samplesizelogisticcasecontrol-package: Sample size and power calculations for case-control studies

In samplesizelogisticcasecontrol: Sample Size and Power Calculations for Case-Control Studies

Sample size and power calculations for case-control studies

Description

This package can be used to calculate the required sample size needed for case-control studies to have sufficient power, or calculate the power of a case-control study for a given sample size. To calculate the sample size, one needs to specify the significance level \alpha, power \gamma, and the hypothesized non-null \theta. Here \theta is a log odds ratio for an exposure main effect or \theta is an interaction effect on the logistic scale. Choosing \theta requires subject matter knowledge to understand how strong the association needs to be to have practical importance. Sample size varies inversely with \theta^{2} and is thus highly dependent on \theta.

Details

The main functions in the package are for different types of exposure variables, where the exposure variable is the variable of interest in a hypothesis test. The functions sampleSize_binary and power_binary can be used for a binary exposure variable (X = 0 or 1), while the functions sampleSize_ordinal and power_ordinal is a more general function that can be used for an ordinal exposure variable (X takes the values 0, 1, ..., k). sampleSize_continuous and power_continuous are useful for a continuous exposure variable and sampleSize_data and power_data can be used when pilot data is available that defines the distribution of the exposure and other confounding variables. Each function will return the sample sizes or power for a Wald-type test and a score test. When there are no adjustments for confounders, the user can specify a general distribution for the exposure variable. With confounders, either pilot data or a function to generate random samples from the multivariate distribution of the confounders and exposure variable must be given.

If the parameter of interest, \theta, is one dimensional, then the test statistic is often asymptotically equivalent to a test of the form T > Z_{1-\alpha}\sigma_{0}n^{-\frac{1}{2}} or T > Z_{1-\alpha}\sigma_{\theta}n^{-\frac{1}{2}}, where Z_{1-\alpha} is the 1-\alpha quantile of a standard normal distribution, n is the total sample size (cases plus controls), and n^{\frac{1}{2}}T is normally distributed with mean 0 and null variance \sigma_{0}^{2}. Depending on which critical value Z_{1-\alpha}\sigma_{0}n^{-\frac{1}{2}} or Z_{1-\alpha}\sigma_{\theta}n^{-\frac{1}{2}} of the test was used, the formulas for sample size are obtained by inverting the equations for power:

n_{1} = (Z_{\gamma}\sigma_{\theta} + Z_{1-\alpha}\sigma_{0})^{2}/\theta^{2} or n_{2} = (Z_{\gamma} + Z_{1-\alpha})^{2}\sigma_{\theta}^{2}/\theta^{2}.

Author(s)

Mitchell H. Gail <[e-mail]>

References

Gail, M.H. and Haneuse, S. Power and sample size for case-control studies. In Handbook of Statistical Methods for Case-Control Studies. Editors: Ornulf Borgan, Norman Breslow, Nilanjan Chatterjee, Mitchell Gail, Alastair Scott, Christopher Wild. Chapman and Hall/CRC, Taylor and Francis Group, New York, 2018, pages 163-187.

Gail, M. H and Haneuse, S. Power and sample size for multivariate logistic modeling of unmatched case-control studies. Statistical Methods in Medical Research. 2019;28(3):822-834,
https://doi.org/10.1177/0962280217737157

samplesizelogisticcasecontrol documentation built on Aug. 21, 2023, 5:07 p.m.