How to Analyze Censored Concentration Data Using Modern Statistical Methods of Survival Analysis: Background and Nonparametric Methods

Quantitative analytical methods for measuring concentrations of chemical substances in aquatic systems typically have acceptable accuracy and precision only for an intermediate range of analyte concentrations. Outside this range, the uncertainty of concentration estimates is too high to justify reporting them as valid measurements for use in statistical analyses. Therefore, concentration estimates falling below the lower reporting limit (LRL) are typically reported as the LRL, along with a code indicating that the measured values fell below the LRL. Such data are called left-censored data. Similarly, concentration estimates falling above the upper reporting limit (URL) are typically reported as the URL, along with a code indicating that the measured values exceeded the URL. Such data are known as right-censored data. Censored data violate assumptions underlying most traditional statistical methods, such as t-tests, regression analysis, and analysis of variance. We briefly review various statistical methods that have been employed for the analysis of censored concentration data, then review in greater detail some modern statistical survival-analysis methods that have become available in standard software within the last 10 years and can be applied to concentration data with both left- and right-censored values. Methods are illustrated with real data.