A mixture of mixed regressions model for longitudinal data, with application to clinical laboratory measurements

We study a statistical model for longitudinal data from a mixture of populations with different mean structures, with a view to analyzing clinical laboratory data. Different configurations of learning data are discussed, including the case where external summary statistics are known for one population. An EM algorithm is used for fitting the model. We discuss the asymptotic properties of the model, and show that there exists a consistent root of the likelihood equations with standard properties. A simulation study with linear and fractional polynomial models to study finite sample bias, variance, as well as parameter standard deviation estimators based on nonparametric bootstrapping and asymptotic distributions, is included. The separation between populations was the most important factor for estimator performance. Nonparametric bootstrapping performed reasonably well in general when separation was large, but was unsatisfactory in some cases with small separation. The asymptotic distributions were in general reasonable for large separation, but very inaccurate in other cases, and seem to be of limited practical value. We also present an example on measurements of cardiac enzymes for data sets comprising both healthy patients and patients with acute myocardial infarction.