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Log-Burr XII regression models with censored data. (English) Zbl 1452.62847

Summary: In survival analysis applications, the failure rate function may frequently present a unimodal shape. In such case, the log-normal or log-logistic distributions are used. In this paper, we shall be concerned only with parametric forms, so a location-scale regression model based on the Burr XII distribution is proposed for modeling data with a unimodal failure rate function as an alternative to the log-logistic regression model. Assuming censored data, we consider a classic analysis, a Bayesian analysis and a jackknife estimator for the parameters of the proposed model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the log-logistic and log-Burr XII regression models. Besides, we use sensitivity analysis to detect influential or outlying observations, and residual analysis is used to check the assumptions in the model. Finally, we analyze a real data set under log-Burr XII regression models.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62J20 Diagnostics, and linear inference and regression
62N05 Reliability and life testing
62-08 Computational methods for problems pertaining to statistics

Software:

Ox
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References:

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