Construction of confidence limits about effect measures: A general approach

Abstract

It is widely accepted that confidence interval construction has important advantages over significance testing for the presentation of research results, as now facilitated by readily available software. However, for a number of effect measures, procedures are either not available or not satisfactory in samples of small to moderate size. In this paper, we describe a general approach for estimating a difference between effect measures, which can also be used to obtain confidence limits for a risk ratio and a lognormal mean. Numerical evaluation shows that this closed-form procedure outperforms existing methods, including the bootstrap.

Towards the Estimation of Effect Measures in Studies Using Respondent-Driven Sampling

“…Of particular strength is that it does not rely on any distributional assumptions on how the confidence limits for each parameter are obtained and thus may be used in the RDS context. 10 Let b π 1 denote the point estimate of the first population proportion of interest, π 1 , with 100(1−α)% confidence limits, l 1 and u 1 , respectively. In a similar spirit, let b π 2 denote the point estimate of the second population proportion of interest, π 2 , with corresponding 100(1−α)% confidence limits, l 2 and u 2 .…”

“…Assuming b π 1 and b π 2 are independent, Zou and Donner 10 provide us with a simple computational form for the 100(1−α)% confidence limits, L and U, for the risk difference, π 1 −π 2 , where…”

“…This is of significant advantage in the analysis of RDS data as the bootstrap CIs obtained from analysis software (e.g., RDSAT 7 ) are typically asymmetric. This approach has been applied to a variety of confidence interval estimation problems, including estimation of confidence intervals for functions of normal means and standard deviations, 9 effect measures, 10 and more generally, linear combinations of parameters. 11 Moreover, the construction of effect measures and confidence intervals using MOVER better quantifies the difference in risk between groups and has higher power than the overlap method, which is known to have low power to conclude that two groups in fact differ.…”

Assessment of Intrasub ject Parallelism in Ex Vivo Bioassay Using Two One-Sided Tolerance Limits

“…deduced the one-sided confidence limit of the quantile (i.e., the one-sided tolerance limit) of the derived variable by using a variation of the modified large-sample theory technique described by Zou and Donner (2008).…”

“…Under the normality assumption in (1),σ 2 l is the sum of the independent statistics, and the (1 − γ/2, 1 − α) lower tolerance limit of li is given by the method of variance estimates recovery (MOVER; Zou and Donner, 2008) as…”