Sample Size Re-estimation for Binary Data via Conditional Power

We extend Lan and Trost’s (1997,1999) conditional power approach for interim sample size re-estimation to binary data for clinical trials with a noninferiority objective. If conditional power is used to extend a trial, the α level will be inflated. On the contrary if it is used to stop a trial early to claim futility, the α level will be reduced. If inflation does not exceed deflation, then the α level will be maintained. Simulations were used to estimate probabilities of Type I error for a range of typical clinical trial situations commonly encountered in Veterinary Medicine. The simulation results demonstrated that the procedure preserves Type I error rate. Throughout, hypothetical examples will be used to illustrate the procedure. This intuitive, simple and flexible procedure is recommended for use in clinical trials. 1. Clinical Trial Setting/introduction Consider the following clinical trial situation. A sponsor was to test a novel compound for Veterinary Medical use. A typical multi-center, double blind, randomized two -arm trial was envisioned. The clinical end point was binary success or failure of the treatment. Due to ethical concerns, a positive control was needed. Per ICH Guideline and preliminary discussion with a regulatory agency, a noninferiority test of the test compound over the positive control was required. The sponsor and the regulatory agency mutually agreed 1) that the minimum sample size per arm should be 100 patients, 2) that the noninferiority margin should be 15 percentage points, and 3) the significance level should be one-sided 5%. Also result of Freedom of Information, the treatment success rate of the positive control was known to be about 75%. Without sufficient early trial information, the sponsor was unsure about the efficacy of the test compound but thought it should be comparable to the positive control (75%). Under a fixed design, the trial statistician performed some sample size/power analyses for true effect sizes of the test compound up to 5% lower than the reference (Table 1). Table 1. Sample Size and Power Percent Success (%) Positive Control Test Power (%)* SS** 77 87 78 76 83 90 75 78 104 74 73 120 73 67 141 72 60 168 71 54 202 75 70 47 246 * denotes power with 100 cases per arm, and ** denotes sample size (SS) per arm to achieve 80% of power What sample size should the sponsor use? If the efficacy was comparable to the positive control, the minimum sample size of 100 required by the agency should be sufficient to achieve a power of approximately 80%. On the other extreme, if the test compound performed 5 percentage points worse than the control, the sample size requirement increased substantially to 246. Conservatively, to ensure success of the trial, a sample size of 246 would be needed. However, if the efficacy of the test was comparable to or better than the control, this would amount to a considerable waste of resources, since 100 subjects per arm would be sufficient. Fortunately, recent advances in flexible/adaptive trial design and interim analysis were used to resolve this dilemma. With concurrence from the regulatory agency, the sponsor proposed to perform an interim analysis to reassess the sample size requirement. Flexible/adaptive trial design and interim data analysis are active areas of research in recent years. Increased knowledge has contributed to greater use of these methods in clinical trials (O’Neill, 1994; ICH E-9, 1999). Gould (2001) provided a comprehensive review of interim sample size re -estimation in methodology developments and their uses in practice. Conditional power (CP) (Lan et al., 1982, 1984; Halperin et al., 1987; Proschan and Hunsberger, 1995; Snapinn, 1992) has been advanced as a useful tool to manage clinical trials. Its properties and uses have been elucidated in Lan and Trost (1997, 1999), Joint Statistical Meetings Biopharmaceutical Section