BACs for PBDEs in biota

Assessment Criteria for Polybrominated Diphenyl Ethers

This document summarises the discussions at OSPAR MIME 2019 on setting Background Assessment Concentrations (BACs) for Polybrominated Diphenyl Ethers (PBDEs). It builds on discussions at MIME in 2017 and 2018.

The first section describes the methodology for estimating BACs. The next section then develops BACs for PBDEs in fish and shellfish.

BAC estimation methodology

BACs are used to test whether concentrations are at background levels for naturally occurring substances, or ‘close to background’ for synthetics. This is done by testing the null hypothesis \({\text{H}_0: \mu \geq \text{BAC}}\) against the alternative hypothesis \({\text{H}_1: \mu < \text{BAC}}\), where \(\mu\) is the mean concentration (in the final monitoring year). The test is precautionary since concentrations are considered to be above background (\({\text{H}_0}\)) unless there is sufficient evidence to show otherwise (\({\text{H}_1}\)).

The BAC is chosen to give a 90% power of rejecting \(\text{H}_0\) when \(\mu = \text{BC}\), where BC is the Background Concentration. The BC of natural occurring substances is estimated using data from near-pristine locations (assuming they exist) or, for sediment concentrations, from cores. The BC of synthetic substances is zero, and to construct the BAC it is necessary to replace the BC by a Low Concentration (LC) which is typically taken to be twice the Quasimeme standard error. For the purposes of this section, the BC (or LC) is assumed known.

Power depends on the statistical test used, the number of years of data, and the variability in the data. It is necessary to standardise these to construct a BAC that can applied across the OSPAR area. Specifically, it is assumed that:

there is a 10-year monitoring programme with the same sampling protocol followed every year (or equivalently and more realistically, a 20-year monitoring programme with sampling every two years)
the test is a one-tailed t-test at the 5% significance level based on the temporal trend regression model fitted to the monitoring data
the variability in the data is typical of that found in MIME monitoring data; this is developed later, but for now it is assumed that the variability is characterised by a parameter \(\psi\)

Assume that the concentration measurements each year are summarised by an annual index on the logarithmic scale (e.g. the median log concentration or the mean log concentration). Let \(\mathbf y\) be the vector (length 10) of annual contaminant indices and assume that

\(\quad \mathbf y = \mathbf f + \mathbf \epsilon\)

where \(\mathbf f\) represents a smooth systematic trend in contaminant levels over time and \(\mathbf \epsilon\) represents random variation, assumed to be independent between years and normally distributed with zero mean and standard deviation \(\psi\). Let \(\mathbf{X}\) be the design matrix used to estimate the systematic trend \(\mathbf f\). The choice of \(\mathbf{X}\) is also discussed later, but it could correspond to a linear trend or a smooth on a fixed number of degrees of freedom. It is assumed that \(\mathbf{X}\) estimates \(\mathbf f\) with no bias. Let \(r\) be the rank of \(\mathbf X\) and \(\nu = 10 - r\) be the residual degrees of freedom associated with \(\mathbf X\). Let

\(\quad \mathbf{H = X(X'X)^{-1}X'}\)

be the hat matrix. The fitted trend is then \(\mathbf {\hat{f} = Hy}\), which has variance \(\mathbf H \psi^2\).

A one-tailed t-test at the 5% significance level is used to test \({\text{H}_0}\) vs \({\text{H}_1}\). Let

\(\quad T = \frac {\hat {\mathbf f} _{10} \text{ }- \text{log BAC}} {\hat \psi \sqrt {\mathbf H_{10,10}} }\)

where the 10 suffix picks out the fitted value and its variance in the final monitoring year, and where \(\hat {\psi^2}\) is the usual unbiased estimator of \(\psi^2\). Then \({\text{H}_0}\) is rejected in favour of \({\text{H}_1}\) if \(T < t_{\text{crit}}\), where \(t_{\text{crit}}\) is the 0.05 quantile of a central t-distribution on \(\nu\) degrees of freedom, denoted \((t ; \nu).\) That is, the value such that

\(\quad \text{Prob} \big( (t ; \nu) < t_{\text{crit}} \big) = 0.05\)

When \(\mathbf f_{10} = \text{log BAC}\), \(T\) has a central t-distribution \(T \sim (t; \nu)\). More generally, T has a non-central t-distribution \(T \sim (t; \nu; \delta)\) on \(\nu\) degrees of freedom and non-centrality parameter

\(\quad \delta = \frac {\mathbf f_{10} - \text{log BAC}} {\psi \sqrt {\mathbf H_{10,10}} }\)

The BAC is chosen to give 90% power when \(\mathbf f_{10} = \text {log BC}\). Let \(\delta _ \text {crit}\) be the value that satisfies

\(\quad \text{Prob} \big( (t ; \nu; \delta _ \text{crit} ) < t_{\text{crit}} \big) = 0.90\)

Then the BAC is given by

\(\quad \text {log BAC} = \text {log BC} - \delta _ \text {crit} \psi \sqrt {\mathbf H_{10,10}}\)

or equivalently

\(\quad \text {BAC} = \text {BC} \text {exp} \big( - \delta _ \text {crit} \psi \sqrt {\mathbf H_{10,10}} \big)\)

Two problems remain: choosing the appropriate form of \(\mathbf X\) and hence \(\mathbf H\) and estimating a suitable value of \(\psi\). The methods for doing both have been updated since the last time BACs were constructed (around 2005 for compounds in other determinand groups) to accommodate developments in the trend assessment methodology. A summary of the changes can be found in the discussions at MIME 2017.

First consider the choice of \(\mathbf X\). A time series with 10 years of data is assessed by fitting a linear trend and smooths on 2 and 3 degrees of freedom (df) and choosing the optimal model based on AICc. In practice, most time series reduce to a linear trend. However, the smooth on 2 df gives BACs that are closest to the previous approach and hence are used here. The corresponding values of \(\delta _ \text{crit}\) and \(\mathbf H\) leads to BACs of the form:

\(\quad \text {BAC} = \text {BC} \text {exp} (2.51 \psi )\)

Now consider the choice of \(\psi\). The concentration measurements are modelled in a mixed modelling framework. This gives estimates of the between-sample and between-year random variation for each time series, denoted here as \(\sigma_{i,\text {sample}}^2\) and \(\sigma_{i,\text {year}}^2\) with the \(i\) used to index the time series. Analytical variability and the number of samples per year have tended to evolve in most time series (getting lower and fewer respectively) so, to characterise recent performance, the analytical variability \(\sigma_{i,\text {analytical}}^2\) for time series was based on the median reported uncertainty in the last three monitoring years. Similarly, the number of samples per year \(n_i\) for time series \(i\) was taken to be the median number of samples in the last three monitoring years. The residual variance for time series \(i\) was then estimated to be

\(\quad \psi _i ^2 = \sigma _ {i, \text {year}} ^2 + \frac 1 {n_i} \big (\sigma _ {i, \text {sample}} ^2 + \sigma _ {i, \text {analytical}} ^2 \big )\)

The value of \(\psi\) typical of MIME monitoring data was then estimated by fitting a robust loess smoother to the \(\text {log} \psi _ i\) as a function of the fitted log mean concentration in the final monitoring year, with a span of 1 and weighted by the number of years in each time series. The (back-transformed) fitted value of the loess smoother at the BC (LC) is taken to be the typical \(\psi\) at background (low) concentrations. When the BC (LC) is outside the range of the data, the fitted value at the closest observed mean concentration is used.

One final important caveat. BACs are statistical constructs and there is no guarantee that they are environmentally relevant. They should be rejected if they are higher than the EAC or equivalent (if it exists) and if they are too high based on expert judgement. For PBDES, the Canadian Federal Environmental Quality Guidelines (FEQGs) are used as EAC equivalents.

BAC estimates for fish and shellfish

MIME agreed to trial BACs of 0.065 \(\mu\)g/kg lw for all PBDE compounds in fish and shellfish

The Quasimeme constant error is 0.005 \(\mu\)g/kg ww for all determinands, so the standard choice of LC is 0.01 \(\mu\)g/kg ww.

To construct BACs on a lipid weight basis, it is necessary to convert the LC to a lipid weight equivalent. Six fish species had a sufficiently high lipid content (>3%) to be assessed on a lipid weight basis. Here are the typical lipid contents for these species. Note that PBDEs were measured in herring muscle.

                      MU.LIPIDWT% LI.LIPIDWT%
Platichthys flesus           0.90       14.70
Limanda limanda              0.70       19.40
Gadus morhua                 0.34       42.00
Clupea harengus              4.62        4.38
Pleuronectes platessa        0.49       11.43
Merlangius merlangus           NA       36.90

The values range from 4.6% to 42.0%, which would suggest multiplying 0.01 by anywhere between 2.4 (cod liver) and 21.7 (herring muscle). The choice is somewhat subjective, but it was decided to use a factor or 3. This is roughly right for the two gadoids, precautionary for the flat fish and very precautionary for herring. However, note that at MIME 2018, there were concerns that an LC of 0.01 \(\mu\)g/kg ww was too high and an LC of 0.005 \(\mu\)g/kg ww was used instead. Multiplying by 3 gives an LC of 0.03 \(\mu\)g/kg lw.

The BACs were estimated using only fish / tissue combinations with a ‘high’ lipid content. The suitability of these BACs for fish / tissue combinations with a low lipid content (assessed on a wet weight basis) and for bivalves (also assessed on a wet weight basis) was then investigated.

The first tab below shows, by determinand, the estimates of \(\psi\) from each time series (assessed on a lipid weight basis) plotted against the estimated mean concentration in the final monitoring year. The fitted loess smoother (black line) with 95% pointwise confidence limits (dashed lines) is also shown. The three vertical lines are the LC (grey), the BAC (blue) constructed using the methodology described earlier and the FEQG (green). Note that some of the FEQGs are not shown because they are off the scale of the plot.

The second tab gives the same information, but with the points coloured by species.

The third tab gives the estimates of \(\psi\) typical of MIME monitoring data at concentrations close to the LC, with lower and upper 95% confidence limits, and the BACs derived from them. The BACs are expressed as \(\mu\)g/kg lw.

The BACs are all well below the FEQGs, so in this sense they are environmentally acceptable. However, the wide variation in BACs between compounds (0.065 - 2.75 \(\mu\)g/kg lw) was considered unsatisfactory, as it tended to reflect variation in analytical performance rather than environnmental characteristics, and as it sometimes resulted in higher BACs for compounds that would be expected to have lower concentrations based on a typical PBDE profile. It was therefore decided to use the BAC for BDE47 of 0.065 \(\mu\)g/kg lw for all compounds. The value for BDE47 was chosen because a) it is based on the most data; b) BDE47 has the lowest value of \(\psi\) and hence the lowest BAC; c) the BAC is below the mean concentration observed in BDE47 time series in areas that would not be considered background (indeed it was below the mean concentration in all BDE47 time series).

The fourth tab shows the estimates of \(\psi\) from all time series plotted against the estimated mean concentration in the final monitoring year. The mean concentrations of those time series assessed on a wet weight basis have been converted to a lipid weight basis using the typical lipid weight for that speices / tissue. The LC of 0.03 and BAC of 0.065 \(\mu\)g/kg lw have been added to the plots (as have the FEQGs). The BAC of 0.065 \(\mu\)g/kg lw looks reasonable for all species / tissue combinations.

The remaining tabs show status plots for each PBDE using a BAC of 0.065 \(\mu\)g/kg lw. Points are coloured

blue if the mean concentration is significantly (p < 0.05) below the BAC
green if the mean concentration is significantly (p < 0.05) below the FEQG
red if the mean concentration is not significantly below the FEQG
orange if there is no FEQG (and above background)

Note that if instead we used an LC of 0.02 \(\mu\)g/kg lw, the BAC would be 0.044 \(\mu\)g/kg lw. Similarly, LCs of 0.05, 0.10 and 0.02 \(\mu\)g/kg lw would correspond to BACs of 0.11, 0.22 and 0.44 \(\mu\)g/kg lw.

Variability by country

Variability by species

BACs

	LC	psi	lower	upper	BAC	FEQG
BDE28	0.030	1.80	0.61	5.31	2.752	2400
BDE47	0.030	0.31	0.22	0.42	0.065	880
BDE66	0.030	0.49	0.20	1.24	0.103
BDE85	0.030
BDE99	0.030	0.65	0.48	0.88	0.154	20
BD100	0.030	0.36	0.23	0.56	0.074	20
BD126	0.030
BD153	0.030	0.50	0.36	0.69	0.105	80
BD154	0.030	0.69	0.42	1.13	0.170	80
BD183	0.030
BD209	0.030

Assessment Criteria for Polybrominated Diphenyl Ethers

BAC estimation methodology

BAC estimates for fish and shellfish

Variability by country

Variability by species

BACs

Variability by tissue

BDE28

BDE47

BDE66

BDE85

BDE99

BD100

BD126

BD153

BD154

BD183

BD209