maczic_power: Power Calculation for Mediation Analysis with Count and Zero-Inflated Count Data

Description

'maczic_power' computes powers to detect average causal mediation effects (indirect effect), average direct effects, and total effect. This function uses simulations of 3 optional covariates (binary, normal, and multinomial), mediator (can be binary or continuous), and outcome (can be Normal, Poisson, Negative Binomial, zero-inflated Poisson/Negative Binomial) based on user-specified parameter values.

Usage

maczic_power(
  nsim,
  nsp,
  mtype,
  boot = FALSE,
  sims = 1000,
  conf.level = 0.95,
  ydist,
  size = 1,
  ymax,
  lpct0 = 0,
  hpct0 = 100,
  px1,
  am,
  bm,
  e1m,
  e2m,
  e3m,
  ag,
  bg,
  gg,
  e1g,
  e2g,
  e3g,
  delta = 0,
  ag2 = 0,
  bg2 = 0,
  gg2 = 0,
  e1g2 = 0,
  e2g2 = 0,
  e3g2 = 0,
  delta2 = 0,
  digits = 3
)

Value

maczic_power returns a data frame with the following components and prints them out in a matrix format:

te.d0, te.d1: average true mediation effects under the control and treatment conditions.
te.z0, te.z1: average true direct effects under the control and treatment conditions.
te.tau: average true total effect.
ee.d0.rej, ee.d1.rej: power to detect mediation effects under the control and treatment conditions.
ee.z0.rej, ee.z1.rej: power to detect direct effects under the control and treatment conditions.
ee.tau.rej: power to detect total effect.
mean.y.z0: mean outcome in control in the simulated data, not available if outcome is normal.
mean.y.z1: mean outcome in treatment in the simulated data, not available if outcome is normal.
mean.y.gt0.z0: mean non-zero outcome in control in the simulated data, not available if outcome is normal.
mean.y.gt0.z1: mean non-zero outcome in treatment in the simulated data, not available if outcome is normal
pct0.y.z0: mean percent zero outcome in control in the simulated data, not available if outcome is normal.
pct0.y.z1: mean percent zero outcome in treatment in the simulated data, not available if outcome is normal.

Arguments

nsim: Number of simulations.
nsp: Sample size.
mtype: Type of mediator, either 'binary' or 'continuous'.
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'.
sims: Number of Monte Carlo draws for nonparametric bootstrap or quasi-Bayesian approximation. Default is 1000.
conf.level: Level of the returned two-sided confidence intervals. The default value, 0.95, is to return the 2.5 and 97.5 percentiles of the simulated quantities.
ydist: Outcome distribution. Can be 'poisson', 'negbin', 'zip', 'zinb', or 'normal'.
size: Dispersion parameter for negative binomial outcome distribution. Default is 1. It's ignored for other outcome distribution.
ymax: Maximum value of outcome allowed.
lpct0: Low bound for percent of zeros in outcome. Default is 0.
hpct0: High bound for percent of zeros in outcome. Default is 100.
px1: Probability of the binary covariate being 1.
am: User-specified value for the intercept in the mediator model.
bm: User-specified value for the treatment coefficient in the mediator model.
e1m: User-specified value for the coefficient of the binary covariate variable in the mediator model.
e2m: User-specified value for the coefficient of the continuous covariate variable in the mediator model.
e3m: User-specified value for the coefficient of the multinomial covariate variable in the mediator model.
ag: User-specified value for the intercept in the outcome model or in the count model of zero-inflated Poisson/Negative Binomial outcome.
bg: User-specified value for the treatment coefficient in the outcome model or in the count model of zero-inflated Poisson/Negative Binomial outcome.
gg: User-specified value for the mediator coefficient in the outcome model or in the count model of zero-inflated Poisson/Negative Binomial outcome.
e1g: User-specified value for the coefficient of the binary covariate variable in the outcome model or in the count model of zero-inflated Poisson/Negative Binomial outcome.
e2g: User-specified value for the coefficient of the continuous covariate variable in the outcome model or in the count model of zero-inflated Poisson/Negative Binomial outcome.
e3g: User-specified value for the coefficient of the multinomial covariate variable in the outcome model or in the count model of zero-inflated Poisson/Negative Binomial outcome.
delta: User-specified value for the treatment-by-mediator interaction coefficient in the outcome model or in the count model of zero-inflated Poisson/Negative Binomial outcome model. Default is 0.
ag2: User-specified value for the intercept in the zero-inflation model of zero-inflated Poisson/Negative Binomial outcome. Note that this argument along with the following argument bg2, gg2, e1g2, e2g2, e3g2 and delta2 only apply to zero-inflated Poisson/Negative Binomial outcome. Default is 0.
bg2: User-specified value for the treatment coefficient in the zero-inflation model of zero-inflated Poisson/Negative Binomial outcome. Default is 0.
gg2: User-specified value for the mediator coefficient in the zero-inflation model of zero-inflated Poisson/Negative Binomial outcome. Default is 0.
e1g2: User-specified value for the coefficient of the binary covariate variable in the zero-inflation model of zero-inflated Poisson/Negative Binomial outcome. Default is 0.
e2g2: User-specified value for the coefficient of the continuous covariate variable in the zero-inflation model of zero-inflated Poisson/Negative Binomial outcome. Default is 0.
e3g2: User-specified value for the coefficient of the multinomial covariate variable in the zero-inflation model of zero-inflated Poisson/Negative Binomial outcome. Default is 0.
delta2: User-specified value for the coefficient of treatment-by-mediator interaction in the zero-inflation model of zero-inflated Poisson/Negative Binomial outcome. Default is 0.
digits: Integer indicating the number of decimal places to round the values to be returned. Default is 3.

Author

Nancy Cheng, Nancy.Cheng@ucsf.edu; Jing Cheng, Jing.Cheng@ucsf.edu.

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.

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.

Examples

Run this code

# For illustration purposes a small number of simulations are used
# Example 1: simulate Poisson outcome with sample size 100, binary mediator
# and 2 covariate (binary and normal) variables
posOut <- maczic_power(nsim = 8, nsp = 100,  mtype = 'binary',
                       sims = 40, ydist = "Poisson", ymax = 60,
                       px1 = 0.5, am = 0.2, bm = 0.5,
                       e1m = 0.1, e2m = 0.1, e3m = 0,
                       ag = 0.1, bg = 0.3, gg = 1,
                       e1g = 0.5, e2g = -0.2, e3g = 0, delta = 0.1)

# Example 2: simulate zero-inflated Poisson outcome with sample size 80,
# continuous mediator and 1 normal covariate variable
zipOut <-maczic_power(nsim = 5, nsp = 80, mtype = 'continuous',
                       sims=30, ydist = "zip", ymax = 88, hpct0 = 60,
                       px1 = 0.5, am = 0.1, bm = 1,
                       e1m = 0, e2m = 0.2, e3m = 0,
                       ag = 0.6, bg = 0.6, gg = 0.2, e1g = 0, e2g = -0.2,
                       e3g = 0, ag2 = -0.7, bg2 = 0.2, gg2 = 0.1,
                       e2g2 = 0.1, delta2 = 0.15)

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