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Current issue: volume 48 (2), July-December 2024

  • Patient-reported outcomes and survival analysis of chronic obstructive pulmonary disease patients: a two-stage joint modelling approach

    Cristina Galán-Arcicollar, Josu Najera-Zuloaga and Dae-Jin Lee

    Abstract: Joint modelling has gained attention in longitudinal studies incorporating biomarkers and survival data. In the context of chronic diseases, patient evolution is often tracked through multiple assessments, with patient-reported outcomes playing a crucial role. The Beta-Binomial distribution is suggested as a suitable model for these longitudinal variables. However, its integration into joint modelling remains unexplored. This study introduces an estimation procedure for analyzing longitudinal patient-reported outcomes and survival data together. We compare different estimation approaches through simulation experiments, including the proposed model. Furthermore, the methodologies are applied to real data from a follow-up study on chronic obstructive pulmonary disease patients

    Keywords: joint modelling, Beta-Binomial regression, patient-reported outcomes, survival analysis

    Pages: 155–182

    DOI:10.57645/20.8080.02.17

  • Non-parametric estimation of the covariate-dependent bivariate distribution for censored gap times

    Ewa Strzalkowska-Kominiak, Elisa M. Molanes-López and Emilio Letón

    Abstract: In many biomedical studies, recurrent or consecutive events may occur during the follow up of the individuals. This situation can be found, for example, in transplant studies, where there are two consecutive events which give rise to two times of interest subject to a common random right-censoring time, the first one being the elapsed time from acceptance into the transplantation program to transplant, and the second one the time from transplant to death. In this work, we incorporate the information of a continuous covariate into the bivariate distribution of the two gap times of interest and propose a non-parametric method to cope with it. We prove the asymptotic properties of the proposed method and carry out a simulation study to see the performance of this approach. Additionally, we illustrate its use with Stanford heart transplant data and colon cancer data.

    Keywords: bivariate distribution, copula function, covariate, serial dependence, random censoring, kernel estimation

    Pages: 183–208

    DOI:10.57645/20.8080.02.18

  • Second-order Markov multistate models

    Mireia Besalú and Guadalupe Gómez Melis

    Abstract: Multistate models are well developed for continuous and discrete times under a first order Markov assumption. Motivated by a cohort of COVID-19 patients, a multistate model was designed based on 14 transitions among 7 states of a patient. Since a preliminary analysis showed that the first-order Markov condition was not met for some transitions, we have developed a second-order Markov model where the future evolution not only depends on the state at the current time but also on the state at the preceding time. Under a discrete time analysis, assuming homogeneity and that past information is restricted to two consecutive times, we expanded the transition probability matrix and proposed an extension of the Chapman-Kolmogorov equations. We propose two estimators for the second-order transition probabilities and illustrate them within the cohort of COVID-19 patients.

    Keywords: multistate models, non-Markov, COVID-19

    Pages: 209–234

    DOI:10.57645/20.8080.02.19

  • Conditional likelihood based inference on single-index models for motor Insurance claim severity

    Catalina Bolancé, Ricardo Cao and Montserrat Guillen

    Abstract: Prediction of a traffic accident cost is one of the major problems in motor insurance. To identify the factors that influence costs is one of the main challenges of actuarial modelling. Telematics data about individual driving patterns could help calculating the expected claim severity in motor insurance. We propose using single-index models to assess the marginal effects of covariates on the claim severity conditional distribution. Thus, drivers with a claim cost distribution that has a long tail can be identified. These are risky drivers, who should pay a higher insurance premium and for whom preventative actions can be designed. A new kernel approach to estimate the covariance matrix of coefficients’ estimator is outlined. Its statistical properties are described and an application to an innovative data set containing information on driving styles is presented. The method provides good results when the response variable is skewed.

    Keywords: covariance matrix of estimator, kernel estimator, marginal effects, telematics covariates, right-skewed cost variable

    Pages: 235–258

    DOI:10.57645/20.8080.02.20

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