Analysis of longitudinal semicontinuous data using marginalized two-part model

Abstract

Background: Connective tissue growth factor (CTGF), is a secreted matricellular factor that has been linked to increased risk of cardiovascular disease in diabetic subjects. Despite the biological role of CTGF in diabetes, it still remains unclear how CTGF expression is regulated. In this study, we aim to identify the clinical parameters that modulate plasma CTGF levels measured longitudinally in type 1 diabetic patients over a period of 10 years. A number of patients had negligible measured values of plasma CTGF that formed a point mass at zero, whereas others had high positive values of CTGF that were measured on a continuous scale. The observed combination of excessive zero and continuous positively distributed non-zero values in the CTGF outcome is referred to as semicontinuous data. Methods: We propose a novel application of a marginalized two-part model (mTP) extended to accommodate longitudinal semicontinuous data in which the marginal mean is expressed in terms of the covariates and estimates of their effect on the mean responses are generated. The continuous component is assumed to follow distributions that stem from the generalized gamma family whereas the binary measure is analyzed using logistic model and both have correlated random effects. Other approaches including the one- and two-part with uncorrelated and correlated random effects models were also applied and their estimates were all compared. Results: Our results using the mTP model identified intensive glucose control treatment and smoking as clinical factors that were associated with decreased and increased odds of observing non-zero CTGF values respectively. In addition, hemoglobin A1c, systolic blood pressure, and high density lipoprotein were all shown to be significant risk factors that contribute to increasing CTGF levels. These findings were consistently observed under the mTP model but varied with the distributions for the other models. Accuracy and precision of the mTP model was further validated using simulation studies. Conclusion: The mTP model identified new clinical determinants that modulate the levels of CTGF in diabetic subjects. Applicability of this approach can be extended to other biomarkers measured in patient populations that display a combination of negligible zero and non-zero values.