The NBDPS is a multi-site population-based case-control study of more than 30 types of major birth defects that started enrollment of women with an estimated date of delivery on or after October 1, 1997.¹⁷ Case infants (live born, stillborn, or induced abortions) were identified using existing birth defects surveillance systems in Arkansas, California, Georgia, Iowa, Massachusetts, New Jersey, New York, North Carolina, Texas, and Utah. Information on birth defects abstracted from hospital records was reviewed by a clinical geneticist at each study center to determine eligibility. The methods used for case classification in the NBDPS have been described in detail elsewhere.¹⁸ Control infants were randomly selected from all live-born infants without any major birth defect from the same geographical area and time period using either hospital birth records (Arkansas, California, Georgia 1997–2000, New York, and Texas) or birth certificates (Georgia 2001–2005, Iowa, Massachusetts, New Jersey, North Carolina, and Utah). Computer-assisted telephone interviews were conducted with the mothers of case and control infants between 6 weeks and 24 months after the estimated date of delivery, including questions on demographic factors, medical and pregnancy history, lifestyle, and occupation. For the time period of interest, the interview participation rate was 69% for case mothers and 66% for control mothers.

In this study, exposure to cannabis was defined as any reported use of marijuana or hashish in the period from 1 month before pregnancy to the end of the third month of pregnancy (periconceptional period). Only case and control infants whose mothers did not report use of any illicit drugs in the 3 months before pregnancy and during the entire index pregnancy, were considered unexposed.

The current study included case and control infants born from October 1, 1997 through December 31, 2005, whose mothers completed the interview (n = 18 745 and 6703, respectively). This dataset overlaps to a large extent with the dataset used by van Gelder et al. to study associations between periconceptional illicit drug use and birth defects,¹³ but it contains 2 additional years of data. Only case infants diagnosed with one of the 20 birth defect categories selected by van Gelder et al.¹³ (n = 14 429) were included in this study. Analogous to our previous study, infants born to women who reported preexisting diabetes type 1 or type 2 (298 cases and 39 controls) were excluded because of the strong association with major birth defects,¹⁹ as well as infants only exposed to other types of illicit drugs (84 cases and 30 controls) or with missing information on illicit drug exposure (188 cases and 78 controls) because of our exposure definition. Eventually, we analyzed data on 13 859 case infants and 6556 control infants.

We first repeated our earlier analyses¹³ using the updated dataset. In these analyses, multivariable logistic regression techniques were used to calculate adjusted odds ratios (aORs) and 95% confidence intervals (CIs) for periconceptional cannabis use and each of the 20 selected birth defects. The same confounder set used in the previous study, consisting of maternal age at delivery, race/ethnicity, level of education, smoking in the periconceptional period, binge drinking in the periconceptional period (≥4 drinks per episode), prepregnancy body mass index, and any use of folic acid or multivitamins containing folic acid in the month before pregnancy or in the first month of pregnancy, was included in all current multivariable analyses. The re-analysis was performed using SPSS version 17.0 for Windows (SPSS Inc., Chicago, IL).

As data on the validity of the interview data on periconceptional cannabis use were not available, we used information on sensitivity of self-reports from the literature. We are not aware of any studies that provide information on accuracy of cannabis reporting among mothers of infants with birth defects. However, we identified 5 studies which determined the sensitivity of interview data on cannabis use among pregnant and postpartum women (Table 1).^20–24 These studies reported sensitivities ranging from 0.58 to 0.82. Because falsely reporting cannabis use is very unlikely, we assumed specificity to be 1.00 in all analyses. These parameters were used in Bayesian models to adjust the cannabis-birth defect associations for non-differential or differential underreporting. These analyses were performed using WinBUGS version 1.4 from within R version 2.12.2 for Windows²⁵ for 7 birth defect groups: all defects that had an elevated OR for periconceptional cannabis use in the frequentist re-analysis (i.e. anencephaly, esophageal atresia, diaphragmatic hernia, and gastroschisis), 1 defect with a decreased OR for periconceptional cannabis use (hypospadias), 1 defect that has been associated with periconceptional cannabis use in previous studies but not in our re-analysis (perimembranous VSD), and 1 defect with a relatively large case group that was not associated with periconceptional cannabis use (cleft lip ± cleft palate).

Following the framework of MacLehose et al.,⁶ we conducted Bayesian uncertainty analyses conditional on prior hypotheses generated from published studies. In short, 3 models, an outcome model, an exposure model, and a measurement model, were jointly estimated, which allowed simultaneous imputation of the true periconceptional cannabis exposure status and estimation of its effect on the risk of the selected birth defects. In the outcome model, the odds of an infant having the selected birth defect was modeled with a logistic regression model conditional on the (unknown) periconceptional cannabis exposure status and the potential confounders assuming no interaction between cannabis use and other factors:

where BD_i is case/control status, β₁ is the effect of periconceptional cannabis use, can_i^true is the unobserved true periconceptional cannabis exposure status, and θ is a vector of effects of the potential confounders in the vector z_i’. We used a non-informative normal distribution with mean = 0 and variance = 10⁶ for the prior distribution of the intercept. Informative priors were placed on the remaining parameters (Table 2). These prior distributions were informed using prior studies, which were discussed among a panel of experienced researchers in the field of birth defects epidemiology, consisting of 2 of the authors and 3 experts outside the study team. As an example, we assumed folic acid supplementation to have no additional protective effect on folate-sensitive birth defects (normal distribution, mean = 0, variance = 0.13), because all pregnant women in our study were exposed to folic acid through food fortification.²⁶ Priors on coefficients for which no information from previous studies was available and the prior on the effect of periconceptional cannabis use on the risk of birth defects were kept relatively vague (normal distribution, mean = 0, variance = 0.67; corresponding to a prior OR of 1.0 with a 95% credible interval of [0.2, 5.0]) as we were uncertain about the magnitude of the ORs for these associations.

In the exposure model, we modeled the probability of true exposure to cannabis in the periconceptional period conditional on a set of predictors:

where ω is a vector of the effects of the predictors in z_i’. The set of predictors consisted of all potential confounders and paternal cannabis use, which is highly predictive of maternal illicit drug use.^27,28 However, as is discussed by MacLehose et al.,⁶ it is difficult to inform priors for parameter estimates because the outcome of interest, true exposure to cannabis, is generally not observed in studies. Therefore, we also placed vague priors (normal distribution, mean = 0, variance = 0.67) on the coefficients in this model.

Finally, in the measurement model we modeled the probability of reporting periconceptional cannabis use during the interview dependent on the true (but unobserved) exposure status and the case/control status, which allowed us to introduce differential misclassification. Because we assumed specificity to be 1.00, we could simplify the measurement model used by MacLehose et al.⁶ to:

Here can_i^int is the periconceptional cannabis exposure status the woman reported in the interview, α₀ is the sensitivity of reported cannabis use among control mothers, , and α₁ is the sensitivity of reported cannabis use among case mothers. The exposure and measurement models were used to impute values of can_i^true in a way similar to that used with Bayesian missing data techniques.⁶ These imputed values were then used to estimate the associations between periconceptional cannabis use and the selected birth defects.

To quantify the potential effects of underreporting of the exposure on the cannabis-birth defect associations observed, we implemented four scenarios that specified α₀ and α₁ in the measurement model. In Scenario 1, the reference scenario, we assumed sensitivity to equal 1.00 (no correction for underreporting), which resulted in a standard Bayesian logistic regression model. Scenario 2 is based on the assumption that cannabis exposure status was non-differentially misclassified with a sensitivity fixed at 3 different values: 0.80, 0.65, and 0.50. In case-control studies of birth defects, there is evidence that maternal reporting is not affected by pregnancy outcome.^29,30 However, since recall bias cannot be excluded, it was assumed that the cannabis exposure status was differentially misclassified for Scenario 3, with the assumed sensitivity to be 0.05 or 0.10 lower among controls than the fixed values of 0.80 and 0.65 among cases. Scenario 4 was based on the assumption that the sensitivities used in the measurement model are not exactly known. For the prior distribution of the sensitivity, a beta distribution (α = 15, β = 6.5) was chosen with prior parameters selected to reflect a priori beliefs concerning reported cannabis use, i.e. sensitivity with a mean of 0.7 and a standard deviation of 0.1. The values for sensitivity among cases and controls were assumed not to be correlated.

We conducted a sensitivity analysis to determine the influence of our prior assumptions in the exposure and outcome models by placing vague priors on all coefficients in every model. All models were fitted using Markov chain Monte Carlo algorithms, which were run for 20 000 iterations with the first 1000 iterations excluded as a burn-in period. We ran three chains from different initial positions; convergence was monitored with trace plots and the Gelman-Rubin statistic. After the burn-in period, the iterations of the algorithm were random draws from the posterior distributions of interest, of which the median was exponentiated to obtain the OR of interest. We exponentiated the 2.5^th and 97.5^th percentile of the random draws to obtain 95% posterior credible intervals (CRIs). To provide a measure of precision of the CRIs, we calculated the half width ratio by dividing the half-width of the CRI by the median. The R script and model specifications used are shown in Appendix S2.