Maximum Cumulative Ratio

Price and Han (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 exposureMaximum 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. For the chronic case long-term individual exposures (estimated by aggregating over the available survey days of each individual) are used.

Risk based, standardised or unweighted exposures

Before calculating the MCR statistics, three optional choices are available, see settings, MCR exposure approach type.

  • Risk based exposures: exposures are multiplied by the relative potency factor (RPF) 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 RPF s equal to 1 for each substance.

Table 192 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 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, with the substance with the highest exposure in parenthesis. 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 192 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 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 MCR 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 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.

../../../_images/mcr1.svg

Figure 71 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 71 can be very dense, in Figure 72, 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).

../../../_images/mcr2.svg

Figure 72 Bivariate distributions MCR vs total exposure

In Figure 73 and Figure 74 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.

../../../_images/mcr1new.svg

Figure 73 Using MCR to identify substances that drive cumulative exposures, scatter distributions (total).

../../../_images/mcr2new.svg

Figure 74 Using MCR to identify substances that drive cumulative exposures, scatter distributions (upper tail 37%).

In Table 193 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<MCR2 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 193 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

To configure the MCR 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).