Fit a mixed-effects meta-analysis model with inclusion of one or more spline terms

Fit a mixed-effects meta-analysis model with inclusion of one or more spline terms

Usage

splinemixmeta(
  smooth = NULL,
  formula,
  se,
  S = se^2,
  manual_fixed = FALSE,
  residual_re = TRUE,
  data,
  random = list(),
  method = "reml",
  bscov = "unstr",
  ...
)

Arguments

smooth

A smoothing term created by mgcv::s(), or a list of such terms.

formula

A formula for the fixed effects part of the model.

se

A vector of standard errors for the response variables.

S

As an alternative to se, S can be provided in several formats to give variance-covariance information for the response variables.

manual_fixed

If TRUE, the fixed-effect component (if any) of any smooth terms is being manually included in the formula and hence should not be obtained as the unpenalized component(s) of smooth. Normally the "fixed-effect component" is the linear component. Hence one should either provide smooth = s(x) with x omitted from formula (e.g. formula = y or formula = y ~ 1) and thus manual_fixed = FALSE, or provide smooth = s(x) with x included in formula (e.g. formula = y ~ x) and manual_fixed = TRUE. The model fits should be identical but the coefficient for x will differ because x will be scaled differently if it was automatically obtained from the spline basis functions (i.e. with manual_fixed = FALSE). In either case, the unpenalized dimensions of the smooth term and not include in the spline random effects.

residual_re

If TRUE, a datum-level random effect for residual variation (beyond the measurement error specified by se or S) is automatically included (similar to the default behavior of mixmeta::mixmeta() when random is not specified). Normally this should be TRUE unless there is a clear reason to set it FALSE.

data

A data frame containing the variables in the model. If not provided, variables are sought from where the function was called.

random

See mixmeta::mixmeta(). This is a list of one-sided formulas specifying additional random effects beyond those that will be created from the smooth argument and residual_re.

method

This must be reml. It is provided as an argument to make clear that only reml is supported for estimating models where spline formulations are set up as random effects. This simplifies catching cases where a user might try to pass a different method value to mixmeta::mixmeta() via ....

bscov

See mixmeta::mixmeta(). This is relevant only if random is provided.

...

Additional arguments passed to mixmeta::mixmeta().'

Value

An object of class splinemixmeta, unless there are no smooth terms, in which case an object of class mixmeta is returned.

Details

This function combines capabilities of mgcv and mixmeta in order to provide spline meta-regression, which means a meta-regression model where the shape of the relationship is unspecified and estimated from the data with smoothing splines. Spline components built from mgcv can be represented as random effects (along with fixed effects, which are unpenalized, typically for linear terms). mixmeta supports fairly flexible specification of fixed and random effects in (univariate or multivariate) meta-analysis regression (meta-regression) models. splinemixmeta takes mgcv-style specifications of smooth (spline) terms, sets them up for mixmeta, and the calls mixmeta to fit the model by REML.

Only a limited set of s arguments and options are supported. Argument k should work. For bs, supported basis functions include "cr", "cs", and "cc". Note that the default choice bs = "tp" does not work well and so results in a warning. (The supported basis functions are those for which mgcv::smoothCon can produce diagonal penalty matrices are supported ("cr", "cs", "cc"), with the exception of "tp". Arguments fx, m, by, id, and sp are not supported should not be provided. Argument xt should work but is untested. Argument pc is untested.

Note that bs="cc" (cyclic cubic regression spline) does not have unpenalized components, so if this is used, manual_fixed is not relevant.

splinemixmeta is not particularly optimized for large data sets.

See also

• predict.splinemixmeta() for predictions based on BLUPs (best linear unbiased predictors) from fitted splinemixmeta models. This is an S3 method that will be called from predict(x) where x is a splinemixmeta object.

• plot.splinemixmeta() for plotting fitted spline meta-regression models. This is an S3 method that will be called from plot(x) where x is a splinemixmeta object.

• blup.splinemixmeta() for obtaining BLUPs (best linear unbiased predictors) from fitted splinemixmeta models. This is used by predict.splinemixmeta, which is typically easier to call directly. This is an S3 method that will be called from blup(x) where x is a splinemixmeta object.

• make_smm_smooth() for the internal function that sets up spline terms for use in splinemixmeta.