## Assessment methodology for imposex

### Overview

Time series of imposex measurements are assessed in three stages:
1. The imposex measurements each year are summarised by an annual index.
2. A generalised linear model is fitted to the annual indices. The type of model depends on the number of years of data:
• 1-2 years: no model
• 3 years: mean
• 4+ years: linear trend
3. The fitted models are used to assess evidence of change in imposex levels over time. The annual indices or the fitted models are used to assess environmental status against available assessment criteria, the choice depending on the availability of individual imposex measurements in the most recent monitoring year.

The methodology for assessing imposex is evolving to make better use of individual measurements.

### Calculating annual indices

Let cti, i = 1 ... nt be the individual imposex measurements on female snails in year t, t = 1 ... T. The annual index in year t is the mean of these measurements:

y_t=\frac{1}{n_t} \sum_i c_{ti}

### Modelling the annual indices

The annual indices are constrained to lie between 0 and 1 by dividing by the largest permissible value (below). For example, the indices for VDS in dog whelks are divided by 6.

 Measure Species Latin name largest value VDS Dog whelk Nucella lapillus 6 VDS Red whelk Neptunea antiqua 4 VDS Netted dog whelk Nassarius reticulatus 6 VDS Sting winkle Ocenebra erinaceus 6 IMPS Common whelk Buccinum undatum 3.5 INTS Common periwinkle Littorina littorea 4

The transformed indices are then modelled using a generalised linear model with a logistic link (McCullagh & Nelder, 1989). Usually, the data are assumed to have a quasi-binomial distribution with weights given by the number of female snails nt. However, the distribution of VDS in dog whelks is specified by a more appropriate mean - variance relationship derived in Fryer & Gubbins (2007). The mean index is given by:

text{logit}(text(E)(y_t))=f(t)

where f(t) is a function of time that depends on the number of years of data:

1-2 years
no model is fitted as there are too few years for formal statistical analysis
3 years
mean model f(t) = µ
there are too few years for a formal trend assessment, but the mean level is summarised by µ and is used to assess status
4+ years
linear model f(t) = µ + βt
the indices vary as a linear logistic function of time; the fitted model is used to assess status and evidence of temporal change

Fryer R & Gubbins M, 2007. Modelling VDSI in Nucella lapillus. ICES Working Group on Statistical Aspects of Environmental Monitoring

McCullagh P & Nelder JA, 1989. Generalized Linear Models (second edition). Chapman & Hall, London.