Adjusting for a cluster effect in the logistic regression model: An illustration of theory and its application

Abstract

When a response having two outcomes is modelled using a logistic model the responses on each observation are often considered to be independent of each other. This assumption may not always be valid and the responses may be correlated with each other as in the case of clustered data, which can occur especially in the case of survey data. When responses are correlated as explained, then the ordinary logistic regression model is unsuitable as the standard errors will be biased, and therefore this model should be adjusted for the cluster effect. In this paper one of the many methods of adjustment suggested in the literature, which is based on robust standard error estimation for cluster sampling data is examined. The objective of this paper is to illustrate the theory and mode of application of this theory by way of using a survey on Paraquet poisoned patients in Sri Lanka. Here, the patients are clustered within hospitals and therefore adjustment of the logistic model for the clustering effect is discussed. Adjusting for the hospital (cluster) effect significantly reduced the standard error of four out of thirty three odds ratios given by the model. That is four odds ratios that were not significant before adjustment became significant after adjustment. There was no change in significance in the other twenty nine odds ratios. On average there is a reduction of 2.29% in the standard error of the odds ratios after adjustment for the cluster effect. This indicates that it is effective and important to adjust for the cluster effect.