Code
data(rmb_datasets, package = "rmb")
rmb_datasets$study_design[rmb_datasets$object == "phototherapy"]
#> [1] "Observational neonatal jaundice cohort used for confounding-adjusted phototherapy analyses."Phototherapy data
This article applies a logistic regression workflow to the phototherapy dataset, examining whether phototherapy reduces the risk of exceeding the transfusion threshold in neonates with jaundice.
1 Introduction
Neonatal jaundice (hyperbilirubinemia) affects the majority of newborns and, when severe, can cause neurological injury. Phototherapy is the first-line treatment to lower total serum bilirubin (TSB), yet observational studies must adjust for gestational age and birth weight because preterm and low-birthweight infants both receive phototherapy more often and are at higher risk of complications. These data were assembled for confounding-adjusted phototherapy analyses described in RMB2e Chapter 9.
Is phototherapy use associated with a reduced rate of exceeding the transfusion threshold after adjusting for gestational age and birth weight?
1.1 Causal assumptions
Code
set.seed(42)
dag <- ggdag::dagify(
ot ~ gest + bwt + pt + tsb,
pt ~ gest + bwt,
labels = c(
ot = "Over transfusion threshold",
pt = "Phototherapy",
gest = "Gestational age",
bwt = "Birth weight",
tsb = "Serum bilirubin"
),
exposure = "pt",
outcome = "ot"
)
ggdag::ggdag(dag, use_labels = "label", text = FALSE) +
ggdag::theme_dag_blank() +
ggplot2::labs(title = "Phototherapy: Causal DAG")
2 Methods
2.1 Study sample
Code
data(phototherapy, package = "rmb")
dat <- phototherapy
dim(dat)
#> [1] 20731 11
summary(haven::zap_labels(dat[c("phototherapy", "over_thresh", "qual_TSB", "birth_wt", "gest_age", "male", "age_days")]))
#> phototherapy over_thresh qual_TSB birth_wt
#> Min. :0.0000 Min. :0.000000 Min. :1.000 Min. :2.000
#> 1st Qu.:0.0000 1st Qu.:0.000000 1st Qu.:1.000 1st Qu.:2.900
#> Median :0.0000 Median :0.000000 Median :2.000 Median :3.300
#> Mean :0.2211 Mean :0.006174 Mean :2.762 Mean :3.324
#> 3rd Qu.:0.0000 3rd Qu.:0.000000 3rd Qu.:4.000 3rd Qu.:3.700
#> Max. :1.0000 Max. :1.000000 Max. :6.000 Max. :6.000
#> gest_age male age_days
#> Min. :35.00 Min. :0.0000 Min. :0.000
#> 1st Qu.:37.00 1st Qu.:0.0000 1st Qu.:1.000
#> Median :39.00 Median :1.0000 Median :2.000
#> Mean :38.37 Mean :0.5796 Mean :2.018
#> 3rd Qu.:40.00 3rd Qu.:1.0000 3rd Qu.:3.000
#> Max. :41.00 Max. :1.0000 Max. :4.0002.2 Statistical analysis
Logistic regression is used to model the binary outcome over_thresh (TSB exceeding the transfusion threshold), with phototherapy as the primary predictor and gestational age and birth weight as confounders (RMB2e Ch. 9).
Code
formula_main <- over_thresh ~ phototherapy + birth_wt + gest_age
formula_main
#> over_thresh ~ phototherapy + birth_wt + gest_age3 Results
3.1 Descriptive statistics
Code
with(dat, table(phototherapy, over_thresh))
#> over_thresh
#> phototherapy 0 1
#> 0 16034 113
#> 1 4569 15
with(dat, prop.table(table(phototherapy, over_thresh), margin = 1))
#> over_thresh
#> phototherapy 0 1
#> 0 0.993001796 0.006998204
#> 1 0.996727749 0.003272251
summary(haven::zap_labels(dat[c("birth_wt", "gest_age", "qual_TSB")]))
#> birth_wt gest_age qual_TSB
#> Min. :2.000 Min. :35.00 Min. :1.000
#> 1st Qu.:2.900 1st Qu.:37.00 1st Qu.:1.000
#> Median :3.300 Median :39.00 Median :2.000
#> Mean :3.324 Mean :38.37 Mean :2.762
#> 3rd Qu.:3.700 3rd Qu.:40.00 3rd Qu.:4.000
#> Max. :6.000 Max. :41.00 Max. :6.000Code
dat$phototherapy_plot <- factor(
dat$phototherapy,
levels = c(0, 1),
labels = c("No", "Yes")
)
ggplot2::ggplot(dat, ggplot2::aes(x = phototherapy_plot, y = gest_age, fill = phototherapy_plot)) +
ggplot2::geom_boxplot() +
ggplot2::scale_fill_manual(values = c("#1b9e77", "#d95f02")) +
ggplot2::labs(
title = "Gestational age by phototherapy group",
x = "Phototherapy",
y = "Gestational age (weeks)"
) +
ggplot2::theme_minimal() +
ggplot2::theme(legend.position = "none")
3.2 Model estimates
Code
fit <- stats::glm(formula_main, data = dat, family = stats::binomial())
summary(fit)
#>
#> Call:
#> stats::glm(formula = formula_main, family = stats::binomial(),
#> data = dat)
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 17.10863 2.24672 7.615 2.64e-14 ***
#> phototherapy -1.21157 0.28061 -4.318 1.58e-05 ***
#> birth_wt 0.39277 0.18993 2.068 0.0386 *
#> gest_age -0.61776 0.06803 -9.081 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 1557.6 on 20730 degrees of freedom
#> Residual deviance: 1443.0 on 20727 degrees of freedom
#> AIC: 1451
#>
#> Number of Fisher Scoring iterations: 83.3 Model diagnostics
Code
data.frame(
model = "adjusted",
AIC = stats::AIC(fit),
deviance = fit$deviance,
null_deviance = fit$null.deviance
)
#> model AIC deviance null_deviance
#> 1 adjusted 1450.997 1442.997 1557.5713.4 Inference
Code
or <- exp(stats::coef(fit))
ci <- exp(stats::confint(fit))
data.frame(
term = names(or),
odds_ratio = unname(or),
conf_low = ci[, 1],
conf_high = ci[, 2],
p_value = summary(fit)$coefficients[, "Pr(>|z|)"]
)
#> term odds_ratio conf_low conf_high p_value
#> (Intercept) (Intercept) 2.692673e+07 3.442282e+05 2.321909e+09 2.638232e-14
#> phototherapy phototherapy 2.977289e-01 1.650710e-01 4.998177e-01 1.577238e-05
#> birth_wt birth_wt 1.481076e+00 1.013495e+00 2.133724e+00 3.864252e-02
#> gest_age gest_age 5.391533e-01 4.711359e-01 6.152494e-01 1.079584e-194 Discussion
After adjustment for gestational age and birth weight, the estimated association between phototherapy use and exceeding the transfusion threshold reflects the confounding-adjusted treatment effect described in RMB2e Chapter 9. Because gestational age and birth weight are both strong predictors of the outcome and strongly related to phototherapy receipt, unadjusted comparisons would be severely confounded. The logistic model framework here illustrates the core confounding-adjustment strategy recommended throughout RMB2e.
5 Source
- UCSF Regression Methods companion data: https://regression.ucsf.edu/sites/g/files/tkssra16191/files/wysiwyg/home/data/phototherapy.dta
- Book: Vittinghoff E, Glidden DV, Shiboski SC, McCulloch CE (2012). Regression Methods in Biostatistics (2nd edition).