tailieunhanh - Báo cáo y học: "Statistics review 14: Logistic regression"

Tuyển tập các báo cáo nghiên cứu về y học được đăng trên tạp chí y học Critical Care cung cấp cho các bạn kiến thức về ngành y đề tài: Statistics review 14: Logistic regression. | Critical Care February 2005 Vol 9 No 1 Bewick et al. Review Statistics review 14 Logistic regression Viv Bewick1 Liz Cheek1 and Jonathan Ball2 Senior Lecturer School of Computing Mathematical and Information Sciences University of Brighton Brighton UK 2Senior Registrar in ICU Liverpool Hospital Sydney Australia Corresponding author Viv Bewick Published online 13 January 2005 This article is online at http content 9 1 112 2005 BioMed Central Ltd Critical Care 2005 9 112-118 DOI cc3045 Abstract This review introduces logistic regression which is a method for modelling the dependence of a binary response variable on one or more explanatory variables. Continuous and categorical explanatory variables are considered. Keywords binomial distribution Hosmer-Lemeshow test likelihood likelihood ratio test logit function maximum likelihood estimation median effective level odds odds ratio predicted probability Wald test Introduction Logistic regression provides a method for modelling a binary response variable which takes values 1 and 0. For example we may wish to investigate how death 1 or survival 0 of patients can be predicted by the level of one or more metabolic markers. As an illustrative example consider a sample of 2000 patients whose levels of a metabolic marker have been measured. Table 1 shows the data grouped into categories according to metabolic marker level and the proportion of deaths in each category is given. The proportions of deaths are estimates of the probabilities of death in each category. Figure 1 shows a plot of these proportions. It suggests that the probability of death increases with the metabolic marker level. However it can be seen that the relationship is nonlinear and that the probability of death changes very little at the high or low extremes of marker level. This pattern is typical because proportions cannot lie outside the range from 0 to 1. The relationship can be described as following an S .