Goodness-of-fit tests based on Kullback-Leibler divergence for bladder cancer survival analysis: Applications to exponentiated exponential distribution
Abstract
Bladder cancer is among the ten most common types of cancer worldwide, with approximately 550,000 new cases occurring each year. It accounts for comprehensively compared to 3% of all newly diagnosed cancer cases and contributes to 2.1% of cancer-related deaths globally. This article introduces goodness-of-fit tests that aim to fit the exponentialized exponential distribution. These tests are based on the Kullback-Leibler difference and have been applied to censored and complete samples of Bladder Cancer Patients. We calculated critical values and statistical power measurements, considering the best and worst bandwidth scenarios. We then comprehensively compared essential values and power across various parameters, accounting for optimal and suboptimal bandwidth choices derived from the Kullback–Leibler difference. In the final phase of our study, we used a dataset of individuals diagnosed with bladder cancer to demonstrate the practical applicability of our proposed research. Finally, this modeling type can benefit researchers and healthcare professionals through time-to-event analysis (survival analysis), investigation of events, medical decision-making, and risk prediction.
Keywords
Censoring, Survival Analysis, Kullback-Leibler Divergence, Goodness of Fit Test, Cancer
Ethical Statement
No approval from the Board of Ethics is required.
References
- F. Bray, J. Ferlay, I. Soerjomataram, R. L. Siegel, L. A. Torre, A. Jemal, Global cancer statistics 2018: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA: A Cancer Journal for Clinicians, 68 (6) (2018) 394-424.
- R. B. D'agostino, M. A. Stephens, Goodness of fit techniques. New York, MDI Press, 1986.
- K. Pearson, On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 50 (302) (1900) 157-175.
- I. Arizono, H. Ohta, A Test for normality based on Kullback-Leibler information, The American Statistician 43 (1989) 20-22.
- B. Şenoğlu, B. Sürücü, Goodness-of-fit tests based on Kullback-Leibler information, IEEE Transactions on Reliability 53 (2004) 357-361.
- B. Choi, K. Kim, S. Heun Song, Goodness-of-fit test for exponentiality based on Kullback–Leibler information, Communications in Statistics - Simulation and Computation 33 (2004) 525-536.
- S. Park, Testing exponentiality based on the Kullback-Leibler information with the type II censored data, IEEE Transactions on Reliability 54 (2005) 22-26.
- J. Lim, S. Park, A goodness of fit tests based on the partial Kullback-Leibler information with the type II censored data, Journal of Applied Statistics 34 (2007) 1051-1064.
- N. Balakrishnan, A. H. Rad, N. R. Arghami, Testing exponentiality based on Kullback-Leibler information with progressively type-II censored data, IEEE Transactions on Reliability 56 (2007) 301-307.
- J. Lim, S. Park, Censored Kullback-Leibler information and goodness-of-fit test with type II censored data, Quality control and applied statistics 54 (1) (2009) 79-80.