- The imposex measurements each year are summarised by an annual index.
- 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

- 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.

Let *c _{ti}, i = *1

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

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

`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 + β*t* - 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.

Temporal trends are assessed for time series with at least 4 years of data using the
model fitted to the annual indices. There is evidence of a
temporal trend if the slope β of the linear logistic regression of *y _{t}* on

Historically, environmental status has been assessed using the model fitted to the annual indices. The upper one-sided 95% confidence limit on the fitted value in the most recent monitoring year is compared to the available assessment criteria. For example, if the upper confidence limit is below the Background Assessment Concentration (BAC), then the mean index in the most recent monitoring year is significantly below the BAC and imposex levels are said to be 'at background'.

However, in many time series, imposex levels have declined so rapidly that the linear models used to assess trends cannot track the change completely. The linear models correctly show evidence of a decline, but over-estimate imposex levels in the final monitoring year suggesting that environmental status is worse than it actually is. To overcome this, an alternative test of status is now used when there are individual measurements in the final monitoring year. A proportional odds model is fitted to the individual measurements and used to place an upper one-sided 95% confidence limit on the annual index in the final monitoring year. This confidence limit is then compared to the available assessment criteria.