## Stopping Criteria

The table showing the probabilities associated with various target improvements can be reviewed by the Data Monitoring Committee. However, although the Bayesian framework is useful for interpreting the current trial's results in an informal manner, it is still useful to have guidelines for when seriously to consider stopping. If the trial is between two treatment arms, then a reasonable criterion is to demand that the posterior probability of one treatment being better, in the light of a sceptical prior belief, is at least 95 per cent; thus cell B should exceed 95 per cent. Alternatively, if a non-zero target improvement is sought, a reasonable criterion might be to accept a posterior probability of 90 per cent; in Table I, for a 5 per cent improvement this would imply that cell C should be at least 90 per cent.

16. CALCULATIONS: SUMMARY

We start with a table giving the observed and expected number of events in each group, as is readily obtained from most survival analysis programs. Nd = + 02 = the total number of deaths observed to data.

Log(hd), the log hazard ratio, can be obtained from equation (6)

Equations (2), (4) and (5) enable Np to be estimated for the sceptical prior:

log(^i) = \og(log(survi)/\og(surv2)) where survx and surv2 are the hypothesised event rates.

Then the list of summary equations can be expanded out, although only the posterior distributions (PI), (P2) and (P3) are used for constructing the table of probabilities of various improvements, 3.

Finally, equation (7) allows log(^) to be evaluated for the improvements ¿>; this value of log(^) can be substituted for log(hd) in (PI), (P2) and (P3), giving the required table of probabilities.

Three worked examples are given, illustrating monitoring of clinical trials such as the oesophageal trial where survival is the main endpoint. These illustrate the calculations for three different arios, and indicate the suggested interpretation of the results. In particular, example 1 (which is a continuation of the example already used in the text) is a trial which might be regarded as beginning to show emerging treatment differences, but is at an early stage of patient recruitment; this trial should be continued. Example 2 is the same trial at a later stage, when early termination would be recommended, and example 3 is a trial which could be terminated because early results suggest there is unlikely to be any treatment dilference.

### 17.1 Worked example 1

The following is an example of what might happen if early results for the OE02 trial were to suggest that there might be a treatment effect, and the Data Monitoring Committee wished to consider the possibility of early termination. We shall adopt the position of a sceptic and mainly focus upon the sceptical prior.

We assume that routine interim analyses are being carried out, say annually. At the time of the first analysis perhaps 200 patients have been entered into the trial, of whom 100 have died (60 in group 1, and 40 in group 2), out of those so far recruited and entered into the trial. Standard survival-analyses techniques allow computation of the expected number of deaths in each group; these values are calculated and printed out by most survival analysis software.

Suppose the following results were obtained at the first interim analysis of the MRC OEQ2 trial:

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