Likelihood and pseudo-likelihood methods for semiparametric joint models for a primary endpoint and longitudinal data

Abstract

Inference on the association between a primary endpoint and features of longitudinal profiles of a continuous response is of central interest in medical and public health research. Joint models that represent the association through shared dependence of the primary and longitudinal data on random effects are increasingly popular; however, existing inferential methods may be inefficient or sensitive to assumptions on the random effects distribution. We consider a semiparametric joint model that makes only mild assumptions on this distribution and develop likelihood-based inference on the association and distribution, which offers improved performance relative to existing methods that is insensitive to the true random effects distribution. Moreover, the estimated distribution can reveal interesting population features, as we demonstrate for a study of the association between longitudinal hormone levels and bone status in peri-menopausal women.

A joint Bayesian approach for the analysis of response measured at a primary endpoint and longitudinal measurements

“…#Below (theta [1],theta [2],theta [3],theta [4]) ¼ # (log(C1),C2,log(sigma2u)) auu < -1/sigma2u sigma2u < -exp(theta [4] [1],-nu-i)) * (mus [2] * pow(lambdas [2],-nu-i)) * (mus [3] * pow(lambdas [3],-nu-i)) * (mus [4] * pow(lambdas [4],-nu-i)) v2[i] < -(pow(exp(loggam(nuþi)),3) * exp(loggam(nu)) * exp(logfact(i))) v3[i] < -exp((nuþi) * (mus [ [4])))}…”

“…1]*theta[1] þ mus[2]*theta[2] þ mus[3]*theta[3] þ mus[4]*theta[4]) -((1/lambdas[1]) * exp(mus[1]*theta[1]) þ (1/lambdas[2]) * exp(mus[2]*theta[2]) þ (1/lambdas[3]) * exp(mus[3]*theta[3]) þ (1/lambdas[4]) * exp(mus[4]*theta…”

Bayesian Nonparametric Regression Analysis of Data with Random Effects Covariates from Longitudinal Measurements

“…Figure 1f implies the two random effects covariates X i 1 and X i 2 are correlated. To check if Gaussian distribution is a realistic assumption for the random effects , we estimated the joint density of X i 1 and X i 2 by the approach of Li, Zhang, and Davidian (2007), which chooses the random effects density via standard model selection criteria. Since all criteria selected Gaussian distribution, we assumed .…”

A fast EM algorithm for fitting joint models of a binary response and multiple longitudinal covariates subject to detection limits

“…This estimating equation strategy was extended by Li et al (2007a) to a model with multiple longitudinal covariates. Li et al (2007b) proposed a semiparametric version of the joint model in which normality of the random effects was not assumed, and then suggested using an EM algorithm or two-stage pseudo-likelihood approach to estimate the parameters in the model. Recently, Hwang et al (2011) extended the EM algorithm approach developed by Wulfsohn and Tsiatis (1997) to the context of a logistic regression submodel for the response.…”