Dependence modeling for multi-type recurrent events via copulas

Multistate modeling and structure selection for multitype recurrent events and terminal event data

In cardiovascular disease studies, a large number of risk factors are measured but it often remains unknown whether all of them are relevant variables and whether the impact of these variables is changing with time or remains constant. In addition, more than one kind of cardiovascular disease events can be observed in the same patient and events of different types are possibly correlated. It is expected that different kinds of events are associated with different covariates and the forms of covariate effects also vary between event types. To tackle these problems, we proposed a multistate modeling framework for the joint analysis of multitype recurrent events and terminal event. Model structure selection is performed to identify covariates with time-varying coefficients, time-independent coefficients, and null effects. This helps in understanding the disease process as it can detect relevant covariates and identify the temporal dynamics of the covariate effects. It also provides a more parsimonious model to achieve better risk prediction. The performance of the proposed model and selection method is evaluated in numerical studies and illustrated on a real dataset from the Atherosclerosis Risk in Communities study.

A copula-based approach for creating an index of micronutrient intakes at household level in Pakistan

Deficiency of micronutrients is considered as the basic cause of health issues. There are a large number of micronutrients to be considered for good health, which are analyzed separately. However, such analyses involve practical as well as methodological complications and it requires construction of an index representing malnutrition of micronutrients. This study proposes copula methodology to categorize malnutrition of micronutrients at household level by combining the dependence structure of various correlated variables. Data of eleven micronutrients are extracted from HIICS- 2015-16 published by Pakistan -Bureau of Statistics. Seven out of the eleven variables are highly correlated, which are considered to construct the index. These include calcium, iron, iodine, zinc, riboflavin, thiamine and phosphorus intakes per capita at household level. Normal probability distribution is found as the best fit to the sample data of all variables. Gaussian copula function is used to derive multivariate probability distribution by combining univariate marginal probability distribution of each micronutrient. The Multivariate distribution of Gaussian copula model is used to calculate cumulative probabilities, which provide a base to categorize households' malnutrition w.r.t. micronutrients. The results show that 60% households lie in very low or low category of micronutrient intakes, 20% of households fall into medium category while 20% fall into high or very high category of micronutrient consumption. The proposed methodology might be helpful to combine other micronutrients as well as a variety of correlated variables in many other fields having a survey data.

Joint analysis of recurrence and termination: A Bayesian latent class approach

Like many other clinical and economic studies, each subject of our motivating transplant study is at risk of recurrent events of non-fatal tissue rejections as well as the terminating event of death due to total graft rejection. For such studies, our model and associated Bayesian analysis aim for some practical advantages over competing methods. Our semiparametric latent-class-based joint model has coherent interpretation of the covariate (including race and gender) effects on all functions and model quantities that are relevant for understanding the effects of covariates on future event trajectories. Our fully Bayesian method for estimation and prediction uses a complete specification of the prior process of the baseline functions. We also derive a practical and theoretically justifiable partial likelihood-based semiparametric Bayesian approach to deal with the analysis when there is a lack of prior information about baseline functions. Our model and method can accommodate fixed as well as time-varying covariates. Our Markov Chain Monte Carlo tools for both Bayesian methods are implementable via publicly available software. Our Bayesian analysis of transplant study and simulation study demonstrate practical advantages and improved performance of our approach.