A simulation study of three sequential methods for the comparison of two treatment groups when the response criterion is censored

Impact of a mis-specification of the response rate under standard treatment in sequential clinical trials

Phase III trials are aimed at assessing whether new treatments have superior efficacy than standards. Sequential methods, such as the single triangular test (STT) and the double triangular test (DTT), allow for early stopping of such trials. They use stopping boundaries which depend, for a binary endpoint, on pi(0) and pi(1) (response rates under standard and new treatment, respectively) and alpha and beta (type I and II errors, respectively). Thus, a wrong estimation of pi(0) at planning phase might have an influence on their statistical properties. We assessed the extent of this influence by simulations regarding alpha, 1--beta, and average sample number (ASN) and compared the two methods with the one-sided and two-sided single-stage designs (SSD). There was no influence on alpha for any test and the power achieved by the one-sided or two-sided SSD was moderately affected by a wrong estimation of pi(0). However, important drifts (whose magnitude depended on chosen design) were observed for sequential methods concerning power and ASN in case of moderate under- or overestimation of pi(0) (+/-20% compared with its 'true' value). For example, when 'true' values of pi(0) and pi(1) are 0.30 and 0.40, respectively, using design values of 0.10 and 0.20, the power is 0.57 and 0.50 for the STT and DTT, respectively, instead of 0.95. When 'true' values of pi(0) and pi(1) are 0.10 and 0.20, respectively, using design values of 0.30 and 0.40, the ASN under H(0) is 1,309 and 2,019 for the STT and DTT, respectively, instead of 392 and 601, respectively, using the right design. Using sequential methods in comparative clinical trials with binary responses requires a precise knowledge of the response rate under standard treatment to avoid losses in power or inappropriate increases in sample size.

Planning and monitoring of placebo-controlled survival trials: comparison of the triangular test with usual interim analyses methods

AIMS

For ethical and economic reasons, interim analysis of phase III clinical trials is essential. This study was conducted to compare the efficiency of two interim analysis procedures, which could be used to allow early termination of a clinical trial.

METHODS

We made a post hoc application of two interim analysis methods (Lan & DeMets with O'Brien-Flemming modification, and the triangular test according to Whitehead) by using individual patient data from four published placebo-controlled survival trials. We determined the date the trial would have been stopped had each method been used, and we estimated consequent results in terms of events and patient numbers included in the trial, the duration of the trial, and on treatment effect.

RESULTS

The triangular test provided the lowest number of events required to reach a conclusion of the trials while providing an accurate estimate of experimental treatment effects. The triangular test thus indicated the smallest number of patients that would have been enrolled, and the shortest trial duration. The difference between the methods was most important with a detrimental effect of experimental treatment: the number of required events was reduced by 75% and the trial duration was shortened by 48% with the triangular test compared to the Lan & DeMets method.

CONCLUSIONS

Stopping a trial early must depend on the clinical context. It is most important to stop a placebo-controlled trial as soon as possible when the experimental treatment can be shown deleterious. In such a situation the triangular test is more appropriate than the Lan & DeMets method. When a treatment effect is no different from, or better than, placebo the triangular test is also superior but the importance of premature termination of the trial in such cases has to be balanced against the inevitable reduction of information that the trial can provide.

Comparison of the two-sided single triangular test to the double triangular test

Comparative clinical trials are designed to determine whether a new treatment has either superior or different efficacy than a standard, that is, if theta represents a measure of treatment difference, to test the null hypothesis H(0): theta = 0 against the alternative hypothesis H(1) of either superior (theta > 0, one-sided) or different (theta not equal 0, two-sided with H(1)(+): theta > 0 and H(-)(1): theta < 0) efficacy. The triangular test (TT), a group sequential method, allows for early stopping of such trials. Its one-sided version (single TT) and two-sided version (double TT) were implemented in the first release of PEST software. The third release of PEST proposed a modification of the single TT, allowing rejection of H(0) in favor of H(-)(1) when very early data show strong inferiority of the new treatment as compared with the standard. Thus, our aim was to compare this modified single TT, referred to as a two-sided test in PEST 3, with the double TT and two-sided single-stage design (SSD). The statistical properties of the SSD and double TT were perfectly similar under all hypotheses. The modified single TT was underpowered as compared to the two others (the probability of falsely accepting H(0) strictly under H(-)(1) was 0.65 instead of 0.05), but the average sample number function was lower than the one of the double TT under all H(-)(1) hypotheses (-56% strictly under H(-)(1)). We conclude that the modified single TT offers a two-sided conclusion with many fewer patients than the double TT, but at the expense of a strong decrease in power under H(-)(1).

Comparison of the spending function method and the Christmas tree correction for group sequential trials

Sequential designs for continuous monitoring can be derived from the theory of a Brownian motion process. In practice, infrequent analyses lead to a discrete monitoring process. In this paper, two methods proposed to correct for discrete monitoring are compared. The methods are used to create procedures similar to both the O'Brien and Fleming test and the triangular test and are compared in terms of the error rates. For the O'Brien and Fleming test, the spending function method is found to achieve the required error rates more accurately than the Christmas tree correction, while for the triangular test, both methods perform as planned.

Application of the triangular test to phase II cancer clinical trials

Phase II cancer clinical trials are primarily designed to determine whether the response rate p to the treatment under study is greater than a specified value p0, that is to test the null hypothesis H0: p less than or equal to p0 against an alternative hypothesis H1 : p greater than p0 specified by p = p1. As an alternative to the single and multistage procedures and to Wald's continuous sequential probability ratio test (SPRT), we applied the group sequential methods proposed by Jones and Whitehead, namely the triangular test (TT) and the discrete SPRT, to the comparison of p with p0, and we expressed H0 and H1 in terms of the log odds-ratio statistic log [p(1 - p0)/p0(1 - p)]. A stimulation study showed that both the TT and the discrete SPRT had type I error and power close to the nominal values, and they compared favourably with multistage methods in terms of the average sample size.

Patient accrual and interim statistical analysis in long-term randomized clinical trials: the French chronic lymphocytic leukemia CLL 80 protocol as a case study

The CLL 80 clinical trial of treatment for chronic lymphocytic leukemia was designed using a three-stage prognostic classification. Within each stage patients received one of two treatments allocated by randomization, two adjacent stages having a common treatment. The fixed-sample design required 850 patients entered over a period of 8.5 years. Active patient recruitment led to 741 patients being randomized in four years. The first interim analysis, carried out at this point, showed a treatment difference in one stage which was statistically significant (p = 0.001) and justified an early termination of the protocol. This paper discusses practical aspects of patient accrual and interim analysis in this study.