Mixture model MCMC

Run the mixture model with MCMC.

Usage

hb_mcmc_mixture(
  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),
  s_delta = 30,
  s_beta = 30,
  s_sigma = 30,
  m_omega = c(0, 0),
  s_omega = c(30, 30),
  p_omega = 1/length(m_omega),
  n_chains = 4,
  n_adapt = 2000,
  n_warmup = 4000,
  n_iterations = 20000,
  quiet = TRUE
)

Arguments

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.
s_delta: Numeric of length 1, prior standard deviation of the study-by-group effect parameters delta.
s_beta: Numeric of length 1, prior standard deviation of the fixed effects beta.
s_sigma: Numeric of length 1, prior upper bound of the residual standard deviations.
m_omega: Numeric with length equal to the number of supposed studies (but only the current study is in the data). m_omega is the prior control group mean of each study. The last element corresponds to the current study, and the others are for historical studies.
s_omega: Numeric with length equal to the number of supposed studies (but only the current study is in the data). s_omega is the prior control group standard deviation of each study. The last element corresponds to the current study, and the others are for historical studies.
p_omega: Numeric with length equal to the number of supposed studies (but only the current study is in the data). p_omega is the prior control group mixture proportion of each study. The last element corresponds to the current study, and the others are for historical studies.
n_chains: Number of MCMC chains to run.
n_adapt: Number of adaptation iterations to run.
n_warmup: Number of warmup iterations per chain to run.
n_iterations: Number of saved MCMC iterations per chain to run.
quiet: Logical of length 1, TRUE to suppress R console output.

Value

A tidy data frame of parameter samples from the posterior distribution. Columns .chain, .iteration, and .draw have the meanings documented in the posterior package.

Details

The study-specific components of the mixture prior are all fixed in advance. Mixture components are normal distributions with means in m_omega and standard deviations in s_omega. These vectors are ordered with historical studies first and the current study last. These mixture components can be computed using hb_mcmc_mixture_hyperparameters() on a full set of data (all the historical studies and the current study together). Then the m_omega and s_omega columns of the output can be plugged directly into hb_mcmc_mixture(). See the examples for a demonstration.

Examples

data_all_studies <- hb_sim_independent(n_continuous = 2)$data
data_all_studies$study <- paste0("study", data_all_studies$study)
hyperparameters <- hb_mcmc_mixture_hyperparameters(
  data = data_all_studies,
  response = "response",
  study = "study",
  study_reference = "study5",
  group = "group",
  group_reference = 1,
  patient = "patient",
  n_chains = 1,
  n_adapt = 100,
  n_warmup = 50,
  n_iterations = 50
)
print(hyperparameters)
#> # A tibble: 5 × 4
#>   study  study_index m_omega s_omega
#>   <chr>        <int>   <dbl>   <dbl>
#> 1 study1           1   0.100  0.285 
#> 2 study2           2  -0.453  0.0933
#> 3 study3           3   0.797  0.0709
#> 4 study4           4  -0.313  0.202 
#> 5 study5           5   0     30     
data_current_study <- dplyr::filter(data_all_studies, study == max(study))
hb_mcmc_mixture(
  data = data_current_study,
  response = "response",
  study = "study",
  study_reference = "study5",
  group = "group",
  group_reference = 1,
  patient = "patient",
  m_omega = hyperparameters$m_omega, # use hyperparams from historical data
  s_omega = hyperparameters$s_omega, # use hyperparams from historical data
  p_omega = rep(1 / nrow(hyperparameters), nrow(hyperparameters)),
  n_chains = 1,
  n_adapt = 100,
  n_warmup = 50,
  n_iterations = 50
)
#> # A tibble: 50 × 19
#>      alpha `beta[1]` `beta[2]` `delta[1]` `delta[2]` `omega[1]` `omega[2]`
#>      <dbl>     <dbl>     <dbl>      <dbl>      <dbl>      <dbl>      <dbl>
#>  1  0.0364     0.592     -1.39     -0.266     -0.228     0.0364     -0.458
#>  2  0.0368     0.619     -1.38     -0.231     -0.202     0.0368     -0.370
#>  3  0.0195     0.691     -1.36     -0.335     -0.257     0.0195     -0.324
#>  4  0.108      0.660     -1.37     -0.348     -0.258     0.108      -0.352
#>  5  0.0420     0.681     -1.39     -0.318     -0.282     0.0420     -0.512
#>  6 -0.0370     0.617     -1.42     -0.262     -0.152    -0.0370     -0.428
#>  7  0.0360     0.618     -1.34     -0.315     -0.232     0.0360     -0.487
#>  8 -0.0284     0.592     -1.40     -0.353     -0.256    -0.0284     -0.568
#>  9  0.0841     0.605     -1.33     -0.309     -0.190     0.0841     -0.370
#> 10  0.179      0.644     -1.36     -0.328     -0.200     0.179      -0.652
#> # ℹ 40 more rows
#> # ℹ 12 more variables: `omega[3]` <dbl>, `omega[4]` <dbl>, `omega[5]` <dbl>,
#> #   `post_p[1]` <dbl>, `post_p[2]` <dbl>, `post_p[3]` <dbl>, `post_p[4]` <dbl>,
#> #   `post_p[5]` <dbl>, sigma <dbl>, .chain <int>, .iteration <int>, .draw <int>

Usage

Arguments

Value

Details

See also

Examples