Inconsistency and drop-minimum data analysis.

Even though consistency is an important issue in multi-regional clinical trials and inconsistency is often anticipated, solutions for handling inconsistency are rare. If a region's treatment effects are inconsistent with that of the other regions, pooling all the regions to estimate the overall treatment effect may not be reasonable. Unlike the multiple center clinical trials conducted in the USA and Europe, in multi-regional clinical trials, different regional regulatory agencies may have their own ways to interpret data and approve new drugs. It is therefore practical to consider the case in which the data from the region with the minimal observed treatment effect is excluded from the analysis in order to attain the regulatory approval of the study drug. Under such cases, what is the appropriate statistical approach for the remaining regions? We provide a solution first formulated within the fixed effects framework and then extend it to discrete random effects models. Copyright © 2016 John Wiley & Sons, Ltd.

Sample size adjustment based on promising interim results and its application in confirmatory clinical trials.

BACKGROUND: For a carefully planned and well-designed Phase 3 confirmatory trial, there is still a potential risk of failing to meet the study objective due to possible differences between Phase 2 and Phase 3 studies. As illustrated by the ENGAGE trial, potential sample size increase at an interim analysis can mitigate the risk for an otherwise underpowered study. Many approaches for sample size adjustment (SSA) require certain modifications to the conventional statistical method, such as changing critical values or using a weighted Z-statistic for final hypothesis testing. Without modification, the type I error rate can be inflated, primarily caused by sample size increase for nonpromising interim observation that is close to null or no treatment effect. As illustrated by the TOPICAL trial, increasing sample size for nonpromising interim result could waste limited resource on ineffective treatment. The modifications in these approaches are therefore unnecessary costs of flexibility/interpretability for unnecessary scenarios of sample size increase. PURPOSE: To discuss and illustrate the appropriateness of SSA based on promising interim results, that is, conditional power being greater than 50% (or CDL approach), in a carefully planned and well-designed Phase 3 confirmatory trial. METHODS: Two clinical trials are used to illustrate the clinical setting for the CDL approach and appropriateness of its application. Operating characteristics are assessed and compared to other methods using numeric computation. Hypothetical trials based on real clinical data are used to illustrate the approach. RESULTS: The CDL approach for SSA leads to a small increase in expected sample size resulting in a small power gain versus the fixed design. This indicates that adding SSA will not on average substantially affect the budget at the portfolio level. However, when the interim result is promising, the CDL approach can dramatically increase the conditional power therefore mitigating the risk of an otherwise underpowered study. LIMITATIONS: Implementation challenges of the SSA methods are not in the scope of this paper. SSA is not intended to replace careful design of a confirmatory trial; instead, it can mitigate the risk for a well-designed trial. CONCLUSIONS: The CDL approach for SSA based on promising interim results, that is, conditional power being greater than 50%, is particularly useful in mitigating the risk for a carefully planned and well-designed Phase 3 confirmatory trial. No modification to the conventional statistical procedure is necessary while the type I error rate is controlled. Such a feature of ''no interference,'' or no change to the conventional statistical procedure with or without sample size adjustment, is important for the interpretation of a confirmatory trial. Similar to the fixed design, carefully planned and well-designed group sequential studies can also benefit from SSA to mitigate the risk of failing to meet the study objective.

A note on sequential monitoring of select-the-winner design.

Consider a trial comparing two treatments or doses A and B with a control C. Based on a unblinded interim look, a winner W between A and B will be chosen, and future patients will be randomized to W and C and compared at the end of a study. The naïve test statistic Z under this setting follows an approximate normal distribution, as shown by Lan et al. (2006) and Shun et al. (2008). Results of these two articles apply only to the fixed sample size design. With simple modifications, this manuscript extends the previous works to the group sequential setting.

Designing multiregional trials under the discrete random effects model.

A discrete random effects model (Lan and Pinheiro, 2012) was proposed recently for multiregional clinical trials for continuous responses. This article elucidates further the application of this model to time-to-event and binary responses. We provide some guidelines on how to design multiregional trials and also show how the same model lends itself naturally to meta-analysis.

Spending functions and continuous-monitoring boundaries.

Clinical trials are monitored periodically for safety, efficacy, and futility. The spending function is a popular tool for efficacy monitoring because it does not require pre-specification of the number or timing of interim analyses. But there are infinitely many spending functions, so some guidance on how to choose one is helpful. We consider spending functions that are generated from different continuous-monitoring boundaries for Brownian motion. We use properties of the continuous-monitoring boundaries to derive properties of the associated spending function.

Design and sample size considerations for simultaneous global drug development program.

Due to the potential impact of ethnic factors on clinical outcomes, the global registration of a new treatment is challenging. China and Japan often require local trials in addition to a multiregional clinical trial (MRCT) to support the efficacy and safety claim of the treatment. The impact of ethnic factors on the treatment effect has been intensively investigated and discussed from different perspectives. However, most current methods are focusing on the assessment of the consistency or similarity of the treatment effect between different ethnic groups in exploratory nature. In this article, we propose a new method for the design and sample size consideration for a simultaneous global drug development program (SGDDP) using weighted z-tests. In the proposed method, to test the efficacy of a new treatment for the targeted ethnic (TE) group, a weighted test that combines the information collected from both the TE group and the nontargeted ethnic (NTE) group is used. The influence of ethnic factors and local medical practice on the treatment effect is accounted for by down-weighting the information collected from NTE group in the combined test statistic. This design controls rigorously the overall false positive rate for the program at a given level. The sample sizes needed for the TE group in an SGDDP for three most commonly used efficacy endpoints, continuous, binary, and time-to-event, are then calculated.

Proposals of statistical consideration to evaluation of results for a specific region in multi-regional trials--Asian perspective.

In recent years, global collaboration has become a conventional strategy for new drug development. To accelerate the development process and to shorten approval time, the design of multi-regional trials incorporates subjects from many countries around the world under the same protocol. After showing the overall efficacy of a drug in all global regions, one can also simultaneously evaluate the possibility of applying the overall trial results to all regions and subsequently support drug registration in each of them. Recently, the trend for simultaneous clinical development in Asian countries being undertaken simultaneously with clinical trials conducted in Europe and the United States has been rapidly rising. In this paper, proposals of statistical consideration to multi-regional trials are provided. More specifically, three aspects are addressed: the definition of the 'Asian region,' the consistency criterion between the 'Asian region' and the overall regions, and the sample size determination for the multi-regional trial.

Interim treatment selection using the normal approximation approach in clinical trials.

We consider a study starting with two treatment groups and a control group with a planned interim analysis. The inferior treatment group will be dropped after the interim analysis, and only the winning treatment and the control will continue to the end of the study. This 'Two-Stage Winner Design' is based on the concepts of multiple comparison, adaptive design, and winner selection. In a study with such a design, there is less multiplicity, but more adaptability if the interim selection is performed at an early stage. If the interim selection is performed close to the end of the study, the situation becomes the conventional multiple comparison where Dunnett's method may be applied. The unconditional distribution of the final test statistic from the 'winner' treatment is no longer normal, the exact distribution of which is provided in this paper, but numerical integration is needed for its calculation. To avoid complex computations, we propose a normal approximation approach to calculate the type I error, the power, the point estimate, and the confidence intervals. Due to the well understood and attractive properties of the normal distribution, the 'Winner Design' can be easily planned and adequately executed, which is demonstrated by an example. We also provide detailed discussion on how the proposed design should be practically implemented by optimizing the timing of the interim look and the probability of winner selection.

Applying the law of iterated logarithm to control type I error in cumulative meta-analysis of binary outcomes.

BACKGROUND: Cumulative meta-analysis typically involves performing an updated meta-analysis every time when new trials are added to a series of similar trials, which by definition involves multiple inspections. Neither the commonly used random effects model nor the conventional group sequential method can control the type I error for many practical situations. In our previous research, Lan et al. (Lan KKG, Hu M-X, Cappelleri JC. Applying the law of iterated logarithm to cumulative meta-analysis of a continuous endpoint. Statistica Sinica 2003; 13: 1135-45) proposed an approach based on the law of iterated logarithm (LIL) to this problem for the continuous case. PURPOSE: The study is an extension and generalization of our previous research to binary outcomes. Although it is based on the same LIL principle, we found the discrete case much more complex and the results from the continuous case do not apply to the binary case. The simulation study presented here is also more extensive. METHODS: The LIL based method ;penalizes' the Z-value of the test statistic to account for multiple tests and for the estimation of heterogeneity in treatment effects across studies. It involves an adjustment factor, which is directly related to the control of type I error and determined through extensive simulations under various conditions. RESULTS: With an adjustment factor of 2, the LIL-based test statistics controls the overall type I error when odds ratio or relative risk is the parameter of interest. For risk difference, the adjustment factor can be reduced to 1.5. More inspections may require a larger adjustment factor, but the required adjustment factor stabilizes after 25 inspections. LIMITATIONS: It will be ideal if the adjustment factor can be obtained theoretically through a statistical model. Unfortunately, real life data are too complex and we have to solve the problem through simulation. However, for large number of inspections, the adjustment factor will have a limited effect and the type I error is controlled mainly by the LIL. CONCLUSIONS: The LIL method controls the overall type I error for a very broad range of practical situations with a binary outcome, and the LIL works properly in controlling the type I error rates as the number of inspections becomes large.

The use of weighted Z-tests in medical research.

Traditionally the un-weighted Z-tests, which follow the one-patient-one-vote principle, are standard for comparisons of treatment effects. We discuss two types of weighted Z-tests in this manuscript to incorporate data collected in two (or more) stages or in two (or more) regions. We use the type A weighted Z-test to exemplify the variance spending approach in the first part of this manuscript. This approach has been applied to sample size re-estimation. In the second part of the manuscript, we introduce the type B weighted Z-tests and apply them to the design of bridging studies. The weights in the type A weighted Z-tests are pre-determined, independent of the prior observed data, and controls alpha at the desired level. To the contrary, the weights in the type B weighted Z-tests may depend on the prior observed data; and the type I error rate for the bridging study is usually inflated to a level higher than that of a full-scale study. The choice of the weights provides a simple statistical framework for communication between the regulatory agency and the sponsor. The negotiation process may involve practical constrains and some characteristics of prior studies.

Over-ruling a group sequential boundary--a stopping rule versus a guideline.

We evaluate the properties of group sequential procedures where the trial is continued even though the boundary for statistical significance (stopping) to demonstrate effectiveness has been crossed. In this case, one may buy-back the previously spent alpha probability to be re-spent or re-distributed at future looks. We show that such plans using an O'Brien-Fleming-like spending function have a negligible effect on the final type I error probability and on the ultimate power of the study. With a Pocock-like bound, however, there is a small additional loss in power. We also show that this approach can be simplified by using a fixed-sample size Z critical value for future looks after buying-back previously spent alpha, such as using a critical Z value of 1.96 for alpha=0.025. We show that this procedure preserves the type I error probability while incurring a minimal loss in power. In this sense, one still has a stopping boundary rather than simply a guideline. This concept is discussed relative to monitoring procedures for inferiority or futility, and cases where both an upper and lower boundary are employed.

Monitoring mortality at interim analyses while testing a composite endpoint at the final analysis.

Mortality is often used as the clinical endpoint in clinical trials for acute diseases and takes precedence over any other outcome. A composite outcome such as death plus disease occurrence (or recurrence) or death plus hospitalization may also be considered, sometimes even as the primary outcome due to practical sample size issues. That is, a composite endpoint should have a higher event rate and thus a smaller sample size than for mortality alone to reach the same power. Two different scenarios are considered: in Scenario 1, the composite outcome is the primary endpoint and the mortality outcome is secondary; in Scenario 2, the mortality outcome is the primary endpoint and the composite outcome is secondary. In either scenario, the trial will be stopped if the simple mortality outcome shows an adverse effect or a significant benefit at an interim analysis, while the composite outcome will be tested at the final analysis if the mortality outcomes fails to show significance. These scenarios are typical in many trials sponsored by industry for regulatory approval. We refer to them as a switching the primary endpoint process. Two switching-endpoint procedures are proposed to calculate the efficacy boundary for the composite test statistic at the final analysis. The Bonferroni method is used in Method 1. In Method 2, the calculation is based upon the joint distribution of the test statistics for the simple mortality and the composite outcomes. A completed clinical trial, prospective randomized amlodipine survival evaluation (PRAISE-1), is used to illustrate the two switching-endpoint procedures. A simulation study shows that the two switching-endpoint procedures allow a trial to be stopped early due to a clinically relevant benefit in the mortality while preserving the overall alpha level.

Increasing the sample size when the unblinded interim result is promising.

Increasing the sample size based on unblinded interim result may inflate the type I error rate and appropriate statistical adjustments may be needed to control the type I error rate at the nominal level. We briefly review the existing approaches which allow early stopping due to futility, or change the test statistic by using different weights, or adjust the critical value for final test, or enforce rules for sample size recalculation. The implication of early stopping due to futility and a simple modification to the weighted Z-statistic approach are discussed. In this paper, we show that increasing the sample size when the unblinded interim result is promising will not inflate the type I error rate and therefore no statistical adjustment is necessary. The unblinded interim result is considered promising if the conditional power is greater than 50 per cent or equivalently, the sample size increment needed to achieve a desired power does not exceed an upper bound. The actual sample size increment may be determined by important factors such as budget, size of the eligible patient population and competition in the market. The 50 per cent-conditional-power approach is extended to a group sequential trial with one interim analysis where a decision may be made at the interim analysis to stop the trial early due to a convincing treatment benefit, or to increase the sample size if the interim result is not as good as expected. The type I error rate will not be inflated if the sample size may be increased only when the conditional power is greater than 50 per cent. If there are two or more interim analyses in a group sequential trial, our simulation study shows that the type I error rate is also well controlled.

Conditional bias of point estimates following a group sequential test.

Repeated significance testing in a sequential experiment not only increases the overall type I error rate of the false positive conclusion but also causes biases in estimating the unknown parameter. In general, the test statistics in a sequential trial can be properly approximated by a Brownian motion with a drift parameter at interim looks. The unadjusted maximum likelihood estimator can be potentially very biased due to the possible early stopping rule at any interim. In this paper, we investigate the conditional and marginal biases with focus on the conditional one upon the stopping time in estimating the Brownian motion drift parameter. It is found that the conditional bias may be very serious for existing point estimation methods, even if the unconditional bias is satisfactory. New conditional estimators are thus proposed, which can significantly reduce the conditional bias from unconditional estimators. The results of Monte-Carlo studies show that the proposed estimators can provide a much smaller conditional bias and MSE than the naive MLE and a Whitebead's bias reduced estimator.