Maximum Cumulative Ratio

Price and Han [Price et al., 2011] propose the Maximum Cumulative Ratio (MCR) 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:

MCR = Cumulative exposure/ Maximum exposure

This MCR statistic is also picked up as a practical device in a recent JRC report [Bopp et al., 2015] to investigate cumulative exposure. If MCR is large, it is important to consider cumulative effects, if MCR is close to 1, the individual exposure will not be much different from a single-substance assessment. The MCR can therefore be interpreted as the degree to which the risk of being exposed is underestimated by not performing a cumulative risk assessment.

The MCR 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, in the chronic case the long-term individual exposures (estimated by aggregating over the available survey days of each individual).

Table 120 shows an artificial example how the MCR 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 relative potency factors (RPF). 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 MCR values within parenthesis the substance with the highest exposure. The MCR 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 MCR value is equal or close to the number of substances, here 4. Day 2 represents an intermediate case. The MCR suggest that for exposure days (or persons) with MCR values close to 1, the need for a cumulative risk assessment is low.

Table 120 Maximum Cumulative Ratios

	Substance A	Substance B	Substance C	Substance D	total exposure	ratio
day 1	0.01	0.99	0	0	1	1.01 (B)
day 2	0.1	0.2	0.3	0.4	1	2.50 (D)
day 3	0.25	0.25	0.24	0.26	1	3.99 (D)

In the example, all days have equal values for total exposure. For real data, total exposure will vary. It is obviously of interest to know if the MCR is high or low at those days (or individuals) where the total exposure is highest.

In Figure 37, French steatosis data (39 substances, 4079 persons) are used to calculate the chronic exposure matrix. For each individual the MCR 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 MCR, the p5, p50 and p95 percentiles are indicated with the black line segments. The red line indicates the ratio with value 5. The dashed green lines indicate the p95 percentiles for the MCR value for different ranges of the total exposure.

Figure 37 Maximum Cumulative Ratios vs total exposure

The plot shows that MCR 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 MCR 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 MCR 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 37 can be very dense, in Figure 38, 95% confidence regions representing bivariate lognormal distributions of MCR 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).

Figure 38 Bivariate distributions MCR vs total exposure

In Figure 39 and Figure 40 scattered MCR distributions for the total and upper tail (here 37%) that drive the cumulative exposure are shown. The red line indicates the MCR threshold, 1.5. The black lines represent the regression lines MCR vs ln(Cumulative exposure) for each tail. Substances with an exposure contribution less than 15% are not displayed.

Figure 39 Using MCR to identify substances that drive cumulative exposures, scatter distributions (total).

Figure 40 Using MCR to identify substances that drive cumulative exposures, scatter distributions (upper tail 37%).

In Table 121 contributions to tail exposures at various percentile are shown. Column MCR = 1 shows the percentage of tail exposure due to individual(day)s with a single substance. Column 1 < MCR \(≤\) 2 shows the percentage of tail exposure due to individual(day)s with multiple substances, but the MCR \(≤\) 2. Column MCR > 2 shows the percentage of tail exposure due to individual(day)s with multiple substances with MCR > 2.

Table 121 Maximum Cumulative Ratio summary

Tail %	% with MCR = 1	Substances	% with 1 < MCR<=2	Substances	% with MCR > 2	Substances
37	20.6	Difeno, Tebu	73.7	Difeno, Tebu	5.7	Difeno, Tebu
50	19.2	Difeno, Tebu	75.6	Difeno, Tebu	5.2	Difeno, Tebu
90	16.3	Difeno, Tebu	78.8	Difeno, Tebu	5.0	Difeno, Tebu
95	15.0	Difeno, Tebu	82.5	Difeno, Tebu	2.5	Difeno, Tebu
99	25.0	Difeno	75.0	Difeno, Tebu Propi	0.0

For MCR settings, see exposure mixture settings.