Censoring Trace-Level Environmental Data: Statistical Analysis Considerations to Limit Bias

Abstract

Trace-level environmental data typically include values near or below detection and quantitation thresholds where health effects may result from low-concentration exposures to one chemical over time or to multiple chemicals. In a cook stove case study, bias in dibenzo­[a,h]­anthracene concentration means and standard deviations (SDs) was assessed following censoring at thresholds for selected analysis approaches: substituting threshold/2, maximum likelihood estimation, robust regression on order statistics, Kaplan–Meier, and omitting censored observations. Means and SDs for gas chromatography–mass spectrometry-determined concentrations were calculated after censoring at detection and calibration thresholds, 17% and 55% of the data, respectively. Threshold/2 substitution was the least biased. Measurement values were subsequently simulated from two log-normal distributions at two sample sizes. Means and SDs were calculated for 30%, 50%, and 80% censoring levels and compared to known distribution counterparts. Simulation results illustrated (1) threshold/2 substitution to be inferior to modern after-censoring statistical approaches and (2) all after-censoring approaches to be inferior to including all measurement data in analysis. Additionally, differences in stove-specific group means were tested for uncensored samples and after censoring. Group differences of means tests varied depending on censoring and distributional decisions. Investigators should guard against censoring-related bias from (explicit or implicit) distributional and analysis approach decisions.

Comment on “Censoring Trace-Level Environmental Data: Statistical Analysis Considerations to Limit Bias”

“…George et al have recently discussed the problem of dealing with data sets which are missing values because some of the measurements are below the detection limit of the analytical method . These are commonly called left-censored data sets, and the problem is what to do with the missing data if one is calculating the central tendency of the data set.…”

Response to Comment on “Censoring Trace-Level Environmental Data: Statistical Analysis Considerations to Limit Bias”

“…These data illustrate the need to understand and limit bias introduced by the handling of nondetects, and our work turned to simulation to assess moderately and highly skewed log-normal data that, by design, complemented the case study. Each estimated distribution mean and standard deviation (SD) from our simulation study, shown in Figure 2, represents the average from 1000 data sets with sample size n = 50. The estimates are for uncensored samples and for samples where the lowest 30%, 50%, and 80% of the data was censored.…”

“…The simulation study is abstract in that its data are not actual analytical measurements, but it has key advantages over a single data set as used in our case study. We noted in the discussion that important distinctions of the simulation study relative to the case study are “(1) the true mean and variance of the underlying population distributions are known, (2) bias estimation based on many samples is, in expectation, more accurate, and (3) the bias estimates are tied only to the distributional characteristics, enhancing generalizability beyond DBA” …”

“…Confidence intervals characterize uncertainty in estimates of the mean . We assessed confidence interval coverage, that is, the percentage of simulated samples where the confidence interval contained the true mean, and found the statistical approaches varied in their estimation performance (Figures S10 and S11). The takeaway is that statistical approaches differ across distributional assumptions, distribution skewness, sample sizes, and amount of censoring.…”

“…A straightforward approach for establishing the functional form of a probability distribution uses distribution parameters; the mean and SD estimates in Figure 2 may be used to estimate the normal, log-normal, and gamma probability distributions corresponding to the simulated samples . Alternatively, an empirical cumulative distribution function (ecdf) may be used in plotting observed quantiles to yield a sample-based distribution function.…”