Probabilistic survival analysis methods

using simulation and cancer data

Yo.Xu, C.P.Tsokos

University of South Florida

Tampa, FL 33620, USA

The object of the present study is to probabilistically evaluate commonly used methods to perform survival analysis of medical patients. Our study includes evaluation of parametric, semi-parametric and nonparametric analysis of probability survival models. We will evaluate the popular Kaplan-Meier (KM), Cox Proportional Hazard (Cox PH), and Kernel density (KD) models using both Monte Carlo simulation and actual breast cancer data. The first part of the evaluation will be based on how these methods measure up to parametric analysis and the second part using actual cancer data. As expected, the parametric survival analysis when applicable gives the best results followed by not commonly used non-parametric Kernel density approach for both evaluations using simulation and actual cancer data.

 

Wikipedia defines survival analysis as a branch of statistics which deals with death in biological organisms and failure in mechanical systems. Scientists have developed and used many different probabilistic survival analysis methods including parametric, nonparametric and semi-parametric models. In the present study we will compare all commonly used methods and propose which ones give the best probabilistic survival results [1-23].

The first part of our study is based on simulating data from a well defined probability failure distribution by identifying the sample size so that the maximum likelihood estimates converge to the assumed parametric values in Monte Carlo simulation procedure. Using this information we develop and compare the parametric estimated probabilistic survival function with the Kernel density (non-parametric), and the popular Kaplan-Meier (KM) model.

The second part of our study uses actual survival time of breast cancer data to compare the above mentioned survival models, in addition to the Cox Proportional (Cox PH) survival hazard function.

Upon completing the evaluation, we will propose a ranking of the analytical methods evaluated for performing survival analysis. The breast cancer data that we used were given by N.A.Ibrahim, whose results and analysis were published in [1, 14]. Some other relevant references that we use in the present study are [2, 11, 12, 13, 15, 18, 19].

In conclusion we note. The present study consists of three parts in which the effectiveness of three survival analysis models, namely, KM, Cox PH and KD, is compared.

Initially, using Monte Carlo simulation we compare the subject models with parametric survival models and find that the proposed KD survival model gives good results, if not better, than KM.

The second part consists of using actual uncensored breast cancer data. Performing similar evaluation, the results support that the proposed KD model gives better estimates than the popular KM and Cox PH models with interactions.

Thirdly, we performed the same analysis with actual censored breast cancer data. Although working with censored data, it is quite difficult to justify such an analysis, we analyzed the data, and the results are similar to Monte Carlo simulation and the case of using the uncensored data.

 

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