hb_summary {historicalborrow}

Model summary

Description

Summarize a fitted model in a table.

Usage

hb_summary(
  mcmc,
  data,
  response = "response",
  study = "study",
  study_reference = max(data[[study]]),
  group = "group",
  group_reference = min(data[[group]]),
  patient = "patient",
  covariates = grep("^covariate", colnames(data), value = TRUE),
  eoi = 0,
  direction = "<"
)

Arguments

mcmc

A wide data frame of posterior samples returned by hb_mcmc_hierarchical() or similar MCMC function.

data

Tidy data frame with one row per patient, indicator columns for the response variable, study, group, and patient, and covariates. All columns must be atomic vectors (e.g. not lists). The data for the mixture and simple models should have just one study, and the others should have data from more than one study. The simple model can be used to get the historical data components of m_omega and s_omega for the mixture model.

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.

covariates

Character vector of column names in data with the columns with baseline covariates. These can be continuous, categorical, or binary. Regardless, historicalborrow derives the appropriate model matrix.

eoi

Numeric of length at least 1, vector of effects of interest (EOIs) for critical success factors (CSFs).

direction

Character of length length(eoi) indicating how to compare the treatment effect to each EOI. ">" means Prob(treatment effect > EOI), and "<" means Prob(treatment effect < EOI). All elements of direction must be either ">" or "<".

Details

The hb_summary() function post-processes the results from the model. It accepts MCMC samples of parameters and returns interpretable group-level posterior summaries such as change from baseline response and treatment effect. To arrive at these summaries, hb_summary() computes marginal posteriors of transformed parameters. The transformations derive patient-level fitted values from model parameters, then derive group-level responses as averages of fitted values. We refer to this style of estimation as "unconditional estimation", as opposed to "conditional estimation", which takes each group mean to be the appropriate linear combination of the relevant alpha and delta parameters, without using beta components or going through fitted values. If the baseline covariates are balanced across studies, unconditional and conditional estimation should produce similar estimates of placebo and treatment effects.

Value

A tidy data frame with one row per group (e.g. treatment arm) and the columns in the following list. Unless otherwise specified, the quantities are calculated at the group level. Some are calculated for the current (non-historical) study only, while others pertain to the combined dataset which includes all historical studies. The mixture model is an exception because the data argument only includes the current study, so other quantities that include historical information will need to borrow from an hb_summary() call on one of the other models.

• group: group label.

• data_mean: observed mean response specific to the current study.

• data_sd: observed standard deviation of the response specific to the current study.

• data_lower: lower bound of a simple frequentist 95% confidence interval of the observed mean specific to the current study.

• data_upper: upper bound of a simple frequentist 95% confidence interval of the observed mean specific to the current study.

• data_n: number of non-missing observations in the combined dataset with all studies.

• data_N: total number of observations (missing and non-missing) in the combined dataset with all studies.

• ⁠data_n_study_*⁠: number of non-missing observations separately for each study. The suffixes of these column names are integer study indexes. Call dplyr::distinct(hb_data(your_data), study, study_label) to see which study labels correspond to these integer indexes. Note: the combined dataset for the mixture model is just the current study. If all the ⁠data_n_study_*⁠ results across all studies are desired, then call hb_summary() on a different model (e.g. pooled).

• ⁠data_N_study_*⁠: same as ⁠data_n_study_*⁠ except both missing and non-missing observations are counted (total number of observations).

• response_mean: Estimated posterior mean of the response from the model specific to the current study. Typically, the raw response is change from baseline, in which case response_mean is estimating change from baseline.

• response_sd: Estimated posterior standard deviation of the mean response from the model specific to the current study.

• response_variance: Estimated posterior variance of the mean response from the model specific to the current study.

• response_lower: Lower bound of a 95% posterior interval on the mean response from the model specific to the current study.

• response_upper: Upper bound of a 95% posterior interval on the mean response from the model specific to the current study.

• response_mean_mcse: Monte Carlo standard error of response_mean.

• response_sd_mcse: Monte Carlo standard error of response_sd.

• response_lower_mcse: Monte Carlo standard error of response_lower.

• response_upper_mcse: Monte Carlo standard error of response_upper.

• diff_mean: Estimated treatment effect from the model specific to the current study.

• diff_lower: Lower bound of a 95% posterior interval on the treatment effect from the model specific to the current study..

• diff_upper: Upper bound of a 95% posterior interval on the treatment effect from the model specific to the current study..

• diff_mean_mcse: Monte Carlo standard error of diff_mean.

• diff_lower_mcse: Monte Carlo standard error of diff_lower.

• diff_upper_mcse: Monte Carlo standard error of diff_upper.

• P(diff > EOI), P(diff < EOI): CSF probabilities on the treatment effect specified with the eoi and direction arguments. Specific to the current study.

• effect_mean: Estimated posterior mean of effect size (treatment difference divided by residual standard deviation). Specific to the current study.

• effect_lower: Lower bound of a 95% posterior interval of effect size from the model. Specific to the current study.

• effect_upper: Upper bound of a 95% posterior interval of effect size from the model. Specific to the current study.

• precision_ratio: For the hierarchical model only, a model-based mean of the precision ratio. Specific to the current study.

• precision_ratio_lower: For the hierarchical model only, lower bound of a model-based 95% posterior interval of the precision ratio. Specific to the current study.

• precision_ratio_upper: For the hierarchical model only, upper bound of a model-based 95% posterior interval of the precision ratio. Specific to the current study.

• ⁠mix_prop_*⁠: For the mixture model only, posterior mixture proportions of each of the mixture components. The last one is for the current study and the first ones are for the historical studies. The suffixes of these column names are the integer study indexes. Call dplyr::distinct(hb_data(your_data), study, study_label) to see which study labels correspond to these integer indexes.

See Also

Other summary: hb_metrics()

Examples

if (!identical(Sys.getenv("HB_TEST", unset = ""), "")) {
data <- hb_sim_pool(n_continuous = 2)$data
data$group <- sprintf("group%s", data$group)
mcmc <- hb_mcmc_pool(
  data,
  n_chains = 1,
  n_adapt = 100,
  n_warmup = 50,
  n_iterations = 50
)
hb_summary(mcmc, data)
}