A Study on the Association between Maternal Childhood Trauma Exposure and Placental-fetal Stress Physiology during Pregnancy
AA Study on the Association between MaternalChildhood Trauma Exposure and Placental-fetalStress Physiology during Pregnancy
Eileen ZhangDepartment of Statistics, University of California, [email protected]
AbstractBackground
It has been found that the effect of childhood trauma (CT) exposure maypass on to the next generation. Scientists have hypothesized that the association betweenCT exposure and placental-fetal stress physiology is the mechanism. A study was con-ducted to examine the hypothesis.
Method
To examine the association between CT exposure and placental corticotrophin-releasing hormone (pCRH), linear mixed effect model and hierarchical Bayesian linearmodel were constructed. In Bayesian inference, by providing conditionally conjugatepriors, Gibbs sampler was used to draw MCMC samples. Piecewise linear mixed effectmodel was conducted in order to adjust to the dramatic change of pCRH at around week20 into pregnancy. Pearson residual, QQ, ACF and trace plots were used to justify themodel adequacy. Likelihood ratio test and DIC were utilized to model selection.
Results
The association between CT exposure and pCRH during pregnancy is obvious.The effect of CT exposure on pCRH varies dramatically over gestational age. Womenwith one childhood trauma would experience 11.9% higher in pCRH towards the end ofpregnancy than those without childhood trauma. The increase rate of pCRH after week20 is almost four-fold larger than that before week 20. Frequentist and Bayesian inferenceproduce similar results.
Conclusion
The findings support the hypothesis that the effect of CT exposure on pCRHover GA exists. The effect changes dramatically at around week 20 into pregnancy.
Keywords linear mixed effect model; Gibbs sampler; variable selection, likelihood ratiotest
Childhood trauma (CT) is the traumatic experience that happens to children aroundage 0-6. It has been indicated that such adverse experience may have an effect on thedeveloping brain [1], the development of depression and anxiety disorders [2]. Traumasurvivors may become vulnerable during the period of time when there is other stress orchanges in their lives[3]. Realizing the widespread consequences of CT, several studieshave been conducted. Among them, an interesting finding is that CT may be transmit-ted between generations and its intergenerational impact will exist [3]. The mechanism1 a r X i v : . [ s t a t . A P ] J a n ehind it remains unsolved. Research results in this area proposed that the traumatizedparents may be functional unavailable for their infant, which resulted in the enhancedsymptomatology with their child [8]. Moreover, through parents’ potential traumatizingbehavior, child trauma may pass on to the next generation [15]. All the findings indicatethe difficulty in searching for the mechanism of CT transmission.It has been studied that the placental corticotrophin-releasing hormone (pCRH) is thekey to communicating between the mother and the unborn child[16]. The concentration ofpCRH is highly related to the fetal and infant health development[17]. The pCRH systemserves as sensor, transducer and effector of the fetal brain development and peripheralsystems [19]. Motivated by these findings, a novel biological pathway has been proposedby Moog, N.K. et al. [16] to explain the mechanism of CT transmission over generations.In their outstanding work, they built the hypothesis that, through the effect of maternalCT exposure on placental-fetal stress physiology, especially pCRH, the intergenerationaltransmission may take place during gestation[16]. Specifically, their study was conductedin a cohort of 295 pregnant women along with their CT exposure measurement. Linearmixed effect model and Bayesian piecewise linear models were implemented to show theassociation between maternal CT exposure and placental-fetal stress physiology.In this study, the dataset consists of pCRH concentrations along with the CT expo-sure measurement and other information is obtained after a sociodemographically-diversecohort of 88 pregnant women. The key scientific questions are to study the effect of CTexposure on pCRH over gestation (using both frequentist and Bayesian inference) andrealize the unneglectable change in the rate of change in pCRH after gestational age goesbeyond 20. Motivated by these, this report aims to provide a solution of those questions. The dataset in this study was collected during a sociodemographically-diverse cohort of88 pregnant women. To measure the CT exposure, Childhood Trauma Questionnairewith 28 items have been assessed. It covered the following five dimensions of childhoodmaltreatments: emotional abuse (EA), physical abuse (PA), sexual abuse (SA), emotionalneglect (EN) and physical neglect (PN). CT-Sum is the total number of those traumasthat a mother had during her childhood. Placental CRH (pCRH) concentrations werealso measured in maternal blood collected during the course of gestation. Besides those,the following information was also collected from each woman: gestation age in weeks(GA), depression score based on a questionnaire by the Center for Epidemiological Studies(DCES), indicator of obstetric risk conditions (OB-risk), pre-pregnancy Body Mass Index(BMI), childhood socioeconomic score using a 15-item measure that characterizes distinctaspects of economic status during childhood (CSES) and number of previous pregnancies(Parity).
The following scientific questions are to be considered:SQ1: Under the framework of frequentist inference, study the effect of CT-Sum on pCRHas gestation (GA) changes while considering all the potential confounding factors.SQ2: Repeat the analysis of SQ1 under the framework of Bayesian inference.2Q3: With the prior information that “the rate of change of pCRH changes remarkablyaround 20 weeks into pregnancy”, modify the models.
As for the preliminary data exploration
The main objective in this section is tostudy pregnant women characteristics during their gestation and how pCRH changes fordifferent level of CT-Sum over GA. Quantitative covariates are presented in their mean,range and skewness along with graphing techniques such as spaghetti plot, regression lineplot and scatterplot; categorical variables are presented in their percentage of the totalpopulation.
As for SQ1
The strategies were based on the following principles:
Linear mixed effect model
Since the current dataset contains multiple observationsper subject and is unbalanced (each individual was measured at different gestation age),linear mixed effect models were employed to study the effect of CT-Sum on pCRH overGA. The assumption is that we assume subjects are independent with each other andlinear relationship between pCRH (or transformed form of pCRH) and CT-Sum exists.
Transform of covariates
It has been indicated that there exists an approximatelyexponential increase rate of pCRH over GA[20]. Following the same strategies of previouswork[4, 6, 7, 10, 16], log-transformation of pCRH has been used in fitting models. Themodel follows that log( pCRH i ) = X i β + Z i b i + (cid:15) i , (1)where i = 1 , , · · · , . The subscript i denotes subject id. β and X i are the coefficientsand design matrix for the fixed effect. Z i and b i are the design matrix and random slopefor the random effects. (cid:15) i are error term within subjects. Variable Selection
To study the effect of CT-Sum on pCRH over GA, covariates CT-Sum, GA and the interaction between them were included in the linear mixed effectmodel. It has been found that there is strong association between the socioeconomicbackground and childhood abuse, which results in the influence on pCRH [12, 18]. Thus,we have strong evidence that CSES should be in the fixed effects. Other covariates areeither psychological or biophysical factors, which may be also associated with CT-Sumor pCRH. For instance, studies show that childhood sexual abuse have strong impacton depression during pregnancy [9, 11]. Childhood trauma survivors may deny theirpregnancy or hide it from others [5, 13, 14], which may result in low number of previouspregnancies. Thus, in this study, we include all the factors in the fixed effects of themodel. To take care of the variability between subjects in the effect of CT-Sum onpCRH, preliminary analysis suggests that the intercept varies across subjects. Moreover,it is also shown that the change rate of log pCRH over GA may also vary across subjects.Hence, we consider to include both of random intercept and slope of GA in the model.Likelihood ratio tests suggests that the random slope may not be necessarily included.Analysis in more details can be found in section 3.2.
As for SQ2
Bayesian inference was implemented to study the effect of CT-Sum onpCRH over GA. The strategies are in the following principles:
Bayesian hierarchical model
With the same argument in SQ1, model (1) was alsoimplemented in this section. To address the question in Bayesian inference, we have the3ollowing prior τ ∼ Inv − χ ( c, d ) , σ (cid:15) ∼ Inv − χ ( a, b ) , β l ∼ N (0 , σ l ) , l = 0 , , · · · , k,b i | τ iid ∼ N (0 , τ ) , (cid:15) ij | σ (cid:15) iid ∼ N (0 , σ (cid:15) ) , i = 1 , , · · · , , j = 1 , , · · · , n i . As is stated in SQ1, we involve intercept in the random effects, which is denoted as b i . β l denotes the coefficient of the covariates in the fixed effect. MCMC estimation
Gibbs sampler was implemented in making inference of parame-ters of interest. The derivation of conditional distribution of parameters can be found inAppendix A. About 20% of MCMC samplers were burned in to make inference of param-eters of interest. Point estimate of parameters was calculated by the sample average. Toget the 95% credible interval, sample quantiles were used to approximate the lower andupper bounds. Besides that, MCMC convergence diagnosis was also conducted.
Variable selection
From previous arguments, we have involved all the factors and theinteraction CT-Sum*GA in the fixed effects and intercept in the random effects. In or-der to determine whether to include random slope of GA, DIC (Deviance InformationCriterion) has been used to compare those two models.
As for SQ3
Piecewise linear mixed effect model was employed in studying the dra-matic change of rate at around 20 weeks. A knot of 20 was made in covariate GA.Based on the model proposed in SQ1, we assume additional slope and intercept whenGA is larger than 20. Likelihood ratio test was conducted to compare models with onlyadditional slope and with both of additional slope and intercept.
To evaluate the model adequacy proposed in SQ1 and SQ3, Pearson residual plots havebeen employed to justify the mean model. QQ plots were also implemented to checkthe normality assumption. To justify the model proposed in SQ2, we employed statistics T ( y, θ ) = − (cid:80) Ni =1 log( p ( y i | θ )). Based on the posterior samplers, data y rep is generated.We calculate the predictive p-value as pB = P r ( T ( y rep , θ ) > T ( y, θ )) . If the value isextremely small, there may be some trouble in model adequacy.
Summary of descriptive statistics of categorical variables is shown in Table 4 (AppendixA). It can be found that almost half of the subjects have no childhood trauma experience.The number of those who experience one to three childhood traumas are roughly the same(17.0%, 14.8% and 12.5%). Only 4.5% of the subjects have 4 childhood traumas. Mostof the pregnant women (68.2%) have low obstetric risk, which compares to 31.8% asthe high obstetric risk. 39.8% of the women have no previous pregnancy and 38.6%of them have one before. Only a small portion of subjects (12.5%) have two previouspregnancies, along with 6.8% have three and 2.3% have four previous pregnancies. Table5 (Appendix A) presents characteristic of quantitative variables in this study. The sampleaverage depression score is 0.65. The pre-pregnancy body mass index is 24.56 on averageand 11.50 is the average childhood socioeconomic score among all the subjects. The4estational age is roughly centered around 26.73 weeks. The placental corticotrophin-releasing hormone has the average of 236.80. Three variables (DECS, CSES and GA) arenot highly skewed (skewness is 0.88, -0.77 and 0.01 respectively). BMI and the responsevariable pCRH are highly skewed.
15 20 25 30 35 40 GA l og ( p CRH )
15 20 25 30 35 40 GA l og ( p CRH ) CT−Sum=0CT−Sum=1CT−Sum=2CT−Sum=3CT−Sum=4 (A) Spaghetti plot of log pCRH (B) Scatter plot overlaid withover GA for each individual regression lines for each CT-SumFigure 1: log pCRH over GA −0.50.00.51.0 0 10 20 30 40
Subject % C on f i den c e I n t e r v a l −1.0−0.50.00.51.0 0 10 20 30 40 Subject % C on f i den c e I n t e r v a l (A) 95% confidence interval of slopes of GA (B) 95% confidence interval of slopes of GAfor individuals without childhood trauma for individuals with childhood traumaFigure 2: 95% confidence interval of slopes of GA5 Subject % C on f i den c e I n t e r v a l −20−100102030 0 10 20 30 40 Subject % C on f i den c e I n t e r v a l (A) 95% confidence interval of intercepts (B) 95% confidence interval of interceptsfor individuals without childhood trauma for individuals with childhood traumaFigure 3: 95% confidence interval of interceptsTo further study the effect of CT-Sum on log pCRH over GA, we conducted prelim-inary analysis. Figure 1(A) shows the spaghetti plots of log pCRH over GA. It can befound that as GA develops, log pCRH increase linearly and the change of rates starts togrow larger when GA is around 25-30 week. After we control for the factor CT-Sum, thespaghetti plots are summarized in Figure 4 (Appendix B). It shows that as GA closesto 15, the value of log pCRH for each individual is not consistent with each other afterwe control for the level of CT-Sum. The same pattern can also be found in Figure 1(A).Figure 3 shows the 95% confidence intervals of the intercept of the fitted linear regressionlines for each subject. It can be seen that after controlling for the factor of CT-Sum, thefitted intercept of each subjects differs from each other and the overlapping is relativelysmall. These findings motivate us to consider a random intercept into the linear mixedeffects model. To further investigate the rate of change of log pCRH over GA, Figure1(B) shows the scatter plot overlaid with regression line after controlling for CT-Sum. Itcan be seen that for each value of CT-Sum, log pCRH increases over GA and the rateof change (slope) differs among different levels of CT-Sum, which indicates the effect ofCT-Sum on log pCRH over GA. Figure 2 presents the 95% confidence intervals of thefitted slopes of GA for different subjects after controlling for CT-Sum. It shows thatthe fitted slope changes dramatically among different subjects especially for the groupwithout childhood trauma. These findings also suggest us to introduce a random slopeof GA in the linear mixed effect model. We will discuss on this in more details in Section3.2. Following the analysis in Section 3.1, a linear mixed effect model was fitted to the dataset.We include all the factors and the interaction CT-Sum*GA in the fixed effects. For therandom effects, we considered two scenarios: random intercept only and both of randomintercept and slope of GA. The two priori models arelog(pCRH ij ) = β + β ∗ GA ij + β ∗ CT-Sum i + β ∗ GA ij ∗ CT-Sum i + β ∗ BMI i + β ∗ CSES i + β ∗ DCES i + β ∗ OB-risk i + β ∗ Parity i + b i + b i ∗ GA ij + (cid:15) ij , (2)6ndlog(pCRH ij ) = β + β ∗ GA ij + β ∗ CT-Sum i + β ∗ GA ij ∗ CT-Sum i + β ∗ BMI i + β ∗ CSES i + β ∗ DCES i + β ∗ OB-risk i + β ∗ Parity i + b i + (cid:15) ij , (3)To further compare model 2 with model 3, a likelihood ratio test was conducted. The χ statistics roughly follows a mixture of χ distributions, χ (1) + χ (2) . The result (pvalue is 0.78) shows that there is no strong evidence to include random slope of GA inthe model.Thus, the proposed model follows thatlog(pCRH ij ) = β + β ∗ GA ij + β ∗ CT-Sum i + β ∗ GA ij ∗ CT-Sum i + β ∗ BMI i + β ∗ CSES i + β ∗ DCES i + β ∗ OB-risk i + β ∗ Parity i + b i + (cid:15) ij , (4)where fixed effects contain all the factors and the interaction GA*CT-Sum; the randomeffect involves intercept.Model diagnosis was conducted in checking the constant variance assumption andnormality assumption. Pearson residual plot in Figure 5 (Appendix C) indicates thatthe constant variance assumption holds since there is not obvious pattern from residuals.QQ plot in Figure 5 indicates normal assumption holds since the graph is closed to a linewith slope 1.Table 1 shows the fixed effect estimates of linear mixed effect model (4). It can befound that covariates of GA, BMI and CT-Sum*GA contribute significantly to the expla-nation of log(pCRH) change. Although CT-Sum does not preform statistical significant,there is no reason to argue that CT-Sum is not a persuasive predictor. Also, previouswork [16] has shown the significance of CT-Sum. Moreover, it is shown from Table 1 thatthe association between CT-Sum and pCRH increases over gestational age (GA) sincethe estimate of CT-Sum*GA is positive.We will exponentiate the estimate to interpret the results. It can be concluded fromthe table that at gestational age 14 (the first time point collected in the dataset), give allthe other factors the same, women with 1 childhood trauma tend to have 1.8% lower inpCRH than those without childhood trauma. However, as gestational age goes up, themedian pCRH is expected to goes up too. For example, if at gestational age 40 (the lasttime point in the dataset), the expected median pCRH value will increase by 11.9% ifthe childhood trauma goes up by 1.In Summary, to address SQ1, we propose model (4) as the final fitted model. The effectof CT-Sum on pCRH over GA varies dramatically. At early gestational age, the effects ofCT-Sum will decrease pCRH and as gestational age goes on, that effect becomes positive.If a pregnant woman experiences 1.2 childhood trauma (the average from the dataset),the expected median pCRH value will be 14.4% higher towards the end of gestationcompared to those without childhood trauma. On the other hand, at gestational age26.7 (the average from the dataset), women with one childhood trauma has 4.7% highermedian pCRH value than those who do not have childhood trauma.7able 1: Fixed effect estimates of linear mixed effect model (4)Covariates of fixed effect Estimate Standard error Degree of freedom T value P value*Intercept 1.750 0.270 113.200 6.502 < . < . Following the argument in section 2.3, Bayesian inference has been made to study theassociation between CT-Sum and pCRH over GA. By similar arguments in section 3.2,we have involved all the factors and the interaction GA*CT-Sum in the fixed effects.DIC was compared to determine whether to include random slope of GA in the model.Results (random intercept and slope: 684.12; random intercept only: 577.75) suggestsonly random intercept included in the model. Thus, we propose model (4) as the finalhierarchical Bayesian linear model as well.Model diagnosis was conducted in checking the convergence of MCMC and also theadequacy of the model. Trace and ACF plots of parameters can be found in Figures 6and 7 (Appendix D). They reveal that all the MCMC samplers are in good mixing andindependent. The Gibbs samplers provide good estimate of the posterior distributionfor each parameter. Figure 8 (Appendix D) compares to observed average test statisticsdefined in section 2.3 with the values obtained from the replicated samples. The estimated pB is 0.58, which implies the model fits the data well.The fixed effect estimates of the proposed model can be found in Table 2. Similar tothe frequentist inference, it shows that intercept, GA and BMI are significant since thecredible interval does not contain 0. Although the interaction GA*CT-Sum covers 0 intheir credible interval, we conclude it is still significant since the lower bound is close to 0.CT-Sum does not preform statistically significant but we can not neglect it by the sameargument in section 3.2. To interpret the results, we will still exponentiate the estimates.The positive value of 0.005 suggests positive association between CT-Sum and pCRH asgestational age increases. To address SQ2, we conclude that the increment of CT-Sumresults in decrease in pCRH at early gestational age. However, as gestational age becomeslarge, increasing the CT-Sum will lead to the increment of pCRH. The arguments aresimilar to the frequentist inference. If a pregnant woman has 1.2 childhood trauma (theaverage of the dataset), the expected median pCRH value will be 14.4% higher at theend of the gestation compared to those without childhood trauma. Moreover, at theaverage gestational age 26.7, women with one childhood trauma will have pCRH value4.7% higher than those without childhood trauma.8able 2: Fixed effect estimates of hierarchical Bayesian model (4)Covariates of fixed effect Posterior mean 95% Probability IntervalIntercept 1.751 (1.152, 2.328)GA 0.141 (0.132, 0.151)CT-Sum -0.088 (-0.265, 0.088)CT-Sum*GA 0.005 (-0.001, 0.011)BMI -0.020 (-0.035, -0.006)CSES -0.018 (-0.049, 0.013)DCES -0.098 (-0.313, 0.118)OB-risk 0.037 (-0.149, 0.225)Parity -0.077 (-0.164, 0.011) To modify model (4) with the additional information, we made a knot of 20 in covariateGA. The question is whether additional slope, or both of additional slope and interceptshould be involved in the fit model. To address this question, models with only additionalslope and both of additional slope and intercept have been fitted. Likelihood ratio test(pvalue is 0.43) suggests that there is no further information indicating the necessityof both of additional intercept and slope. Hence, we will propose the model with onlyadditional slope that followslog(pCRH ij ) = β + β ∗ GA ij + β ∗ CT-Sum i + β ∗ GA ij ∗ CT-Sum i + β ∗ BMI i + β ∗ (GA ij − + + β ∗ CSES i + β ∗ Parity i + β ∗ DCES i + β ∗ OB-risk i + b i + (cid:15) ij , (5)where (GA ij − + = max { GA ij − , } . Model diagnosis was conducted to justify the adequacy, assumption of constant vari-ance and normality. Residual plot can be found in Figure 9 (Appendix D). There is noobvious pattern and the residuals scatters around 0. Also, the QQ plot indicates thevalidity of normal assumption.Summary of fixed effect estimates of model (5) is shown in Table 3. Similar to theresults in SQ1 and SQ2, CT-Sum are not statistically significant. Since the objective isto study the change of effect of CT-Sum on pCRH over GA, there is no reason to removeCT-Sum from the model.Following similar strategies in SQ1 and SQ2, we will exponentiate the estimate ofcoefficients to interpret the results. From Table 3, it is revealed that around 20 gestationalage, there is a dramatic increase of the change rate of pCRH over gestation. In particular,among women whose gestational age is less than 20 and experience 1.2 childhood trauma(the average from the dataset), the expected median pCRH will increase by 3.8% perweek. But after 20 weeks, those women will experience a 17.9% increase of the expectedmedian pCRH per week towards the end of gestation. On the other hand, among thosewomen with 1 childhood trauma (the mode of the dataset), the expected median pCRHincreases by 3.9% per week before week 20, 17.8% per week after week 20. But amongthose without childhood trauma, the expected median pCRH goes up by 3.3% (beforeweek 20) and 17.2% (after week 20). It shows that although at around week 20, theincrement of pCRH becomes dramatic, women without childhood trauma still remain9ower pCRH increase rate compared to those with childhood trauma.Table 3: Fixed effect estimates of linear mixed effect model (5)Covariates of fixed effect Estimate Standard error Degree of freedom T value P value*Intercept 3.729 0.374 300.500 9.961 < . − + < . The objectives of this study were to examine the effect of maternal CT exposure onpCRH and modify the model to realize the difference before and after gestational age 20(in week).In regarding to the first scientific question, linear mixed effect models have beenimplemented. Covariates of all the factors and the interaction GA*CT-Sum were chosenas fixed effects. Intercept was in the random effects. Results indicated that the associationbetween CT exposure and pCRH varied over gestational age. During the first couple ofweeks into pregnancy, women with childhood trauma were likely to have lower pCRHthan those without childhood trauma. However, as gestational age moved on, thosewith childhood trauma experienced much higher increase rate of pCRH. At the end ofpregnancy (GA=40), women with 1 childhood trauma have almost 14.4% higher value inthe expected median pCRH than those without childhood trauma.In regarding to the second scientific question, hierarchical Bayesian linear mixed effectmodel was implemented. By choosing conditionally conjugate priors, Gibbs sampler wasemployed to obtain samplers from the posterior distribution of parameters. The samemodel in SQ1 was proposed after comparing the DIC values. Results are similar tothe frequentist inference. At early gestational age, women with more childhood traumawould experience lower pCRH value. As the pregnancy moves on, more exposure tochildhood trauma lead to much higher increase rate of pCRH. At the average gestationalage (GA=26.7), women with one childhood trauma have 4.7% higher pCRH value thanthose without childhood trauma experience.In regarding to the last scientific question, piecewise linear model with knot at 20 weekwas conducted. The results indicated that after week 20 into pregnancy, the increase ofpCRH over GA became more and more dramatic. The increase rate per week (afterweek 20) is almost four-fold larger than that before week 20. Women without childhood10rauma still remain lower increase rate than those with one childhood trauma before andafter week 20.
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Appendix A
The derivation of conditional distributions in implementing Gibbs sampler. b i | β , τ , σ (cid:15) ∼ N ( (cid:80) n i j =1 (log( pCRH ij ) − X ij β ) /σ (cid:15) n i /σ (cid:15) + 1 /τ , ( n i /σ (cid:15) + 1 /τ ) − ) , β | τ , b i , σ (cid:15) ∼ N ((1 /σ (cid:15) )((1 /σ (cid:15) ) ∗ X T X + Λ ) − X T ˜ Y , ((1 /σ (cid:15) ) ∗ X T X + Λ ) − ) , where X = X X · · · X ,n , Λ = /σ · · ·
00 0 1 /σ k , ˜ Y = (log( pCRH ) − b , · · · , log( pCRH ,n ) − b , ) T .τ | β , b i , σ (cid:15) ∼ Inv − χ (88 + c, (cid:80) i =1 b i + c ∗ d
88 + c ) σ (cid:15) | β , τ , b i ∼ Inv − χ ( (cid:88) i =1 n i + a, (cid:80) i =1 (cid:80) n i j =1 (log( pCRH ij ) − X ij β − b i ) + a ∗ b (cid:80) i =1 n i + a ) . Table 4: Descriptive statistics of categorical variablesVariables Number of observations PercentageNo childhood trauma (CT-Sum=0) 45 51.1%One childhood trauma (CT-Sum=1) 15 17.0%Two childhood trauma (CT-Sum=2) 13 14.8%Three childhood trauma (CT-Sum=3) 11 12.5%Four childhood trauma (CT-Sum=4) 4 4.5%High obstetric risk (OB-risk=1) 28 31.8%Low obstetric risk (OB-risk=0) 60 68.2%No previous pregnancy (Parity=0) 35 39.8%One previous pregnancy (Parity=1) 34 38.6%Two previous pregnancies (Parity=2) 11 12.5%Three previous pregnancies (Parity=3) 6 6.8%Four previous pregnancies (Parity=4) 2 2.3%Table 5: Descriptive statistics of quantitative variablesVariables Mean Range SkewnessDepression score (DCES) 0.65 1.72 0.88Pre-pregnancy body mass index (BMI) 24.56 30.00 1.15Childhood socioeconomic score (CSES) 11.50 11.00 -0.77Gestational age (in weeks) (GA) 26.73 26.00 0.01Placental corticotrophin-releasing hormone (pCRH) 236.80 1337.00 1.9414
Appendix B
15 20 25 30 35 40 GA l og ( p CRH )
15 20 25 30 35 40 GA l og ( p CRH ) CT-Sum=0 CT-Sum=1
15 20 25 30 35 40 GA l og ( p CRH )
15 20 25 30 35 40 GA l og ( p CRH ) CT-Sum=2 CT-Sum=3
15 20 25 30 35 40 GA l og ( p CRH ) CT-Sum=4Figure 4: Spaghetti plots of log pCRH over GA after controlling for CT-Sum15
Appendix C −3 −2 −1 0 1 2 3 − . − . . . . Normal Q−Q Plot
Theoretical Quantiles S a m p l e Q uan t il e s fitted(.) r e s i d ( ., t y pe = " pea r s on " ) −1.0−0.50.00.5 3 4 5 6 7 QQ Plot Pearson Residual plotFigure 5: QQ and Pearson plots of the model in SQ116
Appendix D . . . . . . Iterations be t e_0 − . − . − . − . . . . Iterations be t e_1 . . . . Iterations be t e_2 − . . . . . Iterations be t e_3 − . − . − . − . . . Iterations be t e_4 − . − . − . . . . Iterations be t e_5 − . − . . . Iterations be t e_6 − . . . . Iterations be t e_7 − . − . − . − . − . . . Iterations be t e_8 . . . . Iterations t au_1 . . . . Iterations ep s il on Figure 6: Trace plots of parameters of the model in SQ217 . . . . . . Iterations be t e_0 ACF plot . . . . . . Iterations be t e_1 ACF plot . . . . . . Iterations be t e_2 ACF plot . . . . . . Iterations be t e_3 ACF plot . . . . . . Iterations be t e_4 ACF plot . . . . . . Iterations be t e_5 ACF plot . . . . . . Iterations be t e_5 ACF plot . . . . . . Iterations be t e_6 ACF plot . . . . . . Iterations be t e_7 ACF plot . . . . . . Iterations t au_1 ACF plot . . . . . . Iterations ep s il on ACF plot
Figure 7: ACF plots of parameters of the model in SQ2
Model diagnosis value of T(y,theta) F r equen cy
550 600 650 700
Test statistics based on replicated samplesObserved test statistics
Figure 8: Model diagnosis plot of the model in SQ218 itted(.) r e s i d ( ., t y pe = " pea r s on " ) −1.0−0.50.00.51.0 3 4 5 6 7 −3 −2 −1 0 1 2 3 − . . . . Normal Q−Q Plot
Theoretical Quantiles S a m p l e Q uan t il e ss