This paper examines the problem of hypothesis testing for comparison of time-dependent recurrent events between categorical exposure groups. We compare three methods (a summary chi-square test based on a generalization of the simple Poisson distribution, a chi-square test based on a generalization of the compound Poisson distribution, and a test on risk scores based on individual observed to expected ratios), when the dependent variable may be autocorrelated within an individual, and disease risk may be heterogeneous among subjects. We present a simulation study and an application to a cohort of sickle cell anaemia patients. With autocorrelation or heterogeneous risk present, the simple chi-square test is inappropriate, while the other two methods perform well. An attraction of the risk score method is its relative ease of application.