Robustness of cost-effectiveness analyses of cluster randomized trials assuming bivariate normality against skewed cost data

The bivariate normal multilevel model (MLM) provides a flexible modeling framework for cost-effectiveness analyses (CEAs) alongside cluster randomized trials (CRTs) as well as for sample size calculations of these trials. The bivariate MLM assumes a joint normal distribution for effects and costs, both within (individual level) and between (cluster level) clusters. A typical problem in CEAs is that costs are often associated with right-skewed distributions (e.g., gamma or lognormal), which make it sometimes difficult to justify the modeling of the data based on normality assumptions. The robustness of CEAs of CRTs based on the bivariate normal MLM to non-normal cost distributions at both cluster and individual level are investigated. Normal, gamma, and lognormal distributions are considered using scenarios that differ in the number of clusters, the number of persons per cluster, the covariance parameters of the model, and the level of skewness in the cost data. It is shown that CEA of CRTs, and therefore sample size calculation, based on the bivariate normal MLM, is quite robust against highly skewed costs across a wide range of scenarios. This robustness holds especially with respect to the type I error rate and the power. In terms of bias in variance component estimation and standard errors of fixed effects, large bias can occur in small samples. However, these biases do not appear to translate into any serious deviation of the type I error rate or power from the nominal level.