Scratch that, I found the study. Looks like a 2012 study but still appears to be voluntary response. I will put some of the abstract below. Bently I hope that is ok.
"The birth cohort consisted of 432 pregnant women who gave birth at term (>36 weeks of gestation). Only non-smoking women with singleton pregnancies, 18-35 years of age, and who were free from chronic diseases such as diabetes and hypertension were included in the study. Detailed information on diet over pregnancy was collected through interviews and the measurement of exposure to airborne PAHs was carried out by personal air monitoring during the second trimester of pregnancy. The effect of barbecued meat consumption on birth outcomes (birthweight, length and head circumference at birth) was adjusted in multiple linear regression models for potential confounding factors such as prenatal exposure to airborne PAHs, child’s sex, gestational age, parity, size of mother (maternal prepregnancy weight, weight gain in pregnancy) and prenatal environmental tobacco smoke (ETS)."Reading into it a little further. It looks like the births were from 2001 to 2004 and were only in Krakow, Poland. The women were just given lifestyle questionnaires upon enrollment into the study and then again in the third trimester. I don't consider that reliable data. They were not asked to keep any daily log nor did they have regular check-ins with the study group. Also, they were given a device to measure air pollution (to try and separate airborne PAH from food based) but they only had to keep it with them for one 48 hour period during the test. And once again, this was on the honor system.
Here is a link to the study. After reading it, I am not convinced. The study doesn't seem to focus on any hereditary or genetic history of the parents or any other environmental or lifestyle factors.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3288524/#!po=11.5385