Birth

With a single genetic variant $G_j$ that satisfies the instrumental variable assumptions, the causal effect of the risk factor on the outcome can be consistently estimated as a simple ratio of association estimates: ${\widehat{\mathit{\theta }}}_j=\frac{{\widehat{\mathit{\beta }}}_{Yj}}{{\widehat{\mathit{\beta }}}_{Xj}}$ [16 (link)], where ${\widehat{\mathit{\beta }}}_{Yj}$ is the estimated coefficient from univariable regression of the outcome on the jth genetic variant, and likewise ${\widehat{\mathit{\beta }}}_{Xj}$ from univariable regression of the risk factor on the jth genetic variant. With multiple genetic variants, the ratio estimates from each genetic variant can be averaged using an inverse-variance weighted formula taken from the meta-analysis literature to provide an overall causal estimate known as the inverse-variance weighted (IVW) estimate [17 (link)]. This assumes that the ratio estimates all provide independent evidence on the causal effect; this occurs when the genetic variants are uncorrelated. If the variance terms are taken as $\frac{\mathrm{se}{({\widehat{\mathit{\beta }}}_{Yj})}^2}{{\widehat{\mathit{\beta }}}_{Xj}^2}$ (this is the first term from a delta method expansion for the ratio estimate [18 (link)]), then the pooled estimate (assuming a fixed-effect model) is [19 ]: $$\begin{array}{c}\hfill {\widehat{\mathit{\theta }}}_{IVW}=\frac{{\sum }_j{\widehat{\mathit{\beta }}}_{Yj}{\widehat{\mathit{\beta }}}_{Xj}\mathrm{se}{({\widehat{\mathit{\beta }}}_{Yj})}^{-2}}{{\sum }_j{\widehat{\mathit{\beta }}}_{Xj}^2\mathrm{se}{({\widehat{\mathit{\beta }}}_{Yj})}^{-2}}.\end{array}$$ This same estimate is obtained from the two-stage least squares analysis method for individual-level data when the genetic variants are uncorrelated [20 (link)]. The same estimate can also be obtained from a weighted linear regression of the genetic associations with the outcome ( ${\widehat{\mathit{\beta }}}_{Yj}$ ) on the genetic associations with the risk factor ( ${\widehat{\mathit{\beta }}}_{Xj}$ ) using inverse-variance weights ( $\mathrm{se}{({\widehat{\mathit{\beta }}}_{Yj})}^{-2}$ ) when there is no intercept term in the regression model [14 (link)]: $$\begin{array}{c}\hfill {\widehat{\mathit{\beta }}}_{Yj}={\mathit{\theta }}_{IVW}{\widehat{\mathit{\beta }}}_{Xj}+{\mathit{ϵ}}_{Ij};{\mathit{ϵ}}_{Ij}\sim \mathcal{N}(0,{\mathit{\sigma }}^2\mathrm{se}{({\widehat{\mathit{\beta }}}_{Yj})}^2)\end{array}$$ where ${\widehat{\mathit{\beta }}}_{Yj}$ and ${\widehat{\mathit{\beta }}}_{Xj}$ are the data in the model, ${\mathit{\theta }}_{IVW}$ is the parameter, and ${\mathit{ϵ}}_{Ij}$ is the residual term. To obtain the same standard error for the causal estimate from the regression analysis as from the fixed-effect meta-analysis, the residual standard error in the regression ( $\mathit{\sigma }$ ) must be set to equal one [21 (link)].
If the pleiotropic effects of the genetic variants are all zero ( ${\mathit{\alpha }}_j=0$ for all j; in other words, if all genetic variants are valid instrumental variables), then each of the ${\widehat{\mathit{\theta }}}_j$ will be a consistent estimate of the causal effect, and the overall estimate ${\widehat{\mathit{\theta }}}_{IVW}$ (a weighted mean of the ${\widehat{\mathit{\theta }}}_j$ ) will be a consistent estimate of the causal effect.

We assume that all relationships between variables (in particular, the genetic associations with the risk factor and with the outcome, and the causal effect of the risk factor on the outcome) are linear with no effect modification. We also assume that all genetic variants are uncorrelated (that is, not in linkage disequilibrium), although conventional instrumental variable methods for analysing summarized data from correlated variants have been developed [14 (link)], and similar extensions to the MR-Egger method are discussed later in this paper. The association between genetic variant $G_j$ ( $j=1,2,\dots ,J$ ) and the outcome is denoted ${\mathit{\beta }}_{Yj}$ , and the association between genetic variant $G_j$ and the risk factor is denoted ${\mathit{\beta }}_{Xj}$ .
The genetic association with the outcome can be decomposed into the sum of a direct (pleiotropic) effect and an indirect (causal) effect: $$\begin{array}{c}\hfill {\mathit{\beta }}_{Yj}={\mathit{\alpha }}_j+\mathit{\theta }{\mathit{\beta }}_{Xj}\end{array}$$ where ${\mathit{\alpha }}_j$ is the effect of the genetic variant on the outcome that is not mediated via the risk factor of interest, and $\mathit{\theta }$ is the causal effect of the risk factor on the outcome [15 ]; see Fig. 1. A genetic variant is referred to as pleiotropic if it has associations with more than one risk factor on different causal pathways [16 (link)]. Any such effect is included in the parameter ${\mathit{\alpha }}_j$ ; a genetic variant is pleiotropic if ${\mathit{\alpha }}_j\ne 0$ . A pleiotropic genetic variant is not a valid instrumental variable.Fig. 1

Decomposing association for genetic variant \documentclass[12pt]{minimal}
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\begin{document}$$G_j$$\end{document}Gj with the outcome into a indirect (causal) effect via the risk factor and an direct (pleiotropic) effect (see Eq. 1)

Pregnant CD1 mice were exposed (via direct inhalation) to e-cig vapor containing 2.4% nicotine (Blu^™, 24 mg/ml nicotine) mixed with oxygenated air or oxygenated air alone, 6 times/day; 1 cartridge/day from gestational day 5 (E5) until delivery, and it was continued after delivery until the pups were 7 days old. After birth, the pups would be exposed to nicotine via lactation [40 (link), 41 (link)]. This exposure model was adopted following a study by Sifat et al. who investigated the effects of prenatal electronic cigarette exposure on offspring in mice model [6 (link), 8 (link)]. In our study, Blu^™ was used as this is one of the most popular e-cig brands still on the market, the cig-a-like structure fits well in our smoking apparatus, and there have been previously reported studies using Blu^™ [6 (link), 34 (link), 37 (link)]. A modified CORESTA (Cooperation Centre for Scientific Research Relative to Tobacco) standard smoking protocol adapted to study e-cig exposure (27.5 ml puff depth volume, 3 s puff duration, 2 puffs per 60 s, 32 puffs/session) was followed in the laboratory. E-cig vapor was generated using a Single Cigarette Smoking Machines (SCSM, CH Technologies Inc.) following a previously published method used by our laboratory [6 (link), 34 (link), 37 (link)]. This method was developed to mimic the smoking behavior of a human chronic/heavy smoker/vaper and yields plasma levels of cotinine (111 ng/ml) which is in the range of blood cotinine level (30–250 ng/ml) found in other preclinical rodent models of chronic e-cig exposure [42 (link), 43 (link)]. The smoking exposure was done between 9 a.m. and 2 p.m.

Preterm birth was the primary outcome of this study, which was defined as births before 37 completed weeks of gestation. The World Health Organization (WHO) further subdivided preterm birth based on gestational age: extremely preterm (< 28 weeks), very preterm (28 to < 32 weeks), and moderate or late preterm (32 to < 37 weeks) [23 (link)]. Secondary outcomes were NICU admission, low birthweight and small for gestational age. Low birthweight was defined as a birthweight < 2500 g, and small for gestational age was defined as a birthweight less than the 10th percentile. The following variables were collected: maternal age at delivery (years), race [Asian, Black (Black or African American), White, other (American Indian or Alaska Native, Native Hawaiian or Other Pacific Islander, and more than one race)], education [less than 12 grade, high school/general educational development (GED), some college or associate degree (AA), bachelor or higher], pre-pregnancy weight (lb), pre-pregnancy body mass index (BMI) (BMI < 18.5 kg/m², underweight; BMI = 18.5–24.9 kg/m², normal; BMI = 25.0–29.9 kg/m², overweight; BMI = 30.0–34.9 kg/m², obesity), delivery weight (lb), weight gain (lb), smoking before pregnancy (yes or no), smoking status 1st/2nd/3rd trimester (mother-reported smoking in the three trimesters of pregnancy, yes or no), hypertension eclampsia (yes or no), gestational hypertension (yes or no), pre-pregnancy hypertension (yes or no), number of prenatal visits, the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC, receipt of WIC food for the mother during this pregnancy, yes or no), plurality, prior birth now living, prior birth now dead, prior other terminations, total birth order, gestational age (weeks), newborn sex (female or male), birth weight (g), infertility treatment used (yes or no), pregnancy method (natural pregnancy, pregnancy via ART), method of delivery [spontaneous, non-spontaneous (forceps, vacuum, cesarean)], preterm birth [extremely preterm, very preterm, moderate or late preterm; spontaneous, indicated (forceps, vacuum, cesarean)], NICU admission, low birthweight (yes or no), and small for gestational age (yes or no). WIC is a program intended to help low income pregnant women, infants, and children through age 5 receive proper nutrition by providing vouchers for food, nutrition counseling, health care screenings and referrals; it is administered by the U.S. Department of Agriculture (https://ftp.cdc.gov/pub/Health_Statistics/NCHS/Dataset_Documentation/DVS/natality/UserGuide2019-508.pdf). Infertility treatment referred to using fertility enhancing drugs, artificial insemination, intrauterine insemination, or using ART. ART included in vitro fertilization (IVF), gamete intrafallopian transfer (GIFT), and zygote intrafallopian transfer (ZIFT). Information on variables is available at https://www.cdc.gov/nchs/nvss/index.htm.

This was a cohort study. All data of pregnant women aged 45 or older who were tested for GDM and did not have pre-gestational diabetes were extracted from the NVSS 2014–2019. The NVSS database provides data on births and deaths as well as maternal characteristics in 50 states, New York City, District of Columbia, and 5 territories (Puerto Rico, Virgin Islands, Guam, American Samoa, and Northern Mariana Islands) of the United States [22 (link)]. Participants were excluded according to the following criteria: (1) women with infections presenting or treated during this pregnancy; (2) women with missing information on gestational weeks, neonatal weight, and NICU admission records.