Statistical Analysis of Censored Environmental Data

Measurement data in environmental sciences are often subject to censoring when concentrations of pollutants, biomarkers or physico-chemical parameters fall outside the detection range of analytical instruments. Such censoring can bias summary statistics, distort correlation estimates and undermine inference in regression models if left unaddressed. Statistical techniques have been adapted or developed to accommodate left-, right- and interval-censored observations in a variety of settings: air quality networks, groundwater monitoring, biomonitoring and epidemiological studies. Approaches range from simple substitution of detection-limit values through more sophisticated likelihood-based models, non-parametric estimators and multiple imputation. Recent progress has focused on the integration of robust distributional assumptions with flexible regression frameworks to estimate parameters and associations in the presence of heavy censoring or small sample sizes. These methods improve the accuracy and precision of environmental assessments, support regulatory decision-making and enhance risk evaluation by producing unbiased estimates and valid confidence intervals under realistic sampling conditions.

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Statistical Analysis of Censored Environmental Data publication trend

The graph below shows the total number of articles in statistical analysis of censored environmental data across all publications each year (not limited to Nature Index journals).

Technical terms

Censoring: A condition in which the true value of an observation is only known to lie below, above or within a threshold, rather than measured exactly.

Limit of detection: The lowest concentration of an analyte that can be reliably distinguished from background by an analytical method, below which data are left-censored.

Left censoring: A form of censoring in which observations falling below a specified lower threshold are reported at that threshold rather than at their true values.

Tobit regression: A statistical model that incorporates censored dependent variables into the likelihood function to estimate regression relationships without discarding censored observations.

Multiple imputation: A simulation-based technique that replaces each censored or missing value with a set of plausible values drawn from an estimated distribution to reflect uncertainty.

Robust regression on order statistics (ROS): A method that fits a regression model to the log-transformed uncensored data and predicts censored values on the basis of their expected order statistics under a specified distribution.

References

1. Distorted correlations among censored data: causes, effects, and correction. Behavior Research Methods (2023).
2. Epidemiologic Evaluation of Measurement Data in the Presence of Detection Limits. Environmental Health Perspectives (2004).
3. Combining statistical methods for detecting potential outliers in groundwater quality time series. Environmental Monitoring and Assessment (2022).
4. Assessment of left-censored data treatment methods using stochastic simulation. Revista Brasileira de Recursos Hídricos (2023).