Set prior distributions for the meta-analysis model

Construct a did_priors object specifying the prior distribution for each population-level parameter. Any parameter not supplied takes a default.

Usage

set_priors(
  treatment_effect_mean = normal(0, 10),
  treatment_effect_sd = cauchy(5),
  time_trend_mean = normal(0, 10),
  time_trend_sd = cauchy(5),
  rho_mean = normal(0, 1),
  rho_sd = normal(0, 0.5),
  nu = gamma(2, 0.1),
  delta_rct = normal(0, 10),
  delta_pp = normal(0, 10),
  sigma = cauchy(5),
  beta_cov = normal(0, 10),
  lkj_eta = lkj(2),
  baseline_difference_mean = normal(0, 0.05),
  baseline_difference_sd = cauchy(0.1),
  kappa = normal(0, 0.5),
  multiplier = lognormal(0, 0.7)
)

Arguments

treatment_effect_mean

Prior on the population treatment effect mean. Default: normal(0, 10).

treatment_effect_sd

Prior on the between-study SD. Default: cauchy(5).

time_trend_mean

Prior on the population time-trend mean. Default: normal(0, 10).

time_trend_sd

Prior on the between-study time-trend SD. Default: cauchy(5).

rho_mean

Prior on the mean of the Fisher-z transformed pre-post correlation (only used when hierarchical_rho = TRUE). Default: normal(0, 1).

rho_sd

Prior on the SD of the Fisher-z transformed pre-post correlation (only used when hierarchical_rho = TRUE). Default: normal(0, 0.5).

nu

Prior on the degrees of freedom for between-study heterogeneity (only used when robust_heterogeneity = TRUE). Default: gamma(2, 0.1).

delta_rct

Prior on the RCT design offset relative to DiD (only used when design_effects = TRUE). Default: normal(0, 10).

delta_pp

Prior on the Pre-Post design offset relative to DiD (only used when design_effects = TRUE). Default: normal(0, 10).

sigma

Prior on the study-level observation standard deviations (shared across all designs). Default: cauchy(5).

beta_cov

Prior on the covariate regression coefficients (only used when covariates is specified in meta_did()). Default: normal(0, 10).

lkj_eta

Prior on the Cholesky factor of the correlation matrix between treatment effects and time trends (only used when correlated_effects = TRUE). Default: lkj(2), which gently regularises toward zero correlation.

baseline_difference_mean

Prior on the population mean of the per-study baseline imbalance among non-randomised studies (treatment-arm vs control-arm pre-treatment mean, on the normalised fractional scale). Only used when mu_gamma = "estimated" in meta_did(); under the default mu_gamma = "zero" the population mean is pinned at zero and this prior is ignored. Default: normal(0, 0.05).

The old default was normal(0, 0.5), which was both internally inconsistent with the cauchy(0.1) prior on the between-study SD (it asserted the average imbalance could be far larger than the spread around it) and materially informative about the pooled treatment effect, because baseline imbalance is unidentified for post-only studies and subtracts directly from their estimated effect.

baseline_difference_sd

Prior on the between-study SD of the baseline imbalance among non-randomised studies. Default: cauchy(0.1).

kappa

Prior on the excess-imbalance factor for randomised studies, interpreted as half-normal because kappa is constrained positive. Only used when kappa = "estimate" in meta_did(). kappa^2 is the variance inflation of a randomised study's baseline contrast beyond simple random sampling, so kappa = 0 is perfect randomisation. Default: normal(0, 0.5), which places most mass below kappa = 1 (a doubling of the baseline-contrast variance).

multiplier

Prior on the multiplicative-covariate effect multiplier (only used when multiplicative_covariate is specified in meta_did()). With one or two multiplicative covariates the same prior is applied independently to every estimated non-reference-level factor (of either covariate). Must be a lognormal() prior, placed on the log of the multiplier so it is strictly positive with no boundary at zero. Default: lognormal(0, 0.7) — a median of 1 (the no-multiplicative-effect case), with a central 95% range of roughly [0.25, 3.9] on the natural scale.

Value

A did_priors object.

Examples

# Use defaults
set_priors()
#> Prior distributions:
#>   treatment_effect_mean ~ normal(mean = 0, sd = 10)
#>   treatment_effect_sd ~ cauchy(scale = 5)
#>   time_trend_mean ~ normal(mean = 0, sd = 10)
#>   time_trend_sd ~ cauchy(scale = 5)
#>   rho_mean ~ normal(mean = 0, sd = 1)
#>   rho_sd ~ normal(mean = 0, sd = 0.5)
#>   nu ~ gamma(shape = 2, rate = 0.1)
#>   delta_rct ~ normal(mean = 0, sd = 10)
#>   delta_pp ~ normal(mean = 0, sd = 10)
#>   sigma ~ cauchy(scale = 5)
#>   beta_cov ~ normal(mean = 0, sd = 10)
#>   lkj_eta ~ lkj(eta = 2)
#>   baseline_difference_mean ~ normal(mean = 0, sd = 0.05)
#>   baseline_difference_sd ~ cauchy(scale = 0.1)
#>   kappa ~ normal(mean = 0, sd = 0.5)
#>   multiplier ~ lognormal(meanlog = 0, sdlog = 0.7)

# Override one prior
set_priors(treatment_effect_sd = cauchy(2))
#> Prior distributions:
#>   treatment_effect_mean ~ normal(mean = 0, sd = 10)
#>   treatment_effect_sd ~ cauchy(scale = 2)
#>   time_trend_mean ~ normal(mean = 0, sd = 10)
#>   time_trend_sd ~ cauchy(scale = 5)
#>   rho_mean ~ normal(mean = 0, sd = 1)
#>   rho_sd ~ normal(mean = 0, sd = 0.5)
#>   nu ~ gamma(shape = 2, rate = 0.1)
#>   delta_rct ~ normal(mean = 0, sd = 10)
#>   delta_pp ~ normal(mean = 0, sd = 10)
#>   sigma ~ cauchy(scale = 5)
#>   beta_cov ~ normal(mean = 0, sd = 10)
#>   lkj_eta ~ lkj(eta = 2)
#>   baseline_difference_mean ~ normal(mean = 0, sd = 0.05)
#>   baseline_difference_sd ~ cauchy(scale = 0.1)
#>   kappa ~ normal(mean = 0, sd = 0.5)
#>   multiplier ~ lognormal(meanlog = 0, sdlog = 0.7)