TY - JOUR

T1 - Prediction of an outcome using trajectories estimated from a linear mixed model

AU - Maruyama, Nami

AU - Takahashi, Fumiaki

AU - Takeuchi, Masahiro

PY - 2009/9

Y1 - 2009/9

N2 - In longitudinal data, interest is usually focused on the repeatedly measured variable itself. In some situations, however, the pattern of variation of the variable over time may contain information about a separate outcome variable. In such situations, longitudinal data provide an opportunity to develop predictive models for future observations of the separate outcome variable given the current data for an individual. In particular, longitudinally changing patterns of repeated measurements of a variable measured up to time t, or trajectories, can be used to predict an outcome measure or event that occurs after time t. In this article, we propose a method for predicting an outcome variable based on a generalized linear model, specifically, a logistic regression model, the covariates of which are variables that characterize the trajectory of an individual. Since the trajectory of an individual contains estimation error, the proposed logistic regression model constitutes a measurement error model. The model is fitted in two steps. First, a linear mixed model is fitted to the longitudinal data to estimate the random effect that characterizes the trajectory for each individual while adjusting for other covariates. In the second step, a conditional likelihood approach is applied to account for the estimation error in the trajectory. Prediction of an outcome variable is based on the logistic regression model in the second step. The receiver operating characteristic curve is used to compare the discrimination ability of a model with trajectories to one without trajectories as covariates. A simulation study is used to assess the performance of the proposed method, and the method is applied to clinical trial data.

AB - In longitudinal data, interest is usually focused on the repeatedly measured variable itself. In some situations, however, the pattern of variation of the variable over time may contain information about a separate outcome variable. In such situations, longitudinal data provide an opportunity to develop predictive models for future observations of the separate outcome variable given the current data for an individual. In particular, longitudinally changing patterns of repeated measurements of a variable measured up to time t, or trajectories, can be used to predict an outcome measure or event that occurs after time t. In this article, we propose a method for predicting an outcome variable based on a generalized linear model, specifically, a logistic regression model, the covariates of which are variables that characterize the trajectory of an individual. Since the trajectory of an individual contains estimation error, the proposed logistic regression model constitutes a measurement error model. The model is fitted in two steps. First, a linear mixed model is fitted to the longitudinal data to estimate the random effect that characterizes the trajectory for each individual while adjusting for other covariates. In the second step, a conditional likelihood approach is applied to account for the estimation error in the trajectory. Prediction of an outcome variable is based on the logistic regression model in the second step. The receiver operating characteristic curve is used to compare the discrimination ability of a model with trajectories to one without trajectories as covariates. A simulation study is used to assess the performance of the proposed method, and the method is applied to clinical trial data.

KW - Generalized linear model

KW - Linear mixed model

KW - Longitudinal data

KW - Prediction

KW - ROC curve

KW - Trajectory

UR - http://www.scopus.com/inward/record.url?scp=75149170082&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=75149170082&partnerID=8YFLogxK

U2 - 10.1080/10543400903105174

DO - 10.1080/10543400903105174

M3 - Article

C2 - 20183443

AN - SCOPUS:75149170082

SN - 1054-3406

VL - 19

SP - 779

EP - 790

JO - Journal of Biopharmaceutical Statistics

JF - Journal of Biopharmaceutical Statistics

IS - 5

ER -