Delta method and bootstrap in linear mixed models to estimate a proportion when no event is observed: application to intralesional resection in bone tumor surgery

Resecting bone tumors requires good cutting accuracy to reduce the occurrence of local recurrence. This issue is considerably reduced with a navigated technology. The estimation of extreme proportions is challenging especially with small or moderate sample sizes. When no success is observed, the commonly used binomial proportion confidence interval is not suitable while the rule of three provides a simple solution. Unfortunately, these approaches are unable to differentiate between different unobserved events. Different delta methods and bootstrap procedures are compared in univariate and linear mixed models with simulations and real data by assuming the normality. The delta method on the z-score and parametric bootstrap provide similar results but the delta method requires the estimation of the covariance matrix of the estimates. In mixed models, the observed Fisher information matrix with unbounded variance components should be preferred. The parametric bootstrap, easier to apply, outperforms the delta method for larger sample sizes but it may be time costly. Copyright © 2016 John Wiley & Sons, Ltd.