for the second problem of blinded sample size re-estimation, a method is developed specifically for survival analysis. In both problems, the exponential survival model is assumed. The approach we propose for sample size determination is Bayesian decision theoretical, using explicitly a loss function and a prior distribution. The loss function used is the intrinsic discrepancy loss function introduced by Bernardo and Rueda (2002), and further expounded upon in Bernardo (2011). We use a conjugate prior, and investigate the sensitivity of the calculated sample sizes to specification of the hyper-parameters. For the second problem of blinded sample size re-estimation, we use prior predictive distributions to facilitate calculation of the interim test statistic in a blinded manner while controlling the Type I error. The determination of the test statistic in a blinded manner continues to be nettling problem for researchers. The first problem is typical of traditional experimental designs, while the second problem extends into the realm of adaptive designs. To the best of our knowledge, the approaches we suggest for both problems have never been done hitherto, and extend the current research on both topics. The advantages of our approach, as far as we see it, are unity and coherence of statistical procedures, systematic and methodical incorporation of prior knowledge, and ease of calculation and interpretation. / Statistics