Semiparametric Models with Covariates for Lifetime Data under a General Censoring Scheme with an Application to Contingent Valuation

Nathan Bennett, Srikanth K. Iyer, Sreenivasa Rao Jammalamadaka

Abstract


We are interested in estimating the distribution of lifetimes, also called survival times, subject to a general censoring scheme called ``middle censoring'' (see Jammalamadaka and Mangalam (2003)). Both the Cox proportional hazards (Cox PH) and accelerated failure time (AFT) models are considered since each model has a baseline distribution function that is modified by the presence of covariates. The key contribution presented is the estimation of the effect of the covariate as well as the baseline distribution function. We conclude with an application to a contingent valuation study.

Keywords


middle censoring; Cox PH model; accelerated failure time model (AFT); contingent valuation; willingness to pay

Full Text:

PDF (English)

References


K. ARROW, R. SOLOW (1993). Report of the noaa panel on contingent valuation, Federal Register 58, pp. 4601-14.

M. AYER, H. BRUNK, G. EWING, W. REID, E. SILVERMAN (1955). An empirical distribution function for sampling with incomplete information. The Annals of Mathematical Statistics, 26, no. 4, pp. 641-647.

B. EFRON (1977). The two-sample problem with censored data. In Proc. Fifth Berkeley Symp. Math. Statist. Probab. vol. 4, pp. 831–853.

N. BENNETT, S. IYER, S. JAMMALAMADAKA (2017). Analysis of gamma and weibull lifetime data under a general censoring scheme and in the presence of covariates. Communications in Statistics - Theory and Methods, 46, no. 5, pp. 2277–2289.

J. BRADEN, C. KOLSTAD (1991). Measuring the demand for environmental quality. Contributions to Economic Analysis (Pa´ıses Bajos), 198, pp. 333–355.

D. COX (1972). Regression models and life-tables. Journal of the Royal Statistical Society B, 34, pp. 187–220.

C. HAKANSSON (2007). Cost-Benefit Analysis and Valuation Uncertainty. Ph.D. thesis, Acta Universitatis Agreculturae Sueciae.

N. HANLEY, J. SHOGREN, B. WHITE, E. P. (FIRM) (2001). Introduction to environmental economics. Oxford University Press.

S. IYER, S. JAMMALAMADAKA, D. KUNDU (2008). Analysis of middle-censored data with exponential lifetime distributions. Journal of Statistical Planning and Inference, 138, no. 11, pp. 3550–3560.

S. JAMMALAMADAKA, S. IYER (2004). Approximate self consistency for middle-censored data. Journal of Statistical Planning and Inference, 124, no. 1, pp. 75–86.

S. JAMMALAMADAKA, V. MANGALAM (2003). Nonparametric estimation for middle-censored data. Journal of Nonparametric Statistics, 15, no. 2, pp. 253–265.

S. JAMMALAMADAKA, V. MANGALAM (2009). A general censoring scheme for circular data. Statistical Methodology, 6, no. 3, pp. 280–289.

S. JAMMALAMADAKA, S. PRASAD, P. SANKARAN (2016). A semi-parametric regression model for analysis of middle censored lifetime data. Statistica, 76, no. 1, pp. 27–40.

E. KAPLAN, P. MEIER (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, pp. 457–481.

P. SHEN (2011). The nonparametric maximum likelihood estimator for middle-censored data. Journal of Statistical Planning and Inference, 141, pp. 2494–2499.

V. SMITH (1993). Nonmarket valuation of environmental resources: an interpretive appraisal. Land Economics, 69, no. 1, pp. 1–26.

B. TURNBULL (1976). The empirical distribution function with arbitrarily grouped, censored and truncated data. Journal of the Royal Statistical Society B, 38, pp. 290–295.

J. WELLNER (1982). Asymptotic optimality of the product limit estimator. The Annals of Statistics, 10, pp. 595–602.




DOI: 10.6092/issn.1973-2201/6140

Creative Commons License 

ISSN 1973-2201

Registration at Bologna Court Law no. 2476 on 24th February 1955 (in progress)

The journal is hosted and mantained by ASDD-AlmaDL [privacy]