A joint model for longitudinal continuous and time-to-event outcomes with direct marginal interpretation

Analysis of Recurrent Times-to-Clinical Malaria Episodes and Plasmodium falciparum Parasitemia: A Joint Modeling Approach Applied to a Cohort Data

Background

Recurrent clinical malaria episodes due to Plasmodium falciparum parasite infection are common in endemic regions. With each infection, acquired immunity develops, making subsequent disease episodes less likely. To capture the effect of acquired immunity to malaria, it may be necessary to model recurrent clinical disease episodes jointly with P. falciparum parasitemia data. A joint model of longitudinal parasitemia and time-to-first clinical malaria episode (single-event joint model) may be inaccurate because acquired immunity is lost when subsequent episodes are excluded. This study's informativeness assessed whether joint modeling of recurrent clinical malaria episodes and parasitemia is more accurate than a single-event joint model where the subsequent episodes are ignored.

Methods

The single event joint model comprised Cox Proportional Hazards (PH) sub-model for time-to-first clinical malaria episode and Negative Binomial (NB) mixed-effects sub-model for the longitudinal parasitemia. The recurrent events joint model extends the survival sub-model to a Gamma shared frailty model to include all recurrent clinical episodes. The models were applied to cohort data from Malawi. Simulations were also conducted to assess the performance of the model under different conditions.

Results

The recurrent events joint model, which yielded higher hazard ratios of clinical malaria, was more precise and in most cases produced smaller standard errors than the single-event joint model; hazard ratio (HR) = 1.42, [95% confidence interval [CI]: 1.22, 2.03] vs. HR = 1.29, [95% CI:1.60, 2.45] among participants who reported not to use LLINs every night compared to those who used the nets every night; HR = 0.96, [ 95% CI: 0.94, 0.98] vs. HR = 0.81, [95% CI: 0.75, 0.88] for each 1-year increase in participants' age; and HR = 1.36, [95% CI: 1.05, 1.75] vs. HR = 1.10, [95% CI: 0.83, 4.11] for observations during the rainy season compared to the dry season.

Conclusion

The recurrent events joint model in this study provides a way of estimating the risk of recurrent clinical malaria in a cohort where the effect of immunity on malaria disease acquired due to P. falciparum parasitemia with aging is captured. The simulation study has shown that if correctly specified, the recurrent events joint model can give risk estimates with low bias.

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.

Joint model for left-censored longitudinal data, recurrent events and terminal event: Predictive abilities of tumor burden for cancer evolution with application to the FFCD 2000-05 trial

In oncology, the international WHO and RECIST criteria have allowed the standardization of tumor response evaluation in order to identify the time of disease progression. These semi-quantitative measurements are often used as endpoints in phase II and phase III trials to study the efficacy of new therapies. However, through categorization of the continuous tumor size, information can be lost and they can be challenged by recently developed methods of modeling biomarkers in a longitudinal way. Thus, it is of interest to compare the predictive ability of cancer progressions based on categorical criteria and quantitative measures of tumor size (left-censored due to detection limit problems) and/or appearance of new lesions on overall survival. We propose a joint model for a simultaneous analysis of three types of data: a longitudinal marker, recurrent events, and a terminal event. The model allows to determine in a randomized clinical trial on which particular component treatment acts mostly. A simulation study is performed and shows that the proposed trivariate model is appropriate for practical use. We propose statistical tools that evaluate predictive accuracy for joint models to compare our model to models based on categorical criteria and their components. We apply the model to a randomized phase III clinical trial of metastatic colorectal cancer, conducted by the Fédération Francophone de Cancérologie Digestive (FFCD 2000-05 trial), which assigned 410 patients to two therapeutic strategies with multiple successive chemotherapy regimens.

Mixed models approaches for joint modeling of different types of responses

In many biomedical studies, one jointly collects longitudinal continuous, binary, and survival outcomes, possibly with some observations missing. Random-effects models, sometimes called shared-parameter models or frailty models, received a lot of attention. In such models, the corresponding variance components can be employed to capture the association between the various sequences. In some cases, random effects are considered common to various sequences, perhaps up to a scaling factor; in others, there are different but correlated random effects. Even though a variety of data types has been considered in the literature, less attention has been devoted to ordinal data. For univariate longitudinal or hierarchical data, the proportional odds mixed model (POMM) is an instance of the generalized linear mixed model (GLMM; Breslow and Clayton, 1993). Ordinal data are conveniently replaced by a parsimonious set of dummies, which in the longitudinal setting leads to a repeated set of dummies. When ordinal longitudinal data are part of a joint model, the complexity increases further. This is the setting considered in this paper. We formulate a random-effects based model that, in addition, allows for overdispersion. Using two case studies, it is shown that the combination of random effects to capture association with further correction for overdispersion can improve the model's fit considerably and that the resulting models allow to answer research questions that could not be addressed otherwise. Parameters can be estimated in a fairly straightforward way, using the SAS procedure NLMIXED.