Effective sample size (ESS)

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

hbl_ess(
  mcmc_pool,
  mcmc_hierarchical,
  data,
  response = "response",
  study = "study",
  study_reference = max(data[[study]]),
  group = "group",
  group_reference = min(data[[group]]),
  patient = "patient",
  rep = "rep",
  rep_reference = min(data[[rep]])
)

Arguments

mcmc_pool: A fitted model from hbl_mcmc_pool().
mcmc_hierarchical: A fitted model from hbl_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.
rep: Character of length 1, name of the column in data with the rep ID.
rep_reference: Atomic of length 1, element of the rep column that indicates baseline, i.e. the first rep chronologically. (The other reps may be post-baseline study visits or time points.)

Value

A data frame with one row per discrete time point ("rep") 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 a prior effective sample size: n v0 / v_tau, where n is the number of non-missing historical control patients.

Examples

  set.seed(0)
  data <- hbl_sim_independent(n_continuous = 2)$data
  data$group <- sprintf("group%s", data$group)
  data$study <- sprintf("study%s", data$study)
  data$rep <- sprintf("rep%s", data$rep)
  tmp <- utils::capture.output(
    suppressWarnings(
      pool <- hbl_mcmc_pool(
        data,
        chains = 1,
        warmup = 10,
        iter = 20,
        seed = 0
      )
    )
  )
  tmp <- utils::capture.output(
    suppressWarnings(
      hierarchical <- hbl_mcmc_hierarchical(
        data,
        chains = 1,
        warmup = 10,
        iter = 20,
        seed = 0
      )
    )
  )
  hbl_ess(
    mcmc_pool = pool,
    mcmc_hierarchical = hierarchical,
    data = data
  )
#> # A tibble: 4 × 7
#> # Groups:   rep [4]
#>     rep rep_label     n    v0 v_tau weight   ess
#>   <int> <chr>     <int> <dbl> <dbl>  <dbl> <dbl>
#> 1     1 rep1        400 6.32  0.446 14.2   5667.
#> 2     2 rep2        400 6.06  0.745  8.13  3253.
#> 3     3 rep3        400 6.20  0.900  6.89  2758.
#> 4     4 rep4        400 0.354 0.635  0.558  223.

Arguments

Value

See also

Examples