Tidy a pooled inverse probability weighted result

tidy() returns the estimates of a pool_ipw() result as a tibble using the column names broom conventions use. It holds the rows the results themselves report: for a binary or categorical exposure one row per exposure level, under the term "mean", and then one row per effect measure per contrast of levels; for a continuous exposure one row per reported coefficient. The rows arrive in the order the pooled result stores them and nothing is dropped.

Those columns are the ones the pooled result's own coercion surface reports, so this method is that surface read as a tibble rather than a second assembly of the same table. The covariance of the effects the frame attaches is the one thing that does not travel: it is an attribute rather than a column, and a tidied table is its columns.

The pooling has already happened by the time this method sees the result. Nothing here re-pools and no argument changes an estimate: they say how the table already in the object is reported, which is which of the two readings it is, whether an interval comes with it, the level that interval is reported at, and the scale the ratio rows are put on.

A pooled result reports its effects in one of two readings, and tidy() returns the one the result records unless effects names the other for the call. pool_ipw() pools both readings of the results it is given, so naming one here reports a table the pooling already built rather than pooling again. The marginal reading is the table of pooled causal contrasts described above. The conditional reading is the outcome models' coefficient surface, pooled the same way: one row per coefficient, from the block of the joint estimation that carries the uncertainty of having estimated the weights from the same data. The two readings return the same columns in the same order, with one exception: the contrast column belongs to the marginal reading. A binary and a categorical pool both carry it there, naming the exposure level each mean row belongs to and the pair of levels each effect measure compares, and the conditional reading of either returns the same table one column narrower.

Usage

# S3 method for class 'ipw_pooled'
tidy(
  x,
  conf.int = FALSE,
  conf.level = NULL,
  exponentiate = FALSE,
  ...,
  effects = NULL
)

Arguments

x

An ipw_pooled object, as returned by pool_ipw().

conf.int

Logical. Should the confidence interval bounds be returned in the conf.low and conf.high columns? Defaults to FALSE.

conf.level

The confidence level of the interval. NULL, the default, reports the bounds at the level the pooled result stored, which is the level its own intervals were built at. A number between 0 and 1 rebuilds them at that level instead, from the estimate and its standard error referred to t on the pooled degrees of freedom. Not used when conf.int is FALSE, though it must still be a valid level.

exponentiate

Logical. Should the estimate and its bounds be exponentiated on the rows reported on the log scale? Defaults to FALSE. This behaves exactly as it does on the pooled result's own coercion surface: in the marginal reading the log(rr) and log(or) rows have their estimate and bounds exponentiated and their term relabeled to rr and or, and in the conditional reading the outcome model's link settles the scale for every row at once and no term is relabeled. In both readings the standard error, the test statistic, and the p-value describe the log scale and stay there, which is where the inference was done.

...

These dots are for future extensions and must be empty.

effects

The reading to report, either "marginal" or "conditional". NULL, the default, reports the reading the pooled result records; naming a reading reports that one for the one call and leaves the result as it is. The marginal reading reports the pooled causal contrasts; the conditional reading reports the pooled coefficients of the outcome models, which is the reading exponentiate above puts on the natural scale every row at once. as_marginal() and as_conditional() move a pooled result between the two readings for good rather than for a call.

A reading the pooling could not compute is refused rather than reported under the other one's name. The conditional reading needs the covariance the joint estimation of the weights and the outcome implies, and a linearization fit stacks no such system and records no such block, so a set of those fits pools the marginal reading alone. A result pooled before both readings were kept holds only the one it was pooled in, and asking it for the other is refused the same way.

"fixed" is not among the values this method takes, though tidy() on a single result accepts it. mice::pool() asks for that reading from the tidier of each imputation's own fit, which is where the name arrives and where the tolerance for it belongs; nothing tidies a pooled result on its behalf.

Value

A tibble with one row per pooled estimate and the columns:

term: The effect measure, such as "mean" for a counterfactual mean, or "rd", "log(rr)", "log(or)", "diff", "slope", or "coef" for the measures built from them, or the coefficient name in the conditional reading.
contrast: What the row is about: the exposure level a "mean" row belongs to, such as "0" or "b"; the pair of levels an effect measure compares, such as "1 vs 0" or "b vs a"; or the coefficient name on a surface whose rows are named after their coefficients. Present only in the marginal reading, and there only where a row reports one: the conditional reading names each coefficient in term and returns no contrast column.
estimate: The pooled point estimate.
std.error: The pooled standard error.
statistic: The test statistic, the estimate over its standard error.
df: The pooled degrees of freedom the statistic is referred to. These carry the Barnard-Rubin small-sample adjustment, so the statistic is referred to t on them rather than to the normal.
p.value: The two-sided p-value of that statistic.
conf.low, conf.high: The interval bounds. Present only when conf.int is TRUE.

Examples

set.seed(2024)
n <- 150
x1 <- rnorm(n)
z <- rbinom(n, 1, plogis(0.3 * x1))
y <- rbinom(n, 1, plogis(-0.4 + 0.9 * z + 0.5 * x1))
dat <- data.frame(x1, z, y)
dat$x1[rbinom(n, 1, 0.2) == 1] <- NA

imp <- mice::mice(dat, m = 2, print = FALSE, seed = 1)
fits <- with(imp, {
  ps <- glm(z ~ x1, family = binomial())
  w <- wt_ate(ps)
  om <- glm(y ~ z, family = quasibinomial(), weights = w)
  ipw(ps, om)
})
#> ℹ Using exposure variable "z" from the propensity score model
#> ℹ Treating `.exposure` as binary
#> ℹ Using exposure variable "z" from the propensity score model
#> ℹ Treating `.exposure` as binary

tidy(pool_ipw(fits))
#> # A tibble: 5 × 7
#>   term    contrast estimate std.error statistic    df  p.value
#>   <chr>   <chr>       <dbl>     <dbl>     <dbl> <dbl>    <dbl>
#> 1 mean    0           0.412    0.0595      6.91  136. 1.68e-10
#> 2 mean    1           0.564    0.0551     10.2   138. 1.29e-18
#> 3 rd      1 vs 0      0.152    0.0810      1.88  134. 6.25e- 2
#> 4 log(rr) 1 vs 0      0.315    0.174       1.80  134. 7.33e- 2
#> 5 log(or) 1 vs 0      0.614    0.332       1.85  134. 6.68e- 2

tidy(pool_ipw(fits), conf.int = TRUE, exponentiate = TRUE)
#> # A tibble: 5 × 9
#>   term  contrast estimate std.error statistic    df  p.value conf.low conf.high
#>   <chr> <chr>       <dbl>     <dbl>     <dbl> <dbl>    <dbl>    <dbl>     <dbl>
#> 1 mean  0           0.412    0.0595      6.91  136. 1.68e-10  0.294       0.529
#> 2 mean  1           0.564    0.0551     10.2   138. 1.29e-18  0.455       0.673
#> 3 rd    1 vs 0      0.152    0.0810      1.88  134. 6.25e- 2 -0.00803     0.312
#> 4 rr    1 vs 0      1.37     0.174       1.80  134. 7.33e- 2  0.970       1.93 
#> 5 or    1 vs 0      1.85     0.332       1.85  134. 6.68e- 2  0.958       3.56 

# The outcome models' coefficients, pooled the same way
tidy(pool_ipw(fits), effects = "conditional")
#> # A tibble: 2 × 6
#>   term        estimate std.error statistic    df p.value
#>   <chr>          <dbl>     <dbl>     <dbl> <dbl>   <dbl>
#> 1 (Intercept)   -0.358     0.246     -1.46  136.  0.148 
#> 2 z              0.614     0.332      1.85  134.  0.0668

Usage

Arguments

Value

See also

Examples