Partitioned GMM logistic regression models for longitudinal data

Abstract

Correlation is inherent in longitudinal studies due to the repeated measurements on subjects, as well as due to time-dependent covariates in the study. In the National Longitudinal Study of Adolescent to Adult Health (Add Health), data were repeatedly collected on children in grades 7-12 across four waves. Thus, observations obtained on the same adolescent were correlated, while predictors were correlated with current and future outcomes such as obesity status, among other health issues. Previous methods, such as the generalized method of moments (GMM) approach have been proposed to estimate regression coefficients for time-dependent covariates. However, these approaches combined all valid moment conditions to produce an averaged parameter estimate for each covariate and thus assumed that the effect of each covariate on the response was constant across time. This assumption is not necessarily optimal in applications such as Add Health or health-related data. Thus, we depart from this assumption and instead use the Partitioned GMM approach to estimate multiple coefficients for the data based on different time periods. These extra regression coefficients are obtained using a partitioning of the moment conditions pertaining to each respective relationship. This approach offers a deeper understanding and appreciation into the effect of each covariate on the response.We conduct simulation studies, as well as analyses of obesity in Add Health, rehospitalization in Medicare data, and depression scores in a clinical study.The Partitioned GMM methods exhibit benefits over previously proposed models with improved insight into the nonconstant relationships realized when analyzing longitudinal data.

Use of partitioned GMM marginal regression model with time-dependent covariates: analysis of Chinese Longitudinal Healthy Longevity Study

“…We fit a partitioned GMM logistic regression model [14] to the Chinese Longitudinal Healthy Longevity Study data to determine the effects of time-dependent covariates on the binary outcomes. The model measures the impact of time independent and time-dependent covariates X on the outcome Y measured at four different time points.…”

“…1. Thus, the partitioned GMM logistic regression model [14] provides coefficient estimates for the effect of X on Y when both are measured at the same time, for when X is measured one-time period ahead of Y, for when X is measured two-time periods ahead to Y and for when X is measured three-time periods ahead to Y.…”

“…We do so through a test of bivariate correlation developed by Lalonde, Wilson and Yin [3]. Once the valid moments are identified, the regression parameters are estimated using a GMM approach [14]. We do not rehash the derivations here.…”

Analysis of correlated data with feedback for time-dependent covariates in psychiatry research

“…Although these marginal models provide reasonable estimates of the regression coefficients, they assume that the effects of time-dependent covariates are the same across time. However, a partitioned coefficient model allows for the estimation of current and future effects of time-dependent covariates on binary and continuous outcomes as discussed in Irimata et al 14 Feedback model with time-dependent covariates When analysing longitudinal data with time-dependent covariates, there are usually three questions (Qs) of interest that researchers seek to answer 15 : Q1. What is the cross-sectional relationship/association between the outcome Yit and the covariate Xijt (both X and Y are measured at the same time)?…”

“…While there is merit in the models due to Lai and Small, 12 Zhou et al, 16 Lalonde et al 13 and Irimata et al, 14 they do not always account for the feedback. The two-stage GMM model allows one to account for the feedback effects across different time-periods.…”