Joint modelling of longitudinal and multi‐state processes: application to clinical progressions in prostate cancer

Joint modelling of longitudinal and survival data is increasingly used in clinical trials on cancer. In prostate cancer for example, these models permit to account for the link between longitudinal measures of prostate‐specific antigen (PSA) and time of clinical recurrence when studying the risk of relapse. In practice, multiple types of relapse may occur successively. Distinguishing these transitions between health states would allow to evaluate, for example, how PSA trajectory and classical covariates impact the risk of dying after a distant recurrence post‐radiotherapy, or to predict the risk of one specific type of clinical recurrence post‐radiotherapy, from the PSA history. In this context, we present a joint model for a longitudinal process and a multi‐state process, which is divided into two sub‐models: a linear mixed sub‐model for longitudinal data and a multi‐state sub‐model with proportional hazards for transition times, both linked by a function of shared random effects. Parameters of this joint multi‐state model are estimated within the maximum likelihood framework using an EM algorithm coupled with a quasi‐Newton algorithm in case of slow convergence. It is implemented under R, by combining and extending mstate and JM packages. The estimation program is validated by simulations and applied on pooled data from two cohorts of men with localized prostate cancer. Thanks to the classical covariates available at baseline and the repeated PSA measurements, we are able to assess the biomarker's trajectory, define the risks of transitions between health states and quantify the impact of the PSA dynamics on each transition intensity. Copyright © 2016 John Wiley & Sons, Ltd.     

Subjective prior distributions for modeling longitudinal continuous outcomes with non‐ignorable dropout

Substance abuse treatment research is complicated by the pervasive problem of non‐ignorable missing data—i.e. the occurrence of the missing data is related to the unobserved outcomes. Missing data frequently arise due to early client departure from treatment. Pattern‐mixture models (PMMs) are often employed in such situations to jointly model the outcome and the missing data mechanism. PMMs require non‐testable assumptions to identify model parameters. Several approaches to parameter identification have therefore been explored for longitudinal modeling of continuous outcomes, and informative priors have been developed in other contexts. In this paper, we describe an expert interview conducted with five substance abuse treatment clinical experts who have familiarity with the therapeutic community modality of substance abuse treatment and with treatment process scores collected using the Dimensions of Change Instrument. The goal of the interviews was to obtain expert opinion about the rate of change in continuous client‐level treatment process scores for clients who leave before completing two assessments and whose rate of change (slope) in treatment process scores is unidentified by the data. We find that the experts' opinions differed dramatically from widely utilized assumptions used to identify parameters in the PMM. Further, subjective prior assessment allows one to properly address the uncertainty inherent in the subjective decisions required to identify parameters in the PMM and to measure their effect on conclusions drawn from the analysis. Copyright © 2008 John Wiley & Sons, Ltd.     

An index of local sensitivity to non‐ignorability for multivariate longitudinal mixed data with potential non‐random dropout

Multivariate longitudinal data with mixed continuous and discrete responses with the possibility of non‐ignorable missingness are often common in follow‐up medical studies and their analysis needs to be developed. Standard methods of analysis based on the strong and the unverifiable assumption of missing at random (MAR) mechanism could be highly misleading. A way out of this problem is to start with methods that simultaneously allow modelling non‐ignorable mechanism, which includes somehow troubling computations that are often time consuming, then we can use a sensitivity analysis, in which one estimates models under a range of assumptions about non‐ignorability parameters to study the impact of these parameters on key inferences. A general index of sensitivity to non‐ignorability (ISNI) to measure sensitivity of key inferences in a neighborhood of MAR model without fitting a complicated not MAR (NMAR) model for univariate generalized linear models and for models used for univariate longitudinal normal and non‐Gaussian data with potentially NMAR dropout are well presented in the literature. In this paper we extend ISNI methodology to analyze multivariate longitudinal mixed data subject to non‐ignorable dropout in which the non‐ignorable dropout model could be dependent on the mixed responses. The approach is illustrated by analyzing a longitudinal data set in which the general substantive goal of the study is to better understand the relations between parental assessment of child's antisocial behavior and child's reading recognition skill. Copyright © 2010 John Wiley & Sons, Ltd.     

Multi‐disease analysis of maternal antibody decay using non‐linear mixed models accounting for censoring

Biomedical studies often generate repeated measures of multiple outcomes on a set of subjects. It may be of interest to develop a biologically intuitive model for the joint evolution of these outcomes while assessing inter‐subject heterogeneity. Even though it is common for biological processes to entail non‐linear relationships, examples of multivariate non‐linear mixed models (MNMMs) are still fairly rare. We contribute to this area by jointly analyzing the maternal antibody decay for measles, mumps, rubella, and varicella, allowing for a different non‐linear decay model for each infectious disease. We present a general modeling framework to analyze multivariate non‐linear longitudinal profiles subject to censoring, by combining multivariate random effects, non‐linear growth and Tobit regression. We explore the hypothesis of a common infant‐specific mechanism underlying maternal immunity using a pairwise correlated random‐effects approach and evaluating different correlation matrix structures. The implied marginal correlation between maternal antibody levels is estimated using simulations. The mean duration of passive immunity was less than 4months for all diseases with substantial heterogeneity between infants. The maternal antibody levels against rubella and varicella were found to be positively correlated, while little to no correlation could be inferred for the other disease pairs. For some pairs, computational issues occurred with increasing correlation matrix complexity, which underlines the importance of further developing estimation methods for MNMMs. Copyright © 2015 John Wiley & Sons, Ltd.     

A modeling framework for the analysis of HPV incidence and persistence: A semi‐parametric approach for clustered binary longitudinal data analysis

Human papillomavirus (HPV) infection is a common sexually transmitted disease of growing public health importance, and over 40 genotypes have been identified in genital infections. Current HPV cohort studies often follow participants at pre‐determined visits, such as every 6 months, and data generated from such epidemiology studies can be described as clustered longitudinal binary data where correlation arises in two ways: the directionless clustering due to the multiple genotypes tested within an individual, and the temporal correlation among the repeated measurements on the same genotype along time. Current analyses for identification of risk factors associated with HPV incidence and persistence often either do not fully utilize information in the data set or ignore the correlation between the multiple genotypes. Given the scientific definition of incidence and persistence, conditional probability modeling provides us a natural mathematical tool. We thus present a semi‐parametric regression model for such data where full specification of the joint multivariate binary distribution is avoided by using conditioning argument to handle the temporal correlation and GEE to account for the correlation between the multiple genotypes. The model is applied to the HPV data from the Rakai male circumcision (MC) trial to evaluate the as‐treated efficacy of MC and also identify modifiable risk factors for incidence and persistence of oncogenic HPV types in men. A simulation study is performed to provide empirical information on the number of individuals that is needed for satisfactory power and estimation accuracy of the association parameter estimates in future studies. Copyright © 2010 John Wiley & Sons, Ltd.     

Using longitudinal mixed methods to study the development of professional behaviours during pharmacy work‐based training

Recent longitudinal investigations of professional socialisation and development of professional behaviours during work‐based training are lacking. Using longitudinal mixed methods, this study aimed to explore the development of professional behaviours during a year of intensive work‐based (pre‐registration) training in pharmacy. Twenty trainee pharmacists and their tutors completed semi‐structured interview and professional behaviour questionnaires at four time points during 2011/2012: months 1, 4 and 9 during training and 4 months after registration; tutors participated in months 1 and 9. Interviews were analysed thematically using template analysis, and questionnaires were analysed using ANOVA and t‐tests. Self‐assessed (trainee) and tutor ratings of all elements of professional behaviours measured in questionnaires (appearance, interpersonal/social skills, responsibility, communication skills) increased significantly from the start of pre‐registration training to post‐registration. Some elements, for example, communication skills, showed more change over time compared with others, such as appearance, and continued to improve post‐registration. Qualitative findings highlighted the changing roles of trainees and learning experiences that appeared to facilitate the development of professional behaviours. Trainees’ colleagues, and particularly tutors, played an essential part in trainees’ development through offering support and role modelling. Trainees noted that they would have benefited from more responsibilities during training to ease the transition into practising as a responsible pharmacist. Longitudinal mixed methods can unpack the way in which professional behaviours develop during work‐based training and allow researchers to examine changes in the demonstration of professional behaviours and how they occur. Identifying areas less prone to change allows for more focus to be given to supporting trainees in areas where there is a development need, such as communication skills and holding increasing responsibility.     

‘They’re doing surgery on two people’: a meta‐ethnography of the influences on couples’ treatment decision making for prostate cancer

Background Current orthodoxy suggests that patients need to be provided with full information about their care and that treatment options should be discussed with patients and family members. This imperative is especially challenging when there is a lack of consensus about treatment effectiveness and equivocacy over different types of interventions. In the case of prostate cancer, evidence is contested as to the efficacy of different treatments. Thus, involving patients and their family members in treatment choices is complex and little is known about how patients and their partners process these decisions when there is uncertainty about different outcomes. This paper has reviewed the literature on the way couples approach such decision making in relation to treatment for prostate cancer. Objective A meta‐ethnographic synthesis of published qualitative papers that focused on the influences on patients’, and their partners’ treatment decision making for prostate cancer, was conducted in order to identify and understand barriers and facilitators which impact on this process. Results Our synthesis indicates that the couples’ relationship ‘dynamic’ provides a contextual background against which treatment decisions are negotiated and made. Discussion and conclusions We propose that the findings from this synthesis can enhance the potential for shared decision making for patients, and their partners, when facing a treatment decision for prostate cancer. By understanding the couples’ relationship dynamic pre‐diagnosis, clinicians may be able to tailor the communication and information provision to both patients and their partners, providing a personalized approach to treatment decision making.     

A generalized partially linear mean‐covariance regression model for longitudinal proportional data,with applications to the analysis of quality of life data from cancer clinical trials

Motivated by the analysis of quality of life data from a clinical trial on early breast cancer, we propose in this paper a generalized partially linear mean‐covariance regression model for longitudinal proportional data, which are bounded in a closed interval. Cholesky decomposition of the covariance matrix for within‐subject responses and generalized estimation equations are used to estimate unknown parameters and the nonlinear function in the model. Simulation studies are performed to evaluate the performance of the proposed estimation procedures. Our new model is also applied to analyze the data from the cancer clinical trial that motivated this research. In comparison with available models in the literature, the proposed model does not require specific parametric assumptions on the density function of the longitudinal responses and the probability function of the boundary values and can capture dynamic changes of time or other interested variables on both mean and covariance of the correlated proportional responses. Copyright © 2017 John Wiley & Sons, Ltd.