Code
data(rmb_datasets, package = "rmb")
rmb_datasets$study_design[rmb_datasets$object == "hers_nodm_visit4_only"]
#> [1] "Cross-sectional Visit 4 subset of HERS participants without diabetes."Table 11.1/11.2 HERS data
This article examines missing glucose data patterns at Visit 4 in HERS participants without diabetes, illustrating missing data mechanisms described in RMB2e Chapter 11.
1 Introduction
Missing data are a pervasive challenge in longitudinal clinical studies. In HERS, fasting glucose was measured repeatedly but subject to informative missingness— women who missed visits or had missing glucose values may differ systematically from completers. RMB2e Chapter 11 uses this dataset to illustrate missing-at-random (MAR) and missing-not-at-random (MNAR) mechanisms.
We ask: among HERS participants without diabetes at Visit 4, is missingness of fasting glucose associated with BMI category and other baseline characteristics, suggesting non-random missingness?
1.1 Causal assumptions
Code
set.seed(42)
dag <- ggdag::dagify(
miss ~ bmi + age + smoke + htn + drink,
labels = c(
miss = "Missing glucose",
bmi = "BMI category",
age = "Age",
smoke = "Smoking",
htn = "HTN meds",
drink = "Alcohol use"
),
outcome = "miss"
)
ggdag::ggdag(dag, use_labels = "label", text = FALSE) +
ggdag::theme_dag_blank() +
ggplot2::labs(title = "HERS visit 4: Missing data DAG")
2 Methods
2.1 Study sample
Code
data(hers_nodm_visit4_only, package = "rmb")
dat <- hers_nodm_visit4_only
dim(dat)
#> [1] 1871 31
summary(haven::zap_labels(dat[c("miss_gluc", "bmi_cat", "age", "csmker", "htnmeds", "drinkany")]))
#> miss_gluc bmi_cat age csmker
#> Min. :0.0000 Min. :1.000 Min. :44.00 Min. :0.0000
#> 1st Qu.:0.0000 1st Qu.:2.000 1st Qu.:61.00 1st Qu.:0.0000
#> Median :0.0000 Median :3.000 Median :66.00 Median :0.0000
#> Mean :0.2368 Mean :2.997 Mean :65.93 Mean :0.1322
#> 3rd Qu.:0.0000 3rd Qu.:4.000 3rd Qu.:71.00 3rd Qu.:0.0000
#> Max. :1.0000 Max. :5.000 Max. :79.00 Max. :1.0000
#> NAs :110 NAs :63
#> htnmeds drinkany
#> Min. :0.000 Min. :0.0000
#> 1st Qu.:1.000 1st Qu.:0.0000
#> Median :1.000 Median :0.0000
#> Mean :0.853 Mean :0.3938
#> 3rd Qu.:1.000 3rd Qu.:1.0000
#> Max. :1.000 Max. :1.0000
#> NAs :632.2 Statistical analysis
We fit logistic regression to predict glucose missingness (miss_gluc) from BMI category, age, smoking status, hypertension medication use, and alcohol consumption.
Code
formula_miss <- miss_gluc ~ bmi_cat + age + csmker + drinkany + htnmeds
formula_miss
#> miss_gluc ~ bmi_cat + age + csmker + drinkany + htnmeds3 Results
3.1 Descriptive statistics
Code
miss_by_bmi <- with(dat, tapply(miss_gluc, bmi_cat, mean, na.rm = TRUE))
miss_df <- data.frame(
bmi_cat = names(miss_by_bmi),
prop_missing = as.numeric(miss_by_bmi)
)
ggplot2::ggplot(miss_df, ggplot2::aes(x = bmi_cat, y = prop_missing)) +
ggplot2::geom_col(fill = "grey70") +
ggplot2::labs(
title = "HERS Visit 4: Glucose missingness by BMI quintile",
x = "BMI category (quintile)",
y = "Proportion with missing glucose"
) +
ggplot2::theme_minimal()
3.2 Model estimates
Code
fit_miss <- stats::glm(formula_miss, data = dat, family = stats::binomial())
summary(fit_miss)
#>
#> Call:
#> stats::glm(formula = formula_miss, family = stats::binomial(),
#> data = dat)
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 0.996734 0.678388 1.469 0.14176
#> bmi_cat -0.094452 0.043663 -2.163 0.03053 *
#> age -0.030779 0.009536 -3.228 0.00125 **
#> csmker 0.072864 0.175978 0.414 0.67884
#> drinkany 0.158861 0.120222 1.321 0.18637
#> htnmeds -0.106962 0.162695 -0.657 0.51090
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 1779.5 on 1722 degrees of freedom
#> Residual deviance: 1761.3 on 1717 degrees of freedom
#> (148 observations deleted due to missingness)
#> AIC: 1773.3
#>
#> Number of Fisher Scoring iterations: 43.3 Model diagnostics
Code
data.frame(
model = "missingness model",
AIC = stats::AIC(fit_miss),
n_obs = nobs(fit_miss)
)
#> model AIC n_obs
#> 1 missingness model 1773.338 17233.4 Inference
Code
or <- exp(stats::coef(fit_miss))
ci <- exp(stats::confint(fit_miss))
inf <- data.frame(
term = names(or),
odds_ratio = unname(or),
conf_low = ci[, 1],
conf_high = ci[, 2],
p_value = summary(fit_miss)$coefficients[, "Pr(>|z|)"]
)
inf
#> term odds_ratio conf_low conf_high p_value
#> (Intercept) (Intercept) 2.7094193 0.7150214 10.2317462 0.141759606
#> bmi_cat bmi_cat 0.9098718 0.8350393 0.9910184 0.030527487
#> age age 0.9696895 0.9516996 0.9879715 0.001248205
#> csmker csmker 1.0755841 0.7564607 1.5095678 0.678836465
#> drinkany drinkany 1.1721747 0.9253774 1.4828658 0.186369687
#> htnmeds htnmeds 0.8985597 0.6567238 1.2438365 0.5108985124 Discussion
Missingness of fasting glucose at Visit 4 is associated with BMI category and other participant characteristics, indicating that the missing data mechanism is not completely at random (MCAR). This pattern motivates the multiple imputation approach demonstrated in RMB2e Chapter 11, where MAR-based imputation accounts for the observed predictors of missingness to produce valid inference about the glucose outcome.
5 Source
- UCSF companion data
- Book: Vittinghoff E, Glidden DV, Shiboski SC, McCulloch CE (2012). Regression Methods in Biostatistics (2nd edition).