Dataset Information

Sample size and power calculations in Mendelian randomization with a single instrumental variable and a binary outcome.

ABSTRACT:

Background

Sample size calculations are an important tool for planning epidemiological studies. Large sample sizes are often required in Mendelian randomization investigations.

Methods and results

Resources are provided for investigators to perform sample size and power calculations for Mendelian randomization with a binary outcome. We initially provide formulae for the continuous outcome case, and then analogous formulae for the binary outcome case. The formulae are valid for a single instrumental variable, which may be a single genetic variant or an allele score comprising multiple variants. Graphs are provided to give the required sample size for 80% power for given values of the causal effect of the risk factor on the outcome and of the squared correlation between the risk factor and instrumental variable. R code and an online calculator tool are made available for calculating the sample size needed for a chosen power level given these parameters, as well as the power given the chosen sample size and these parameters.

Conclusions

The sample size required for a given power of Mendelian randomization investigation depends greatly on the proportion of variance in the risk factor explained by the instrumental variable. The inclusion of multiple variants into an allele score to explain more of the variance in the risk factor will improve power, however care must be taken not to introduce bias by the inclusion of invalid variants.

SUBMITTER: Burgess S

PROVIDER: S-EPMC4052137 | biostudies-literature |

REPOSITORIES: biostudies-literature

ACCESS DATA

Similar Datasets

Project description:Background/aimsGeneralized estimating equations are commonly used to fit logistic regression models to clustered binary data from cluster randomized trials. A commonly used correlation structure assumes that the intracluster correlation coefficient does not vary by treatment arm or other covariates, but the consequences of this assumption are understudied. We aim to evaluate the effect of allowing variation of the intracluster correlation coefficient by treatment or other covariates on the efficiency of analysis and show how to account for such variation in sample size calculations.MethodsWe develop formulae for the asymptotic variance of the estimated difference in outcome between treatment arms obtained when the true exchangeable correlation structure depends on the treatment arm and the working correlation structure used in the generalized estimating equations analysis is: (i) correctly specified, (ii) independent, or (iii) exchangeable with no dependence on treatment arm. These formulae require a known distribution of cluster sizes; we also develop simplifications for the case when cluster sizes do not vary and approximations that can be used when the first two moments of the cluster size distribution are known. We then extend the results to settings with adjustment for a second binary cluster-level covariate. We provide formulae to calculate the required sample size for cluster randomized trials using these variances.ResultsWe show that the asymptotic variance of the estimated difference in outcome between treatment arms using these three working correlation structures is the same if all clusters have the same size, and this asymptotic variance is approximately the same when intracluster correlation coefficient values are small. We illustrate these results using data from a recent cluster randomized trial for infectious disease prevention in which the clusters are groups of households and modest in size (mean 9.6 individuals), with intracluster correlation coefficient values of 0.078 in the control arm and 0.057 in an intervention arm. In this application, we found a negligible difference between the variances calculated using structures (i) and (iii) and only a small increase (typically <5%) for the independent correlation structure (ii), and hence minimal effect on power or sample size requirements. The impact may be larger in other applications if there is greater variation in the ICC between treatment arms or with an additional covariate.ConclusionThe common approach of fitting generalized estimating equations with an exchangeable working correlation structure with a common intracluster correlation coefficient across arms likely does not substantially reduce the power or efficiency of the analysis in the setting of a large number of small or modest-sized clusters, even if the intracluster correlation coefficient varies by treatment arm. Our formulae, however, allow formal evaluation of this and may identify situations in which variation in intracluster correlation coefficient by treatment arm or another binary covariate may have a more substantial impact on power and hence sample size requirements.