The effect of mRNA Vaccination on Small Gestational Age
Test Report
Busenur Kizilaslan
The aim is to examine whether administration at least one dose of the mRNA-based vaccine in pregnancy is associated with shorter gestational age at birth. Data Summary
Garbage in, garbage out!
The most important thing is to understand what is the data structure, in this manner we need to ask a lot of questions to the data set.
Is the data properly defined?
Are there any outliers and missing observations?
The data set has 12590 observations and 20 variables. All variables are entered as numeric variables.
## 'data.frame': 12590 obs. of 20 variables:
## $ pin : num 1 2 3 4 5 6 7 8 9 10 ...
## $ vaccination : num 0 0 0 0 0 0 0 0 0 0 ...
## $ gestationalweekofvaccination: num NA NA NA NA NA NA NA NA NA NA ...
## $ sarscov2_infection : num 0 1 1 0 0 0 0 0 0 1 ...
## $ ibu_prepreg : num 0 0 0 0 0 0 0 0 0 0 ...
## $ paracet_prepreg : num 1 1 1 1 1 1 1 1 1 0 ...
## $ opioid_prepreg : num 0 0 0 0 1 0 0 0 0 0 ...
## $ diabetes : num 0 1 1 0 0 0 0 0 0 1 ...
## $ depression_severity : num 6 5.9 5.2 5.4 4.6 ...
## $ pain : num 0 0 0 1 0 0 0 0 0 0 ...
## $ headache : num 0 0 0 1 0 0 0 1 1 1 ...
## $ pelvicgirdlepain : num 0 1 0 0 1 0 1 1 1 0 ...
## $ smoking : num 0 NA 0 0 0 0 0 0 0 0 ...
## $ bmipp : num 25.4 33.1 27.9 25.6 20.8 ...
## $ age : num 33.5 32.3 34.3 32.1 32 ...
## $ parity : num 0 1 0 1 0 1 0 1 1 1 ...
## $ education : num 1 1 0 1 1 1 0 1 0 1 ...
## $ birthweight : num 4195 4001 4908 3697 4064 ...
## $ gestage : num 266 280 260 281 269 ...
## $ malform : num 0 0 0 0 0 0 0 0 0 0 ...Factor variables are fixed for the reliable analysis. Also, the data set has possible outliers and missing values that have to be examined.
## 'data.frame': 12590 obs. of 20 variables:
## $ pin : num 1 2 3 4 5 6 7 8 9 10 ...
## $ vaccination : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ gestationalweekofvaccination: num NA NA NA NA NA NA NA NA NA NA ...
## $ sarscov2_infection : Factor w/ 2 levels "0","1": 1 2 2 1 1 1 1 1 1 2 ...
## $ ibu_prepreg : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ paracet_prepreg : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 1 ...
## $ opioid_prepreg : Factor w/ 2 levels "0","1": 1 1 1 1 2 1 1 1 1 1 ...
## $ diabetes : Factor w/ 2 levels "0","1": 1 2 2 1 1 1 1 1 1 2 ...
## $ depression_severity : num 6 5.9 5.2 5.4 4.6 ...
## $ pain : Factor w/ 2 levels "0","1": 1 1 1 2 1 1 1 1 1 1 ...
## $ headache : Factor w/ 2 levels "0","1": 1 1 1 2 1 1 1 2 2 2 ...
## $ pelvicgirdlepain : Factor w/ 2 levels "0","1": 1 2 1 1 2 1 2 2 2 1 ...
## $ smoking : Factor w/ 2 levels "0","1": 1 NA 1 1 1 1 1 1 1 1 ...
## $ bmipp : num 25.4 33.1 27.9 25.6 20.8 ...
## $ age : num 33.5 32.3 34.3 32.1 32 ...
## $ parity : Factor w/ 2 levels "0","1": 1 2 1 2 1 2 1 2 2 2 ...
## $ education : Factor w/ 2 levels "0","1": 2 2 1 2 2 2 1 2 1 2 ...
## $ birthweight : num 4195 4001 4908 3697 4064 ...
## $ gestage : num 266 280 260 281 269 ...
## $ malform : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...Outliers
Outliers can have many causes, such as: measurement or input error, missing values, true outlier observation. There is no precise way to define and identify outliers in general because of the specifics of each dataset. Instead, researcher and an expert, must interpret the raw observations and decide whether a value is an outlier or not. The data set examined as univariate and multivariate perspective in order to create a road map.
Univariate Outlier Evaluation
Univariate outlier check is done with boxplot. It is seen that each variable has outliers both upper and lower level. (This is an interactive plot, you can add or exclude variables in a one click on variable label, and you can see the points and thresholds on the plot)
The outliers are examined. An observation can be observed as an outlier in more than one variable. For this reason, the intersection must be checked (7 intersecting observations were counted only once). Total number of outliers are equal to 458, 23 of these observations belong to the vaccinated observations. 435 of these observations belong to the non-vaccinated observations.
At this point, the important question is what is the rate of vaccinated and non-vaccinated observations in the data? The data set has 207 vaccinated, and 12383 non-vaccinated observations. When we compare each group within itself, it is seen that, in case of removing outliers from the data set, 3.64% of total observations are lost. Although this rate is small, it is a significant loss because the rate also equal to 11.11% of vaccinated and 3.51% of non-vaccinated observations.
Multivariate Outlier Evaluation
Multivariate outlier check is done by using spatial signs which is fast algorithm for identifying multivariate outliers in high-dimensional and/or large data sets. The computation of the distances is based on Mahalanobis distances.
The data set has 295 possible outliers from multivariate perspective. When we compare each group within itself, it is seen that, in case of removing outliers from the data set, %2.34 of total observations are lost. They are equal to 1.45% of vaccinated and 2.36% of non-vaccinated observations.
🎯 Decision
The decision of which outliers to be eliminated should be made together with the domain expert. In this case study, the intersection of outliers that is both univariate and multivariate possible outlier set are selected as final outliers.
In the final case, 14 of outliers are eliminated which belong to non-vaccinated observations.
Missing Values
After the outlier elimination, the missing values should be checked and examined. It can be seen that, \(98.25\%\) of gestational week of vaccination observation is missing. This rate also equal to the number of non-vaccinated observations. As expected, a non-vaccinated observation does not have a vaccination week information. For this reason, gestational week of vaccination variable is excluded from the data set before imputation.
| Missing Value(%) | |
|---|---|
| gestationalweekofvaccination | 98.2446386 |
| depression_severity | 0.5798253 |
| smoking | 1.0722796 |
| bmipp | 0.1191422 |
| education | 0.2779984 |
| gestage | 0.4289118 |
Under the assumption that data were missing at random (MAR), the missing values are imputed. For imputation, Generates Multivariate Imputations by Chained Equations (MICE) package is used that creates multiple imputations for multivariate missing data. The method is based on Fully Conditional Specification, where each incomplete variable is imputed by a separate model. In this study, m is selected as 5 because the substantive conclusions are unlikely to change as a result of raising m beyond \(m=5\) (Van Buuren 2018).
In the beginning of imputation step, the data set is splitted into two group which are vaccinated and non-vaccinated because of interactions. Each group is imputed and then combined the imputed data sets (Van Buuren 2018).
After the normality test, Bayesian linear regression is used for bmipp and birthweight variables which are normally distributed. Predictive mean matching is used for other variables for multiple imputation.
🎯 Decision
Except for the gestational week of vaccination variable, all missing observations are imputed.
Data Modifications
In this study, the association between vaccine and small gestational age at birth is examined. For this purpose, some of variables are converted for usage and some new variables are created.
At this point, gestage (in days) values are converted from day to week.
Gestatinal Week of Vaccination
As mentioned before, gestational week of vaccination variable has a lot of missing value because the data set has a lot of non-vaccinated observations. In order to use this important variable in the analysis both vaccinated and non-vaccinated group, the continuous variable converted to factor variable by using trimesters. This transformation also provides ease of interpretation.
| value | trimesters | meaning |
|---|---|---|
| 0 | NA | No vaccination |
| 1 | 0 - 13 weeks | vaccination in 1st trimester |
| 2 | 14 - 26 weeks | vaccination in 2nd trimester |
| 3 | 27 - 40 weeks | vaccination in 3rd trimester |
Determination of Small/Short Gestational Age (SGA)
Small for gestational age (SGA) newborns are those who are smaller in size than normal for the gestational age, most commonly defined as a weight below the 10th percentile (threshold) for the gestational age (MedlinePlus). In this study, SGA determination is done with the proposed table (Talge et al. 2014). Thus, a new factor variable gestatinal.age (\(SGA = 1\), \(AGA = 0\)) is generated using the birthweight and gestage variables. Also, the variable gestage (in days) is converted to week format for computational convenience.
Method
It is seen that, the vaccination variable has unbalanced groups as vaccinated and non-vaccinated. For this reason, inverse probability of treatment weighting (IPTW) is used to balance groups using a propensity score matching weight approach.
The association between vaccination and small gestational age at birth is examined with logistic regression because the gestational.age variable is binary. In this manner, gestatinal.age and vaccination variables are considered as response and explanatory variables, respectively. The logistic regression is applied both before and after IPTW for comparison purpose.
The Summary of Variables Before/After Inverse Probability of Treatment Weighting (IPTW)
In the IPTW method, the propensity score is defined as the probability of being vaccinated. It is obtained from a logistic regression model where the vaccination variable is considered as a binary dependent variable and the following list of covariates is considered as the independent variables.
## [1] "ibu_prepreg" "paracet_prepreg" "opioid_prepreg"
## [4] "diabetes" "depression_severity" "pain"
## [7] "headache" "pelvicgirdlepain" "smoking"
## [10] "bmipp" "age" "parity"
## [13] "education" "malform" "sarscov2_infection"Balance before and after IPTW assessed using the standardized mean difference (SMD) between vaccination groups. A SMD of greater that 0.1 is usually considered to indicate a significant imbalance(Austin 2009).
After the missing data imputation, 5 imputed data sets are obtained. In the next, firstly, we present results for the first imputation data sets (\(m = 1\)). Then, the combination of all imputed data set results are presented.
Unweighted distribution of baseline characteristics of the study population for \(m=1\).
## Stratified by vaccination
## 0 1 SMD
## n 12369 207
## ibu_prepreg = 1 (%) 3172 (25.6) 59 (28.5) 0.064
## paracet_prepreg = 1 (%) 10310 (83.4) 176 (85.0) 0.046
## opioid_prepreg = 1 (%) 1239 (10.0) 26 (12.6) 0.080
## diabetes = 1 (%) 1764 (14.3) 32 (15.5) 0.034
## depression_severity (mean (SD)) 4.99 (1.00) 5.70 (0.85) 0.762
## pain = 1 (%) 982 ( 7.9) 10 ( 4.8) 0.127
## headache = 1 (%) 3891 (31.5) 75 (36.2) 0.101
## pelvicgirdlepain = 1 (%) 6798 (55.0) 113 (54.6) 0.007
## smoking = 1 (%) 749 ( 6.1) 180 (87.0) 2.772
## bmipp (mean (SD)) 26.49 (3.12) 26.19 (3.05) 0.099
## age (mean (SD)) 32.09 (2.24) 32.00 (2.21) 0.039
## parity = 1 (%) 6218 (50.3) 69 (33.3) 0.349
## education = 1 (%) 9269 (74.9) 152 (73.4) 0.034
## malform = 1 (%) 566 ( 4.6) 26 (12.6) 0.288
## sarscov2_infection = 1 (%) 920 ( 7.4) 0 ( 0.0) 0.401It is concluded that 7 variables have a SMD of greater than 0.1.
Propensity Score Estimation
For \(m = 1\), IPTW performed for a set of the selected covariates using the propensity score. Logistic regression is fitted to estimate the probability of vaccination groups.
##
## Call: glm(formula = vaccination ~ ibu_prepreg + paracet_prepreg + opioid_prepreg +
## diabetes + depression_severity + pain + headache + pelvicgirdlepain +
## smoking + bmipp + age + parity + education + malform + sarscov2_infection,
## family = binomial(link = "logit"), data = merged.data.rev1)
##
## Coefficients:
## (Intercept) ibu_prepreg1 paracet_prepreg1
## -12.495992 0.213107 0.162699
## opioid_prepreg1 diabetes1 depression_severity
## 0.059400 1.271233 1.369380
## pain1 headache1 pelvicgirdlepain1
## -0.264455 0.188465 -0.110322
## smoking1 bmipp age
## 4.973338 -0.020595 -0.007185
## parity1 education1 malform1
## -0.931643 -0.193988 0.001348
## sarscov2_infection1
## -18.178769
##
## Degrees of Freedom: 12575 Total (i.e. Null); 12560 Residual
## Null Deviance: 2111
## Residual Deviance: 1035 AIC: 1067##
## Call:
## glm(formula = vaccination ~ ibu_prepreg + paracet_prepreg + opioid_prepreg +
## diabetes + depression_severity + pain + headache + pelvicgirdlepain +
## smoking + bmipp + age + parity + education + malform + sarscov2_infection,
## family = binomial(link = "logit"), data = merged.data.rev1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6360 -0.0782 -0.0448 -0.0245 4.1528
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -12.495992 1.616186 -7.732 1.06e-14 ***
## ibu_prepreg1 0.213107 0.191144 1.115 0.265
## paracet_prepreg1 0.162699 0.237279 0.686 0.493
## opioid_prepreg1 0.059400 0.261738 0.227 0.820
## diabetes1 1.271233 0.278083 4.571 4.84e-06 ***
## depression_severity 1.369380 0.111083 12.328 < 2e-16 ***
## pain1 -0.264455 0.385929 -0.685 0.493
## headache1 0.188465 0.179808 1.048 0.295
## pelvicgirdlepain1 -0.110322 0.172889 -0.638 0.523
## smoking1 4.973338 0.228490 21.766 < 2e-16 ***
## bmipp -0.020595 0.026802 -0.768 0.442
## age -0.007185 0.038240 -0.188 0.851
## parity1 -0.931643 0.180559 -5.160 2.47e-07 ***
## education1 -0.193988 0.195619 -0.992 0.321
## malform1 0.001348 0.275040 0.005 0.996
## sarscov2_infection1 -18.178769 488.240139 -0.037 0.970
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2110.8 on 12575 degrees of freedom
## Residual deviance: 1034.7 on 12560 degrees of freedom
## AIC: 1066.7
##
## Number of Fisher Scoring iterations: 19The matching weight method (Li and Greene 2013) is used for creating weights. The matching weight is defined as the smaller of the predicted probabilities of receiving or not receiving the treatment (vaccination) over the predicted probability of being assigned to the patient is actually in. After weighting, all the standardized mean differences are below 0.1.
## Stratified by vaccination
## 0 1 SMD
## n 165.1 175.1
## ibu_prepreg = 1 (%) 46.7 (28.3) 48.0 (27.4) 0.020
## paracet_prepreg = 1 (%) 138.1 (83.6) 148.2 (84.6) 0.027
## opioid_prepreg = 1 (%) 20.6 (12.5) 21.8 (12.5) <0.001
## diabetes = 1 (%) 22.7 (13.7) 19.9 (11.4) 0.071
## depression_severity (mean (SD)) 5.46 (0.84) 5.52 (0.76) 0.082
## pain = 1 (%) 7.2 ( 4.3) 8.7 ( 5.0) 0.029
## headache = 1 (%) 55.1 (33.4) 60.8 (34.7) 0.029
## pelvicgirdlepain = 1 (%) 91.2 (55.3) 96.9 (55.3) 0.002
## smoking = 1 (%) 137.8 (83.5) 148.1 (84.6) 0.030
## bmipp (mean (SD)) 26.05 (3.36) 26.11 (3.07) 0.017
## age (mean (SD)) 32.12 (2.32) 32.10 (2.18) 0.009
## parity = 1 (%) 59.2 (35.8) 61.3 (35.0) 0.018
## education = 1 (%) 122.8 (74.4) 129.7 (74.1) 0.006
## malform = 1 (%) 19.9 (12.1) 21.1 (12.1) 0.001
## sarscov2_infection = 1 (%) 0.0 ( 0.0) 0.0 ( 0.0) <0.001In the next table and figure, after and before IPTW results of baseline characteristics and SMD values of considered independent variables are presented.
## Unweighted
## Group No Vaccination Vacination SMD
## n 12369 207
## ibu_prepreg = 1 (%) 3172 (25.6) 59 (28.5) 0.064
## paracet_prepreg = 1 (%) 10310 (83.4) 176 (85.0) 0.046
## opioid_prepreg = 1 (%) 1239 (10.0) 26 (12.6) 0.080
## diabetes = 1 (%) 1764 (14.3) 32 (15.5) 0.034
## depression_severity (mean (SD)) 4.99 (1.00) 5.70 (0.85) 0.762
## pain = 1 (%) 982 ( 7.9) 10 ( 4.8) 0.127
## headache = 1 (%) 3891 (31.5) 75 (36.2) 0.101
## pelvicgirdlepain = 1 (%) 6798 (55.0) 113 (54.6) 0.007
## smoking = 1 (%) 749 ( 6.1) 180 (87.0) 2.772
## bmipp (mean (SD)) 26.49 (3.12) 26.19 (3.05) 0.099
## age (mean (SD)) 32.09 (2.24) 32.00 (2.21) 0.039
## parity = 1 (%) 6218 (50.3) 69 (33.3) 0.349
## education = 1 (%) 9269 (74.9) 152 (73.4) 0.034
## malform = 1 (%) 566 ( 4.6) 26 (12.6) 0.288
## sarscov2_infection = 1 (%) 920 ( 7.4) 0 ( 0.0) 0.401
## Weighted
## Group No Vaccination Vacination SMD
## n 165.1 175.1
## ibu_prepreg = 1 (%) 46.7 (28.3) 48.0 (27.4) 0.020
## paracet_prepreg = 1 (%) 138.1 (83.6) 148.2 (84.6) 0.027
## opioid_prepreg = 1 (%) 20.6 (12.5) 21.8 (12.5) <0.001
## diabetes = 1 (%) 22.7 (13.7) 19.9 (11.4) 0.071
## depression_severity (mean (SD)) 5.46 (0.84) 5.52 (0.76) 0.082
## pain = 1 (%) 7.2 ( 4.3) 8.7 ( 5.0) 0.029
## headache = 1 (%) 55.1 (33.4) 60.8 (34.7) 0.029
## pelvicgirdlepain = 1 (%) 91.2 (55.3) 96.9 (55.3) 0.002
## smoking = 1 (%) 137.8 (83.5) 148.1 (84.6) 0.030
## bmipp (mean (SD)) 26.05 (3.36) 26.11 (3.07) 0.017
## age (mean (SD)) 32.12 (2.32) 32.10 (2.18) 0.009
## parity = 1 (%) 59.2 (35.8) 61.3 (35.0) 0.018
## education = 1 (%) 122.8 (74.4) 129.7 (74.1) 0.006
## malform = 1 (%) 19.9 (12.1) 21.1 (12.1) 0.001
## sarscov2_infection = 1 (%) 0.0 ( 0.0) 0.0 ( 0.0) <0.001This analysis is conducted before and after IPTW for \(m = 1\).
The logistic regression results for the main model (gestation.age and vaccination variables) before IPTW are given as follows.
##
## Call:
## glm(formula = (gestational.age == 1) ~ vaccination, family = binomial(link = "logit"),
## data = merged.data.rev1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.1709 -0.0685 -0.0685 -0.0685 3.4801
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.0533 0.1859 -32.560 < 2e-16 ***
## vaccination1 1.8338 0.6106 3.003 0.00267 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 446.24 on 12575 degrees of freedom
## Residual deviance: 440.52 on 12574 degrees of freedom
## AIC: 444.52
##
## Number of Fisher Scoring iterations: 9The logistic regression results for the main model after IPTW results are given as follows.
##
## Call:
## glm(formula = (gestational.age == 1) ~ vaccination, family = quasibinomial(),
## data = merged.data.rev1, weights = ps_weights)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.17543 -0.00896 -0.00509 -0.00281 2.89200
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.4077 0.1174 -37.544 <2e-16 ***
## vaccination1 0.2413 0.1551 1.556 0.12
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasibinomial family taken to be 0.02705635)
##
## Null deviance: 49.253 on 12575 degrees of freedom
## Residual deviance: 49.187 on 12574 degrees of freedom
## AIC: NA
##
## Number of Fisher Scoring iterations: 7Final Analysis
In this part, the analysis conducted with all imputed data sets (m is selected 5) after IPTW, and the results are combined with pool function.
## Class: mipo m = 5
## term m estimate ubar b t dfcom df riv lambda
## 1 (Intercept) 5 -6.053305 0.006912759 0 0.006912759 62878 62859.83 0 0
## 2 vaccination1 5 1.833798 0.074559817 0 0.074559817 62878 62859.83 0 0
## fmi
## 1 3.18153e-05
## 2 3.18153e-05## [1] "Odd ratio before IPTW: 6.26"The effect of vaccination variable on the response variable gestational.age is explained using an odds ratio (OR). Since \(OR>1\), vaccinated observations has a higher odds of having the SGA compared with the non-vaccinated group.
Based on the above results, since OR before IPTW is 6.26, vaccinated observations have more risk for SGA event than non-vaccinated observations. This result based on imbalanced data set.
In the next, the analysis conducted with all imputed data sets (m is selected 5) after IPTW, and the results are combined with pool function.
## Class: mipo m = 5
## term m estimate ubar b t dfcom df riv lambda
## 1 (Intercept) 5 -4.4160371 0.002778721 0 0.002778721 62878 62859.83 0 0
## 2 vaccination1 5 0.2518516 0.004828786 0 0.004828786 62878 62859.83 0 0
## fmi
## 1 3.18153e-05
## 2 3.18153e-05## [1] "Odd ratio after IPTW: 1.29"Based on the above results, since OR after IPTW is 1.29, vaccinated observations have slightly more risk for SGA event than non-vaccinated observations. This result based on balanced data set. Hence, it is observed that OR decreases significantly using IPTW.
Limitations
The number of vaccinated observations are limited, and also observations were predominantly vaccinated during the second and third trimesters.
In the data set, previous history of preterm or SGA at birth were not available, it can be important for prosperity. Family-based studies showed that gestational age at birth is partially (from 25% to 40%) determined by genetic factors (Clausson, Lichtenstein, and Cnattingius 2000).
Because of the time constraint, a lot of method could not be applied such as relative risk ratios, sensitivity analysis, possible machine learning techniques.
The lack of domain knowledge for outlier and missing value evaluation.
Packages and Details
In this study, R statistical software(R Core Team 2022) (version 4.2.0) is used. The interactive report is prepared with R Markdown. The packages used in the study are listed below.
readr, tidyverse, magrittr, naniar, mice, dplyr, GGally, finalfit, usethis, devtools, psych, ltm, VIM, plotly, nortest, car, Hmisc, purrr, reshape2, MVN, mvoutlier, kableExtra, grid, shadowtext, tableone, Matching, survey, ggplot2🚀 References
Austin, Peter C. 2009. “Balance Diagnostics for Comparing the Distribution of Baseline Covariates Between Treatment Groups in Propensity-Score Matched Samples.” Statistics in Medicine 28 (25): 3083–3107.
Clausson, Britt, Paul Lichtenstein, and Sven Cnattingius. 2000. “Genetic Influence on Birthweight and Gestational Length Determined by Studies in Offspring of Twins.” BJOG: An International Journal of Obstetrics & Gynaecology 107 (3): 375–81.
Li, Liang, and Tom Greene. 2013. “A Weighting Analogue to Pair Matching in Propensity Score Analysis.” The International Journal of Biostatistics 9 (2): 215–34.
R Core Team. 2022. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
Talge, Nicole M, Lanay M Mudd, Alla Sikorskii, and Olga Basso. 2014. “United States Birth Weight Reference Corrected for Implausible Gestational Age Estimates.” Pediatrics 133 (5): 844–53.
Van Buuren, S. 2018. Flexible Imputation of Missing Data. CRC press. https://stefvanbuuren.name/fimd/.