arXiv subjects

Kevin Burke

Publications and source records attributed to Kevin Burke.

26 records · Page 2Linked to original sources

arXiv2019

An Alternative Formulation of Coxian Phase-type Distributions with Covariates: Application to Emergency Department Length of Stay

In this paper we present a new methodology to model patient transitions and length of stay in the emergency department using a series of conditional Coxian phase-type distributions, with covariates. We reformulate the Coxian models (standard Coxian, Coxian with multiple absorbing states, joint Coxian, and conditional Coxian) to take into account heterogeneity in patient characteristics such as arrival mode, time of admission and age. The approach differs from previous research in that it reduces the computational time, and it allows the inclusion of patient covariate information directly into the model. The model is applied to emergency department data from University Hospital Limerick in Ireland.

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arXiv2019

On the Non-uniqueness of Representations of Coxian Phase-Type Distributions

Parameter estimation in Coxian phase-type models can be challenging due to their non-unique representation leading to a multi-modal likelihood. Since each representation corresponds to a different underlying data-generating mechanism, it is of interest to identify those supported by given data (i.e., find all likelihood modes). The standard approach is to simply refit using various initial values, but this has no guarantee of working. Thus, we develop new properties specific to this class of models, and employ these to determine all the equivalent model representations. The proposed approach only requires fitting the model once, and is guaranteed to find all representations.

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arXiv2019

Penalized Variable Selection in Multi-Parameter Regression Survival Modelling

Multi-parameter regression (MPR) modelling refers to the approach whereby covariates are allowed to enter the model through multiple distributional parameters simultaneously. This is in contrast to the standard approaches where covariates enter through a single parameter (e.g., a location parameter). Penalized variable selection has received a significant amount of attention in recent years: methods such as the least absolute shrinkage and selection operator (LASSO), smoothly clipped absolute deviation (SCAD), and adaptive LASSO are used to simultaneously select variables and estimate their regression coefficients. Therefore, in this paper, we develop penalized multi-parameter regression methods and investigate their associated performance through simulation studies and real data; as an example, we consider the Weibull MPR model.

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arXiv2019

A Multi-parameter regression model for interval censored survival data

We develop flexible multi-parameter regression survival models for interval censored survival data arising in longitudinal prospective studies and longitudinal randomised controlled clinical trials. A multi-parameter Weibull regression survival model, which is wholly parametric, and has non-proportional hazards, is the main focus of the paper. We describe the basic model, develop the interval-censored likelihood and extend the model to include gamma frailty and a dispersion model. We evaluate the models by means of a simulation study and a detailed re-analysis of data from the Signal Tandmobiel$^{\circledR}$ study. The results demonstrate that the multi-parameter regression model with frailty is computationally efficient and provides an excellent fit to the data.

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arXiv2019

Semiparametric multi-parameter regression survival modelling

We consider a log-linear model for survival data, where both the location and scale parameters depend on covariates and the baseline hazard function is completely unspecified. This model provides the flexibility needed to capture many interesting features of survival data at a relatively low cost in model complexity. Estimation procedures are developed and asymptotic properties of the resulting estimators are derived using empirical process theory. Finally, a resampling procedure is developed to estimate the limiting variances of the estimators. The finite sample properties of the estimators are investigated by way of a simulation study, and a practical application to lung cancer data is illustrated.

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arXiv2019

A Bivariate Power Generalized Weibull Distribution: a Flexible Parametric Model for Survival Analysis

We are concerned with the flexible parametric analysis of bivariate survival data. Elsewhere, we have extolled the virtues of the "power generalized Weibull" (PGW) distribution as an attractive vehicle for univariate parametric survival analysis: it is a tractable, parsimonious, model which interpretably allows for a wide variety of hazard shapes and, when adapted (to give an adapted PGW, or APGW, distribution), covers a wide variety of important special/limiting cases. Here, we additionally observe a frailty relationship between a PGW distribution with one value of the parameter which controls distributional choice within the family and a PGW distribution with a smaller value of the same parameter. We exploit this frailty relationship to propose a bivariate shared frailty model with PGW marginal distributions: these marginals turn out to be linked by the so-called BB9 or "power variance function" copula. This particular choice of copula is, therefore, a natural one in the current context. We then adapt the bivariate PGW distribution, in turn, to accommodate APGW marginals. We provide a number of theoretical properties of the bivariate PGW and APGW models and show the potential of the latter for practical work via an illustrative example involving a well-known retinopathy dataset, for which the analysis proves to be straightforward to implement and informative in its outcomes. The novelty in this article is in the appropriate combination of specific ingredients into a coherent and successful whole.

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arXiv2019

A Flexible Parametric Modelling Framework for Survival Analysis

We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic, Burr type XII, Weibull, Gompertz), and includes defective distributions (i.e., cure models). This generality is achieved using four basic distributional parameters: two scale-type parameters and two shape parameters. Generalising to covariate dependence, the scale-type regression components correspond to accelerated failure time (AFT) and proportional hazards (PH) models. Therefore, this general formulation unifies the most popular survival models which allows us to consider the practical value of possible modelling choices for survival data. Furthermore, in line with our proposed flexible baseline distribution, we advocate the use of multi-parameter regression in which more than one distributional parameter depends on covariates - rather than the usual convention of having a single covariate-dependent (scale) parameter. While many choices are available, we suggest introducing covariates through just one or other of the two scale parameters, which covers AFT and PH models, in combination with a `power' shape parameter, which allows for more complex non-AFT/non-PH effects, while the other shape parameter remains covariate-independent, and handles automatic selection of the baseline distribution. We explore inferential issues in simulations, both with and without a covariate, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by investigating differences between treatment groups using data from a lung cancer study and a melanoma study. Censoring is accommodated throughout.

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arXiv2019

Multi-Parameter Regression Survival Modelling: An Alternative to Proportional Hazards

It is standard practice for covariates to enter a parametric model through a single distributional parameter of interest, for example, the scale parameter in many standard survival models. Indeed, the well-known proportional hazards model is of this kind. In this paper we discuss a more general approach whereby covariates enter the model through more than one distributional parameter simultaneously (e.g., scale and shape parameters). We refer to this practice as "multi-parameter regression" (MPR) modelling and explore its use in a survival analysis context. We find that multi-parameter regression leads to more flexible models which can offer greater insight into the underlying data generating process. To illustrate the concept, we consider the two-parameter Weibull model which leads to time-dependent hazard ratios, thus relaxing the typical proportional hazards assumption and motivating a new test of proportionality. A novel variable selection strategy is introduced for such multi-parameter regression models. It accounts for the correlation arising between the estimated regression coefficients in two or more linear predictors -- a feature which has not been considered by other authors in similar settings. The methods discussed have been implemented in the mpr package in R.

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