Formatting Multiple Imputation Results

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

This vignette demonstrates how to use the svypooled() function to format pooled regression model outputs from mice package objects into clean, fallacy-safe tables.

Formatting Results from Multiple Imputation

Beyond survey data, a common analytical challenge is presenting results from models fitted to multiply imputed datasets. The svyTable1 package provides the svypooled() function to address this. It takes a pooled model object (mipo) from mice and produces publication-ready regression tables.

A key feature of svypooled() is its ability to create a fallacy-safe table. This approach displays results for the primary exposure only while listing adjustment covariates in a footnote, preventing misinterpretation of covariate p-values.

Example: Handling Missing Data in a Survey Design

The following sections illustrate the recommended workflow. Data are taken from the NHANES example dataset supplied in the NHANES package.

Data Preparation

library(svyTable1)
library(mice)
library(dplyr)
library(survey)
library(NHANES)
library(knitr)
library(mitools)

We prepare an analytic dataset, define obesity, categorize age, define a binary smoking variable, and select variables needed for both imputation and the survey design.

data(NHANESraw, package = "NHANES")
nhanes_analytic <- NHANESraw %>%
  filter(Age >= 20 & WTMEC2YR > 0) %>% 
  mutate(
    Obese = factor(ifelse(BMI >= 30, "Yes", "No"), levels = c("No", "Yes")),
    AgeCat = cut(Age, breaks = c(19, 39, 59, 80), labels = c("20-39", "40-59", "60-80")),
    Smoke100 = factor(Smoke100, levels = c("No", "Yes"))
  ) %>%
  select(Obese, AgeCat, Smoke100, Education, SDMVPSU, SDMVSTRA, WTMEC2YR)

Pooling from Imputed Data

We run mice(), fit a survey-weighted logistic regression model to each imputed dataset using svyglm(), and combine the results using pool(). This pooled model object is accepted directly by svypooled().

imputed_data <- mice(nhanes_analytic, m = 2, maxit = 2, seed = 123, printFlag = FALSE)

fit_list <- list()
for (i in 1:imputed_data$m) {
  completed_data <- complete(imputed_data, i)
  design_i <- svydesign(
    id = ~SDMVPSU,
    strata = ~SDMVSTRA,
    weights = ~WTMEC2YR,
    nest = TRUE,
    data = completed_data
  )
  fit_list[[i]] <- svyglm(
    Obese ~ Smoke100 + AgeCat + Education,
    design = design_i,
    family = quasibinomial()
  )
}

pooled_results <- pool(fit_list)

Generating Tables with svypooled()

Fallacy-Safe Table

This is the recommended format (Westreich and Greenland 2013). It presents results only for the main exposure and lists adjustment variables as a single footnote.

svypooled(
 pooled_model = pooled_results,
 main_exposure = "Smoke100",
 adj_var_names = c("AgeCat", "Education"),
 measure = "OR",
 title = "Adjusted Odds of Obesity (Fallacy-Safe)"
)

Adjusted Odds of Obesity (Fallacy-Safe)

Characteristic	OR (95% CI)	p-value
Smoke100
Yes	0.86 (0.77, 0.96)	0.012
Adjusted for: AgeCat, Education

Full Table (Appendix-Style)

This version displays results for every variable in the model. It is useful for supplemental materials or internal reporting but should not be used for primary interpretation.

svypooled(
 pooled_model = pooled_results,
 main_exposure = "Smoke100",
 adj_var_names = c("AgeCat", "Education"),
 measure = "OR",
 title = "Adjusted Odds of Obesity (Full Table for Appendix)",
 fallacy_safe = FALSE
)

Adjusted Odds of Obesity (Full Table for Appendix)

Characteristic	OR (95% CI)	p-value
Smoke100
Yes	0.86 (0.77, 0.96)	0.012
AgeCat
40-59	1.37 (1.20, 1.56)	<0.001
60-80	1.30 (1.12, 1.50)	0.001
Education
9 - 11th Grade	1.07 (0.89, 1.28)	0.451
High School	1.12 (0.92, 1.35)	0.243
Some College	1.14 (0.99, 1.31)	0.070
College Grad	0.64 (0.51, 0.80)	<0.001

References

Westreich, Daniel, and Sander Greenland. 2013. “The Table 2 Fallacy: Presenting and Interpreting Confounder and Modifier Coefficients.” American Journal of Epidemiology 177 (4): 292–98.