Quantify borrowing with effective sample size (ESS) as cited and explained in the methods vignette at https://wlandau.github.io/historicalborrow/articles/methods.html.

## Arguments

- mcmc_pool
A fitted model from

`hb_mcmc_pool()`

.- mcmc_hierarchical
A fitted model from

`hb_mcmc_hierarchical()`

.- data
A tidy data frame or

`tibble`

with the data.- response
Character of length 1, name of the column in

`data`

with the response/outcome variable.`data[[response]]`

must be a continuous variable, and it*should*be the change from baseline of a clinical endpoint of interest, as opposed to just the raw response. Treatment differences are computed directly from this scale, please supply change from baseline unless you are absolutely certain that treatment differences computed directly from this quantity are clinically meaningful.- study
Character of length 1, name of the column in

`data`

with the study ID.- study_reference
Atomic of length 1, element of the

`study`

column that indicates the current study. (The other studies are historical studies.)- group
Character of length 1, name of the column in

`data`

with the group ID.- group_reference
Atomic of length 1, element of the

`group`

column that indicates the control group. (The other groups may be treatment groups.)- patient
Character of length 1, name of the column in

`data`

with the patient ID.

## Value

A data frame with one row and the following columns:

`v0`

: posterior predictive variance of the control group mean of a hypothetical new study given the pooled model. Calculated as the mean over MCMC samples of`1 / sum(sigma_i ^ 2)`

, where each`sigma_i`

is the residual standard deviation of study`i`

estimated from the pooled model.`v_tau`

: posterior predictive variance of a hypothetical new control group mean under the hierarchical model. Calculated by averaging over predictive draws, where each predictive draw is from`rnorm(n = 1, mean = mu_, sd = tau_)`

and`mu_`

and`tau_`

are the`mu`

and`tau`

components of an MCMC sample.`n`

: number of non-missing historical control patients.`weight`

: strength of borrowing as a ratio of variances:`v0 / v_tau`

.`ess`

: strength of borrowing as an effective sample size:`n v0 / v_tau`

, where`n`

is the number of non-missing historical control patients.

## See also

Other summary:
`hb_summary()`

## Examples

```
data <- hb_sim_independent(n_continuous = 2)$data
data$group <- sprintf("group%s", data$group)
data$study <- sprintf("study%s", data$study)
pool <- hb_mcmc_pool(
data,
n_chains = 1,
n_adapt = 100,
n_warmup = 50,
n_iterations = 50
)
hierarchical <- hb_mcmc_hierarchical(
data,
n_chains = 1,
n_adapt = 100,
n_warmup = 50,
n_iterations = 50
)
hb_ess(
mcmc_pool = pool,
mcmc_hierarchical = hierarchical,
data = data
)
#> # A tibble: 1 × 5
#> ess weight n v0 v_tau
#> <dbl> <dbl> <int> <dbl> <dbl>
#> 1 8.24 0.0206 400 0.226 11.0
```