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Sample size estimation for stratified individual and cluster randomized trials with binary outcomes.

ABSTRACT: Individual randomized trials (IRTs) and cluster randomized trials (CRTs) with binary outcomes arise in a variety of settings and are often analyzed by logistic regression (fitted using generalized estimating equations for CRTs). The effect of stratification on the required sample size is less well understood for trials with binary outcomes than for continuous outcomes. We propose easy-to-use methods for sample size estimation for stratified IRTs and CRTs and demonstrate the use of these methods for a tuberculosis prevention CRT currently being planned. For both IRTs and CRTs, we also identify the ratio of the sample size for a stratified trial vs a comparably powered unstratified trial, allowing investigators to evaluate how stratification will affect the required sample size when planning a trial. For CRTs, these can be used when the investigator has estimates of the within-stratum intracluster correlation coefficients (ICCs) or by assuming a common within-stratum ICC. Using these methods, we describe scenarios where stratification may have a practically important impact on the required sample size. We find that in the two-stratum case, for both IRTs and for CRTs with very small cluster sizes, there are unlikely to be plausible scenarios in which an important sample size reduction is achieved when the overall probability of a subject experiencing the event of interest is low. When the probability of events is not small, or when cluster sizes are large, however, there are scenarios where practically important reductions in sample size result from stratification.

SUBMITTER: Kennedy-Shaffer L

PROVIDER: S-EPMC7247053 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Risk-prediction models for health outcomes are used in practice as part of clinical decision-making, and it is essential that their performance be externally validated. An important aspect in the design of a validation study is choosing an adequate sample size. In this paper, we investigate the sample size requirements for validation studies with binary outcomes to estimate measures of predictive performance (C-statistic for discrimination and calibration slope and calibration in the large). We aim for sufficient precision in the estimated measures. In addition, we investigate the sample size to achieve sufficient power to detect a difference from a target value. Under normality assumptions on the distribution of the linear predictor, we obtain simple estimators for sample size calculations based on the measures above. Simulation studies show that the estimators perform well for common values of the C-statistic and outcome prevalence when the linear predictor is marginally Normal. Their performance deteriorates only slightly when the normality assumptions are violated. We also propose estimators which do not require normality assumptions but require specification of the marginal distribution of the linear predictor and require the use of numerical integration. These estimators were also seen to perform very well under marginal normality. Our sample size equations require a specified standard error (SE) and the anticipated C-statistic and outcome prevalence. The sample size requirement varies according to the prognostic strength of the model, outcome prevalence, choice of the performance measure and study objective. For example, to achieve an SE < 0.025 for the C-statistic, 60-170 events are required if the true C-statistic and outcome prevalence are between 0.64-0.85 and 0.05-0.3, respectively. For the calibration slope and calibration in the large, achieving SE < 0.15 would require 40-280 and 50-100 events, respectively. Our estimators may also be used for survival outcomes when the proportion of censored observations is high.

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Sample size estimation for stratified individual and cluster randomized trials with binary outcomes.

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