mediate_zi_vcoef {maczic}

Mediation Sensitivity Analysis for Count and Zero-Inflated Count Data with a Post-Treatment Confounder

Description

'mediate_zi_vcoef' is modified from mediate_zi function with 3 confounder-related parameters ('model.u', 'delta.beta.u', and 'confounder') added. It is used to estimate causal mediation effects when there is a treatment-induced mediator-outcome confounder, and the coefficient of treatment in the confounder model is specified by users. Users can perform sensitivity analysis with a range of specified coefficient values when there is a post-treatment confounder.

Usage

mediate_zi_vcoef(
  model.u,
  delta.beta.u,
  model.m,
  model.y,
  sims = 1000,
  boot = FALSE,
  treat = "treat.name",
  mediator = "med.name",
  confounder = "confd.name",
  covariates = NULL,
  outcome = NULL,
  control = NULL,
  conf.level = 0.95,
  control.value = 0,
  treat.value = 1,
  long = TRUE,
  dropobs = FALSE,
  robustSE = FALSE,
  cluster = NULL,
  ...
)

Arguments

model.u

A fitted model object for confounder. Can be of class 'lm', 'polr', 'bayespolr', 'glm', 'bayesglm', 'gam', 'rq', or 'survreg'.

delta.beta.u

Sensitivity parameter as difference from the estimated treatment coefficient in the confounder model (model.u) based on the observed data.

model.m

A fitted model object for mediator. Can be of class 'lm', 'polr', 'bayespolr', 'glm', 'bayesglm', 'gam', 'rq', or 'survreg'.

model.y

A fitted model object for outcome. Can be of class 'lm', 'polr', 'bayespolr', 'glm', 'bayesglm', 'gam', 'vglm', 'rq', 'survreg', or 'zeroinfl'

sims

Number of Monte Carlo draws for nonparametric bootstrap or quasi-Bayesian approximation.

boot

A logical value. if 'FALSE' a quasi-Bayesian approximation is used for confidence intervals; if 'TRUE' nonparametric bootstrap will be used. Default is 'FALSE'.

treat

A character string indicating the name of the treatment variable used in the models. The treatment can be either binary (integer or a two-valued factor) or continuous (numeric).

mediator

A character string indicating the name of the mediator variable used in the models.

confounder

A character string indicating the name of the confounder variable used in the models.

covariates

A list or data frame containing values for a subset of the pre-treatment covariates in 'model.m' and 'model.y'. If provided, the function will return the estimates conditional on those covariate values.

outcome

A character string indicating the name of the outcome variable in ‘model.y’. Only necessary if 'model.y' is of class 'survreg'; otherwise ignored.

control

A character string indicating the name of the control group indicator. Only relevant if 'model.y' is of class 'gam'. If provided, 'd0', 'z0' and 'n0' are allowed to differ from 'd1', 'z1' and 'n1', respectively.

conf.level

Level of the returned two-sided confidence intervals. Default is to return the 2.5 and 97.5 percentiles of the simulated quantities.

control.value

Value of the treatment variable used as the control condition. Default is 0.

treat.value

Value of the treatment variable used as the treatment condition. Default is 1.

long

A logical value. If 'TRUE', the output will contain the entire sets of simulation draws of the the average causal mediation effects, direct effects, proportions mediated, and total effect. Default is 'TRUE'.

dropobs

A logical value indicating the behavior when the model frames of 'model.m' and 'model.y' (and the 'cluster' variable if included) are composed of different observations. If 'TRUE', models will be re-fitted using common data rows. If 'FALSE', error is returned. Default is 'FALSE'.

robustSE

A logical value. If 'TRUE', heteroskedasticity-consistent standard errors will be used in quasi-Bayesian simulations. Ignored if 'boot' is 'TRUE' or neither 'model.m' nor 'model.y' has a method for vcovHC in the sandwich package. Default is 'FALSE'.

cluster

A variable indicating clusters for standard errors. Note that this should be a vector of cluster indicators itself, not a character string for the name of the variable.

...

other arguments passed to vcovHC in the sandwich package: typically the 'type' argument, which is ignored if 'robustSE' is 'FALSE'. Arguments to the boot in the boot package may also be passed, e.g. 'parallel' and 'ncpus'.

Value

mediate_zi_vcoef returns an object of class "mediate", (or "mediate.order" if the outcome model used is 'polr' or 'bayespolr'), a list that contains the components listed below. Some of these elements are not available if 'long' is set to 'FALSE' by the user.

The function summary (i.e., summary.mediate, or summary.mediate.order) can be used to obtain a table of the results. The function plot (i.e., plot.mediate, or plot.mediate.order) can be used to produce a plot of the estimated average causal mediation, average direct, and total effects along with their confidence intervals.

d0, d1

point estimates for average causal mediation effects under the control and treatment conditions.

d0.ci, d1.ci

confidence intervals for average causal mediation effects. The confidence level is set at the value specified in 'conf.level'.

d0.p, d1.p

two-sided p-values for average causal mediation effects.

d0.sims, d1.sims

vectors of length 'sims' containing simulation draws of average causal mediation effects.

z0, z1

point estimates for average direct effect under the control and treatment conditions.

z0.ci, z1.ci

confidence intervals for average direct effects.

z0.p, z1.p

two-sided p-values for average causal direct effects.

z0.sims, z1.sims

vectors of length 'sims' containing simulation draws of average direct effects.

n0, n1

the "proportions mediated", or the size of the average causal mediation effects relative to the total effect.

n0.ci, n1.ci

confidence intervals for the proportions mediated.

n0.p, n1.p

two-sided p-values for proportions mediated.

n0.sims, n1.sims

vectors of length 'sims' containing simulation draws of the proportions mediated.

tau.coef

point estimate for total effect.

tau.ci

confidence interval for total effect.

tau.p

two-sided p-values for total effect.

tau.sims

a vector of length 'sims' containing simulation draws of the total effect.

d.avg, z.avg, n.avg

simple averages of d0 and d1, z0 and z1, n0 and n1, respectively, which users may want to use as summary values when those quantities differ.

d.avg.ci, z.avg.ci, n.avg.ci

confidence intervals for the above.

d.avg.p, z.avg.p, n.avg.p

two-sided p-values for the above.

d.avg.sims, z.avg.sims, n.avg.sims

vectors of length 'sims' containing simulation draws of d.avg, z.avg and n.avg, respectively.

boot

logical, the 'boot' argument used. If 'FALSE' a quasi-Bayesian approximation was used for confidence intervals; if 'TRUE' nonparametric bootstrap was used

boot.ci.type

a character string 'perc' indicating percentile bootstrap confidence intervals were estimated if the argument boot = TRUE

treat

a character string indicating the name of the 'treat' variable used in the models.

mediator

a character string indicating the name of the 'mediator' variable used in the models.

INT

a logical value indicating whether the model specification allows the effects to differ between the treatment and control conditions.

conf.level

the confidence level used.

model.y

the outcome model used.

model.m

the mediator model used.

control.value

value of the treatment variable used as the control condition.

treat.value

value of the treatment variable used as the treatment condition.

nobs

number of observations in the model frame for 'model.m' and 'model.y'. May differ from the numbers in the original models input to 'mediate' if 'dropobs' was 'TRUE'.

robustSE

‘TRUE’ or ‘FALSE’.

cluster

the clusters used.

Author(s)

Nancy Cheng, [e-mail]; Jing Cheng, [e-mail].

References

Cheng, J., Cheng, N.F., Guo, Z., Gregorich, S., Ismail, A.I., Gansky, S.A (2018) Mediation analysis for count and zero-inflated count data. Statistical Methods in Medical Research. 27(9):2756-2774.

Ismail AI, Ondersma S, Willem Jedele JM, et al. (2011) Evaluation of a brief tailored motivational intervention to prevent early childhood caries. Community Dentistry and Oral Epidemiology 39: 433–448.

Tingley, D., Yamamoto, T., Hirose, K., Imai, K. and Keele, L. (2014). "mediation: R package for Causal Mediation Analysis", Journal of Statistical Software, Vol. 59, No. 5, pp. 1-38.

Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2011). Unpacking the Black Box of Causality: Learning about Causal Mechanisms from Experimental and Observational Studies, American Political Science Review, Vol. 105, No. 4 (November), pp. 765-789.

Imai, K., Keele, L. and Tingley, D. (2010) A General Approach to Causal Mediation Analysis, Psychological Methods, Vol. 15, No. 4 (December), pp. 309-334.

Imai, K., Keele, L. and Yamamoto, T. (2010) Identification, Inference, and Sensitivity Analysis for Causal Mediation Effects, Statistical Science, Vol. 25, No. 1 (February), pp. 51-71.

Imai, K., Keele, L., Tingley, D. and Yamamoto, T. (2009) "Causal Mediation Analysis Using R" in Advances in Social Science Research Using R, ed. H. D. Vinod New York: Springer.

See Also

plot_sensitivity, mediate_zi, summary.mediate, plot.mediate

Examples

data("midvd_bt100")
uFit <- glm (PDVisit_6 ~ intervention + BrushTimes_W2 + HealthyMeals_W2
                         + PDVisit_W2,
             family = 'binomial', data = midvd_bt100)
mFit <- glm (PBrushBedt_6 ~ intervention + BrushTimes_W2 + HealthyMeals_W2
                            + PBrush_W2 + PDVisit_6,
             family = 'binomial', data = midvd_bt100)
yFit <- zeroinfl(Untreated_W3 ~ intervention + PBrushBedt_6 + BrushTimes_W2
                                + HealthyMeals_W2 + PBrush_W2+ PDVisit_6,
                 data = midvd_bt100)
# For illustration purposes a small number of simulations are used
# Estimation via Quasi-Bayesian approximation
ee <-mediate_zi_vcoef(uFit, delta.beta.u = 0.01, mFit, yFit, sims = 100,
                      treat = "intervention", mediator = "PBrushBedt_6",
                      confounder ="PDVisit_6")
summary(ee)