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Pool Estimates from Several Imputations with Rubin's Rules

Source: R/pool_imputations.R
pool_imputations.Rd

Combines the same model fitted to each of `m` imputed data sets into one estimate per term: the mean of the estimates, the within-imputation variance, the between-imputation variance and the total variance \(T = \bar{U} + (1 + 1/m) B\), with Rubin's degrees of freedom and a t-based interval and p-value.

Usage

pool_imputations(
  x,
  imputation_col = "imputation",
  conf_level = 0.95,
  exponentiate = FALSE,
  df_complete = NULL
)

Arguments

x

A list of data frames, or a stacked data frame.

imputation_col

Name of the imputation column when `x` is stacked.

conf_level

Confidence level.

exponentiate

Return `estimate`, `conf.low` and `conf.high` exponentiated.

df_complete

Optional complete-data degrees of freedom (for example `N - k`). When given, the Barnard-Rubin (1999) small-sample adjustment is used, \(\nu_{adj} = (1/\nu + 1/\nu_{obs})^{-1}\) with \(\nu_{obs} = \frac{df+1}{df+3} df (1 - \lambda)\), instead of the large-sample \(\nu\). Terms are pooled over the union of terms across imputations; a term missing in any imputation is an error.

Value

A tibble with `term`, `m`, `estimate`, `std.error` (of the pooled estimate), `within_var`, `between_var`, `total_var`, `df`, `statistic`, `p.value`, `conf.low`, `conf.high` and `fmi` (fraction of missing information).

Input

Either a list of `m` data frames (for example `lapply(imputed, function(d) broom::tidy(fit(d)))`) or one stacked data frame with a column naming the imputation. Each needs `term`, `estimate` and `std.error`. Pool on the scale the estimates are approximately normal (log hazard ratio, not hazard ratio); use `exponentiate = TRUE` to report on the ratio scale.

Rubin's rules assume proper multiple imputation (draws from a posterior predictive distribution). A single imputation, such as one run of [impute_piecewise_lmm()], gives no between-imputation variance, so impute several times with different seeds first.

Examples

set.seed(1)
fits <- lapply(1:5, function(i) {
  data.frame(term = c("x", "z"), estimate = c(0.5, -0.2) + rnorm(2, sd = 0.05),
             std.error = c(0.1, 0.08))
})
pool_imputations(fits)
#> # A tibble: 2 × 13
#>   term      m estimate std.error within_var between_var total_var    df
#>   <chr> <int>    <dbl>     <dbl>      <dbl>       <dbl>     <dbl> <dbl>
#> 1 x         5    0.499    0.106      0.01       0.00110   0.0113  292. 
#> 2 z         5   -0.186    0.0950     0.0064     0.00219   0.00903  47.2
#> # ℹ 5 more variables: statistic <dbl>, p.value <dbl>, conf.low <dbl>,
#> #   conf.high <dbl>, fmi <dbl>