# A single predictor in a multiple binary logistic regression

A power calculator is given here for upto two binary covariates using Demidenko (2007, 2008) and were here although it is anticipated this page could reappear pending a redesign of the http://biostat.hitchcock.org/ website (April 2017). An example of using Demidenko's programme is here.

Hsieh FY (1989) gives formulae and tables for odds ratios between 0.6 and 3.0 and ONE-tailed type I error to compute power for given total sample size in a multiple binary logistic regression for continuous covariates associated with a change of 1 sd in the value of the covariate. These calculations can be done using a spreadsheet.

Hsieh, Bloch and Larsen (1998) showed that sample size for multiple logistic regression predictors could be approximated using t-tests for a single predictor. A spreadsheet to compute power using their approach for a binary covariate is given here and using a continuous covariate here. The odds ratio in the latter represents an increase of one standard deviation in the covariate.

(The following is reproduced from this website). A less complex approach is based upon the work of Peduzzi et al. (1996) who offer the following guideline for a minimum number of cases to include in your study.

Whitaker HJ, Farrington, CP, Spiessens B and Musonda P (2005) give simple sample size formulae for an odds which takes the length of the risk period into account e.g. what fraction of the observation period you are exposed to an adverse event (see also Musonda et al here.)

References

Demidenko E (2007) Sample size determination for logistic regression revisited. *Statistics in Medicine* **26** 3385-3397.

Demidenko E (2008) Sample size and optimal design for logistic regression with binary interaction. *Statistics in Medicine*, **27** 36-46.

Hsieh FY (1989) Sample size tables for logistic regression. *Statistics in Medicine* **8** 795-802.

Hsieh, FY, Block, DA, and Larsen, MD (1998). A Simple Method of Sample Size Calculation for Linear and Logistic Regression. Statistics in Medicine, Volume 17, pages 1623-1634.

Musonda P, Farrington CP and Whitaker HJ. (2005) Sample sizes for self-controlled case series studies. Research report:The Open University.

Whitaker HJ, Farrington, CP, Spiessens B and Musonda P (2005). Tutorial in biostatistics: the self-controlled case series method. *Statistics in Medicine* **24** 4035-4044.