Proportional hazards model under ranked setsampling scheme using censored data of coronaryheart disease

Proportional hazards model under ranked setsampling scheme using censored data of coronaryheart disease

The proportional hazards model is one of the most common model for analyzing survivaldata. Only proportional hazards assumption is required to apply this model. Using ap-propriate sampling methods is an important part of modelling data and estimation ofparameters. In literature there is a few studies based on sampling methods in survivalanalysis and most of them are related with non-parametric estimations of survival func-tions, sample size calculation etc. The main innovation of our approach is to examinethe sampling methods for the proportional hazards model. This paper describes usage ofranked set sampling design in the proportional hazards model. In order to analyze theperformance of our methods, we use a real data and conduct a simulation study. Weconclued that ranked set sampling is more efficient than simple random sampling.

___

  • [1]A.I. Al-Omari,Ratio estimation of the population mean using auxiliary informationin simple random sampling and median ranked set sampling, Statist. Probab. Lett.82, 1883-1890, 2012.
  • [2]M.F. Al-Saleh and A.I. Al-Omari,Multistage ranked set sampling, J. Statist. Plann.Inference102, 273286, 2002.
  • [3]D. G. Altman, B.L. De Stavola, S.B. Love and K. A. Stepniewska,Review of survivalanalyses published in cancer journals, British Journal of Cancer72(2), 511, 1995.
  • [4]N. Ata Tutkun, N. Koyuncu and U. Karabey,Discrete-time survival analysis underranked set sampling: an application to Turkish motor insurance data, J. Stat. Comput.Simul.89(4), 660-667, 2019.
  • [5]S.K. Ashour and M.S. Abdallah,New distribution function estimators and tests ofperfect ranking in concomitant-based ranked set sampling, Comm. Statist. SimulationComput. 1-26, 2019.
  • [6]M. J. Bradburn, T. G. Clark, S. B. Love, and D. G. Altman,Survival analysis part II:multivariate data analysisan introduction to concepts and methods, British Journal ofCancer89(3), 431-436, 2003.
  • [7]J. Borucka,Methods of handling tied events in the Cox proportional hazard model,Studia Oeconomica Posnaniensia2(2), 91-106, 2014.
  • [8]N.E. Breslow,Covariance analysis of censored survival data, Biometrics30, 89-99,1974.
  • [9]H. Che,Cutoff sample size estimation for survival data: a simulation study, Unpub-lished Master Thesis, Department of Statistics, Uppsala University, Sweden, 2013.
  • [10]D. Collett,Modelling survival data in medical research, Chapman and Hall, UK, 1994.
  • [11]D.R. Cox,Regression models and life tables (with discussion), J. R. Stat. Soc. Ser. B.Stat. Methodol.34,187-220, 1972.
  • [12]B. Efron,The efficiency of Coxs likelihood function for censored data, J. Amer. Statist.Assoc.76, 312-319, 1977.
  • [13]J. Frey,Nonparametric mean estimation using partially ordered sets, Environmentaland Ecological Statistic19, 309-326, 2012.
  • [14]N.M. Gemayel, E.A. Stasny, J.A. Tackett and D. A. Wolfe,Ranked set sampling: Anauditing application. Review of Quantitative Finance and Accounting39, 413-422,2012.
  • [15]F.Y. Hsieh and P. W. Lavori,Sample-size calculations for the Cox proportional haz-ards regression model with nonbinary covariates, Controlled Clinical Trials21,552560,2000.
  • [16]A.A. Jemain and A.I. Al-Omari,Multistage median ranked set samples for estimatingthe population mean, Pakistan Journal of Statistics22,195207, 2006.
  • [17]A.A. Jemain, A.I. Al-Omari and K. Ibrahim,Multistage extreme ranked set samplingfor estimating the population mean, J. Stat. Theory Appl.6(4),456471, 2007.
  • [18]J.D. Kalbfleisch and R.L. Prentice,The statistical analysis of failure time data, Wiley,New York, 1980.
  • [19]M. Mahdizadeh, and E. Zamanzade,Smooth estimation of a reliability function inranked set sampling, Statistics52, 750-768, 2018.
  • [20]M. Mahdizadeh, and E. Zamanzade,Interval estimation ofP(X < Y)in ranked setsampling, Comput. Statist.33, 1325-1348, 2018.
  • [21]M. Mahdizadeh, and E. Zamanzade,Efficient body fat estimation using multistagepair ranked set sampling, Stat. Methods Med. Res.28: 223-234, 2019.
  • [22]M. G. Marmot, M. J. Shipley and G. Rose,Inequalities in deathspecific explanationsof a general pattern, The Lancet323(8384), 1003-1006, 1984.
  • [23]G.A. McIntyre,A method for unbiased selective sampling, using ranked sets, Aus-tralian Journal of Agricultural Research3, 385390, 1952.
  • [24]M. Moerbeek,Sufficient sample sizes for discrete-time survival analysis mixture mod-els, Structural Equation Modelling: A Multidisipliniary Journal21(1), 63-67, 2014.
  • [25]O. Ozturk,Sampling from partially rank-ordered sets, Environmental and EcologicalStatistics18, 757-779, 2011.
  • [26]H. M. Samawi, A. Helu, H. Rochani, J. Yin, L. Yu and R. Vogel,Reducing samplesize needed for accelerated failure time model using more efficient sampling methods,J. Stat. Theory Pract.12(3), 530-541, 2018.
  • [27]D. Schoenfeld,Sample-size formula for the proportional-hazards regression model,Biometrics39,499503, 1983.
  • [28]P. Royston, G. Ambler, and W. Sauerbrei,The use of fractional polynomials tomodel continuous risk variables in epidemiology, International Journal of Epidemi-ology,28(5), 964-974, 1999.
  • [29]S. Wang, J. Zhang and W. Lu,Sample size calculation for the proportional hazardsmodel with a time-dependent covariate, Comput. Statist. Data Anal.74, 217-227,2014.
  • [30]E. Zamanzade and M. Vock,Variance estimation in ranked set sampling using aconcomitant variable, Statist. Probab. Lett.105, 1-5, 2015.
  • [31]E. Zamanzade and M. Mahdizadeh,A more efficient proportion estimator in rankedset samplingStatist. Probab. Lett.129, 28-33, 2017.
  • [32]E. Zamanzade and M. Mahdizadeh,Distribution function estimation usingconcomitant-based ranked set sampling, Hacet. J. Math. Stat.47(3), 755-761, 2018.
  • [33]E. Zamanzade and M. Mahdizadeh,Estimating the population proportion in pairranked set sampling with application to air quality monitoring, J. Appl. Stat.45(3),426-437, 2018.
  • [34]E. Zamanzade and M. Mahdizadeh,Using ranked set sampling with extreme ranks inestimating the population proportion, Stat. Methods Med. Res.29(1), 165-177, 2020.