A retrospective analysis of conditional power assumptions in clinical trials with continuous or binary endpoints

Abstract

Background: Adaptive clinical trials may use conditional power (CP) to make decisions at interim analyses, requiring assumptions about the treatment effect for remaining patients. It is critical that these assumptions are understood by those using CP in decision-making, as well as timings of these decisions.

Methods: Data for 21 outcomes from 14 published clinical trials were made available for re-analysis. CP curves for accruing outcome information were calculated using and compared with a pre-specified objective criteria for original and transformed versions of the trial data using four future treatment effect assumptions: (i) observed current trend, (ii) hypothesised effect, (iii) 80% optimistic confidence limit, (iv) 90% optimistic confidence limit.

Results: The hypothesised effect assumption met objective criteria when the true effect was close to that planned, but not when smaller than planned. The opposite was seen using the current trend assumption. Optimistic confidence limit assumptions appeared to offer a compromise between the two, performing well against objective criteria when the end observed effect was as planned or smaller.

Conclusion: The current trend assumption could be the preferable assumption when there is a wish to stop early for futility. Interim analyses could be undertaken as early as 30% of patients have data available. Optimistic confidence limit assumptions should be considered when using CP to make trial decisions, although later interim timings should be considered where logistically feasible.

Keywords: Adaptive designs; Clinical trials; Conditional power; Futility; Sample size re-estimation.

Fig. 1

a, b Stability of the treatment estimate during trial progression for IMPROVE (log(OR)) and CASPER Plus (mean difference) studies respectively, showing estimates and 95% confidence intervals given patient enrolment occurred in original sequential order, reverse order, and simulated random re-ordering for 1000 random samples (median and 2.5, 25, 75, 97.5 percentiles). c, d Conditional power curves for the original trial data for IMPROVE and CASPER Plus respectively, calculated using four assumptions of future treatment effect. A 10% futility boundary is also shown (dashed line)

Fig. 2

Conditional power curves for all re-analysed trials using the current trend assumption (a, b), the hypothesised assumption (c, d), the 80% optimistic confidence limit assumption (e, f), and the 90% confidence limit assumption (g, h), split by statistical significance in the original analysis: non-significant (a, c, e, g) and significant (b, d, f, h)

Fig. 3

Conditional power curves for trials with continuous outcome data following data transformations such that observed final estimate equals: a ∂ = ∂_plan; b $\partial =\frac{2}{3}{\partial }_{\mathit{plan}}$; c ∂ = 0. For each data transformation scenario, four future treatment effect assumptions are used in the conditional power calculation

Fig. 4

Conditional power curves for trials with binary outcome data following data transformations such that observed final estimate equals: a ∂ = ∂_plan; b $\partial =\frac{2}{3}{\partial }_{\mathit{plan}}$; c ∂ = 0. For each data transformation scenario, four future treatment effect assumptions are used in the conditional power calculation