Frequentist and Bayesian approaches for a joint model for prostate cancer risk and longitudinal prostate-specific antigen data

Joint modeling of longitudinal CD4 count data and time to first occurrence of composite outcome

In this study, we jointly modeled longitudinal CD4 count data and survival outcome (time-to-first occurrence of composite outcome of death, cardiac tamponade or constriction) in other to investigate the effects of Mycobacterium indicus pranii immunotherapy and the CD4 count measurements on the hazard of the composite outcome among patients with HIV and tuberculous (TB) pericarditis. In this joint modeling framework, the models for longitudinal and the survival data are linked by an association structure. The association structure represents the hazard of the event for 1-unit increase in the longitudinal measurement. Models fitting and parameter estimation were carried out using R version 4.2.3. The association structure that represents the strength of the association between the hazard for an event at time point j and the area under the longitudinal trajectory up to the same time j provides the best fit. We found that 1-unit increase in CD4 count results in 2 % significant reduction in the hazard of the composite outcome. Among HIV and TB pericarditis individuals, the hazard of the composite outcome does not differ between of M.indicus pranii versus placebo. Application of joint models to investigate the effect of M.indicus pranii on the hazard of the composite outcome is limited. Hence, this study provides information on the effect of M.indicus pranii on the hazard of the composite outcome among HIV and TB pericarditis patients.

Joint models for dynamic prediction in localised prostate cancer: a literature review

BACKGROUND

Prostate cancer is a very prevalent disease in men. Patients are monitored regularly during and after treatment with repeated assessment of prostate-specific antigen (PSA) levels. Prognosis of localised prostate cancer is generally good after treatment, and the risk of having a recurrence is usually estimated based on factors measured at diagnosis. Incorporating PSA measurements over time in a dynamic prediction joint model enables updates of patients' risk as new information becomes available. We review joint model strategies that have been applied to model time-dependent PSA trajectories to predict time-to-event outcomes in localised prostate cancer.

METHODS

We identify articles that developed joint models for prediction of localised prostate cancer recurrence over the last two decades. We report, compare, and summarise the methodological approaches and applications that use joint modelling accounting for two processes: the longitudinal model (PSA), and the time-to-event process (clinical failure). The methods explored differ in how they specify the association between these two processes.

RESULTS

Twelve relevant articles were identified. A range of methodological frameworks were found, and we describe in detail shared-parameter joint models (9 of 12, 75%) and joint latent class models (3 of 12, 25%). Within each framework, these articles presented model development, estimation of dynamic predictions and model validations.

CONCLUSIONS

Each framework has its unique principles with corresponding advantages and differing interpretations. Regardless of the framework used, dynamic prediction models enable real-time prediction of individual patient prognosis. They utilise all available longitudinal information, in addition to baseline prognostic risk factors, and are superior to traditional baseline-only prediction models.

Bayesian survival analysis with BUGS

Survival analysis is one of the most important fields of statistics in medicine and biological sciences. In addition, the computational advances in the last decades have favored the use of Bayesian methods in this context, providing a flexible and powerful alternative to the traditional frequentist approach. The objective of this article is to summarize some of the most popular Bayesian survival models, such as accelerated failure time, proportional hazards, mixture cure, competing risks, multi-state, frailty, and joint models of longitudinal and survival data. Moreover, an implementation of each presented model is provided using a BUGS syntax that can be run with JAGS from the R programming language. Reference to other Bayesian R-packages is also discussed.

Bayesian joint modelling of longitudinal and time to event data: a methodological review

BACKGROUND

In clinical research, there is an increasing interest in joint modelling of longitudinal and time-to-event data, since it reduces bias in parameter estimation and increases the efficiency of statistical inference. Inference and prediction from frequentist approaches of joint models have been extensively reviewed, and due to the recent popularity of data-driven Bayesian approaches, a review on current Bayesian estimation of joint model is useful to draw recommendations for future researches.

METHODS

We have undertaken a comprehensive review on Bayesian univariate and multivariate joint models. We focused on type of outcomes, model assumptions, association structure, estimation algorithm, dynamic prediction and software implementation.

RESULTS

A total of 89 articles have been identified, consisting of 75 methodological and 14 applied articles. The most common approach to model the longitudinal and time-to-event outcomes jointly included linear mixed effect models with proportional hazards. A random effect association structure was generally used for linking the two sub-models. Markov Chain Monte Carlo (MCMC) algorithms were commonly used (93% articles) to estimate the model parameters. Only six articles were primarily focused on dynamic predictions for longitudinal or event-time outcomes.

CONCLUSION

Methodologies for a wide variety of data types have been proposed; however the research is limited if the association between the two outcomes changes over time, and there is also lack of methods to determine the association structure in the absence of clinical background knowledge. Joint modelling has been proved to be beneficial in producing more accurate dynamic prediction; however, there is a lack of sufficient tools to validate the prediction.

A continuous-time hidden Markov model for cancer surveillance using serum biomarkers with application to hepatocellular carcinoma

Hepatocellular carcinoma (HCC) is the fourth most common cause of cancer deaths worldwide, and its early detection is a critical determinant of whether curative treatment is achievable. Early stage HCC is typically asymptomatic. Thus, screening programmes are used for cancer detection in patients at risk of tumour development. Radiological screening methods are limited by imperfect data, cost and associated risks, and additionally are unable to detect lesions until they have grown to a certain size. Therefore, some screening programmes use additional blood/serum biomarkers to help identify individuals in whom to target diagnostic cancer investigations. The GALAD score, combining the levels of several blood biomarkers, age and sex, has been developed to identify patients with early HCC. Here we propose a Bayesian hierarchical model for an individual's longitudinal GALAD scores whilst in HCC surveillance to identify potentially significant changes in the trend of the GALAD score, indicating the development of HCC, aiming to improve early detection compared to standard methods. An absorbent two-state continuous-time hidden Markov model is developed for the individual level longitudinal data where the states correspond to the presence/absence of HCC. The model is additionally informed by the information on the diagnosis by standard clinical practice, taking into account that HCC can be present before the actual diagnosis so that there may be false negatives within the diagnosis data. We fit the model to a Japanese cohort of patients undergoing HCC surveillance and show that the detection capability of this proposal is greater than using a fixed cut-point.

The longitudinal increments of serum alanine aminotransferase increased the incidence risk of metabolic syndrome: A large cohort population in China

BACKGROUND

Although alanine aminotransferase (ALT) is well known to be associated with metabolic syndrome (MetS), prospective data on longitudinal increments in ALT activities and incident cases of MetS are limited. We analyzed the impact of longitudinal increments of ALT on MetS based on a health check-up population in China.

METHODS

A total of 4491 subjects free of MetS who completed at least two annual health examinations during March 2010 to April 2016 were enrolled in this cohort study. The MetS was defined according to the Joint Interim Statement criteria 2009. The RRs of incident MetS were estimated by using the Cox model and the Joint model in R software.

RESULTS

The cumulative incidence of MetS was 18.55% during the 7 years of follow-up. In the Cox model, the estimated RR of developing MetS was 1.751 (95% CI =1.532-2.000) for 1 unit augmented in LNALT-0 level. In the Joint model, the estimated RR of developing MetS was 3.626 (95% CI = 2.721-4.831) for 1 unit augmented in LNALT activity longitudinally.

CONCLUSIONS

The longitudinal increment of individuals' ALT activity over time increased the incidence risk of MetS and the effects generated by longitudinal increments of ALT on MetS was higher than that generated by baseline ALT.

Bayesian joint modeling of bivariate longitudinal and competing risks data: An application to study patient-ventilator asynchronies in critical care patients

Mechanical ventilation is a common procedure of life support in intensive care. Patient-ventilator asynchronies (PVAs) occur when the timing of the ventilator cycle is not simultaneous with the timing of the patient respiratory cycle. The association between severity markers and the events death or alive discharge has been acknowledged before, however, little is known about the addition of PVAs data to the analyses. We used an index of asynchronies (AI) to measure PVAs and the SOFA (sequential organ failure assessment) score to assess overall severity. To investigate the added value of including the AI, we propose a Bayesian joint model of bivariate longitudinal and competing risks data. The longitudinal process includes a mixed effects model for the SOFA score and a mixed effects beta regression model for the AI. The survival process is defined in terms of a cause-specific hazards model for the competing risks death or alive discharge. Our model indicates that the SOFA score is strongly related to vital status. PVAs are positively associated with alive discharge but there is not enough evidence that PVAs provide a more accurate indication of death prognosis than the SOFA score alone.

Bayesian joint ordinal and survival modeling for breast cancer risk assessment

We propose a joint model to analyze the structure and intensity of the association between longitudinal measurements of an ordinal marker and time to a relevant event. The longitudinal process is defined in terms of a proportional‐odds cumulative logit model. Time‐to‐event is modeled through a left‐truncated proportional‐hazards model, which incorporates information of the longitudinal marker as well as baseline covariates. Both longitudinal and survival processes are connected by means of a common vector of random effects.

General inferences are discussed under the Bayesian approach and include the posterior distribution of the probabilities associated to each longitudinal category and the assessment of the impact of the baseline covariates and the longitudinal marker on the hazard function. The flexibility provided by the joint model makes possible to dynamically estimate individual event‐free probabilities and predict future longitudinal marker values.

The model is applied to the assessment of breast cancer risk in women attending a population‐based screening program. The longitudinal ordinal marker is mammographic breast density measured with the Breast Imaging Reporting and Data System (BI‐RADS) scale in biennial screening exams. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.