= A single predictor in a multiple binary logistic regression =

A power calculator is given [http://www.dartmouth.edu/~eugened/power-samplesize.php here] for upto two binary covariates using Demidenko (2007, 2008) and [http://biostat.hitchcock.org/MeasurementError/Analytics/SampleSizeCalculationsforLogisticRegression.asp here.]

Hsieh FY (1989) gives formulae to compute total sample size for given power 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 [attachment:llog1.xls spreadsheet.] Hsieh, Bloch and Larsen (1998) showed that sample size for multiple logistic regression predictors could be approximated using t-tests for a single binary predictor. A spreadsheet to compute sample size for a binary covariate is given [attachment:hblbin.xls here.]

[http://www.medcalc.org/manual/logistic_regression.php (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.

Let p be the smallest of the proportions of negative or positive cases in the population and k the number of covariates (the number of independent variables), then the minimum number of cases to include is:

N = 10 k / p

For example: you have 3 covariates to include in the model and the proportion of positive cases in the population is 0.20 (20%). The minimum number of cases required is

N = 10 x 3 / 0.20 = 150

If the resulting number is less than 100 you should increase it to 100 as suggested by Long (1997).

__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.

[attachment:logN.pdf Hsieh, FY, Block, DA, and Larsen, MD (1998). A Simple Method of Sample Size Calculation for Linear and Logistic Regression.] ''Statistics in Medicine'' '''17''' 1623-1634. (Pdf file taken from [http://personal.health.usf.edu/ywu/logistic.pdf here]).

Long, JS (1997). Regression Models for categorical and limited dependent variables. Thousand Oaks, CA: Sage Publications.

Peduzzi, P, Concato, J, Kemper, E, Holford, TR, Feinstein, AR (1996). A simulation study of the number of events per variable in logistic regression analysis. ''Journal of Clinical Epidemiology'' '''49''' 1373-1379.