gms | German Medical Science

Background: In the Fr1da trial (ClinicalTrials.gov identifier: NCT04039945), trial numbers were based on oral insulin halving the exponentially distributed hazard of the events dysglycemia and diabetes as compared with placebo. After recruitment of 163 children, a blinded sample size re-estimation was planned to review the original assumptions that 220 children randomized 1:1 provide 86.6% power to observe a significant difference at the two-sided alpha level 0.033 if two-year event-free survival was 70% in the placebo arm, recruitment time 55 months, additional follow-up 36 months, and drop-out 13%.

Methods: Data on event-free survival, drop-outs, and a randomization ratio of 81:82 was available. Group allocation was unknown. Now, 1,000 samples were created, all by randomly drawing, without replacement, 82 children for a hypothetical placebo arm. Assuming exponential distribution, the event hazard was estimated in both resulting treatment groups. Sample size re-estimation was based on these hazard estimates and the original assumptions. The sample size estimation formula of Schoenfeld and Richter [1] was used.

Results: Median observation time for the 163 children was 23 months. Twenty-eight events were recorded. With 81.4% at 2 years [95% confidence interval: 73.3; 82.2%], event-free survival probabilities were higher than expected. For 19 of 163 children, a drop-out was observed. Treating events and censoring as competing risks, 2-year probability for drop-out was 9.2%. Supposing that results for the unknown real allocation into the two arms would follow the original assumption of twice the hazard for placebo, in dependence on the estimated hazards, re-calculated sample sizes ranged between 254 and 266 (based on n=10 samples) and between 214 and 224, if power was reduced to 80.0%. However, changes were considerable, if the hazard ratio of placebo to insulin treatment was smaller (sample sizes from 620 to 250 for ratios from 1.5 to 1.9) or larger (sample sizes from 196 to 132 for ratios from 2.1 to 2.5). For the re-calculated sample sizes, thirteen percent drop-outs were considered.

Conclusion: The observation of higher event-free survival probabilities i.e. fewer events than anticipated resulted in higher re-estimated samples sizes. Ten samples with hazard ratio 2.0 confirmed that a final sample size of 220 would be reasonable if all assumptions and the estimated current overall hazard were correct and a power reduction to 80.0% was acceptable. However, in interpreting data, caution needs to be exercised as considerable variation in sample sizes with small changes in the hazard ratio indicated that restricted information was provided by the current data.

The authors declare that they have no competing interests.

The authors declare that a positive ethics committee vote has been obtained.