Application of bootstrap sample-resample method in logistic regression in analysis of breast cancer data

The purpose of this study was to assess the accuracy of the bootstrap method in logistic regression and to explore the method's use in logistic regression models in cases where the sample size is insufficient. We use data from 150 patients who had undergone surgery at the Cancer Institute, Emam Khomeini hospital during from 1999 to 2001. Then we drew repeated samples of size 50 from these 150 patients. Applying ordinary logistic regression, an appropriate model we fitted to the initial data. Then confidence intervals and standard errors were computed for all regression coefficients. There are many situations where the sample size is insufficient and conditions for using ordinary logistic regression are not met. In these cases the use of the bootstrap method not only produces more accurate estimations of regression coefficients, but with repeated sampling, produces estimates very close to the true values. This holds for the estimation of regression coefficients, confidence intervals and standard errors of coefficients. In this study we show the optimal number of replications and the optimal sample size when using the bootstrap method in studies involving relatively small sample sizes.