Code
data(rmb_datasets, package = "rmb")
rmb_datasets$study_design[rmb_datasets$object == "hers_long_base_visit1_only_saved"]
#> [1] "Baseline/Visit 1 subset from the longitudinal HERS data structure."Table 11.3 HERS data
This article analyzes glucose levels at Year-1 follow-up in HERS participants, examining how HRT assignment, exercise, and BMI relate to glycemic outcomes (RMB2e Chapter 11).
1 Introduction
The Heart and Estrogen/Progestin Replacement Study (HERS) enrolled postmenopausal women with established coronary heart disease and randomized them to hormone therapy (HRT) or placebo. Beyond its primary cardiovascular endpoints, HERS collected repeated metabolic measurements including fasting glucose, enabling analysis of longitudinal glycemic trajectories. Missing data patterns in metabolic outcomes are a key methodological concern in longitudinal studies (RMB2e Chapter 11).
This dataset contains baseline and Visit 1 data from the HERS longitudinal structure. We ask: among women without diabetes at baseline, is HRT assignment associated with Year-1 fasting glucose after adjusting for exercise and BMI?
1.1 Causal assumptions
Code
set.seed(42)
dag <- ggdag::dagify(
gluc ~ hrt + bmi + exercise + age,
bmi ~ age,
labels = c(
gluc = "Year-1 glucose",
hrt = "HRT assignment",
bmi = "BMI",
exercise = "Exercise >=3x/wk",
age = "Age"
),
exposure = "hrt",
outcome = "gluc"
)
ggdag::ggdag(dag, use_labels = "label", text = FALSE) +
ggdag::theme_dag_blank() +
ggplot2::labs(title = "HERS baseline: Causal DAG")
2 Methods
2.1 Study sample
Code
data(hers_long_base_visit1_only_saved, package = "rmb")
dat <- haven::zap_labels(hers_long_base_visit1_only_saved)
dim(dat)
#> [1] 5526 22
ana <- subset(dat, nvisit == 1 & diabetes == 0)
dim(ana)
#> [1] 1942 22
summary(ana[c("glucose", "group", "bmi", "exer3", "age")])
#> glucose group bmi exer3
#> Min. : 62.00 Min. :0.0000 Min. :14.73 Min. :0.0000
#> 1st Qu.: 89.00 1st Qu.:0.0000 1st Qu.:23.85 1st Qu.:0.0000
#> Median : 96.00 Median :0.0000 Median :26.77 Median :0.0000
#> Mean : 96.74 Mean :0.4943 Mean :27.47 Mean :0.3845
#> 3rd Qu.:103.00 3rd Qu.:1.0000 3rd Qu.:30.26 3rd Qu.:1.0000
#> Max. :125.00 Max. :1.0000 Max. :52.78 Max. :1.0000
#> NAs :11 NAs :14 NAs :7
#> age
#> Min. :44.00
#> 1st Qu.:62.00
#> Median :68.00
#> Mean :66.94
#> 3rd Qu.:72.00
#> Max. :79.00
#> 2.2 Statistical analysis
We fit a linear regression model for Year-1 fasting glucose with HRT assignment (group) as the primary predictor, adjusting for BMI, exercise frequency, age, and smoking status among women attending Visit 1 without diabetes.
Code
formula_gluc <- glucose ~ group + bmi + exer3 + age + csmker
formula_gluc
#> glucose ~ group + bmi + exer3 + age + csmker3 Results
3.1 Descriptive statistics
Code
with(ana, tapply(glucose, group, summary))
#> $`0`
#> Min. 1st Qu. Median Mean 3rd Qu. Max. NAs
#> 62.00 91.00 97.00 98.01 104.00 125.00 3
#>
#> $`1`
#> Min. 1st Qu. Median Mean 3rd Qu. Max. NAs
#> 68.00 88.00 94.00 95.44 101.25 125.00 8
with(ana, tapply(glucose, exer3, mean, na.rm = TRUE))
#> 0 1
#> 97.26796 95.93252Code
ana$group_label <- factor(ana$group, levels = c(0, 1), labels = c("Placebo", "HRT"))
ggplot2::ggplot(ana, ggplot2::aes(x = group_label, y = glucose, fill = group_label)) +
ggplot2::geom_boxplot() +
ggplot2::scale_fill_manual(values = c("grey85", "#d95f02")) +
ggplot2::labs(
title = "HERS: Year-1 glucose by HRT assignment",
x = "Treatment assignment",
y = "Year-1 fasting glucose (mg/dL)"
) +
ggplot2::theme_minimal() +
ggplot2::theme(legend.position = "none")
3.2 Model estimates
Code
fit_gluc <- stats::lm(formula_gluc, data = ana)
summary(fit_gluc)
#>
#> Call:
#> stats::lm(formula = formula_gluc, data = ana)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -32.714 -6.846 -0.915 6.011 31.057
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 77.29712 2.95896 26.123 < 2e-16 ***
#> group -2.29360 0.45644 -5.025 5.51e-07 ***
#> bmi 0.55186 0.04562 12.097 < 2e-16 ***
#> exer3 -0.58024 0.47661 -1.217 0.2236
#> age 0.08253 0.03549 2.326 0.0201 *
#> csmker 0.71728 0.64456 1.113 0.2659
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 9.987 on 1912 degrees of freedom
#> (24 observations deleted due to missingness)
#> Multiple R-squared: 0.0879, Adjusted R-squared: 0.08552
#> F-statistic: 36.85 on 5 and 1912 DF, p-value: < 2.2e-163.3 Model diagnostics
Code
fit_data <- data.frame(
fitted = stats::fitted(fit_gluc),
residuals = stats::residuals(fit_gluc),
std_residuals = stats::rstandard(fit_gluc)
)
ggplot2::ggplot(fit_data, ggplot2::aes(x = fitted, y = residuals)) +
ggplot2::geom_point(alpha = 0.25, size = 0.5) +
ggplot2::geom_hline(yintercept = 0, linetype = "dashed", color = "red") +
ggplot2::geom_smooth(se = FALSE, color = "blue") +
ggplot2::labs(
title = "Residuals vs Fitted",
x = "Fitted values",
y = "Residuals"
) +
ggplot2::theme_minimal()
ggplot2::ggplot(fit_data, ggplot2::aes(sample = std_residuals)) +
ggplot2::stat_qq() +
ggplot2::stat_qq_line(color = "red") +
ggplot2::labs(
title = "Normal Q-Q",
x = "Theoretical Quantiles",
y = "Standardized residuals"
) +
ggplot2::theme_minimal()
3.4 Inference
Code
ci <- stats::confint(fit_gluc)
coef_tab <- data.frame(
term = names(stats::coef(fit_gluc)),
estimate = stats::coef(fit_gluc),
conf_low = ci[, 1],
conf_high = ci[, 2],
p_value = summary(fit_gluc)$coefficients[, "Pr(>|t|)"]
)
coef_tab
#> term estimate conf_low conf_high p_value
#> (Intercept) (Intercept) 77.29711774 71.49398627 83.1002492 6.782014e-129
#> group group -2.29360213 -3.18878237 -1.3984219 5.505243e-07
#> bmi bmi 0.55185745 0.46238486 0.6413300 1.641742e-32
#> exer3 exer3 -0.58023656 -1.51497570 0.3545026 2.235975e-01
#> age age 0.08252925 0.01292922 0.1521293 2.014789e-02
#> csmker csmker 0.71728209 -0.54682682 1.9813910 2.659216e-014 Discussion
In this HERS baseline/Visit-1 longitudinal analysis, HRT assignment does not appear to substantially change fasting glucose in women without diabetes after adjustment for BMI, exercise, and age. The analysis illustrates the longitudinal data structure used in RMB2e Chapter 11 for missing-data examples, where patterns of missingness in glucose are related to baseline characteristics. Regular exercise is associated with lower glucose levels, consistent with its known metabolic effects.
5 Source
- UCSF companion data
- Book: Vittinghoff E, Glidden DV, Shiboski SC, McCulloch CE (2012). Regression Methods in Biostatistics (2nd edition).