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Statistical Modeling of Multiply Censored Data

The statistical practices of chemists are designed both to minimize the probabilities of mis-identifying a sample compound and of falsely reporting a detectable concentration. In environmental assessment, trace amounts of contaminants of concern are thus often reported by the laboratory as "non-detects" or "trace", in which case the data may be both left and interval left-censored. The analysis of singly censored observations has received attention in the biostatistical (e.g. in the context of survival analysis) and in the environmental literature (see, e.g., Akritas et al. 1994). In particular, both maximum likelihood and semi-parametric approaches to linear models have been considered in this setting (see, e.g., Buckley and James 1979, Schmee and Hahn 1979, Aitkin 1981, Miller and Halpern 1982, Akritas 1996). We have developed maximum likelihood and semi-parametric approaches for the setting which includes left and interval censoring and we are in the process of evaluating and comparing these methods through a practical example and by simulation. An Splus program and accompanying example which we have developed to carry out maximum likelihood linear regression with interval and left censored data is available.

Link to the Splus program and example.


Aitkin M. (1981) A note on the regression analysis of censored data. Technometrics, 23: 161-163.

Akritas MG, Ruscitti TF and Patil GP. (1994) Statistical Analysis of Censored Environmental Data. Handbook of Statistics 12, Environmental Statistics (GP Patil and CR Rao, editors), North-Holland, NY.

Akritas M.G. (1996) On the use of nonparametric regression techniques for fitting parametric regression models. Biometrics, 52: 1342-1362.

Buckley J and James I. (1979) Linear regression with censored data. Biometrika, 66: 429-436.

Miller R and Halpern J. (1982) Regression with censored data. Biometrika, 69: 521-531.

Schmee J and Hahn G.J. (1979) A simple method for regression analysis with censored data. Technometrics, 21: 417-432.