Maximum Cumulative Ratio¶
Price and Han [38] 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 [8] 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 109 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.
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 35, French steatosis data (39 substances, 4079 persons) are used to calculate the chronic exposure matrix. For each indiviual the MCR is calculated and plotted against the total exposure. The different colors 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 35 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 35 can be very dense, in Figure 36, 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 36 Bivariate distributions MCR vs total exposure¶