Sains Malaysiana 46(12)(2017): 2529–2539

http://dx.doi.org/10.17576/jsm-2017-4612-31

 

Bootstrap Intervals in the Presence of Left-Truncation, Censoring and Covariates with a Parametric Distribution

(Selang Butstrap dalam Kehadiran Pemangkasan Kiri, Penapisan dan Kovariat dengan Taburan Parametrik)

 

THIRUNANTHINI MANOHARAN*, JAYANTHI ARASAN, HABSHAH MIDI

& MOHD BAKRI ADAM

 

Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor Darul Ehsan, Malaysia

 

Laboratory of Computational Statistics and Operations Research, Universiti Putra Malaysia

43400 UPM Serdang, Selangor Darul Ehsan, Malaysia

 

Received: 29 March 2016/Accepted: 18 April 2017

 

ABSTRACT

Left-truncated and censored survival data are commonly encountered in medical studies. However, traditional inferential methods that heavily rely on normality assumptions often fail when lifetimes of observations in a study are both truncated and censored. Thus, it is important to develop alternative inferential procedures that ease the assumptions of normality and unconventionally relies on the distribution of data in hand. In this research, a three parameter log-normal parametric survival model was extended to incorporate left-truncated and right censored medical data with covariates. Following that, bootstrap inferential procedures using non-parametric and parametric bootstrap samples were applied to the parameters of this model. The performance of the parameter estimates was assessed at various combinations of truncation and censoring levels via a simulation study. The recommended bootstrap intervals were applied to a lung cancer survival data.

 

Keywords: Bootstrap method; covariate; left-truncation; random censoring

 

ABSTRAK

Data terpangkas kiri dan tertapis wujud dalam bidang perubatan dan kaedah inferensi tradisi yang sangat bergantung kepada andaian normal sering kali gagal apabila data tidak lengkap akibat mekanisme terpangkas dan tertapis data. Oleh itu, adalah menjadi keperluan untuk mengkaji kaedah selang keyakinan alternatif yang kurang bergantung dengan andaian lazim semata-mata, sebaliknya bergantung kepada taburan data yang sedia ada. Dalam kajian ini, model mandiran log-lazim dengan kehadiran kovariat dipertimbangkan untuk data perubatan yang terpangkas kiri dan tertapis. Seterusnya, kesesuaian selang keyakinan butstrap yang berasaskan persampelan parametrik dan bukan parametrik diuji untuk setiap parameter yang wujud dalam model mandirian log-lazim menerusi kajian kebarangkalian liputan. Simulasi data jangka hayat dijalankan pada pelbagai kombinasi peratusan data terpangkas dan tertapis. Berikutan hasil kajian tersebut, kaedah selang keyakinan yang dicadangkan telah diuji dengan data pesakit kanser paru-paru.

 

Kata kunci: Kaedah butstrap; kovariat; terpangkas kiri; tertapis rawak

REFERENCES

 

Arasan, J. & Lunn, M. 2008. Alternative interval estimation for parameters of bivariate exponential model with time varying covariate. Computational Statistics 23(4): 605-622.

Balakrishnan, N. & Mitra, D. 2014. Some further issues concerning likelihood inference for left truncated and right censored lognormal data. Communications in Statistics: Simulation and Computation 43(2): 400-416.

Carpenter, J. & Bithell, J. 2000. Bootstrap confidence intervals: When, which, what? A practical guide for medical statisticians for parameters of bivariate exponential model with time varying covariate. Statistics in Medicine 19(9): 1141-1164.

Efron, B. 1981. Censored data and the bootstrap. Journal of the American Statistical Association 76(374): 312-319.

Gross, S.T. & Lai, T.L. 1996. Nonparametric estimation and regression analysis with left-truncated and right-censored data. Journal of the American Statistical Association 91(435): 1166-1180.

Grover & Sabharwal 2012

Guo, G. 1992. Event-history analysis for left-truncated data. Sociological Methodology 23(1): 217-243.

Hjort, N.L. 1992. On inference in parametric survival data models. International Statistical Review/Revue Internationale de Statistique 60(3): 355-387.

Manoharan, T., Arasan, J., Midi, H. & Adam, M.B. 2015. A coverage probability on the parameters of the log-normal distribution in the presence of left-truncated and right-censored survival data. Malaysian Journal of Mathematical Sciences 9(1): 127-144.

Pan, W. & Chappell, R. 2002. Estimation in the cox proportional hazards model with left-truncated and interval-censored data. Biometrics 58(1): 64-70.

Robinson, J. 1983. Bootstrap confidence intervals in location-scale models with progressive censoring. Technometrics 25(2): 179-817.

Shen, P.S. 2012. Proportional hazards regression with interval-censored and left-truncated data. Journal of Statistical Computation and Simulation 84(2): 1-9.

Tai, P., Chapman, J.A.W., Yu, E., Jones, D., Yu, C., Yuan, F. & Sang-Joon, L. 2007. Disease specific survival for limited-stage small-cell lung cancer affected by statistical method of assessment. BMC Cancer 7(1): 31-39.

Wang, M.C. 1991. Nonparametric estimation from cross-sectional survival data. Journal of the American Statistical Association 86(413): 13-143.

 

 

*Corresponding author; email: mthirunanthini@gmail.com

 

 

 

 

previous