Joint modeling of event time and nonignorable missing longitudinal data

A Joint Model Based on Post-Treatment Longitudinal Prognostic Nutritional Index to Predict Survival in Nasopharyngeal Carcinoma

BACKGROUND

a low PNI in patients with NPC is linked to poor survival, but prior studies have focused on single-timepoint measurements. Our study aims to employ joint modeling to analyze longitudinal PNI data from each routine visit, exploring its relationship with overall survival.

METHODS

In this retrospective study using data from the Chang Gung Research Database (2007-2019), we enrolled patients with NPC undergoing curative treatment. We analyzed the correlation between patient characteristics, including the PNI, and overall survival. A joint model combining a longitudinal sub-model with a time-to-event sub-model was used to further evaluate the prognostic value of longitudinal PNI.

RESULTS

A total of 2332 patient were enrolled for the analysis. Separate survival analyses showed that longitudinal PNI was an independent indicator of a reduced mortality risk (adjusted HR 0.813; 95% CI, 0.805 to 0.821). Joint modeling confirmed longitudinal PNI as a consistent predictor of survival (HR 0.864; 95% CI, 0.850 to 0.879). An ROC analysis revealed that a PNI below 38.1 significantly increased the risk of 90-day mortality, with 90.0% sensitivity and 89.6% specificity.

CONCLUSIONS

Longitudinal PNI data independently predicted the overall survival in patients with NPC, significantly forecasting 90-day survival outcomes. We recommend routine PNI assessments during each clinic visit for these patients.

A two‐level copula joint model for joint analysis of longitudinal and competing risks data

In this article, we propose a two-level copula joint model to analyze clinical data with multiple disparate continuous longitudinal outcomes and multiple event-times in the presence of competing risks. At the first level, we use a copula to model the dependence between competing latent event-times, in the process constructing the submodel for the observed event-time, and employ the Gaussian copula to construct the submodel for the longitudinal outcomes that accounts for their conditional dependence; these submodels are glued together at the second level via the Gaussian copula to construct a joint model that incorporates conditional dependence between the observed event-time and the longitudinal outcomes. To have the flexibility to accommodate skewed data and examine possibly different covariate effects on quantiles of a non-Gaussian outcome, we propose linear quantile mixed models for the continuous longitudinal data. We adopt a Bayesian framework for model estimation and inference via Markov Chain Monte Carlo sampling. We examine the performance of the copula joint model through a simulation study and show that our proposed method outperforms the conventional approach assuming conditional independence with smaller biases and better coverage probabilities of the Bayesian credible intervals. Finally, we carry out an analysis of clinical data on renal transplantation for illustration.

Changes in Thoroughbred speed and stride characteristics over successive race starts and their association with musculoskeletal injury

BACKGROUND

Certain stride characteristics have been shown to affect changes in biomechanical factors that are associated with injuries in human athletes. Determining the relationship between stride characteristics and musculoskeletal injury (MSI) may be key in limiting injury occurrence in the racehorse.

OBJECTIVES

This study aimed to determine whether changes in race day speed and stride characteristics over career race starts are associated with an increased risk of MSI in racehorses.

STUDY DESIGN

Case-control study.

METHODS

Speed, stride length, and stride frequency data were obtained from the final 200 m sectional of n = 5660 race starts by n = 584 horses (case n = 146, control n = 438). Multivariable joint models, combining longitudinal and survival (time to injury) analysis, were generated. Hazard ratios and their 95% confidence intervals (CI) are presented.

RESULTS

The risk of MSI increased by 1.18 (95% CI 1.09, 1.28; P < 0.001) for each 0.1 m/s decrease in speed and by 1.11 (95% CI 1.02, 1.21; P = 0.01) for each 10 cm decrease in stride length over time (career race starts). A more marked rate of decline in speed and stride length was observed approximately 6 races prior to injury. Risk of MSI was highest early in the horse's racing career.

MAIN LIMITATIONS

Only final sectional stride characteristics were assessed in the model. The model did not account for time between race starts.

CONCLUSIONS

Decreasing speed and stride length over multiple races is associated with MSI in racehorses. Monitoring stride characteristics over time may be beneficial for the early detection of MSI.

Bivariate joint models for survival and change of cognitive function

Changes in cognitive function over time are of interest in ageing research. A joint model is constructed to investigate. Generally, cognitive function is measured through more than one test, and the test scores are integers. The aim is to investigate two test scores and use an extension of a bivariate binomial distribution to define a new joint model. This bivariate distribution model the correlation between the two test scores. To deal with attrition due to death, the Weibull hazard model and the Gompertz hazard model are used. A shared random-effects model is constructed, and the random effects are assumed to follow a bivariate normal distribution. It is shown how to incorporate random effects that link the bivariate longitudinal model and the survival model. The joint model is applied to the English Longitudinal Study of Ageing data.

Modelling of viral load dynamics and CD4 cell count progression in an antiretroviral naive cohort: using a joint linear mixed and multistate Markov model

Background

Patients infected with HIV may experience a succession of clinical stages before the disease diagnosis and their health status may be followed-up by tracking disease biomarkers. In this study, we present a joint multistate model for predicting the clinical progression of HIV infection which takes into account the viral load and CD4 count biomarkers.

Methods

The data is from an ongoing prospective cohort study conducted among antiretroviral treatment (ART) naïve HIV-infected women in the province of KwaZulu-Natal, South Africa. We presented a joint model that consists of two related submodels: a Markov multistate model for CD4 cell count transitions and a linear mixed effect model for longitudinal viral load dynamics.

Results

Viral load dynamics significantly affect the transition intensities of HIV/AIDS disease progression. The analysis also showed that patients with relatively high educational levels (β = − 0.004; 95% confidence interval [CI]:-0.207, − 0.064), high RBC indices scores (β = − 0.01; 95%CI:-0.017, − 0.002) and high physical health scores (β = − 0.001; 95%CI:-0.026, − 0.003) were significantly were associated with a lower rate of viral load increase over time. Patients with TB co-infection (β = 0.002; 95%CI:0.001, 0.004), having many sex partners (β = 0.007; 95%CI:0.003, 0.011), being younger age (β = 0.008; 95%CI:0.003, 0.012) and high liver abnormality scores (β = 0.004; 95%CI:0.001, 0.01) were associated with a higher rate of viral load increase over time. Moreover, patients with many sex partners (β = − 0.61; 95%CI:-0.94, − 0.28) and with a high liver abnormality score (β = − 0.17; 95%CI:-0.30, − 0.05) showed significantly reduced intensities of immunological recovery transitions. Furthermore, a high weight, high education levels, high QoL scores, high RBC parameters and being of middle age significantly increased the intensities of immunological recovery transitions.

Conclusion

Overall, from a clinical perspective, QoL measurement items, being of a younger age, clinical attributes, marital status, and educational status are associated with the current state of the patient, and are an important contributing factor to extend survival of the patients and guide clinical interventions. From a methodological perspective, it can be concluded that a joint multistate model approach provides wide-ranging information about the progression and assists to provide specific dynamic predictions and increasingly precise knowledge of diseases.

Joint model robustness compared with the time-varying covariate Cox model to evaluate the association between a longitudinal marker and a time-to-event endpoint

BACKGROUND

The recent progress in medical research generates an increasing interest in the use of longitudinal biomarkers for characterizing the occurrence of an outcome. The present work is motivated by a study, where the objective was to explore the potential of the long pentraxin 3 (PTX3) as a prognostic marker of Acute Graft-versus-Host Disease (GvHD) after haematopoietic stem cell transplantation. Time-varying covariate Cox model was commonly used, despite its limiting assumptions that marker values are constant in time and measured without error. A joint model has been developed as a viable alternative; however, the approach is computationally intensive and requires additional strong assumptions, in which the impacts of their misspecification were not sufficiently studied.

METHODS

We conduct an extensive simulation to clarify relevant assumptions for the understanding of joint models and assessment of its robustness under key model misspecifications. Further, we characterize the extent of bias introduced by the limiting assumptions of the time-varying covariate Cox model and compare its performance with a joint model in various contexts. We then present results of the two approaches to evaluate the potential of PTX3 as a prognostic marker of GvHD after haematopoietic stem cell transplantation.

RESULTS

Overall, we illustrate that a joint model provides an unbiased estimate of the association between a longitudinal marker and the hazard of an event in the presence of measurement error, showing improvement over the time-varying Cox model. However, a joint model is severely biased when the baseline hazard or the shape of the longitudinal trajectories are misspecified. Both the Cox model and the joint model correctly specified indicated PTX3 as a potential prognostic marker of GvHD, with the joint model providing a higher hazard ratio estimate.

CONCLUSIONS

Joint models are beneficial to investigate the capability of the longitudinal marker to characterize time-to-event endpoint. However, the benefits are strictly linked to the correct specification of the longitudinal marker trajectory and the baseline hazard function, indicating a careful consideration of assumptions to avoid biased estimates.

Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues

Background

Available methods for the joint modelling of longitudinal and time-to-event outcomes have typically only allowed for a single longitudinal outcome and a solitary event time. In practice, clinical studies are likely to record multiple longitudinal outcomes. Incorporating all sources of data will improve the predictive capability of any model and lead to more informative inferences for the purpose of medical decision-making.

Methods

We reviewed current methodologies of joint modelling for time-to-event data and multivariate longitudinal data including the distributional and modelling assumptions, the association structures, estimation approaches, software tools for implementation and clinical applications of the methodologies.

Results

We found that a large number of different models have recently been proposed. Most considered jointly modelling linear mixed models with proportional hazard models, with correlation between multiple longitudinal outcomes accounted for through multivariate normally distributed random effects. So-called current value and random effects parameterisations are commonly used to link the models. Despite developments, software is still lacking, which has translated into limited uptake by medical researchers.

Conclusion

Although, in an era of personalized medicine, the value of multivariate joint modelling has been established, researchers are currently limited in their ability to fit these models routinely. We make a series of recommendations for future research needs.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-016-0212-5) contains supplementary material, which is available to authorized users.

Joint modeling of HIV data in multicenter observational studies: A comparison among different approaches

Disease process over time results from the combination of event history information and longitudinal process. Commonly, separate analyses of longitudinal and survival outcomes are performed. However, discharging the dependence between these components may cause misleading results. Separate analyses are difficult to interpret whenever one deals with observational retrospective multicenter cohort studies where the biomarkers are poorly monitored over time, while the survival component may be affected by several sources of bias, such as multiple endpoints, multiple time-scales, and informative censoring. We discuss how joint modeling of longitudinal and survival data represents an effective strategy to incorporate all information simultaneously and to provide valid and efficient inferences, thus allowing to produce a better insight into the biological mechanisms underlying the phenomenon under study. Accounting for the whole dynamics of the disease process is crucial in retrospective longitudinal studies. In this work, we present different approaches for modeling longitudinal and time-to-event data, retrieved from 648 HIV-infected patients enrolled in the Italian cohort of the CASCADE (Concerted Action on SeroConversion to AIDS and Death in Europe) study, one of the largest AIDS collaborative cohort studies. In particular, we evaluate CD4 lymphocyte evolution over time (from the date of seroconversion) and overall survival, CD4 being one of the most important immunologic biomarker for HIV progression. Besides a standard separate modeling approach, we consider two alternative joint models: the traditional joint model and the joint latent class mixed model. Advantages and disadvantages of the different approaches are discussed. To compare the performances of these models, cross-validation procedures are also performed.

Analysis of longitudinal health-related quality of life data with terminal events

Longitudinal health-related quality of life data arise naturally from studies of progressive and neurodegenerative diseases. In such studies, patients' mental and physical conditions are measured over their follow-up periods and the resulting data are often complicated by subject-specific measurement times and possible terminal events associated with outcome variables. Motivated by the "Predictor's Cohort" study on patients with advanced Alzheimer disease, we propose in this paper a semiparametric modeling approach to longitudinal health-related quality of life data. It builds upon and extends some recent developments for longitudinal data with irregular observation times. The new approach handles possibly dependent terminal events. It allows one to examine time-dependent covariate effects on the evolution of outcome variable and to assess nonparametrically change of outcome measurement that is due to factors not incorporated in the covariates. The usual large-sample properties for parameter estimation are established. In particular, it is shown that relevant parameter estimators are asymptotically normal and the asymptotic variances can be estimated consistently by the simple plug-in method. A general procedure for testing a specific parametric form in the nonparametric component is also developed. Simulation studies show that the proposed approach performs well for practical settings. The method is applied to the motivating example.

Factors related to recurrence of spontaneous pneumothorax

OBJECTIVES

The purpose of this retrospective study was to identify factors associated with recurrent spontaneous pneumothorax (SP) in southern China, and to compare the therapeutic effectiveness of different procedures.

METHODS

A total of 182 consecutive patients (89.0% male; mean age, 38.9 years), admitted with their first episode of pneumothorax, were reviewed retrospectively. Follow up was available in 138 patients (75.8%), including 68 treated by chemical pleurodesis and 70 by chest tube drainage alone. The cumulative recurrence rates with different therapeutic procedures and different chemical sclerosing agents were compared, and the factors that influenced the recurrence rate were analysed using Cox's proportional hazard model.

RESULTS

The most common pre-existing lung disease responsible for pneumothorax was COPD (69.7%), followed by tuberculosis (16.5%). Recurrence was significantly more common in taller patients, patients with lower weight, and patients with secondary spontaneous pneumothorax. The cumulative recurrence rates in the pleurodesis therapy group after 6 months, 1 and 3 years were 13, 16 and 27%, respectively, whereas in the chest tube drainage group the recurrence rates were 26, 33 and 50%, respectively (P < 0.05). There was no significant difference in the recurrence rate for those receiving tetracycline compared with those who received gentamicin.

CONCLUSIONS

Spontaneous pneumothorax patients who are taller, weigh less or have secondary spontaneous pneumothorax are more likely to have recurrences. The risk of recurrence is reduced in patients who undergo chemical pleurodesis. Since there was no significant difference between intrapleural tetracycline and gentamicin, gentamicin should be considered as a potential chemical sclerosing agent.

Variables dépendantes du temps dans le modèle de Cox Théorie et pratique

In survival analysis, exposure that appears or changes during the follow-up of subjects must be taken into account as a time-dependent covariate in the Cox proportional hazards model. Two types of time-dependent covariates are defined: covariates with unique change, and covariates with multiple changes. The way of taking into account such changes in the exposure is presented in theory and illustrated from a small sample of 5 subjects enrolled in a French HIV cohort. The problems raised by missing data as well as alternative but more sophisticated solutions are also evocated. Annexes include programs for SAS software, and results from the "Log" and "Results" windows.