Three algorithms and SAS macros for estimating power and sample size for logistic models with one or more independent variables of interest in the presence of covariates.

David Keith Williams,Zoran Bursac

doi:10.1186/1751-0473-9-24

Abstract

BackgroundCommonly when designing studies, researchers propose to measure several independent variables in a regression model, a subset of which are identified as the main variables of interest while the rest are retained in a model as covariates or confounders. Power for linear regression in this setting can be calculated using SAS PROC POWER. There exists a void in estimating power for the logistic regression models in the same setting.MethodsCurrently, an approach that calculates power for only one variable of interest in the presence of other covariates for logistic regression is in common use and works well for this special case. In this paper we propose three related algorithms along with corresponding SAS macros that extend power estimation for one or more primary variables of interest in the presence of some confounders.ResultsThe three proposed empirical algorithms employ likelihood ratio test to provide a user with either a power estimate for a given sample size, a quick sample size estimate for a given power, and an approximate power curve for a range of sample sizes. A user can specify odds ratios for a combination of binary, uniform and standard normal independent variables of interest, and or remaining covariates/confounders in the model, along with a correlation between variables.ConclusionsThese user friendly algorithms and macro tools are a promising solution that can fill the void for estimation of power for logistic regression when multiple independent variables are of interest, in the presence of additional covariates in the model.Electronic supplementary materialThe online version of this article (doi:10.1186/1751-0473-9-24) contains supplementary material, which is available to authorized users.

Highlights

The purpose of this work is to propose and demonstrate the %LRpowerCorr10 algorithm which estimates power and sample size for logistic models in settings where one or more predictors are of primary interest (Additional file 1)
The motivation for this work stems from methods that are in use to estimate power and sample size for standard linear regression models [1,2,3,4]
In the third and final example we present the use and the results of the %LRpowerCorr10C macro which provides an approximate power curve for the user specified range of sample sizes

Summary

Introduction

The purpose of this work is to propose and demonstrate the %LRpowerCorr algorithm (and two related algorithms) which estimates power and sample size for logistic models in settings where one or more predictors are of primary interest (Additional file 1). Suppose an investigator proposes a linear model with four total predictors X1, X2, X3, and X4 but is primarily interested in X1 and X2 while controlling for X3 and X4. To power this setting the full model would be:. The short SAS code below would return a power value of 0.864

Objectives

Methods

Conclusion