msm_fit {qgcomp}

Fitting marginal structural model (MSM) within quantile g-computation

Description

This is an internal function called by qgcomp, qgcomp.glm.boot, and qgcomp.glm.noboot, but is documented here for clarity. Generally, users will not need to call this function directly.

Usage

msm_fit(
  f,
  qdata,
  intvals,
  expnms,
  rr = TRUE,
  main = TRUE,
  degree = 1,
  id = NULL,
  weights,
  bayes = FALSE,
  MCsize = nrow(qdata),
  hasintercept = TRUE,
  ...
)

Arguments

f

an r formula representing the conditional model for the outcome, given all exposures and covariates. Interaction terms that include exposure variables should be represented via the AsIs function

qdata

a data frame with quantized exposures

intvals

sequence, the sequence of integer values that the joint exposure is 'set' to for estimating the msm. For quantile g-computation, this is just 0:(q-1), where q is the number of quantiles of exposure.

expnms

a character vector with the names of the columns in qdata that represent the exposures of interest (main terms only!)

rr

logical, estimate log(risk ratio) (family='binomial' only)

main

logical, internal use: produce estimates of exposure effect (psi) and expected outcomes under g-computation and the MSM

degree

polynomial bases for marginal model (e.g. degree = 2 allows that the relationship between the whole exposure mixture and the outcome is quadratic. Default=1)

id

(optional) NULL, or variable name indexing individual units of observation (only needed if analyzing data with multiple observations per id/cluster)

weights

"case weights" - passed to the "weight" argument of glm or bayesglm

bayes

use underlying Bayesian model (arm package defaults). Results in penalized parameter estimation that can help with very highly correlated exposures. Note: this does not lead to fully Bayesian inference in general, so results should be interpreted as frequentist.

MCsize

integer: sample size for simulation to approximate marginal zero inflated model parameters. This can be left small for testing, but should be as large as needed to reduce simulation error to an acceptable magnitude (can compare psi coefficients for linear fits with qgcomp.zi.noboot to gain some intuition for the level of expected simulation error at a given value of MCsize)

hasintercept

(logical) does the model have an intercept?

...

arguments to glm (e.g. family)

Details

This function first computes expected outcomes under hypothetical interventions to simultaneously set all exposures to a specific quantile. These predictions are based on g-computation, where the exposures are ‘quantized’, meaning that they take on ordered integer values according to their ranks, and the integer values are determined by the number of quantile cutpoints used. The function then takes these expected outcomes and fits an additional model (a marginal structural model) with the expected outcomes as the outcome and the intervention value of the exposures (the quantile integer) as the exposure. Under causal identification assumptions and correct model specification, the MSM yields a causal exposure-response representing the incremental change in the expected outcome given a joint intervention on all exposures.

See Also

qgcomp.glm.boot, and qgcomp

Examples

set.seed(50)
dat <- data.frame(y=runif(200), x1=runif(200), x2=runif(200), z=runif(200))
X <- c('x1', 'x2')
qdat <- quantize(dat, X, q=4)$data
mod <- msm_fit(f=y ~ z + x1 + x2 + I(x1*x2),
        expnms = c('x1', 'x2'), qdata=qdat, intvals=1:4, bayes=FALSE)
summary(mod$fit) # outcome regression model
summary(mod$msmfit) # msm fit (variance not valid - must be obtained via bootstrap)