In observational and clinical studies, it is often of interest to model the distribution of a given outcome as a function of one or more predictors (or treatments, or exposures). For example, pediatric growth charts consist of a series of percentile curves to model the distribution of certain body measurements in children as a function of age. Phenomena like human growth, certain disease mechanisms and the effects of harmful environmental substances such as lead and mercury, may show strong nonlinearities over time. Data collection to investigate this kind of effects typically involves repeated measurements on the same subject for a period of time. In clinical trials, for example, it is now common to collect biological specimens repeatedly throughout the duration of the study. Cohort studies follow-up individuals from their birth or early childhood throughout extended periods of life. Mixed-effects models represent a popular statistical approach to the modeling of longitudinal and other types of clustered data. However, the normality assumptions in mean regression imply that all individuals in a population are affected by the exposure in the same exact way. A growing body of empirical findings in the medical literature shows that this is not the case in a number of studies. Mean effects may average out stronger and weaker effects, or even cancel out effects of opposite sign. Quantile regression (QR) is a flexible statistical tool with a vast number of applications and has been rapidly emerging in the medical field in the recent years. Its ability to allow inference about the effects of an exposure in subjects that deviate from the `population mean', its robustness to outliers and to distributional assumptions, are among the reasons why QR is a successful tool in many fields of science. Although the foundations of QR theory have been laid out, some inferential and computational issues in nonlinear modelling of longitudinal/clustered data in are yet to be explored. This project aims at developing advanced statistical methods to address complex issues often encountered in pediatric research when assessing the association between an outcome of interest and a set of predictors. We propose to develop nonlinear quantile mixed models (NLQMMs) to model nonlinear quantile effects when the data are longitudinal or clustered. The proposed methods will specifically cope with three aspects: deviations from normality, nonlinearity and clustering. By building on established methods and software developed by the PI, this project will fill a hole in the statistical literatue and will provide innovative analytical methods to address important research questions in a number of fields, including the medical and health sciences.
The proposed research addresses important statistical methodology developments for the analysis of longitudinal/clustered data with applications in child health research, including the study of the effects of succimer on blood lead levels; the association between blood lead and blood pressure; and the temporal trajectories of physical activity and inactivity in children. There is a tremendous need to model the data appropriately in order to quantify more accurately medical and economic costs associated with a given risk factor, or to assess the benefits of a medical treatment for patients who deviate from the 'average'. The key element of the proposed models is to provide a framework of analysis for assessing nonlinear effects of exposures on health outcomes in subjects who rank lower or higher in the distribution (e.g., preterm and low birthweight, obese, sedentary, hypotensive, hypertensive, socio-economically disadvantaged): these are individuals that may experience higher mortality, morbidity or social exclusion and may require targeted interventions.
