Code
data(rmb_datasets, package = "rmb")
rmb_datasets$study_design[rmb_datasets$object == "nhanes3"]
#> [1] "Complex multistage cross-sectional sample from NHANES III."NHANES data
This article applies survey-weighted logistic regression to NHANES III data to estimate associations between age, sex, and race/ethnicity and diabetes prevalence in a nationally representative US sample (RMB2e Chapter 12).
1 Introduction
The Third National Health and Nutrition Examination Survey (NHANES III, 1988–1994) used a complex multistage probability sample to produce nationally representative estimates of health and nutrition in the US population. Because sampling probabilities differ across demographic strata, unweighted analyses would give biased prevalence estimates and incorrect standard errors. Survey-weighted regression using sampling weights, primary sampling units (PSUs), and strata is required for valid inference from NHANES III data (RMB2e Ch. 12).
Are age, sex, and race/ethnicity associated with diabetes prevalence in a nationally representative US sample?
1.1 Causal assumptions
Code
set.seed(42)
dag <- ggdag::dagify(
dm ~ age + sex + aa + ma,
labels = c(
dm = "Diabetes",
age = "Age per 10yr",
sex = "Female",
aa = "African American",
ma = "Mexican American"
),
outcome = "dm"
)
ggdag::ggdag(dag, use_labels = "label", text = FALSE) +
ggdag::theme_dag_blank() +
ggplot2::labs(title = "NHANES III: Causal DAG")
2 Methods
2.1 Study sample
Code
data(nhanes3, package = "rmb")
dat <- nhanes3
dim(dat)
#> [1] 18162 9
summary(haven::zap_labels(dat[c("diabetes", "female", "aframer", "mexamer", "age10")]))
#> diabetes female aframer mexamer
#> Min. :0.00000 Min. :0.0000 Min. :0.000 Min. :0.0000
#> 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
#> Median :0.00000 Median :1.0000 Median :0.000 Median :0.0000
#> Mean :0.07387 Mean :0.5327 Mean :0.281 Mean :0.2703
#> 3rd Qu.:0.00000 3rd Qu.:1.0000 3rd Qu.:1.000 3rd Qu.:1.0000
#> Max. :1.00000 Max. :1.0000 Max. :1.000 Max. :1.0000
#> NAs :22
#> age10
#> Min. :1.700
#> 1st Qu.:2.900
#> Median :4.300
#> Mean :4.687
#> 3rd Qu.:6.400
#> Max. :9.000
#> 2.2 Statistical analysis
A survey design object is constructed using PSUs, strata, and sampling weights, then survey-weighted logistic regression is fitted for diabetes on age (per 10 years), sex, African American ethnicity, and Mexican American ethnicity (RMB2e Ch. 12).
Code
nhanes_design <- survey::svydesign(
id = ~sdppsu6,
strata = ~sdpstra6,
weights = ~wtpfqx6,
data = dat,
nest = TRUE
)
formula_main <- diabetes ~ female + aframer + mexamer + age10
formula_main
#> diabetes ~ female + aframer + mexamer + age103 Results
3.1 Descriptive statistics
Code
survey::svymean(~diabetes, nhanes_design)
#> mean SE
#> diabetes NA NaN
survey::svyby(~diabetes, ~aframer, nhanes_design, survey::svymean)
#> aframer diabetes se
#> 0 0 NA NaN
#> 1 1 NA NaN
survey::svyby(~diabetes, ~mexamer, nhanes_design, survey::svymean)
#> mexamer diabetes se
#> 0 0 NA NaN
#> 1 1 NA NaNCode
dm_by_age <- survey::svyby(~diabetes, ~age10, nhanes_design, survey::svymean)
ggplot2::ggplot(dm_by_age, ggplot2::aes(x = age10, y = diabetes)) +
ggplot2::geom_line(color = "#1b9e77", linewidth = 1) +
ggplot2::geom_point(color = "#1b9e77", size = 3) +
ggplot2::labs(
title = "NHANES III: Diabetes prevalence by age (survey-weighted)",
x = "Age group (per 10yr)",
y = "Weighted diabetes prevalence"
) +
ggplot2::theme_minimal()
3.2 Model estimates
Code
fit <- survey::svyglm(formula_main, design = nhanes_design, family = stats::binomial())
summary(fit)
#>
#> Call:
#> svyglm(formula = formula_main, design = nhanes_design, family = stats::binomial())
#>
#> Survey design:
#> survey::svydesign(id = ~sdppsu6, strata = ~sdpstra6, weights = ~wtpfqx6,
#> data = dat, nest = TRUE)
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -5.79408 0.19487 -29.733 < 2e-16 ***
#> female -0.01954 0.09392 -0.208 0.836
#> aframer 0.59845 0.09508 6.294 1.14e-07 ***
#> mexamer 0.64715 0.09797 6.606 3.93e-08 ***
#> age10 0.53286 0.02774 19.211 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for binomial family taken to be 0.8635979)
#>
#> Number of Fisher Scoring iterations: 63.3 Model diagnostics
Code
fit_age_only <- survey::svyglm(diabetes ~ age10, design = nhanes_design, family = stats::binomial())
stats::anova(fit_age_only, fit, test = "Chisq")
#> Working (Rao-Scott) LRT for female aframer mexamer
#> in svyglm(formula = formula_main, design = nhanes_design, family = stats::binomial())
#> Working 2logLR = 43.9424 p= 2.2564e-06
#> (scale factors: 1.9 0.87 0.24 )3.4 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(>|t|)"]
)
#> term odds_ratio conf_low conf_high p_value
#> (Intercept) (Intercept) 0.003045541 0.002056872 0.004509432 3.160774e-31
#> female female 0.980651263 0.811642396 1.184852964 8.361362e-01
#> aframer aframer 1.819299812 1.502228919 2.203293896 1.141043e-07
#> mexamer mexamer 1.910096525 1.568047072 2.326759700 3.926636e-08
#> age10 age10 1.703792188 1.611221551 1.801681351 2.568224e-234 Discussion
Older age, African American ethnicity, and Mexican American ethnicity are all associated with higher diabetes prevalence in the US population after mutual adjustment, consistent with well-documented patterns of diabetes disparities (RMB2e Ch. 12). Using survey weights is essential: the complex NHANES III sampling design over-represents certain demographic groups, and unweighted estimates would misrepresent national prevalence. This analysis illustrates the survey-weighted GLM approach that is required whenever data come from complex probability samples with unequal selection probabilities.
5 Source
- UCSF Regression Methods companion data: https://regression.ucsf.edu/sites/g/files/tkssra16191/files/wysiwyg/home/data/nhanes3.dta
- Book: Vittinghoff E, Glidden DV, Shiboski SC, McCulloch CE (2012). Regression Methods in Biostatistics (2nd edition).