The Design and Sample Size Requirement for a Cluster Randomized Non-Inferiority Trial with Two Binary Co-Primary Outcomes.

This paper will discuss the design and sample size requirement for a cluster randomized non-inferiority trial with two binary co-primary outcomes. A hypothetical study (the EXAMPLE Trial) will be considered. Lets assume the EXAMPLE Trial will consist of two separate binomial noninferiority two-sample trials. Trial 1: the Coronary Artery Disease known population (co-primary 1) and Trial 2: the Coronary Artery Disease unknown population (co-primary 2). A physician-month cluster randomization scheme will be used. That is, for each trial (trial 1 and trial 2) every month for a 12-month period, each physician participating in the EXAMPLE Trial will be allocated a randomized cluster of size 10. The physician will need to consent and enroll 10 patients each month for the 12-month period for each trial (trial 1 and trial 2). Each cluster will be specific to a treatment group (either EXPERIMENTAL or CONTROL). The design and sample size method discussed by Bland (2003) and Donner and Klar (2000) will be used. The EXAMPLE Trial will be declared a success if statistical significance is demonstrated at the pre-specified nominal alpha-level for both co-primary outcomes. Lets assume the EXAMPLE Trial will consist of two separate binomial non-inferiority two-sample trials. Trial 1: the CAD known population (co-primary 1) and Trial 2: the CAD unknown population (co-primary 2). A physician-month cluster randomization scheme will be used. That is, for each trial (trial 1 and trial 2) every month for a 12-month period, each physician participating in the EXAMPLE Trial will be allocated a randomized cluster of size 10. The physician will need to consent and enroll 10 patients each month for the 12-month period for each trial (trial 1 and trial 2). Each cluster will be specific to a treatment group (either EXPERIMENTAL or CONTROL). The design and sample size method discussed by Bland (2003) and Donner and Klar (2000) will be used. The EXAMPLE Trial will be declared a success if statistical significance is demonstrated at the pre-specified nominal α -level for all co-primary outcomes. Therefore, non-inferiority must be demonstrated with respect to both co-primary 1 and co-primary 2 in order for the EXAMPLE Trial to be considered a success. Since both co-primary outcomes are required to be met, no adjustment to the significance level (α = 0.025; 1-sided) is required (EMEA: CPMP/EWP/908/99; 2002; section 2.1.1 and Sankoh AJ et al.; 2003; section 3.1.1). The EMEA document states: “ In this situation, there is no intention or opportunity to select the most favourable result and, consequently, the individual type I error levels are set equal to the overall type I error level α , i.e., no reduction is necessary”. However, the EMEA document notes: “This procedure inflates the relevant type II error (here: falsely accepting that at least one null hypothesis is true), which in the worst case scenario is the sum of the type II errors connected with the individual hypotheses. This inflation must be taken into account for a proper estimation of the sample size for the trial”. Therefore, we will need to set the type II error rate for each co-primary outcome at a value which, in the worst case scenario, will sum to a value no greater than 0.20 (since, for this trial, we want an overall type II error rate = 0.20; that is power = 80%). Thus, we will use β =0.10 for each co-primary outcome. EAST 5.2. 0 will be used to determine the sample size (East, 2008). Trial 1: Sample Size Calculation for Co-Primary 1: Lets assume the study design consists of two treatment groups. CONTROL is the active control group and EXPERIMENTAL is the experimental treatment group. Co-primary 1 will be treated as a binomial non-inferiority two-sample trial. The goal is to establish that the death rate of the experimental treatment group is no worse than that of the active control group. A difference in proportions is considered. Co-Primary 1: Coronary Artery Disease (CAD) known: Death rate at 12 months. Denote c π as the death rate for the active control group and t π as the death rate for the experimental treatment group. Page 1 Hosted by The Berkeley Electronic Press