The relationship between a primary endpoint and features of longitudinal profiles of a continuous response is often of interest, and a relevant framework is that of a generalized linear model with covariates that are subject-specific random effects in a linear mixed model for the longitudinal measurements. Naive implementation by imputing subject-specific effects from individual regression fits yields biased inference, and several methods for reducing this bias have been proposed. These require a parametric (normality) assumption on the random effects, which may be unrealistic. Adapting a strategy of Stefanski and Carroll (1987, Biometrika74, 703-716), we propose estimators for the generalized linear model parameters that require no assumptions on the random effects and yield consistent inference regardless of the true distribution. The methods are illustrated via simulation and by application to a study of bone mineral density in women transitioning to menopause.

Joint models are formulated to investigate the association between a primary endpoint and features of multiple longitudinal processes. In particular, the subject-specific random effects in a multivariate linear random-effects model for multiple longitudinal processes are predictors in a generalized linear model for primary endpoints. Li, Zhang, and Davidian (2004, Biometrics60, 1-7) proposed an estimation procedure that makes no distributional assumption on the random effects but assumes independent within-subject measurement errors in the longitudinal covariate process. Based on an asymptotic bias analysis, we found that their estimators can be biased when random effects do not fully explain the within-subject correlations among longitudinal covariate measurements. Specifically, the existing procedure is fairly sensitive to the independent measurement error assumption. To overcome this limitation, we propose new estimation procedures that require neither a distributional or covariance structural assumption on covariate random effects nor an independence assumption on within-subject measurement errors. These new procedures are more flexible, readily cover scenarios that have multivariate longitudinal covariate processes, and can be implemented using available software. Through simulations and an analysis of data from a hypertension study, we evaluate and illustrate the numerical performances of the new estimators.

Summary. We consider nonparametric regression analysis in a generalized linear model (GLM) framework for data with covariates that are the subject-specific random effects of longitudinal measurements. The usual assumption that the effects of the longitudinal covariate processes are linear in the GLM may be unrealistic and if this happens it can cast doubt on the inference of observed covariates. Allowing the regression functions to be unknown, we propose to apply Bayesian cubic smoothing spline models for the possible nonlinearity and use an additive model in this complex setting. To improve computational efficiency, we propose the use of a data augmentation scheme. The approach allows flexible covariance structures for the random effects and within-subject measurement errors of the longitudinal processes. The posterior model space is explored through a Markov Chain Monte Carlo (MCMC) sampler. The proposed method is illustrated and compared to existing methods via simulations and by an application that investigates the relationship between obesity in adulthood and childhood growth curves.

Determination of urolith mineral composition is critical for management of urolithiasis in dogs and cats. Using computed tomography, urolith physical density, and hence chemical composition, can be quantified using mean beam attenuation measurements (Hounsfield units; HU). This study was designed to establish in vitro reference ranges for three types of compositionally pure uroliths retrieved from dogs. Sixty-six canine uroliths (22 uric acid, 21 calcium oxalate, 14 struvite, nine mixed or compound) were placed in a phantom array. Uroliths were scanned at 120 kVp, 200 mA, and 80 kVp, 200 mA. The region of interest (ROI) for mean HU calculation was determined using two techniques, and reference ranges were calculated for each kVp using either ROI technique. HU for urolith types of pure composition were statistically different (Wilcoxon's two-sample test, P < 0.0083 [Bonferonni correction with six comparisons for total P < 0.05]) using both ROI techniques at either kVp. Struvite uroliths were not statistically different from mixed or compound uroliths. The accuracy for determination of composition of pure uroliths ranged from 86% to 93%; the prediction accuracy for each urolith mineral type and for all uroliths in general was highest when the ROI was hand-drawn just within the visible urolith border at 80 kVp. Technique of ROI determination and kVp that yielded the highest sensitivity, specificity, and positive and negative predictive values varied for each urolith type. Therefore, in this study, HU could be used to differentiate three types of uroliths of pure mineral composition in vitro. Further studies are needed to determine the predictive value of HU in vivo.

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.