maczic_power {maczic}

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
)

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.

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.

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.

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

mediate_zi

Examples

# 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)