Price and Han (2011) propose the Maximum Cumulative Ratio () which is defined as the ratio of the cumulative exposure received by an individual on an intake day to the largest exposure received from a single substance:
This statistic is also picked up as a practical device in a recent JRC report, Bopp et al. (2015), to investigate cumulative exposure. If is large, it is important to consider cumulative effects. If is close to 1, the individual exposure will not be much different from a single-substance assessment. The can therefore be interpreted as the degree to which the risk of being exposed is underestimated by not performing a cumulative risk assessment.
The statistic is implemented in MCRA for both the acute risk and the chronic risk cases. In the acute risk case the short-term (single-day) exposures are used. For the chronic case long-term individual exposures (estimated by aggregating over the available survey days of each individual) are used.
Risk based exposures: exposures are multiplied by the relative potency factor () of each substance and thus exposures for different substances are on the same and comparable scale.
Standardised exposures: all exposures are standardised to equal variance (unit variance).
Unweighted exposures: exposures are taken as such, this is equivalent to s equal to 1 for each substance.
Table 192 shows an artificial example how the is calculated in the acute risk case. First the cumulative exposure per day is calculated by cumulating the exposure of each substance multiplied by the . Then, for each day, the cumulative exposure (in equivalents of the reference substance) is divided by the maximum exposure of a single substance on that day. The last column shows the values, with the substance with the highest exposure in parenthesis. The has a value of 1 or close to 1 for mixtures where the exposure is dominated by one substance (e.g. day 1, substance B). When all substances have approximately equal exposure (e.g. day 3) the value is equal or close to the number of substances, here 4. Day 2 represents an intermediate case. The suggest that for exposure days (or persons) with values close to 1, the need for a cumulative risk assessment is low.
In this artificial example, all days have equal values for total exposure (= 1). For real data, total exposure will vary. It is obviously of interest to know if the is high or low at those days (or individuals) where the total exposure is highest.
In Figure 71, French steatosis data (39 substances, 4079 persons) are used to calculate the chronic exposure matrix. For each individual the is calculated and plotted against the total exposure. The different colours are used to identify the single substances with maximum exposure. From the original 39 substances, 10 different substances have the largest exposures. For the total exposure and , the , and percentiles are indicated with the black line segments. The red line indicates the ratio with value 5. The dashed green lines indicate the percentiles for the value for different ranges of the total exposure.
The plot shows that values with Imazalil as risk driving substance (purple) are predominantly found in the lower part of the plot for relatively high values of the total exposure. A second finding is that values decline when total exposure increases. This implies that cumulative exposure for most individuals is driven by multiple substances. At the right site of the plot, individuals are found with high exposure. Because values tend to be lower here, higher exposures are received from one predominant substance and not because many substances are above the average level. For those individuals a cumulative risk assessment has less value.
Because Figure 71 can be very dense, in Figure 72, 95% confidence regions representing bivariate lognormal distributions of and total exposure are plotted. The latter figure facilitates interpretation of the first figure. Note that substances with just one or two observations cannot be plotted in this display (substances with 2 observations are represented by a line).
In Figure 73 and Figure 74 scattered distributions for the total and upper tail (here 37%) that drive the cumulative exposure are shown. The red line indicates the threshold, 1.5. The black lines represent the regression lines vs ln(Cumulative exposure) for each tail. Substances with an exposure contribution less than 15% are not displayed.
In Table 193 contributions to tail exposures at various percentile are shown. Column shows the percentage of tail exposure due to individual(day)s with a single substance. Column shows the percentage of tail exposure due to individual(day)s with multiple substances, but the 2. Column shows the percentage of tail exposure due to individual(day)s with multiple substances with .
To configure the plot, see dietary exposures settings, human monitoring analysis settings and exposures settings with options to display the ratio total exposure/ maximum for individual(day) exposures (MCR plot), to specify tail percentiles of the exposure distribution, e.g. 95, 97.5 and 99% (MCR plot) or to set the minimum percentage contribution per substance to the tail exposure (MCR plot).