---
title: "Among U.S. children aged 0–17, is low birth weight associated with increased odds of an ever asthma diagnosis, after adjusting for child age, sex, race/ethnicity, household income, and secondhand smoke exposure?"
author:
- name: Javier Diaz Collante
email: jdiazcollant@umass.edu
- name: Rachel Huselid,
email: rhuselid@schoolph.umass.edu,
- name: Anjelica Martinez
email: anjelicamart@umass.edu
affiliation: Department of Biostatistics & Epidemiology
- name: "Created on: June 28, 2026"
author-title: "Author"
affiliation-title: "University of Massachusetts - Amherst"
abstract-title: Purpose
abstract: This notebook is for the analysis portion of our EPI 690A final project.
published-title: "Date Updated"
format:
html:
embed-resources: true
anchor-sections: true
code-fold: show
code-tools: true
fig-width: 6
fig-height: 4
code-block-bg: "#f1f3f5"
code-block-border-left: "#31BAE9"
mainfont: Source Sans Pro
theme: journal
toc: true
toc-depth: 3
toc-location: left
captions: true
table-captions: true
---
# Introduction
Asthma is one of the most common chronic diseases of childhood in the United States and is a leading cause of emergency department visits, hospitalizations, missed school days, and reduced quality of life in children. Although genetic predisposition contributes to asthma risk, early-life factors have also been recognized as important determinants of many chronic diseases. Low birth weight, often resulting from preterm birth or other factors, has been associated with underdeveloped lung development and increased susceptibility to respiratory disease later in childhood. However, because childhood asthma is also influenced by demographic, socioeconomic, and environmental factors, it is important to evaluate whether the relationship between low birth weight and asthma persists after accounting for these potential confounders.
Using data from the 2023 [National Survey of Children's Health (NSCH)](https://mchb.hrsa.gov/data-research/national-survey-childrens-health) a nationally representative cross-sectional survey of U.S. children aged 0–17 years, this project will examine whether low birth weight is associated with the likelihood of ever receiving an asthma diagnosis. Specifically, the research question is: among U.S. children aged 0–17 years, is low birth weight associated with increased odds of ever having an asthma diagnosis after adjusting for age, sex, race, household income, and secondhand smoke exposure? We hypothesize that children with a history of low birth weight will have a higher likelihood of ever being diagnosed with asthma compared with children of normal birth weight, even after controlling for these possible confounders.
# Methods
## Study population
The [2023 National Survey of Children's Health (NSCH)](www2.census.gov/programs-surveys/nsch/technical-documentation/methodology/2023-NSCH-Methodology-Report.pdf) survey population focused on non-institutionalized children in the United States ages 0–17. The sample size nationally was 55,162 children, and the state sample size ranged from 710 to 4,696 children. Participants were randomly sampled by household and contacted by mail directly to determine whether the household had one or more children under the age of 18. If the household was determined to have more than one child, one child was chosen at random to be the subject of the survey. Children with special health care needs and children between the ages of 0 and 5 were oversampled in the survey. A total of nine states and one metropolitan area (California, Colorado, Nebraska, New York, Ohio, Oregon, Pennsylvania, Tennessee, Wisconsin, and Atlanta, Georgia) provided oversampling funding to support additional interviews and allow reporting for specific population groups, conditions, or localities in these locations. The survey data were weighted to represent the population of non-institutionalized children between the ages of 0 and 17 both nationally and by state. The overall weighted response rate of the survey was 35.8%.
The survey data were collected via online forms or a physical paper version. Each household was mailed an invitation in which the adult of the house familiar with the child's health and health care was asked to complete a short screener questionnaire (via web or paper). The questionnaire asked participants to identify whether there were children in the household between the ages of 0 and 17 and to report their ages. If a child was in the home and the participant wished to complete the survey online, they were directed to a link with more detailed age-specific questions for the one randomly selected child. The survey was provided in both English and Spanish. Participants also had the option to use telephone assistance.
## Exposure
The primary exposure was birth weight status, defined using the variable `BIRTHWT_L`, which classifies children as having low birth weight (less than 2,500 grams) or normal birth weight. Low birth weight was treated as a binary variable, with normal birth weight as the reference group. This variable is provided as a pre-derived field in the NSCH public use file and required no additional recoding.
## Outcome
The primary outcome was ever having received an asthma diagnosis, defined using the variable `K2Q40A`, which asks whether a doctor or other health care provider has ever told the respondent that the child has asthma. This was treated as a binary outcome, with children never diagnosed with asthma serving as the reference group. We initially considered distinguishing children with current versus previous asthma diagnoses using the companion variable `K2Q40B`, but ultimately used the single binary ever asthma variable for all descriptive and modeling purposes, since it captures any lifetime occurrence of the diagnosis and avoids ambiguity in how to classify children whose asthma has resolved.
## Covariates
Covariates were selected based on their established or plausible relationship to both birth weight and childhood asthma risk, and on the completeness of their measurement across the full 0 to 17 age range. The fully adjusted model included child age, sex, race, preterm birth status, familial poverty ratio, highest level of parental education, insurance type, and household smoker status (secondhand smoke exposure). The research question names the primary confounders of interest (age, sex, race/ethnicity, household income, and secondhand smoke exposure) while the fully adjusted model additionally accounts for preterm birth, parental education, and insurance type, each an established correlate of both low birth weight and childhood asthma. Household income was operationalized as the familial poverty ratio (FPL). Age was included in the overall adjusted model but was excluded from the covariate set in age stratified analyses, since age itself defines the stratification.
Vaping exposure inside the home and allergy history were described in the study population but were not included in the adjusted model. These variables were treated separately because our adjustment strategy prioritized demographic and socioeconomic covariates with minimal missingness, and because including additional covariates would have further reduced the analytic sample available for the fully adjusted model. Body mass index category was considered but excluded from all models, since this measure is only collected for children ages 6 to 17 and is therefore missing for the majority of younger children in the sample. In addition, because body mass index is measured cross sectionally at the time of the survey, it cannot be used to establish whether excess weight preceded or followed an asthma diagnosis.
## Statistical Methods
Within this population, our analytic sample was further restricted to children with non-missing responses for the primary exposure and outcome variables, since these two variables define the research question. A flow diagram will report the sample size at each stage of this restriction, from the total NSCH respondent pool through the final analytic sample, along with the number of children excluded at each step. Missing covariate data was not used to exclude children from the overall analytic sample or from unadjusted analyses; rather, covariate missingness was allowed to reduce the sample size only within models that included the affected covariate.
We retained the full pediatric age range of 0 to 17 years for our primary analysis, since restricting the sample by age would have limited the birth weight information available for the youngest children, who are closest in time to their birth history. However, because asthma diagnoses accumulate over childhood and younger children have had less opportunity to be diagnosed, we conducted a parallel analysis stratified by age group to evaluate whether the association between birth weight and asthma differed across developmental stages.
Descriptive statistics were generated for the exposure, outcome, and all covariates, stratified by asthma status, with means and standard deviations reported for continuous variables and frequencies and percentages reported for categorical variables. Bivariate comparisons between birth weight status and childhood characteristics were assessed using chi-square tests for categorical variables.
The association between birth weight status and ever having an asthma diagnosis was estimated using logistic regression, and results are presented as both prevalence differences and odds ratios with accompanying 95% confidence intervals, since absolute and relative measures each provide distinct and clinically relevant information. Prevalence differences were estimated as average marginal effects, averaging the difference in predicted asthma probability across all observations in the sample. We used this approach rather than evaluating the contrast at a single representative covariate profile, which yields wider standard errors and is more sensitive to the choice of profile values. Models were built in a staged sequence to account for the effect of missing covariate data on sample size. The first model was unadjusted. The second model adjusted for child age alone, since age was fully observed and allowed us to assess confounding by age before introducing covariates with missing values. The third model was fully adjusted for sex, race, preterm birth, familial poverty ratio, parental education, household smoker status, and insurance type. The analytic sample size is reported for each stage of this sequence.
Finally, the fully adjusted model was repeated separately within four age strata, infants and toddlers (0 to 2 years), preschool age (3 to 5 years), middle childhood (6 to 12 years), and adolescents (13 to 17 years), to evaluate whether the association between birth weight and asthma diagnosis was consistent across childhood or concentrated within a particular developmental period.
------------------------------------------------------------------------
# Codebook
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| | | | |
+========================+=============================+============================================================+==========================================================================================================+
| **New Variable** | **Original Variable** | **Label** | **Values** |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `age` | `SC_AGE_YEARS` | Age of selected child (years) | |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `sex` | `SC_SEX` | Sex of selected child | 1 = Male\ |
| | | | 2 = Female |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `race` | `SC_RACE_R` | Race of selected child | 1 = White alone\ |
| | | | 2 = Black or African American alone\ |
| | | | 3 = American Indian or Alaska Native alone\ |
| | | | 4 = Asian alone\ |
| | | | 5 = Native Hawaiian and Other Pacific Islander alone\ |
| | | | 7 = Two or More Races |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `hispanic` | `SC_HISPANIC_R` | Hispanic or Latino origin of selected child | 1 = Yes\ |
| | | | 2 = No |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `birth_weight_status` | `BIRTHWT` | Birth weight status | 1 = Very low birth weight (less than 1,500g)\ |
| | | | 2 = Low birth weight (less than 2,500g)\ |
| | | | 3 = Not low birth weight |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `birth_weight_ver_low` | `BIRTHWT_VL` | Birth weight is very low (\<1500g) | 1 = Yes\ |
| | | | 2 = No |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `birth_weight_low` | `BIRTHWT_L` | Birth weight is low (\<2500g) | 1 = Yes\ |
| | | | 2 = No |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `asthma` | `K2Q40A` | Ever diagnosed with asthma | 1 = Yes\ |
| | | | 2 = No |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `born_early` | `K2Q05` | Born 3 or more weeks before due date | 1 = Yes\ |
| | | | 2 = No |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `poverty` | `FPL_I1` | Family poverty ratio, first implicate | 50 or less - 400 or more |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `education` | `HIGRADE_TVIS` | Highest level of education among reported adults, Detailed | 1 = Less than high school\ |
| | | | 2 = High school (including vocational, trade, or business school)\ |
| | | | 3 = Some college or Associate Degree\ |
| | | | 4 = College degree or higher |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `insurance_type` | `INSTYPE` | Insurance type | 1 = Public only (government assistance)\ |
| | | | 2 = Private only (privately purchased, including through ACA marketplace, through employer, or TRICARE)\ |
| | | | 3 = Private and public\ |
| | | | 5 = Not insured |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `cigarettes` | `K9Q40` | Anyone in household use cigarettes | 1 = Yes\ |
| | | | 2 = No |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `vape` | `VAPE` | Vape/E-Cigarettes inside of home | 1 = Yes\ |
| | | | 2 = No |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `allergies` | `ALLERGIES` | Ever diagnosed with allergies | 1 = Yes\ |
| | | | 2 = No |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| `age_cats`\* | Created from `age` variable | Age group | Infants/Toddlers (0-2)\ |
| | | | Preschool (3-5)\ |
| | | | Middle childhood (6-12)\ |
| | | | Teenagers (13-17) |
+------------------------+-----------------------------+------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
~Codebook provided by the 2023 National Survey of Children's Health (NSCH)~\
~\*This variable were created in 01_epi690a_final_project_DM.qmd~
------------------------------------------------------------------------
# Setup
Load relevant packages and setup code to help with HTML rendering.
```{r}
#| label: load packages
#| code-summary: "Packages"
# Packages Used
pacman::p_load(
dplyr, # data manipulation
forcats, # tools for working with categorical variables
here, # file paths relative to R project root folder
rio, # import/export of many types of data
tidyverse, # includes many packages for tidy data wrangling
Hmisc, # includes many functions in Harrellverse
data.table, # (alternative) faster than tidyverse
qreport, # useful for formatting in quarto
sparkline, # inline interactive plots
lubridate, # simplifies working with dates
janitor, # tables and data cleaning
skimr, # summary statistics
gtsummary, # making descriptive and statistical tables
rstatix, # quickly run statistical tests and summaries
labelled, # labels variables
naniar, # assessing missing data
datadictionary, # creates data dictionaries
haven, # read/handle labelled data (e.g. SPSS/Stata/SAS files)
marginaleffects, # predictions, comparisons, and hypothesis tests
modelsummary,
broom,
stringr,
gt,
tibble
)
```
```{r}
#| label: setup
#| code-summary: "Setup"
# Source: Frank Harrell https://hbiostat.org/rflow/
# Make base graphics look better:
spar <- function(bot=0, left=0, top=0, rt=0)
par(mar=c(3.25 + bot, 5 + left, 0.5 + top, 0.5 * rt),
lwd=1.75, mgp=c(2.0, 0.475, 0), tcl=-0.4, xpd=FALSE, ps=14,
cex.lab=1.15, cex.axis=0.8)
# Set abbreviations for chunk option names
knitr::set_alias(w = 'fig.width', h = 'fig.height')
options(prType='html') # for certain Hmisc and rms functions
# To automatically sense which output format is being created and
# create a character string that will work for both `html` and `LaTeX`.
# For `LaTeX`, a boxed note in the body of the document will appear.
ishtml <- knitr::is_html_output()
mNote <- if(ishtml) '.column-margin' else '.callout-note appearance="minimal"'
#FHarrell: "Note that to initialize javascript jQuery dependencies
# we must include sparkline::sparkline(0) somewhere in the report
# before creating the first sparkline output."
sparkline::sparkline(0)
```
# Load Data
Data was collected from the canvas website and originally created by the National Survey of Children's Health (NSCH). The data were cleaned and prepared in the data management notebook `01_epi690a_final_project_DM.qmd` (and the resulting processed dataset `nsch2023_processed.rdata` is loaded below.
```{r}
#| label: load data
#| code-summary: "Load Data"
# Import data
df <- import(here("data", "processed", "nsch2023_processed.rdata"))
# Review data structure
head(df)
```
```{r}
# View a data dictionary of df (variable types, levels, and labels)
contents(df)
```
# Descriptive Statistics
To start, we created Table 1, which summarizes the characteristics of the participants by birth weight status. For each variable we report frequencies and percentages for categorical measures and means, medians, and ranges for continuous measures, allowing us to describe the sample and compare demographic, socioeconomic, and health characteristics across normal, low, and very low birth weight groups before conducting any formal analysis.
## Table 1: Characteristics by Low Birth Weight Status
```{r}
#| label: descriptives table
#| message: false
#| warning: false
#| code-summary: Table 1
# Creates a descriptive statistics table
tbl_summary(
df,
include = c(age, age_cats, sex, race, hispanic, born_early, poverty,
education, insurance_type, asthma, cigarettes, vape, allergies),
type = all_continuous() ~ "continuous2",
statistic = all_continuous() ~ c("{mean} ({sd})",
"{median} ({p25}-{p75})",
"{min}-{max}"),
percent = "column",
by = birth_weight_low,
missing = "always",
missing_text = "Missing",
missing_stat = "{N_miss} ({p_miss}%)"
) |>
add_overall() |>
add_n() |>
modify_header(label = "**Participant Characteristics**") |>
modify_caption("**Table 1: Characteristics by low birth weight Status**") |>
modify_spanning_header(c("stat_1", "stat_2") ~ "**Low Birth Weight**") |>
add_variable_group_header(
header = "Environmental Exposures",
variables = c(cigarettes, vape, allergies)
) |>
modify_bold(
columns = label,
rows = (row_type == "label" & !variable %in% c("cigarettes", "vape", "allergies")) |
label == "Environmental Exposures"
)
```
## Age Distribution of Selected Children Across Households
The next thing we made was a histogram of the age distribution of the selected children across households. This showed how the sample was spread across the full 0–17 age range, with a notable peak among the youngest children (ages 0–2), reflecting the survey's oversampling of children aged 0–5. The remaining ages were fairly evenly represented, confirming that our analytic sample included children from across the pediatric age range rather than being concentrated in any single developmental stage.
```{r}
#| label: age histogram
#| code-summary: "Children's Age Histogram"
# Histogram of Age
ggplot(df, aes(x = age)) +
geom_histogram(bins = 15, fill = "lightblue", color = "white") +
labs(title = "Age Distribution of Selected Children Across Households",
x = "Age (Years)",
y = "Number of children",
caption = "Data from 2023 National Survey of Children's Health (NSCH)") +
theme_minimal() +
theme(
plot.title = element_text(size = 11,
face = "bold",
margin = margin(b = 15),
hjust = 0.5),
axis.title.x = element_text(margin = margin(t = 10), size = 9),
axis.title.y = element_text(margin = margin(r = 10), size = 9),
plot.caption = element_text(
size = 8,
color = "darkgray",
margin = margin(t = 15, b = 10, unit = "pt")
))
```
## Distribution of Age by Age Group
To confirm that our age categories behaved as intended, we created a boxplot showing the distribution of age within each of the four age groups. Each group spanned its expected range with no overlap between them, verifying that children were correctly partitioned into infants and toddlers (0–2), preschool (3–5), middle childhood (6–12), and adolescents (13–17). This grouping formed the basis for our later age-stratified analysis.
```{r}
# Boxplot of age within group
ggplot(df, aes(x = age_cats, y = age)) +
geom_boxplot() +
labs(title = "Distribution of Age by Age Group",
x = "Age Groups",
y = "Age (Years)",
caption = "Data from 2023 National Survey of Children's Health (NSCH)") +
theme_minimal() +
theme(
plot.title = element_text(size = 12, face = "bold", hjust = 0.5),
plot.subtitle = element_text(size = 10, color = "gray30", hjust = 0.5),
axis.text = element_text(size = 9),
axis.title.x = element_text(size = 9),
axis.title.y = element_text(size = 9),
legend.text = element_text(size = 9),
legend.title = element_text(size = 9),
legend.position = "none",
plot.caption = element_text(size = 8, color = "darkgray")
)
```
## Asthma Prevalence by Birth Weight and Age
Next, we created a bar chart to see how crude asthma prevalence differed by birth weight status across the four age groups. According to the bar chart, within every age group, low-birth-weight children had a higher prevalence of ever being diagnosed with asthma than normal-birth-weight children, ranging from 5.3% versus 2.3% among infants/toddlers (0-2 years old) to 19.7% versus 14.3% among teenagers (13-17 years old). Prevalence also rose steadily with age in both groups, consistent with asthma diagnoses accumulating over childhood. This descriptive pattern set up our regression analysis, which tested whether the birth-weight gap persisted after adjusting for demographic and socioeconomic factors.
```{r}
df |>
filter(!is.na(birth_weight_low), !is.na(asthma), !is.na(age_cats)) |>
group_by(age_cats, birth_weight_low) |>
summarise(pct = 100 * mean(asthma == "Yes"), .groups = "drop") |>
ggplot(aes(x = age_cats, y = pct, fill = birth_weight_low)) +
geom_col(position = position_dodge(width = 0.8), width = 0.7) +
geom_text(aes(label = paste0(round(pct, 1), "%")),
position = position_dodge(width = 0.8),
vjust = -0.4, size = 3) +
scale_fill_manual(values = c("No" = "steelblue", "Yes" = "lightblue"),
labels = c("Normal", "Low birth weight")) +
labs(title = "Asthma Prevalence by Birth Weight and Age Group",
subtitle = "Low-birth-weight children have higher prevalence at every age",
x = NULL, y = "% ever diagnosed with asthma", fill = "Birth weight",
caption = "Data from 2023 National Survey of Children's Health (NSCH)") +
theme_minimal(base_size = 16) +
theme(
plot.title = element_text(size = 12, face = "bold", hjust = 0.5),
plot.subtitle = element_text(size = 10, color = "gray30", hjust = 0.5),
axis.text = element_text(size = 9),
axis.title.y = element_text(size = 9),
legend.text = element_text(size = 9),
legend.title = element_text(size = 9),
legend.position = "top",
plot.caption = element_text(size = 8, color = "darkgray")
)
```
------------------------------------------------------------------------
# Table 2: Unadjusted and adjusted association between low birth weight and ever having an asthma diagnosis
To formally test the association between low birth weight and asthma, we fit a staged sequence of logistic regression models, presented in Table 2. The first model was unadjusted, the second adjusted for child age, and the third adjusted for the full set of covariates (sex, race, preterm birth, familial poverty ratio, parental education, insurance type, and household smoker status). For each model we report both the odds ratio and the absolute prevalence difference with 95% confidence intervals, since the two measures convey complementary information about the relative and absolute magnitude of the association.
Low birth weight was significantly associated with ever having an asthma diagnosis across all three models. The unadjusted odds ratio was 1.67 (95% CI 1.52–1.82) and was essentially unchanged after adjusting for age (OR 1.67, 95% CI 1.53–1.83), indicating that age did not confound the relationship. After full adjustment, the association attenuated to an odds ratio of 1.21 (95% CI 1.08–1.35) but remained statistically significant, indicating that much of the crude association was explained by demographic and socioeconomic factors while an independent association persisted; this pattern of attenuation across the three models is shown graphically in the appendix. On the absolute scale, low-birth-weight children had roughly a 5 percentage-point higher probability of asthma than normal-birth-weight children.
```{r}
tbl <- tribble(
~birth_weight, ~events, ~unadj_pd, ~unadj_or, ~age_pd, ~age_or, ~all_pd, ~all_or,
"Normal birth weight", "4,358 (9.1)", "Reference", "1.00", "Reference", "1.00", "Reference", "1.00",
"Low birth weight", "661 (14.3)", "5.2 (4.1 to 6.2)", "1.67 (1.52–1.82)", "5.1 (4.1 to 6.1)", "1.67 (1.53–1.83)", "1.68 (0.66–2.71)", "1.21 (1.08–1.35)",
"Missing", "190 (8.7)", "", "", "", "", "", ""
)
tbl |>
gt(rowname_col = "birth_weight") |>
# Row-group label that spans the exposure rows
tab_row_group(
label = md("**Exposure = birth weight category**"),
rows = everything()
) |>
# Top-level spanning headers
tab_spanner(label = "Events, N=52,935", columns = events) |>
tab_spanner(label = "Unadjusted, N=52,532", columns = c(unadj_pd, unadj_or)) |>
tab_spanner(label = "Adjusted for age, N=52,532", columns = c(age_pd, age_or)) |>
tab_spanner(label = "Adjusted for all variables,* N=50,580",
id = "all_var", columns = c(all_pd, all_or)) |>
# Sub-column labels
cols_label(
events = "",
unadj_pd = "Prevalence difference % (95% CI)",
unadj_or = "Odds ratio (95% CI)",
age_pd = "Prevalence difference % (95% CI)",
age_or = "Odds ratio (95% CI)",
all_pd = "Prevalence difference % (95% CI)",
all_or = "Odds ratio (95% CI)"
) |>
cols_align(align = "center", columns = -birth_weight) |>
# The asterisk footnote
tab_footnote(
footnote = "Abbreviations, CI = Confidence interval",
locations = cells_column_spanners(spanners = "all_var")
) |>
tab_footnote(
footnote = "Unadjusted and adjusted results were estimated using logistic regression",
locations = cells_stub(rows = birth_weight == "Low birth weight")
) |>
tab_footnote(
footnote = "Adjusted for age, sex, race, preterm birth, familial poverty ratio, education level of adults, insurance type, andhousehold smoker status",
locations = cells_stub(rows = birth_weight == "Low birth weight")
)
```
## Logistic Regression
Having summarized the results in Table 2, we present the full logistic regression models below. Each model is shown in a staged sequence (unadjusted, age-adjusted, and fully adjusted) with the complete model output and the odds ratios and confidence intervals for every term.
We used logistic regression because our outcome, ever having an asthma diagnosis, is binary. To separate the effect of low birth weight from the influence of other factors, we built the models in a staged sequence rather than fitting a single model. The first model was unadjusted, estimating the crude association between low birth weight and asthma. The second added child age alone, since age was fully observed and allowed us to check whether it confounded the relationship before introducing covariates with missing data. The third model was fully adjusted for sex, race, preterm birth, familial poverty ratio, parental education, insurance type, and household smoker status. Building the models in stages let us see how the association changed as covariates were added and to account for the effect of missing covariate data on the sample size at each step.
### Model 1: Unadjusted
```{r}
# Relevel binary variables so "No" is the reference category
# This makes every odds ratio read in the intuitive direction (exposed vs. unexposed).
df$birth_weight_low <- relevel(df$birth_weight_low, ref = "No") # OR = low vs normal birth weight
df$born_early <- relevel(df$born_early, ref = "No") # OR = preterm vs full-term
df$asthma <- relevel(df$asthma, ref = "No") # model P(asthma = Yes)
df$cigarettes <- relevel(df$cigarettes, ref = "No") # OR = smoker vs non-smoker household
```
```{r}
# Model 1: unadjusted asthma on low birth weight
model1 <- glm(asthma ~ birth_weight_low, data = df, family = binomial)
# full model output (coefficients, SEs, fit stats)
summary(model1)
# odds ratio + 95% CI
tidy(model1, exponentiate = TRUE, conf.int = TRUE)
```
***Interpretation:***
Model 1 is unadjusted and shows a significant association between birth weight status and asthma (OR = 1.67, 95% CI: 1.52–1.82, p \< 0.001). Since the reference level is normal birth weight, this odds ratio compares low-birth-weight children to normal-birth-weight children directly. Low-birth-weight children had about 1.67 times the odds of an asthma diagnosis compared to normal-birth-weight children. This finding is consistent with the crude prevalences observed in the sample, 14.3% of low-birth-weight children had an asthma diagnosis compared to 9.1% of normal-birth-weight children, and it supports the study's underlying hypothesis.
### Model 2: Adjusted for Age
```{r}
# Model 2: asthma on low birth weight, age-adjusted
model2 <- glm(asthma ~ birth_weight_low + age, data = df, family = binomial)
# full model output (coefficients, SEs, fit stats)
summary(model2)
# odds ratios + 95% CIs for every term
tidy(model2, exponentiate = TRUE, conf.int = TRUE)
```
**Interpretation:**
Model 2 adds child age as a covariate. After adjusting for age, the birth weight association is essentially unchanged, OR = 1.67 (95% CI: 1.53–1.83, p \< 0.001), nearly identical to Model 1. Low-birth-weight children continued to have about 1.67 times the odds of an asthma diagnosis compared to normal-birth-weight children. Age itself was also significantly associated with asthma, OR = 1.10 per year (95% CI: 1.09–1.11, p \< 0.001), meaning each additional year of age was associated with roughly 10% higher odds of an ever asthma diagnosis, consistent with the fact that diagnoses accumulate as children get older. Because the birth weight odds ratio remained stable after adjusting for age, this indicates that age is not confounding the relationship between birth weight and asthma.
### Model 3: Adjusted for age, sex, race, preterm birth, familial poverty ratio, education level of adults, insurance type, and household smoker status
```{r}
# Model 3: fully adjusted logistic regression of asthma
model3 <- glm(asthma ~ birth_weight_low + age + sex + race + born_early
+ poverty + education + insurance_type + cigarettes,
data = df, family = binomial)
# full model output (coefficients, SEs, fit stats)
summary(model3)
# odds ratios + 95% CIs for every term
tidy(model3, exponentiate = TRUE, conf.int = TRUE)
```
**Interpretation**
Model 3 adds the full covariate set, sex, race, preterm birth, familial poverty ratio, education level of adults, insurance type, and household smoker status, on top of age. After this full adjustment, the birth weight association attenuates meaningfully: OR = 1.21 (95% CI: 1.08–1.35, p \< 0.001), down from OR = 1.67 in both Model 1 and Model 2. Low-birth-weight children had about 1.21 times the odds, a 21% increase in odds, of an ever asthma diagnosis compared to normal-birth-weight children, holding the other covariates constant. However, this association remains statistically significant, since the 95% confidence interval does not cross 1.00, though the magnitude is now notably smaller than in the unadjusted and age-adjusted models.
This attenuation indicates that part of the crude birth weight-asthma association was confounded by the additional covariates introduced in this model, rather than reflecting a direct effect of birth weight alone. Race is the strongest driver of this attenuation: Black children had substantially higher odds of an asthma diagnosis than White children (OR ≈ 1.87, p \< 0.001), the largest independent association of any covariate in the model. Preterm birth also contributed meaningfully (OR ≈ 1.62, p \< 0.001) and is strongly correlated with low birth weight, so some of the crude birth weight effect seen in Models 1 and 2 was likely capturing the combined influence of race and prematurity rather than low birth weight operating independently. Insurance type was also significantly associated with asthma diagnosis, contributing further to the attenuation. Familial poverty ratio, by contrast, was not significantly associated with asthma in this model (p = 0.458), despite being included in the adjustment set.
Because the birth weight odds ratio drops substantially once these covariates are added, race, preterm birth, and insurance type appear to confound part of the crude birth weight-asthma relationship. Even so, a statistically significant association between low birth weight and asthma persists after full adjustment, suggesting that low birth weight retains an independent relationship with asthma risk beyond what these covariates alone can explain.
### Model 3 Visualizations
To make the model results easier to interpret, we created several visualizations. First, a predicted-probability plot shows how the estimated probability of an asthma diagnosis changes across age for low- versus normal-birth-weight children, translating the model's odds ratios onto the more intuitive probability scale. Second, a coefficient plot displays the adjusted odds ratios for every predictor in the fully adjusted model on a single axis, allowing quick comparison of which factors raise or lower the odds of asthma and which are statistically significant. Together, these plots summarize the fully adjusted model both in terms of its central finding (the birth-weight effect across age) and its full set of covariates.
#### Predicted Probabilities Plot
```{r}
# Predicted asthma probability by age and birth weight (Model 3)
plot_predictions(model3, condition = c("age", "birth_weight_low")) +
scale_color_discrete(labels = c("Normal", "Low birth weight")) +
scale_fill_discrete(labels = c("Normal", "Low birth weight")) +
labs(title = "Predicted Asthma Probability by Age and Birth Weight",
subtitle = "Low-birth-weight children have higher predicted probability at every age",
x = "Age (Years)", y = "Predicted probability of asthma",
color = "Birth weight", fill = "Birth weight",
caption = "Adjusted model (Model 3). Data from 2023 NSCH") +
theme_minimal() +
theme(
plot.title = element_text(size = 12,
face = "bold",
hjust = 0.5),
plot.subtitle = element_text(size = 10, hjust = 0.5),
axis.title.x = element_text(margin = margin(t = 10), size = 10),
axis.title.y = element_text(margin = margin(r = 10), size = 10),
plot.caption = element_text(
size = 9,
color = "darkgray",
margin = margin(t = 15, b = 10, unit = "pt")
))
```
***Interpretation:***
*Predicted asthma probability rises steadily with age in both groups, from about 4–5% at birth to 16–19% by age 17 which is consistent with the age odds ratio of 1.10 (asthma diagnoses accumulate as children get older). Low-birth-weight children (blue) sit above normal-birth-weight children (red) at every age, showing the adjusted birth-weight effect (OR = 1.21) holds across all of childhood. The gap between the two curves widens in absolute terms at older ages. This is expected on the probability scale, since a constant odds ratio produces a larger percentage-point difference when the baseline probability is higher. The confidence bands overlap modestly, reflecting that the adjusted birth-weight association, while significant, is smaller than the crude one.*
#### Coefficient Plot
```{r}
#| message: false
#| warning: false
labels <- c(
"birth_weight_lowYes" = "Low birth weight",
"age" = "Age (per year)",
"sexFemale" = "Female",
"raceBlack or African American" = "Black",
"raceAmerican Indian or Alaska Native" = "American Indian/Alaska Native",
"raceAsian" = "Asian",
"raceNative Hawaiian and other Pacific Islander" = "Native Hawaiian/Pacific Islander",
"raceTwo or more races" = "Two or more races",
"born_earlyYes" = "Preterm birth",
"poverty" = "Poverty ratio",
"educationHigh school" = "High school",
"educationSome college" = "Some college",
"educationCollege degree or higher" = "College degree or higher",
"insurance_typePrivate" = "Private insurance",
"insurance_typePrivate and Public" = "Private and public insurance",
"insurance_typeNot insured" = "Not insured",
"cigarettesYes" = "Household smoker"
)
modelplot(model3, coef_map = rev(labels), exponentiate = TRUE) +
geom_vline(xintercept = 1, linetype = "dashed", color = "gray50") +
labs(title = "Adjusted Odds Ratios for Ever Asthma Diagnosis (Model 3)",
subtitle = "Reference line at OR = 1; intervals crossing it are not significant",
x = "Odds ratio (95% CI)", y = NULL,
caption = "Model 3 (fully adjusted). Data from 2023 NSCH") +
theme_minimal() +
theme(
plot.title = element_text(size = 11, face = "bold", hjust = 0.5),
plot.subtitle = element_text(size = 9, hjust = 0.5),
axis.title.x = element_text(margin = margin(t = 10), size = 9),
plot.caption = element_text(size = 8, color = "darkgray",
margin = margin(t = 15, b = 10, unit = "pt"))
)
```
**Interpretation**
*Each point is a covariate's adjusted odds ratio from Model 3, with its 95% CI; the dashed line at OR = 1 marks no association, and intervals crossing it are not statistically significant. Higher asthma odds (right of 1, CI excludes 1): Black race shows the largest increase (OR \~1.87), followed by preterm birth (\~1.62), two or more races (\~1.39), some college (\~1.31), private and public insurance (\~1.19), low birth weight (\~1.21), and age (\~1.10 per year). Lower asthma odds (left of 1, CI excludes 1): female sex (\~0.70), Asian race (\~0.82), private insurance (\~0.74), and not insured (\~0.65).*
*On the significance boundary, household smoker (\~1.10) sits just right of 1 with its CI lower bound touching 1, a borderline positive association. No significant association (CI crosses 1): poverty ratio (\~1.00), American Indian/Alaska Native, Native Hawaiian/Pacific Islander, high school, and college degree or higher.*
*Overall, the strongest independent predictors of asthma in the fully adjusted model are Black race and preterm birth, while low birth weight (the exposure of interest) remains modestly but significantly associated after accounting for all covariates.*
------------------------------------------------------------------------
## Odds Ratios
To compare the birth-weight association directly across the three models, we extracted the odds ratio and 95% confidence interval for low birth weight from each one and reported them alongside each model's sample size. Isolating this single term across the unadjusted, age-adjusted, and fully adjusted models lets us see how the estimate changed as covariates were added, while the sample sizes show how covariate missingness reduced the analytic sample at the fully adjusted stage.
We then created a forest plot of the fully adjusted model, displaying the adjusted odds ratio and confidence interval for every predictor on a single axis. Plotting all covariates together, with a reference line at an odds ratio of 1, makes it easy to see which factors were associated with higher or lower odds of asthma and which were statistically significant.
```{r}
overall <- bind_rows(
tidy(model1, exponentiate = TRUE, conf.int = TRUE) |>
mutate(model = "Unadjusted"),
tidy(model2, exponentiate = TRUE, conf.int = TRUE) |>
mutate(model = "Age-adjusted"),
tidy(model3, exponentiate = TRUE, conf.int = TRUE) |>
mutate(model = "Fully adjusted")
) |>
filter(str_detect(term, "birth_weight_low")) |>
mutate(model = factor(model, levels = c("Fully adjusted", "Age-adjusted", "Unadjusted")))
ggplot(overall, aes(x = estimate, y = model)) +
geom_vline(xintercept = 1, linetype = "dashed", color = "gray50") +
geom_pointrange(aes(xmin = conf.low, xmax = conf.high)) +
labs(
title = "Low Birth Weight and Asthma Odds Across Models",
subtitle = "Association attenuates with adjustment but remains significant",
x = "Odds ratio (95% CI)", y = NULL,
caption = "Data from 2023 National Survey of Children's Health (NSCH)"
) +
theme_minimal() +
theme(
plot.title = element_text(
size = 11,
face = "bold",
hjust = 0.5
),
plot.subtitle = element_text(size = 10, hjust = 0.5),
axis.title.x = element_text(margin = margin(t = 10), size = 9),
axis.title.y = element_text(margin = margin(r = 10), size = 9),
plot.caption = element_text(
size = 8,
color = "darkgray",
margin = margin(t = 15, b = 10, unit = "pt")
)
)
```
```{r}
# Model 1: odds ratio + CI for low birth weight
tidy(model1, exponentiate = TRUE, conf.int = TRUE) |>
filter(str_detect(term, "birth_weight_low"))
# Model 2: same, age-adjusted
tidy(model2, exponentiate = TRUE, conf.int = TRUE) |>
filter(str_detect(term, "birth_weight_low"))
# Model 3: same, fully adjusted
tidy(model3, exponentiate = TRUE, conf.int = TRUE) |>
filter(str_detect(term, "birth_weight_low"))
```
```{r}
# Sanity check: confirm nobs() matches manual listwise deletion.
# If these two numbers differ for any model, NAs are being dropped
# somewhere unexpected (or a variable isn't in the model formula).
check_obs <- function(label, model) {
vars <- all.vars(formula(model))
manual <- df |> select(all_of(vars)) |> drop_na() |> nrow()
cat("===============", label, "===============\n")
cat("Observations after manual removal:", manual, "\n")
cat("Observations in model:", nobs(model), "\n\n")
}
cat("Total observations in df:", nrow(df), "\n\n")
check_obs("MODEL 1", model1)
check_obs("MODEL 2", model2)
check_obs("MODEL 3", model3)
```
***Interpretation***
*The birth weight–asthma association is significant in all three models and consistent in direction (reference = low birth weight, so not-low-birth-weight children have higher odds). Adjusting for age alone changes nothing (from 1.67 to 1.67), age is not a confounder. Full adjustment attenuates the OR from 1.67 to 1.21, so demographic and socioeconomic covariates explain a substantial part of the crude association, though a significant independent association remains. Model 3 dropped around1,952 observations (52,532 dropped from 50,580) due to missing data on the added covariates, so it isn't fit on quite the same sample as Models 1–2. The comparison is still valid but not strictly apples-to-apples.*
------------------------------------------------------------------------
## Prevalence Difference % (95% CI)
Because odds ratios describe the association on a relative scale, we also estimated the absolute difference in asthma probability between low- and normal-birth-weight children. We first computed this contrast using predicted probabilities from `predictions()` and a hypothesis test, which evaluates the difference at a single representative covariate profile. We then computed it as an average marginal effect using `avg_comparisons()`, which averages the difference in predicted probability across all children in the sample using their actual covariate values. Because the average marginal effect reflects the true covariate distribution of the sample and provides a more precise population-level estimate, we report the `avg_comparisons()` results in Table 2. Reporting the prevalence difference alongside the odds ratio conveys the absolute public-health impact of low birth weight, which the odds ratio alone does not capture.
```{r}
# Model 1: Unadjusted ===============================================
# predicted asthma probability, No vs Yes
pred_model1 <- predictions(model1,
newdata = datagrid(
birth_weight_low = c("No", "Yes")))
# Checks if the two predictions differ
hypotheses(pred_model1, hypothesis = "b2 = b1")
# Model 2: Age-adjusted =============================================
# same predictions, now controlling for age
pred_model2 <- predictions(model2,
newdata = datagrid(
birth_weight_low = c("No", "Yes")))
# Checks if the two predictions differ
hypotheses(pred_model2, hypothesis = "b2 = b1")
# Model 3: Fully adjusted (multiple covariates) =====================
# same predictions, now controlling for *almost* everything
pred_model3 <- predictions(model3,
newdata = datagrid(
birth_weight_low = c("No", "Yes")))
# Checks if the two predictions differ
hypotheses(pred_model3, hypothesis = "b2 = b1")
```
```{r}
# Event counts for the full sample
df |>
group_by(birth_weight_low) |>
summarise(n = n(),
events = sum(asthma == "Yes", na.rm = TRUE),
pct = round(100 * events / sum(!is.na(asthma)), 1))
# Adjusted prevalence differences (probability scale), Low vs Normal
avg_comparisons(model1, variables = "birth_weight_low") # unadjusted
avg_comparisons(model2, variables = "birth_weight_low") # adjusted
avg_comparisons(model3, variables = "birth_weight_low")
```
***Interpretation***
On the absolute (probability) scale, low-birth-weight children had roughly 5 percentage points higher predicted probability of asthma than normal-birth-weight children in both the unadjusted and age-adjusted models (prevalence difference ≈ 5.1 to 5.2 percentage points, 95% CI roughly 4 to 6 percentage points, p \< 0.001). This is consistent with the crude prevalences (14.3% versus 9.1%) and with the corresponding odds ratios, both scales point toward the same conclusion that low birth weight is associated with higher asthma risk.
After full adjustment in Model 3, the prevalence difference narrows to about 1.7 percentage points (95% CI: 0.7 to 2.7), mirroring the attenuation already seen in the odds ratio (1.67 to 1.21) and reflecting that much of the crude absolute difference is explained by the covariates added in that model. Reporting both the odds ratio and the prevalence difference is useful because the odds ratio captures the relative strength of the association while the prevalence difference conveys its absolute, population-level impact.
------------------------------------------------------------------------
# Table 3. Adjusted Associations between Birth Weight Status and Ever Asthma Diagnosis, Stratified by Age Group\*
Because asthma diagnoses accumulate over childhood and younger children have had less time to be diagnosed, we conducted a parallel analysis stratified by age group to examine whether the association between low birth weight and asthma differed across developmental stages. We repeated the fully adjusted model separately within each of the four age strata (infants and toddlers \[0–2\], preschool \[3–5\], middle childhood \[6–12\], and adolescents \[13–17\]) excluding age from the covariate set, since age no longer varies meaningfully within a stratum. As in Table 2, we report both the odds ratio and the absolute prevalence difference with 95% confidence intervals for each age group, summarized in Table 3. The individual stratified models are shown below.
+-------------------+---------------------+---------------+--------------------------+------------------+
| Age group | Birth weight status | Events, N (%) | Prevalence difference %\ | Odds ratio\ |
| | | | (95% CI) | (95% CI) |
+===================+=====================+===============+==========================+==================+
| Toddler\ | Normal birth weight | 193 (2.3%) | Reference | 1.00 |
| (0-2 years) | | | | |
+-------------------+---------------------+---------------+--------------------------+------------------+
| | Low birth weight | 38 (5.3%) | 0.8 (−0.5 to 2.2) | 1.37 (0.86–2.14) |
+-------------------+---------------------+---------------+--------------------------+------------------+
| Preschool\ | Normal birth weight | 671 (6.4%) | Reference | 1.00 |
| (3-5 years) | | | | |
+-------------------+---------------------+---------------+--------------------------+------------------+
| | Low birth weight | 119 (11.3%) | 2.6 (0.5 to 4.6) | 1.44 (1.11–1.86) |
+-------------------+---------------------+---------------+--------------------------+------------------+
| Middle childhood\ | Normal birth weight | 1527 (10.0%) | Reference | 1.00 |
| (6-12 years) | | | | |
+-------------------+---------------------+---------------+--------------------------+------------------+
| | Low birth weight | 241 (15.9%) | 1.8 (−0.1 to 3.8) | 1.21 (1.00–1.45) |
+-------------------+---------------------+---------------+--------------------------+------------------+
| Teenager\ | Normal birth weight | 1967 (14.3%) | Reference | 1.00 |
| (13-17 years) | | | | |
+-------------------+---------------------+---------------+--------------------------+------------------+
| | Low birth weight | 263 (19.7%) | 1.1 (−1.1 to 3.4) | 1.09 (0.92–1.30) |
+-------------------+---------------------+---------------+--------------------------+------------------+
~Adjusted results estimated using logistic regression, run separately within each age stratum, adjusted for sex, race/ethnicity, preterm birth, familial poverty ratio, education level of adults, insurance type, and household smoker status~
***Table 3 Notes:***
*Only preschool (3-5) is significant on both scales (prevalence diff CI excludes 0, OR CI excludes 1). Middle childhood (6-12) is borderline on both (OR lower bound = 1.00, prevalence diff lower bound = −0.1). Toddlers and teens are non-significant. The overall pattern: the low-birth-weight/asthma association is strongest in early childhood and fades with age.*
------------------------------------------------------------------------
## Age-Stratified Models (Table 3)
### Infants to Toddlers (0-2 years) Model
```{r}
# Toddlers (0-2 years)
# fit the asthma model for infants to toddlers
model_toddler <- glm(asthma ~ birth_weight_low + sex + race + born_early
+ poverty + education + insurance_type + cigarettes,
data = filter(df, age_cats == "Infants/Toddlers (0-2)"),
family = binomial)
# pull the odds ratio + CI for low birth weight
tidy(model_toddler, exponentiate = TRUE, conf.int = TRUE) |>
filter(str_detect(term, "birth_weight_low"))
# checks how many kids the model used
nobs(model_toddler)
# predicted asthma probability, No vs Yes
pred_toddler <- predictions(model_toddler,
newdata = datagrid(
birth_weight_low = c("No", "Yes")))
# check if the two predictions differ
hypotheses(pred_toddler, hypothesis = "b1 = b2")
```
**Interpretation**
*The birth weight association is not significant in this age group. OR = 1.37 (95% CI: 0.86–2.14, p = 0.17) as the CI crosses 1. The sample size is 8,788 toddlers. Among toddlers, low birth weight shows no statistically significant association with asthma on either scale. The OR points in the same direction as the overall analysis but is imprecise, likely because asthma is rarer and less established at this age (fewer cases to detect an effect).*
### Preschoolers (3-5 years) Model
```{r}
# Preschool (3-5 years)
# fit the asthma model for preschoolers
model_prek <- glm(asthma ~ birth_weight_low + sex + race + born_early +
poverty + education + insurance_type + cigarettes,
data = filter(df, age_cats == "Preschool (3-5)"),
family = binomial)
# pull the odds ratio + CI for low birth weight
tidy(model_prek, exponentiate = TRUE, conf.int = TRUE) |>
filter(str_detect(term, "birth_weight_low"))
# Checks how many kids did the model use
nobs(model_prek)
# Predicted asthma probability, No vs Yes
pred_prek <- predictions(model_prek,
newdata = datagrid(
birth_weight_low = c("No", "Yes")))
# Checks if the two predictions differ
hypotheses(pred_prek, hypothesis = "b1 = b2")
```
**Interpretation**
*The birth weight association is significant here. OR = 1.44 (95% CI: 1.11–1.86, p = 0.006) as the CI excludes 1. Same direction as the overall analysis (reference = low birth weight, so not-low-birth-weight kids have higher odds). The sample size is 11,115 preschoolers. Among preschoolers, low birth weight is significantly associated with asthma on the relative (odds) scale, unlike toddlers where it wasn't. The absolute difference remains modest.*
### Middle Childhood (6-12 years) Model
```{r}
# Middle childhood (6-12)
# fit the asthma model for middle childhood
model_middle <- glm(asthma ~ birth_weight_low + sex + race + born_early +
poverty + education + insurance_type + cigarettes,
data = filter(df, age_cats == "Middle childhood (6-12)"),
family = binomial)
# pull the odds ratio + CI for low birth weight
tidy(model_middle, exponentiate = TRUE, conf.int = TRUE) |>
filter(str_detect(term, "birth_weight_low"))
# checks how many kids did the model use
nobs(model_middle)
# Predicted asthma probability, No vs Yes
pred_middle <- predictions(model_middle,
newdata = datagrid(
birth_weight_low = c("No", "Yes")))
# # check if the two predictions differ
hypotheses(pred_middle, hypothesis = "b1 = b2")
```
**Interpretation**
*The birth weight association is borderline and just misses significance. OR = 1.21 (95% CI: 0.998–1.45, p = 0.051). The CI barely touches 1. This is the largest subsample with16,280 kids. Among middle-childhood kids, low birth weight shows a suggestive but not quite statistically significant association with asthma (p right at 0.05, CI's lower bound essentially at 1). The effect size (OR 1.21) matches the overall fully-adjusted estimate, so it's consistent in direction and magnitude, just short of the significance threshold in this subgroup.*
### Teenagers (13-17 years) Model
```{r}
# Teenagers (13-17)
# Fit the asthma model for teens
model_teens <- glm(asthma ~ birth_weight_low + sex + race + born_early +
poverty + education + insurance_type + cigarettes,
data = filter(df, age_cats == "Teenagers (13-17)"),
family = binomial)
# Pull the odds ratio + CI for low birth weight
tidy(model_teens, exponentiate = TRUE, conf.int = TRUE) |>
filter(str_detect(term, "birth_weight_low"))
# Checks how many teens the model used
nobs(model_teens)
# Predicted asthma probability, No vs Yes
pred_teens <- predictions(model_teens,
newdata = datagrid(
birth_weight_low = c("No", "Yes")))
# Checks if the two predictions differ
hypotheses(pred_teens, hypothesis = "b1 = b2")
```
**Interpretation**
*The birth weight association is not significant. OR = 1.09 (95% CI: 0.92–1.30, p = 0.32) (CI crosses 1). The sample size is14,397 teens. Among teenagers, low birth weight shows no significant association with asthma on either scale. This is the weakest effect of all age groups (OR closest to 1), suggesting any early birth-weight association has largely faded by adolescence.*
```{r}
# Information for filling out Table 3
# Gives the covariate-adjusted prevalence difference on the probability scale.
avg_comparisons(model_toddler, variables = "birth_weight_low")
avg_comparisons(model_prek, variables = "birth_weight_low")
avg_comparisons(model_middle, variables = "birth_weight_low")
avg_comparisons(model_teens, variables = "birth_weight_low")
```
**Interpretation**
*These are the covariate-adjusted absolute differences (low vs normal birth weight) within each age stratum, and they populate the prevalence-difference column of Table 3. Only preschool (3–5) reaches significance (2.6 pp, 95% CI 0.5–4.6). Toddlers (0.8 pp), middle childhood (1.8 pp), and teenagers (1.1 pp) all have confidence intervals that cross zero. The pattern mirrors the odds ratios: the absolute effect of low birth weight on asthma risk is largest in early childhood and diminishes with age.*
------------------------------------------------------------------------
# Results
## Sample and descriptive findings
Our analytic sample came from the 2023 NSCH, covering children ages 0 to 17. Table 1 shows characteristics by birth weight group. In the raw counts (Table 2), 661 of the low birth weight children had ever been diagnosed with asthma (14.3%), compared to 4,358 of the normal birth weight children (9.1%). Another 190 children with missing birth weight (8.7% with asthma) were not carried into the models. Crude asthma prevalence was also higher among low birth weight children in every age band, not just overall.
## Staged regression models
We fit three logistic regression models in stages and report both the odds ratio and the prevalence difference for each. The prevalence differences were estimated as average marginal effects using `avg_comparisons()`.
In the unadjusted model (Model 1), low birth weight had an odds ratio of 1.67 (95% CI 1.52 to 1.82) and a prevalence difference of 5.2 percentage points (95% CI 4.1 to 6.2). Adding age (Model 2) barely changed either estimate (OR 1.67, 95% CI 1.53 to 1.83; prevalence difference 5.1, 95% CI 4.1 to 6.1). After adjusting for the full covariate set (Model 3), both estimates dropped but stayed significant: OR 1.21 (95% CI 1.08 to 1.35) and prevalence difference 1.68 percentage points (95% CI 0.66 to 2.71). Model 3 was fit on a smaller sample (50,580 versus 52,532) because some covariates had missing values. Among the other covariates, preterm birth and Black race were associated with higher odds of asthma and female sex with lower odds.
## Age stratified models
We re-ran the fully adjusted model separately within each age group (Table 3), dropping age as a covariate inside each stratum. The association was statistically significant only among preschoolers ages 3 to 5 (OR 1.44, 95% CI 1.11 to 1.86; prevalence difference 2.6, 95% CI 0.5 to 4.6). Toddlers ages 0 to 2 had an odds ratio in the same direction (1.37) but a wide interval crossing the null (0.86 to 2.14). Middle childhood ages 6 to 12 was borderline, with a lower confidence bound at exactly 1.00. Teenagers ages 13 to 17 showed no significant association (OR 1.09, 95% CI 0.92 to 1.30).
------------------------------------------------------------------------
# Conclusions
We found that low birth weight was associated with a higher prevalence of ever being diagnosed with asthma among U.S. children. The crude association was fairly strong (OR 1.67), and while it weakened substantially after adjusting for demographic and socioeconomic factors, it did not go away (adjusted OR 1.21, adjusted prevalence difference of about 1.7 percentage points). This tells us two things at once. First, part of what looks like a birth weight effect is really being carried by other correlated factors like preterm birth and socioeconomic status. Second, even after accounting for those factors, low birth weight still carries its own association with asthma.
The age stratified results add some detail to this. The association is not uniform across childhood. It shows up most clearly in preschool aged children and essentially disappears by adolescence. One reasonable interpretation is that low birth weight is linked to earlier onset asthma, and that by the teenage years other pathways to an asthma diagnosis have caught up, diluting the birth weight signal. We cannot confirm that from this data, but it fits the pattern we see.
From a public health standpoint, the odds ratio and the prevalence difference tell complementary stories. The adjusted odds ratio of 1.21 is modest, so low birth weight is not one of the strongest predictors of asthma we looked at. But because childhood asthma is common, even a modest association translates into a meaningful number of additional cases at the population level, which is what the prevalence difference is capturing.
# Strengths
This project had some clear strengths. It drew on a large, nationally representative sample of U.S. children, which gives the estimates decent precision and makes them more generalizable than a single clinic or regional sample would be. We also ran both a staged multivariable analysis and age stratified analyses, which let us assess potential confounding and see how the association changes across childhood rather than assuming it holds steady at every age. Finally, we reported both the odds ratio and the prevalence difference, so the results capture the relative strength of the association and its absolute magnitude at the population level.
# Limitations
There are several limitations worth being upfront about.
First, and most importantly, this is a cross sectional study. The NSCH measures children at one point in time, so we are capturing the prevalence of an existing asthma diagnosis, not the incidence of new cases. This is why we reported prevalence differences rather than risk differences. It also means we cannot establish temporality or claim causation, so everything here should be read as an association, not a proven effect.
Second, the exposure, outcome, and most covariates are parent reported rather than taken from medical records, which opens the door to recall bias and misclassification. A parent may not report a child's birth weight accurately, and "ever diagnosed with asthma" depends on the child having had access to care in the first place.
Third, we used complete case analysis and let each model drop only the cases missing the variables it used. This keeps the simpler models from shrinking unnecessarily, but it means Model 3 is fit on a smaller sample than Models 1 and 2, so the attenuation across models is not entirely clean. We documented the missingness rather than imputing it.
Fourth, there is almost certainly residual confounding. Variables like environmental exposures, family history of asthma, and maternal health during pregnancy are not in this dataset, and any of them could explain part of the association we are attributing to birth weight. Relatedly, preterm birth is included as a covariate even though it is often the cause of low birth weight rather than an independent confounder. Adjusting for a variable on the exposure's own causal pathway can remove part of the effect we are trying to estimate, so the drop from an odds ratio of 1.67 to 1.21 likely reflects some over-adjustment alongside genuine confounding. The fully adjusted estimate may therefore understate the total association between low birth weight and asthma.
Fifth, we excluded BMI because it is only collected for children ages 6 to 17 and cannot be placed in the right time order relative to birth weight. That was the right call for temporality, but it kept us from exploring a variable that plausibly sits on the pathway.
Finally, the NSCH uses a complex survey sampling design. A fully rigorous analysis would incorporate the survey weights, so our confidence intervals in particular should be read with some caution.
Despite these limitations, the pattern is consistent and lines up with prior literature: low birth weight is associated with higher asthma prevalence in children, the association is partly but not fully explained by other factors, and it is most apparent in early childhood.
------------------------------------------------------------------------
# Appendix
## Forest Plot: Odds Ratios Across Models
This appendix figure presents a forest plot summarizing the birth-weight odds ratios across the three overall models. Plotting the unadjusted, age-adjusted, and fully adjusted estimates together on a single axis, with a reference line at an odds ratio of 1, provides a visual summary of how the association attenuated as covariates were added. It presents the same results reported in Table 2 in graphical form.
```{r}
# Combine the four age-stratified models into one table of odds ratios with 95% CIs.
strat <- bind_rows(
tidy(model_toddler, exponentiate = TRUE, conf.int = TRUE) |> mutate(age_group = "Toddler (0-2)"),
tidy(model_prek, exponentiate = TRUE, conf.int = TRUE) |> mutate(age_group = "Preschool (3-5)"),
tidy(model_middle, exponentiate = TRUE, conf.int = TRUE) |> mutate(age_group = "Middle childhood (6-12)"),
tidy(model_teens, exponentiate = TRUE, conf.int = TRUE) |> mutate(age_group = "Teenager (13-17)")
) |>
filter(str_detect(term, "birth_weight_low")) |>
mutate(age_group = factor(age_group,
levels = c("Teenager (13-17)", "Middle childhood (6-12)",
"Preschool (3-5)", "Toddler (0-2)")))
# Plot odds ratios with confidence intervals by age group.
ggplot(strat, aes(x = estimate, y = age_group)) +
geom_vline(xintercept = 1, linetype = "dashed", color = "gray50") +
geom_pointrange(aes(xmin = conf.low, xmax = conf.high)) +
labs(title = "Low Birth Weight and Asthma Odds by Age Group",
subtitle = "Association is strongest in early childhood and fades with age",
x = "Odds ratio (95% CI)", y = NULL,
caption = "Each age stratum adjusted separately. Data from 2023 NSCH") +
theme_minimal() +
theme(
plot.title = element_text(size = 11,
face = "bold",
hjust = 0.5),
plot.subtitle = element_text(size = 9, hjust = 0.5),
axis.title.x = element_text(margin = margin(t = 10), size = 9),
axis.title.y = element_text(margin = margin(r = 10), size = 9),
plot.caption = element_text(
size = 8,
color = "darkgray",
margin = margin(t = 15, b = 10, unit = "pt")
))
```
