Monday, November 21, 2016

Haybittle–Peto Boundary for Stopping the Trial for Efficacy or Futility at Interim Analysis

In clinical trials with group sequential design or the clinical trials with formal interim analysis for efficacy, we will need to deal with the alpha spending issue. To maintain the overall experimental wide alpha level at 0.05, the final analysis will usually tested at a significance level less than 0.05 due to the alpha spending at the interim analyses. Various approaches in handling the multiplicity issue due to the interim analyses have been proposed. The O'Brien-Fleming approach is the most common approach. 

In an article by Schulz and Grimes (Lancet 2005) "Multiplicity in randomised trials II: subgroup and interim analyses", three approaches were listed where the stop boundaries were expressed in p-value format:

In the middle is the approach proposed by Peto. In practice, Peto approach is more commonly referred as Haybittle-Peto boundaries.

In an online course by "Treatment Effects Monitoring; Safety Monitoring", there is a following table comparing the different approaches for boundaries and Haybittle-Peto boundary is one of them.

In a lecture note by Dr Koopmeiners, the Haybitle-Peto boundaries are summarized as below with the boundaries expressed in critical values:

In short, the Haybittle–Peto boundary states that if an interim analysis shows a probability of equal to a very small alpha or greater than a very large critical value that a difference as extreme or more between the treatments is found, given that the null hypothesis is true, then the trial should be stopped early. The final analysis is still evaluated at almost the normal level of significance (usually 0.05). The main advantage of the Haybittle–Peto boundary is that the same threshold is used at every interim analysis, unlike other the O'Brien–Fleming boundary, which changes at every analysis. Also, using the Haybittle–Peto boundary means that the final analysis is performed using a 0.05 level of significance as normal, which makes it easier for investigators and readers to understand. The main argument against the Haybittle–Peto boundary is that some investigators believe that the Haybittle–Peto boundary is too conservative and makes it too difficult to stop a trial.

I have seen several high profiles clinical trials where the Haybittle-Peto boundary is used. In a very recent paper by Finn et al (NEJM 2016) "Palbociclib and Letrozole in Advanced Breast Cancer", the Haybittle-Peto boundary was used for the interim analysis.
We planned for the data and safety monitoring committee to conduct one interim analysis
after approximately 65% of the total number of events of disease progression or death were observed to allow for the study to be stopped early owing either to compelling evidence of efficacy (using a pre-specified Haybittle–Peto efficacy boundary with an alpha level of 0.000013) or to a lack of efficacy.
In a paper by Eikelboom et al (NEJM 2017) "Rivaroxaban with or without Aspirin in Stable
Cardiovascular Disease", the modified Haybittle-Peto boundary was used:
Two formal interim analyses of efficacy were planned, when 50% and 75% of primary efficacy events had occurred. A modified Haybittle–Peto rule was used, which required a difference of 4 SD at the first interim analysis that was consistent over a period of 3 months, and a consistent difference of 3 SD at the second interim analysis
In a paper by Sitbon et al (NEJM 2015) "Selexipag for the Treatment of Pulmonary
Arterial Hypertension", the Haybittle-Peto boundary was also used for the interim analysis. Notice that the overall alpha for this study was 0.005, not the typical 0.05. While it was not mentioned in the NEJM publication, the alpha level for interim analysis was 0.0001 according to FDA's statistical review of the NDA.
An independent data and safety monitoring committee performed an interim analysis,
which had been planned after 202 events had occurred, with stopping rules for futility
and efficacy that were based on Haybittle–Peto boundaries. The final analysis used a one-sided significance level of 0.00499.
In both case, we can see that with Haybittle-Peto boundaries, the boundaries are set up very high - making it almost impossible to stop the trial for efficacy (or futility).

In choosing the stop boundaries for interim analysis, Haybittle-Peto boundaries may be chosen when a sponsor has no real intention to stop the trial early, but give Data Monitoring Committee a chance to take a peek into the study results in in the middle of the study.

Haybittle-Peto boundaries are included in the major sample size calculation software such as Cytel's EAST SEQUENTIAL and SAS Proc SEQDESIGN.

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