MOSAIC_SSD: A new web tool for species sensitivity distribution to include censored data by maximum likelihood

Abstract

Censored data are seldom taken into account in species sensitivity distribution (SSD) analysis. However, they are found in virtually every dataset and sometimes represent the better part of the data. Stringent recommendations on data quality often entail discarding a lot of these meaningful data, resulting in datasets of reduced size which lack representativeness of any realistic community. However, it is reasonably simple to include censored data in SSD by using an extension of the standard maximum likelihood method. The authors detail this approach based on the use of the R-package fitdistrplus, dedicated to the fit of parametric probability distributions. The authors present the new Web tool MOSAIC_SSD, that can fit an SSD on datasets containing any type of data, censored or not. The MOSAIC_SSD Web tool predicts any hazardous concentration and provides bootstrap confidence intervals on the predictions. Finally, the authors illustrate the added value of including censored data in SSD, taking examples from published data.

Comparative Assessment of Vegetative and Reproductive Terrestrial Plant Species Endpoints from Exposure to Herbicides and Potential Environmental Implications: A Review

“…Censored values are difficult to include in numeric evaluations, for example, in a species sensitivity distribution (SSD), in particular if the censored values are not the lowest or highest but are framed by higher or lower actual numeric values (e.g., Dickerson ). However, to provide a more comprehensive overview, we implemented further statistical analysis, conceptually either by replacing censored values by 10th or 90th percentiles respectively (e.g., Amemiya ; Helsel ), that is, maximum‐likelihood–estimation approaches involving bootstrapping SSDs (following Helsel ; Kon Kam King et al , details not shown), and alternatively by including censored values with a simple correction coefficient of 2 (censored greater‐than endpoints were multiplied by 2, and censored less‐than endpoints were divided by 2). For brevity only results with the simplistic approach are presented here; for further details, see Christl ().…”

Sensitivity of a Large and Representative Sample of Antarctic Marine Invertebrates to Metals

“…The SSDs were constructed both empirically and on the log‐normal distribution using the method described by Kon Kam King (). This log‐normal distribution method allows for the inclusion of right‐, left‐, and interval‐censored data as well as point estimates, using R‐script from the online tool MOdeling and StAtistical tools for ecotoxICology_SSD (MOSAIC_SSD see http://pbil.univ-lyon1.fr/software/mosaic/ssd/).…”

“…Previous construction of SSDs with rapid test data has used either Bayesian statistics (Hickey et al ; Kefford et al ; Dowse et al ; Kon Kam King et al ), which requires considerable statistical expertise (Kon Kam King et al ), or the Kaplan–Meier function (Kefford et al , , , ; Dunlop et al ; Dowse et al ). The Kaplan–Meier function has several undesirable properties:1) it can only incorporate interval data by transforming them to the mid‐point of the interval (Kon Kam King et al ); 2) it is empirical, that is, the estimation of an HC1 value requires ≥100 species to be included; and 3) the confidence intervals (CIs) produced are not of the PC x values but are approximately the x % itself, so it provide estimates of the concentration at which x ± d % of species will be protected.…”

In Response: Some species sensitivity distribution statistics revisited—A governmental perspective

“…A similar approach to censored values using Bayesian concepts is followed by Kon Kam King et al with the R‐based web‐tool MOSAIC_SSD. Figure shows the lower bound of the censored values.…”

“…It does not convey how the method of maximum likelihood takes censoring into account. For that, Kon Kam King et al and Helsel supply the details.…”