Introduction

Rubin´s Rules (RR) are designed to pool parameter estimates, such as mean differences, regression coefficients, standard errors and to derive confidence intervals and p-values. The standard errors of the multiple imputation solution are slightly smaller than in the complete-case analysis.

# Examples
# impute missing data, analyse and pool using the classic MICE workflow
library(mice)
## 
## Attaching package: 'mice'
## The following object is masked from 'package:stats':
## 
##     filter
## The following objects are masked from 'package:base':
## 
##     cbind, rbind
imp <- mice(nhanes, maxit = 2, m = 2)
## 
##  iter imp variable
##   1   1  bmi  hyp  chl
##   1   2  bmi  hyp  chl
##   2   1  bmi  hyp  chl
##   2   2  bmi  hyp  chl
fit <- with(data = imp, exp = lm(bmi ~ hyp + chl))

summary(pool(fit))
##          term    estimate std.error  statistic       df   p.value
## 1 (Intercept) 21.68958724 6.3605374  3.4100243 1.575945 0.1052522
## 2         hyp -0.48166025 2.6607294 -0.1810256 4.215992 0.8647196
## 3         chl  0.02680028 0.0240484  1.1144309 4.237083 0.3242825
fit2 <- ( lm(bmi ~ hyp + chl,data = nhanes ))

summary( (fit2))
## 
## Call:
## lm(formula = bmi ~ hyp + chl, data = nhanes)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -6.425 -3.296  0.035  3.123  7.632 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 20.10564    5.70716   3.523  0.00551 **
## hyp         -0.68459    3.39596  -0.202  0.84428   
## chl          0.03783    0.03054   1.239  0.24370   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.66 on 10 degrees of freedom
##   (12 observations deleted due to missingness)
## Multiple R-squared:  0.143,  Adjusted R-squared:  -0.02846 
## F-statistic: 0.834 on 2 and 10 DF,  p-value: 0.4624
# missing exist