Sequential trials

Looked at in terms of the number of trials that are run by the pharmaceutical industry, sequential trials are relatively unimportant. However, since such trials are often run where the number of patients needed is suspected to be great, they are relatively more important in terms of numbers of patients and also of cost. Nevertheless, it remains true that there are many indications in drug development where such trials are never or rarely used and I think it is only fair that I should warn the reader that in all my time in the pharmaceutical industry I never designed or analysed one myself. But since leaving 

Statistical Issues in Drug Development, 2nd Edition. Stephen Senn 2007 John Wiley Sons, Ltd ISBN 978-0-470-01877-4 

It is assumed that a number of inspections may be made of the trial results as they accrue. 

In the light of the type of measurement to be taken and using the likelihood under a suitable model, a statistic Z is defined which summarizes the treatment difference at inspection i. (This statistic is related to the cumulative treatment difference.) For example, for a binary outcome, the statistic would be (S - Sq) /2 where S and Sc are the successes in experimental and treatment arms, respectively. 

A further statistic, Vj, is defined which measures the variability of Z, under the null hypothesis of no treatment effect. For the binary example, this statistic is SF/(4n) where S, F and n are the total number of successes, failures and patients, respectively. 

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Fig. 7.10 (Continued) (b) VN-x inhibits response to female urine by male guinea-pig X-2 sequential trials (duration, sec. x s.e.) (from Beauchamp et al., 1982). (c) Inter-strain (domestic vs. wild) discrimination by male domestic guinea pig of female urines [sequential testing sec/4 min, s.e., Ss above each bar intact/sham-VN-x. above]. WF= wild female, F = domestic female (from Beauchamp et al., 1982). (d) Effects of VN-x on maternal chemoinvestigation ewe responses to lambs, including tongue-manipulation of palate [c.f. Fig. 7.6(d)], procaine = MOE inhibition, a sign, versus control (from Booth and Katz, 2000).

The purpose of interim analyses in group sequential trials is to determine if the clinical trial should be terminated at that point. The rationale for interim analyses of data that are accumulating over time in a clinical trial was established almost 40 years ago, and considerable attention has subsequently focused on the development of statistical approaches and decision-making processes that facilitate the implementation of data monitoring and interim analyses for the early termination of a clinical trial (Chow and Liu, 2004). 

Groenveld GJ, Veldirik JH, Varr der Tweel I, Kalmijrr S, Beijer C, de Visser M, Wokke JH, Franssen H, varr derr Berg LH (2003) A randomized sequential trial of creatine irr amyotr ophic lateral sclerosis. AnnNeur ol 53 437 445. 

Coninx P, Nasca S, Lebrun D, Panis X, Lucas P, Garbe E, Legros M. Sequential trial of initial chemotherapy for advanced cancer of the head and neck. DDP versus DDP + 5-fluorouracil. Cancer 1988 62(9) 1888-92. 

A common concern for a group sequential trial utilizing repeated interim ANOVA analysis is an inflated chance of observing a spurious result leading to an inflated Type I (false positive) error rate. Table 31.1 (24) illustrates the impact on the Type I error rate (a) based on the number of interim analyses each controlled at a = 0.05. 

Sit by a sequential trial long enough and significance will come floating by unless you take steps to sink it. 

Sequential trials are not generally relevant to drug development... 

It would thus seem that the sort of serious and life-threatening diseases where sequential trials are run ought to be an exception to the two-trials rule. However, this raises a problem with the standard of evidence. As we saw in Chapter 12, one interpretation of the two-trials rule is that it reflects the fact that higher standards of evidence are required in practice than suggested by the conventional 5% significance level. If we do not have a two-trials rule, then it simply means that our standards of evidence are lower for the sorts of indications in which sequential trials are run than for other areas of drug development. This may seem to be appropriate for serious diseases, where more is at stake and we intuitively feel that it is unreasonable to carry on in the search for proof of efficacy where belief is already strong. 

Naive estimators associated with sequential tests may also be biased in the sense that the expectation of standard fixed trial estimators taken over all possible trials run to the same stopping rule may not be equal to the true treatment effect. Adjustments for estimators and associated intervals are possible but raise similar issues to those discussed under section 19.2.1. For example, suppose that we have a fixed parallel-group trial and calculate, as a conventional treatment estimate, the difference between the mean outcomes in each group. Suppose we then notice, however, on looking at the results for the patients ordered over time, that had we run this trial as a given sequential trial with three looks at equal intervals, then we would have stopped exactly at the point dictated by the fixed trial, which happens to correspond to the second look of the sequential trial. Had we carried out the sequential trial we should have adjusted the treatment estimator, but since we have carried out a fixed trial we shall not. 

A source of potential embarrassment with sequential trials is that having decided on the basis of results to date to stop the recruitment of patients because the results are convincing, further information will continue to accrue. For example, in a trial where survival is the main outcome we will continue to follow up patients we have treated. Those recruited most recently will usually still be alive and thus have, at the time of stopping, censored and relatively uninformative survival times. In such a trial it is actually the number of deaths which affects the power of the study, rather than the number of patients per se. Thus, as time goes on, further information will be obtained and it is always theoretically possible that this will tend to contradict results to date, so that once the further information is received we are no longer as convinced as when we stopped that the treatment is efficacious. 

This feature seems to be embarrassing for frequentist systems where there seems to be no formal way of declaring a hypothesis not rejected once it has been rejected. It does not appear to be a reversible process. However, this is not the only interpretation of what goes on in a sequential analysis with over-running. One view is that the only analysis which counts is the final one, once the further information has been collected. The trial has been stopped earlier on the practical grounds that it seems as if a decision of efficacy is now possible. There is no question of unrejecting Hq. It was not rejected in the first place. After all, in a fixed sample size trial, we would have made a decision when to stop the trial and then some time later we would either have found that the result would or would not have been significant. The only difference with the sequential trial is that the decision when to stop has made some use of the results. 

If it is considered desirable and feasible to run a double-blind trial in a given indication, the fact that a sequential trial is being run with repeated looks at accumulating data has the capacity, as O Neill (1993) puts it, to influence parts of the trial conduct such as types of patients entered, definitions of endpoints, exclusion criteria etc. (p. 606). Sometimes the data-monitoring board is kept in the dark as to which treatment is which and results are presented to it without revealing the treatment labels. This is not always possible for example, where an asymmetric stopping rule is being used, as may be the case when trials can be stopped for lack of efficacy. 

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