Statistical Analysis for Prediction of DINP Intake by Young Children

Bob Proctor

Intro Stat

Nov. 22, 05

Statistical Analysis for Prediction of DINP Intake by Young Children

Michael A. Green, Ph.D., 1998

In the late 1990s researchers discovered that diisononyl phthalate (DINP), asubstance used in the production of children’s toys including rattlers andyellow rubber duckies, caused chronic toxic effects to the liver and otherorgans in animals. The article my paper is about was the 1998 study conductedto determine the rates at which 3-26 month year old babies were ingesting DINPby putting their toys in their mouths.

The study first determined the rate at which DINP entered the body. 10adult volunteers were administered 11-square-centimeter disks sliced out ofyellow rubber duckies. That size area was chosen because it was believed to bethe same surface area as an object likely to be mouthed by a child (if exactprocedures were used to obtain this size, none were specified in the article),

four disks per subject. Each human provided measurements for fourfifteen-minute periods for a total of 40 measurements.

The distribution of migration rates has a skewed appearance with an arithmeticmean of 8.20 (all units are in micrograms per square centimeter per hour),median of 4.8 sq. cm. and standard deviation (SD) of 9.83. The study alsoutilized The Shapiro-Wilk statistic, which is a test for the fit of the normaldistribution. The Shapiro-Wilk statistic for the transformed data was 0.97 witha p value of 0.55. The Shaprio-Wilk statistic was 0.66 with a p value of lessthan 0.0001.

The paper utilized logarithms to reduce variation in the data. Lognormaldistribution models were made for the two groups. Transforming to logs produceda mean of 1.66, median of 1.57, SD of 0.91. The skewness and normality testsuggested that the log transformation was successful in fitting a normaldistribution.

The second part of the study was to determine how long children havetheir toysin their mouth. The children were divided into two groups: 3-12 month olds and 13-26month

olds. The researchers decided to do this, “because the amount of time thesechildren were observed to engage in mouthing behavior was very different.”

The arithmetic mean mouthing time for the 3-12 month age groupwas 24.4 minutes, the median was 15.3 min. and the standard deviation was 32.9min. The data did not fit the normal distribution, so the researchers used whatwas referred to as a skewness statistic to measure the degree of non-normality.The skewness statistic was 2.85, with the Shapiro Wilk of 0.6530 (p < .0001).The researchers decided to use a log transformation to correct the extreme

skewness. The log transformed versions had corresponding statistics of mean=2.49 and SD = 1.37. The value of the skewness statistic was = -0.6840. TheShapiro Wilk statistic was 0.9559 (p = .4976).

The paper also utilized a term called the geometric mean, which itdefined as, “a typical measure of the center of a skewed distribution, and infact, for the lognormal distribution, the geometric mean is an estimate for themedian or 50th percentile of the data.” The mean value following the logtransformation, corresponded to a geometric mean in the original data of 5.24.

From the transformed data, the geometric mean mouthing time was 12.03 minuteswith an estimated 95% confidence interval of 6.2 to 23.3 minutes.

The researchers noted that children spend far more time mouthing otherobjects

such as fingers and pacifiers. For 3-12 month old children the average usage ofpacifiers was 45 minutes per day and fingers was 11 minutes per day.

The arithmetic mean mouthing time for children aged 13-26 months was2.54 minutes with a median of 1.49 minutes, a SD of 2.94 minutes, skewness of1.4117 and Shapiro Wilk W statistic of 0.8161 (p = 0.0006) . Again, theresearchers felt it necessary to correct the skewness using logtransformations. Also, there were five subjects who did not suck their toys atall, recording times of zero. The researchers considered three methods to dealwith these extreme observations. One possibility would be to replace the zeroswith very small quantities. However the researchers decided that this would“induce negative skewness, that is, it would create the opposite outlierproblem as found with the original values” so the strategy was rejected. Thetwo other approaches were dropping the 5 cases with zeroes and thentransforming to logs or using the month of age of the subject to average theobservations before taking the logs. This second strategy had the desiredresult of reducing the number of zeroes to one for the child age 24 months, butat the cost of artificially lowering the standard deviation of the data. The twoprocesses ultimately yielded very similar means (.74 and .77), and since thesecond process had the undesirable effect of lowering the SD, the zeros weredropped. The geometric mean was 2.1 with a 95% confidence interval of 1.22 to3.62 minutes.

The study then attempted to determine the average child’s intake ofDINP. Aformula was derived for daily exposure: DE= (M)(D)/(BW) M= rate of DINPmigration D=duration product is likely to be in the subject’s mouth, andBW=body weight of subjects.

For children between ages 3 and 12 months, the results showed ageometric meanaverage daily intake of 5.7 micrograms per day with a 95% confidence interval2.5 to 12.9. The distribution was very skewed. The 95th percentile exposure was94.3 micrograms with a 95% confidence interval of 50.1 to 225.6. For children13-26 months old, there was a geometric mean of daily exposure of 0.69micrograms per 10.7 kg per day, with a 95% confidence interval of 0.32 to 1.55.The estimated 95th percentile exposure was 7.6 micrograms with a 95% confidence

interval of 4.4 to 16.2 micrograms.

The researchers also checked to see if migration rates correlated withanyspecific variables. First, researchers tested whether migration rates differed by type ofspecimen.Products were classified as ‘teethers‘, ‘mouth toys‘, and ‘others.’ Theresearchers used a “Kolmogorov-Smirnov” test “to determine whether the datacould be assumed to come from the same underlying process.” The p value forthis test was 0.58, which meant that there was no reason to believe that anyproduct had a migration rate higher than any other product.

Second, models were estimated to determine if migration rates could beexplained by the characteristics of the products, including DINP content byweight, the type of manufacturing process (e.g. injection molding, rotation,etc.) and the thickness of the product. The regression models did not produce avalue of R greater than 0.33 which was not considered useful in predicting DINPmigration rates. Also, the nature of migration rates of DINP can createvariation within a single specimen.

Third, an analysis of variance procedure (ANOVA) was applied to themigration rates to determine if there were any, gender effects, disk effects,or systematic variation in migration rates over the fifteen minute period forthe testing on the 10 volunteers. Using the log of the migration rate as theresponse variable, only the disk effect was statistically significant with a p

value ofp=0.0119. The researchers decided that they should not treat the disksas exact replicates of each other in their analysis.

Researchers concluded that there was a minimal to nonexistent healththreat to children based on DINP intake. DINP was banned from the making ofchildren's toys, anyway. The article was clear in its methodology and thoroughin its search for correlation of other variables. The article also took thetime to define its terms, so even though I was not familiar with several of theprocedures, the article was still quite accessible.