Analyzing longitudinal data with patients in different disease states during follow-up and death as final state

Joint Models of Longitudinal and Time-to-Event Data with More Than One Event Time Outcome: A Review

Methodological development and clinical application of joint models of longitudinal and time-to-event outcomes have grown substantially over the past two decades. However, much of this research has concentrated on a single longitudinal outcome and a single event time outcome. In clinical and public health research, patients who are followed up over time may often experience multiple, recurrent, or a succession of clinical events. Models that utilise such multivariate event time outcomes are quite valuable in clinical decision-making. We comprehensively review the literature for implementation of joint models involving more than a single event time per subject. We consider the distributional and modelling assumptions, including the association structure, estimation approaches, software implementations, and clinical applications. Research into this area is proving highly promising, but to-date remains in its infancy.

Modelling the distribution of health-related quality of life of advanced melanoma patients in a longitudinal multi-centre clinical trial using M-quantile random effects regression

Health-related quality of life assessment is important in the clinical evaluation of patients with metastatic disease that may offer useful information in understanding the clinical effectiveness of a treatment. To assess if a set of explicative variables impacts on the health-related quality of life, regression models are routinely adopted. However, the interest of researchers may be focussed on modelling other parts (e.g. quantiles) of this conditional distribution. In this paper, we present an approach based on quantile and M-quantile regression to achieve this goal. We applied the methodologies to a prospective, randomized, multi-centre clinical trial. In order to take into account the hierarchical nature of the data we extended the M-quantile regression model to a three-level random effects specification and estimated it by maximum likelihood.

A prospective study on quality of life and functional outcome in children and adolescents after malignant bone tumor surgery

BACKGROUND

Few longitudinal data are available concerning quality of life (QoL) and functioning of young patients undergoing surgical procedures for malignant bone tumors around the knee joint. Aim of the present study was to evaluate patients' quality of life, functional ability, and physical activity during a 2-year postoperative period.

METHODS

This prospective study included patients who underwent surgery for a malignant bone tumor around the knee joint between 2004 and 2008. Assessments were done at 3, 6, 9, 12, 18, and 24 months after surgery. QoL was measured with the TNO-AZL Children's or Adult's Quality of Life Questionnaires (TACQOL and TAAQOL), the Short Form-36 (SF-36) and Bone tumor (Bt)-DUX; functional ability with the Toronto Extremity Salvage Scale (TESS), the 6-minute walk test (6 MWT) and four functional performance tests; and physical activity with the Baecke questionnaire and the ActiLog® activity monitor. Statistical analysis included linear mixed model analysis.

RESULTS

Forty-four patients (27 males, 17 females, mean age 14.9 (SD 4.8) years) were included, 27 (61%) underwent limb-salvage and 17 (39%) ablative surgery. Twenty patients were lost during the 2 years follow-up as a consequence of oncological complications. Over the first year, survivors showed significant improvement of QoL, functional ability and physical activity, except for the mental dimension of the SF-36 and the activity monitor results. Over the second year, these improvements were less pronounced.

CONCLUSIONS

In the first 2 years after bone tumor surgery, survivors improved significantly with respect to QoL, functional ability, and physical activity levels.

Slope estimation for informatively right censored longitudinal data modelling the number of observations using geometric and Poisson distributions: application to renal transplant cohort

Analysis of longitudinal data is often complicated by the presence of informative right censoring. This type of censoring should be accounted for in the analysis so that valid slope estimates are attained. In this study, we developed a new likelihood-based approach wherein the likelihood function is integrated over random effects to obtain a marginal likelihood function. Maximum likelihood estimates for the population slope were acquired by direct maximisation of the marginal likelihood function and empirical Bayes estimates for the individual slopes were generated using Gaussian quadrature. The performance of the model was assessed using the geometric and Poisson distributions to model the number of observations for every individual subject. Our model generated valid estimates for the slopes under both distributions with minimal bias and mean squared errors. Our sensitivity analysis confirmed the robustness of the model to assumptions pertaining to the underlying distribution and demonstrated its insensitivity to normality assumptions. Moreover, superiority of the model in terms of accuracy of slope estimates was consistently shown across the different levels of censoring in comparison to the naïve and bootstrap approaches. This model was illustrated using the cohort of renal transplant patients and estimates of the slopes that are adjusted for informative right censoring were acquired.