Abstract
Abstract The linear correlation coefficient of Bravais-Pearson is considered a powerful indicator when the dependency relationship is linear and the error variate is normally distributed. Unfortunately in finance and in survival analysis the dependency relationship may not be linear. In such case, the use of rank-based measures of dependence, like Kendall’s tau or Spearman rho are recommended. In this direction, under length-biased sampling, measures of the degree of dependence between the survival time and the covariates appear to have not received much intention in the literature. Our goal in this paper, is to provide an alternative indicator of dependence measure, based on the concept of information gain, using the parametric copulas. In particular, the extension of the Kent’s [18] dependence measure to length-biased survival data is proposed. The performance of the proposed method is demonstrated through simulations studies.
Highlights
Survival data occur in many areas such as medicine, epidemiology, biology, economics and manufacturing
We provide some examples of parametric copulas and we discuss goodness-of- t procedures
This paper provides a measure of dependence for length-biased survival data, by extending the dependence measure of [18], under length-biased sampling
Summary
Survival data occur in many areas such as medicine, epidemiology, biology, economics and manufacturing. Most of the literature on length-biased sampled data concentrates on statistical methods for the survival function (e.g., [7]; [32], estimating the density function (e.g., [4]; [17]), kernel smoothing [33], proportional hazards models [35] and covariate bias induced by length-biased sampling of failure times (e.g., [3]). The phenomena of length-biased sampling appears naturally in many areas of research, see for instance [24] in land economics, [36] in screening and early detection of disease, [34] in epidemiology and geriatric medicine. For further examples of length-biased sampling see for example [26]
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