Impact of cystic fibrosis on birthweight: a population based study of children in Denmark and Wales

Background Poor growth during infancy and childhood is a characteristic feature of cystic fibrosis (CF). However, the impact of CF on intrauterine growth is unclear. We studied the effect of CF on birth weight in Denmark and Wales, and assessed whether any associations are due to differences in gestational age at birth. Methods We conducted national registry linkage studies in two countries, using data for 2.2 million singletons born in Denmark (between 1980 and 2010) and Wales (between 1998 and 2015). We used hospital inpatient and outpatient data to identify 852 children with CF. Using causal mediation methods, we estimated the direct and indirect (via gestational age) effect of CF on birth weight after adjustment for sex, parity and socioeconomic background. We tested the robustness of our results by adjusting for additional factors such as maternal smoking during pregnancy in subpopulations where these data were available. Results Babies with CF were more likely to be born preterm and with low birth weight than babies with no CF (12.7% vs 5% and 9.4% vs 5.8% preterm; 11.9% vs 4.2% and 11% vs 5.4% low birth weight in Denmark and Wales, respectively). Using causal mediation methods, the total effect of CF on birth weight was estimated to be −178.8 g (95% CI −225.43 to −134.47 g) in the Danish population and −210.08 g (95% CI −281.97 to −141.5 g) in the Welsh population. About 40% of this effect of CF on birth weight was mediated through gestational age. Conclusions CF significantly impacts on intrauterine growth and leads to lower birth weight in babies with CF, which is only partially explained by shorter gestation.

: Distribution of gestation age (left panel) and birth weight (right panel) in the Welsh study population is shown by the red histogram. The dashed line indicates the fitted distribution of the primary sub-population, the dotted line the distribution of the secondary sub-population and the solid line and the grey shaded region the fitted distribution for the whole population. The raw data and the fitted models represent the entire population and do not distinguish between CF and non-CF cases.

S.3 Testing main effects for significance by backward elimination
The full model was initially fitted and main effects terms were removed individually from the submodel for birthweight, the sub-model for gestational age and both sub-models. Likelihood ratio tests were carried out to assess the significance of the covariates. All covariates were found to be significant at the 5% level. Tables S1 and S2 show the deviances and p-values from the likelihood ratio tests for the Welsh and the Danish populations, respectively.  S.4 Estimated effects in the primary and secondary populations

Primary Sub-population
In the primary sub-population, babies with CF were estimated to be born about a quarter of a week earlier than non-CF babies (-0.26 weeks 95%CI -0.39 to -0.13). The difference in gestational age between first-borns and non-first-borns was estimated to be 0.12 weeks (95%CI 0.12 to 0.13). While the effect of sex was negligible, differences in maternal education were estimated to have effects of up to a quarter of a week increase in gestational age with increased education (see Table S3 for details).
The birthweight of babies with CF in the primary component was estimated to be 107.65g (95%CI 70.16g to 147.03g) less than that of non-CF babies of the same gestational age, sex, first born status and maternal education. Per week gestation, birth weight was estimated to increase by 137.72g (95%CI 137.03g to 138.64g). This leads to an additional indirect effect of CF on birth weight through gestational age of -36.34g (95%CI -54.2g to -18.2g). In total, CF babies in the primary sub-population were therefore estimated to be 143.99g lighter (95%CI 100.28g to 190.09g) than non-CF babies.
Females and first-borns were estimated to be lighter than males and not-first-borns and birthweight was estimated to increase with increasing maternal education (see Table S4 for details).

Secondary Sub-population
In the secondary sub-population, CF babies were estimated to be born between one and two and a half weeks earlier than non-CF-babies (-1.84 95%CI -2.52 to -1.03). Sex and first-born status were also found to have large effect sizes with males and first-borns being born earlier. Maternal education did appear to affect gestational age, in particular babies born to mothers with education level 5 or 6 were born later than those born to mothers with education level 1, however, there was no clear increasing trend of gestational age with maternal education (see Table S3).
The direct effect of CF on birthweight was estimated to be -201.48g (95%CI -298.02g to -100.15g).
Birthweight was estimated to increase by 178.85g (95%CI 177.05g to 180.17g) per week gestation leading to an additional indirect effect of CF on birthweight of -329.5 (95%CI: -449.34g, -184.2g). Thus, in total, CF babies in the secondary sub-population were estimated to be 530.98g (95%CI:353.27g to 688.07g) lighter than non-CF babies. First-borns and females were again estimated to be lighter than non-first-borns and males. The effect of maternal education on birthweight in the secondary subpopulation was unclear (see Table S4 for details).

Findings in the Welsh population
Primary Sub-population

Secondary Sub-population
In the secondary sub-population the effect of CF on gestational age was estimated to be -1.55 weeks (95%CI -3.3 to 0.16)). Sex, first-born status and socio-economic status were also found to have large effect sizes with males, first-borns and more deprived children being born earlier. The effects of gender, first-born status and deprivation were estimated to be smaller in this subpopulation compared to the primary one, yet showing the same trends (see Table S4).  Interaction effects between CF and any of the other main effects were tested for significance using the likelihood ratio test. None of the interaction effects were found to be significant at the 5% level. Tables S5 and S6 show the resulting deviances and p-values.
In both populations, the interaction effect between CF and first-born status on gestational age was only marginally not significant and may therefore be of interest. We thus fitted the model in both populations including this interaction term and found that it did not significantly change the estimated effects CF has on birthweight. As we could also not find a possible biological explanation for this phenomena we have not included this in the main article.  S.6 Interaction between CF and gestational age in the birthweight sub-model In the Danish population we found a significant interaction effect between CF and gestational age on birthweight (see Table S7), meaning that the effect of gestational age on birthweight differs between CF and non-CF babies. Taking into account this interaction term, the effects of CF and all covariates on gestational age remained unchanged, as did the effects of first-born status, sex, and maternal education on birthweight (see Table S9). Table S8 summaries the effects of gestational age and the direct and indirect effects of CF on birthweight when taking into account the interaction term (see below for details on the derivation of the direct and indirect effects). The direct and indirect effects of CF are comparable to the results when no interaction effect between CF and gestational age is taken into account.

Calculation of direct and indirect effects from the regression parameters when there is an exposuremediator interaction
The information given in this section is a restatement of previous findings. For more details and the derivation of the estimators, see [1,2].
The estimation of direct and indirect affects requires four key assumptions: 1) No unmeasured exposure-outcome confounding 2) No unmeasured mediator-outcome confounding 3) No unmeasured exposure-mediator confounding 4) No variable exists, that is affected by the exposure and confounds the mediator-outcome relationship Under these assumptions, the natural direct and indirect effect are identified and can be estimated as follows. Let Y denote the outcome of interest, A the exposure, M the potential mediator and C the baseline covariates. A linear regression of the outcome Y on the exposure, mediator and covariates including an exposure-mediator interaction is then given by [ | , , ] = 0 + 1 + 2 + 3 + 4 ′ .
A linear regression of the mediator on the exposure and the baseline covariates is The natural direct and indirect effect are then given by where and * are two different levels of exposure; in our example =1 and * =0 indicate CF and no CF, respectively. Note that when there is no exposure-mediator interaction (i.e. when 3 = 0 ) then the direct effect is estimated by 1 and the indirect effect is estimated by 2 1 .
The estimated direct effect is dependent on baseline covariates. Table 8 below gives the direct effect at reference covariate levels, for females, and individuals with education level 6 (compared to males and education level 1, which are the reference levels). The estimates only vary negligibly. Table 9 gives the estimates for the remaining parameters.

One child per mother
The analyses including only one baby from each mother resulted in a slightly higher point estimate of the direct effect of CF on birthweight in Wales and slighter lower point estimate in Denmark, though the estimates were within the previously stated confidence limits. All other effects also remained consistent with the results presented previously, with the exception for first-born status the effect of which decreased in both populations. Tables S10 and S11 show the parameter estimates and associated standard errors found in the analysis. For comparison, the tables also contain the estimates and standard errors from the analysis shown in the main paper.

Additional covariates
Data on maternal smoking during pregnancy and age at birth were available on a subset of 119,712 individuals including 65 CF babies in Wales. In Denmark we had data on mode of delivery, diabetes during index pregnancy, and pre-eclampsia during index pregnancy in addition to maternal age at birth and smoking during pregnancy in 1,032,281 individuals including 257 CF babies. Tables S12 and S13 show the parameter estimates and associated standard errors from fitting the model to the subpopulation for whom the additional data were available. For comparison, the model was initially fitted to the same population without the additional covariates and then refitted adding in these covariates.
In Wales the estimates for the effects of CF on both gestational age and birthweight were lower in this sub-population than in the previously stated results but within the previously stated confidence limits.
There was no significant difference between the estimates for the effect of CF from the model with and without the adjustment for smoking and maternal age. The only variable affected was deprivation, the effect of which on birthweight decreased substantially after maternal smoking during pregnancy and maternal age at birth were adjusted for. This is unsurprising as there are strong correlations between all three variables.
In Denmark the estimates for the effects of CF on gestational age and birthweight remained consistent with previous results after adjustment for the additional factors. Similar to the results from the Welsh analysis, maternal education was the only covariate affected by the inclusion of the additional factors.

Sensitivity to misclassification of CF cases
In order to assess the potential impact of misclassification of CF cases on our results, we repeated the analyses using a more stringent criterion for CF cases. In Denmark, only those individuals who had a CF code as primary or supplementary diagnosis in the Danish National Patient Register and who had been admitted to hospital more than once were classified as having CF in this sensitivity analysis. This resulted in 379 CF cases out of 1,736,783 individuals. In Wales, we only classified those individuals with CF code in the Congenital Anomaly Register and Information Service has having CF. This lead to 181 individuals with CF out of 442,664 individuals. Tables S14 and S15 below give the parameter estimates and standard errors for the sensitivity analyses as well as the original analysis (control analysis) in Denmark and Wales, respectively. Table S16 gives the estimated direct, indirect and total effects of CF in the total population in Denmark and Wales, as well as the results from the original analysis for comparison.
In Denmark the estimated parameters and effect of CF on birthweight did not differ markedly in the sensitivity compared to the original analysis. In Wales, the point estimates for the total and the direct effect increased compared to the original analysis, whereas the indirect effect decreased slightly. The confidence intervals, however, were compatible with the results from the original analysis.   (-306.35 , -148.78) -210.08 (-281.97 , -141.5) -183.26 (-223.59, -113.1) -178.8 (-225.43 , -134.47) S.8 The probability of having low birthweight In our fitted model the probability for a baby to be born with low birthweight depends on its covariate values, c, and the model parameters, . Let ( | , ) denote the cumulative distribution function of birthweight for given sets of values of c and θ. Our best guess at the probability of low birth-weight for a given set of values for c is (2500| ,̂) where ̂ is the maximum likelihood estimate of θ. To allow for the uncertainty in ̂ we proceed as follows.
Draw an independent random sample of size 10 000 from the multivariate Normal sampling distribution of ̂. For each sampled value, θi say , calculate ( ) = (2500| , ) for each set of possible values of c. Our Monte Carlo estimates of the probability of low birth-weight are the sample means, q(c) say, of the qi(c). We carried out the above simulation study initially using a model which did not include an adjustment for gestational age and therefore captured the total effect of CF on birthweight. We then repeated the study using the model in the main article, which includes an adjustment for gestational age. We estimated the probabilities of low birthweight at gestational ages 35 weeks, 37 weeks and 39 weeks. This does not take into account that babies with CF are born earlier but comparing the probabilities with and without adjustment for gestational age shows that the difference between the probabilities of being born with low birthweight for CF and non-CF babies is not solely explained by differences in gestational age.
We repeated the simulation studies for all possible combinations of covariate values.
The results are given in Tables S18-S25 below.
The probability for CF babies to be born with low birthweight is between 1.3 and 1.8 and between 1.2 and 2.1 times that of non-CF babies in Wales and Denmark, respectively, and depends on sex, first-born status, deprivation and gestational age. The ratio between the probabilities for CF and non-CF babies to be born with low birthweight increases with increasing gestational age. For all of the combinations of sex, first born status and gestational age, the probability of being born with low birthweight decreases slightly with decreasing deprivation. This is the case for both, CF and non-CF babies.