effect_draw: Make predictive draws from baggr model

Description

The function effect_draw and its alias, posterior_predict, take the sample of hyperparameters from a baggr model (typically hypermean and hyper-SD, which you can see using treatment_effect) and draws values of new realisations of treatment effect, i.e. an additional draw from the "population of studies". This can be used for both prior and posterior draws, depending on baggr model. By default this is done for a single new effect, but for meta-regression models you can specify values of covariates with the newdata argument, same as in predict.

Usage

effect_draw(
  object,
  draws = NULL,
  newdata = NULL,
  transform = NULL,
  summary = FALSE,
  message = TRUE,
  interval = 0.95
)

Value

A vector (with draws values) for models with one treatment effect parameter, a matrix (draws rows and same number of columns as number of parameters) otherwise. If newdata are specified, an array is returned instead, where the first dimension corresponds to rows of newdata.

Arguments

object: A baggr class object.
draws: How many values to draw? The default is as long as the number of samples in the baggr object (see Details).
newdata: an optional data frame containing new values of covariates that were used when fitting the baggr model
transform: a transformation (an R function) to apply to the result of a draw.
summary: logical; if TRUE returns summary statistics rather than samples from the distribution;
message: logical; use to disable messages prompted by using this function with no pooling models
interval: uncertainty interval width (numeric between 0 and 1), if summary=TRUE

Details

The predictive distribution can be used to "combine" heterogeneity between treatment effects and uncertainty in the mean treatment effect. This is useful both in understanding impact of heterogeneity (see Riley et al, 2011, for a simple introduction) and for study design e.g. as priors in analysis of future data (since the draws can be seen as an expected treatment effect in a hypothetical study).

The default number of samples is the same as what is returned by Stan model implemented in baggr, (depending on such options as iter, chains, thin). If n is larger than what is available in Stan model, we draw values with replacement. This is not recommended and warning is printed in these cases.

Under default settings in baggr, a posterior predictive distribution is obtained. But effect_draw can also be used for prior predictive distributions when setting ppd=T in baggr. The two outputs work exactly the same way.

If the baggr model used by the function is a meta-regression (i.e. a baggr model with covariates), by specifying the predicted values can be adjusted for known levels of fixed covariates by passing newdata (same as in predict). If no adjustment is made, the returned value should be interpreted as the effect when all covariates are 0.

References

Riley, Richard D., Julian P. T. Higgins, and Jonathan J. Deeks. "Interpretation of Random Effects Meta-Analyses". BMJ 342 (10 February 2011)..

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