The ICLIFETEST Procedure

Data that have certain values below a limit of detection (LOD) are frequently encountered by toxicologists and environmental scientists. Such data are usually analyzed by imputing the unobserved values by LOD/2 or LOD/. This type of practice often raises the question of whether the population distributions can be estimated without bias. Gillespie et al. (2010) propose using a reverse Kaplan-Meier estimator, or equivalently, Turnbull’s method (1976) by treating the unobserved data as left-censored. When the assumption of independent censoring holds, these estimators can unbiasedly estimate the population distribution functions.

The following hypothetical data have two values, 3 and 10, that are below the limit of detection:

data temp;  
   input C1 C2;
   datalines;
  .     3
  4     4
  6     6
  8     8
  .     10
  12    12
;

The following statements invoke PROC ICLIFETEST to estimate the population distribution function by using Turnbull’s method:

proc iclifetest data=temp method=turnbull plots=survival(failure)
                impute(seed=1234);
   time (c1,c2);
run;

Specifying the PLOTS=SURVIVAL(FAILURE) option requests a failure probability plot. Results are shown in Output 50.1.1. Note that because the first Turnbull interval is , the failure probability function is undefined within that interval.

Output 50.1.1: Failure Probability Plot for Fictitious Nondetection Data

Output 50.1.2 presents the estimated failure probability, with standard errors that are estimated by the method of multiple imputations.