PowerUpR (version 1.1.0)

med_pn: Partially Nested Designs Probing Multilevel Mediation

Description

Two/One partially nested design occurs when subjects are recruited into groups for the treatment condition, but the remaining participants (or waiting list) are left for the control group (without any intervention clusters). If the interest is to design a sufficiently powered study to detect mediation effect in Two/One design, use power.med_pn21().

Three/One partially nested design occurs when subjects are recruited into groups, and a number of groups are guided by the same leader for the treatment condition, but the remaining participants (or waiting list) are left for the control group (without any intervention clusters). If the interest is to design a sufficiently powered study to detect mediation effect in Three/One design, use power.med_pn31().

Three/Two partially nested design occurs when subjects are recruited into groups, and a number of groups are guided by the same leader for the treatment condition, however, separate from Two/One and Three/One designs, the remaining participants are nested within providers in the control group (without any intervention clusters, but with nested structure). If the interest is to design a sufficiently powered study to detect mediation effect in Three/Two design, use power.med_pn31().

Usage

power.med_pn21(esa = .50, esB = .50, esb1 = .10,
               two.tailed = TRUE, alpha = .05,
               mc = TRUE, nsims = 1000, ndraws = 1000,
               rhom_trt = .20, rho_trt = .20,
               r2m1_ctrl = .20, r2m1_trt = .20, r2m2_trt = .20,
               r2y1z_trt = 0, r2y2z_trt = 0,
               r2y1_trt = NULL, r2y2_trt = NULL,
               g1_ctrl = 0, n_ctrl =  20,
               g2_trt = 0, n_trt = 30, J_trt = 20)
power.med_pn31(esa = .50, esB = .50, esb1 = .10,  esb2 = .10,
               two.tailed = TRUE, alpha = .05,
               mc = TRUE, nsims = 1000, ndraws = 1000,
               rhom3_trt = .20, rhom2_trt = .20,
               rho3_trt = .20, rho2_trt = .20,
               r2m1_ctrl = .20, r2m1_trt = .20, r2m2_trt = .20, r2m3_trt = .20,
               r2y1z_trt = 0, r2y2z_trt = 0, r2y3z_trt = 0,
               r2y1_trt = NULL, r2y2_trt = NULL, r2y3_trt = NULL,
               g1_ctrl = 0, n_ctrl =  20,
               g3_trt = 0, n_trt = 30, J_trt = 20, K_trt = 20)
power.med_pn32(esa = .50, esB = .50, esb1 = .10,  esb2 = .10,
               two.tailed = TRUE, alpha = .05,
               mc = TRUE, nsims = 1000, ndraws = 1000,
               rhom2_ctrl = .20, rhom3_trt = .20, rhom2_trt = .20,
               rho3_trt = .20, rho2_trt = .20,
               r2m1_ctrl = .20, r2m2_ctrl = .20,
               r2m1_trt = .20, r2m2_trt = .20, r2m3_trt = .20,
               r2y1z_trt = 0, r2y2z_trt = 0, r2y3z_trt = 0,
               r2y1_trt = NULL, r2y2_trt = NULL, r2y3_trt = NULL,
               g2_ctrl = 0, n_ctrl = 30, J_ctrl = 20,
               g3_trt = 0, n_trt =  20, J_trt = 20,  K_trt = 20)

Arguments

esa

Standardized mean difference in mediator values between treatment and control groups (esa = esa_trt - esa_ctrl).

esB

Standardized regression coefficient for mediator - outcome path, capturing level 1 and level 2 (between intervention clusters) effects (esB = esb1 + esb2 for Two/One design, or esB = esb1 + esb2 + esb3 for Three/One or Three/Two designs).

esb1

Standardized regression coefficient for mediator - outcome path at level 1 in the treatment group (within first intervention clusters).

esb2

Standardized regression coefficient for aggregate mediator - outcome path at level 2 in the treatment group (between first intervention clusters).

alpha

probability of type I error.

two.tailed

logical; TRUE for two-tailed hypothesis testing, FALSE for one-tailed hypothesis testing.

rhom2_ctrl

Proportion of unconditional mediator variance between level 2 units (intervention clusters) in the control group.

rhom3_trt

Proportion of unconditional mediator variance between level 3 units (second intervention clusters) in the treatment group.

rhom2_trt

Proportion of unconditional mediator variance between level 2 units (first intervention clusters) in the treatment group.

rhom_trt

Proportion of unconditional mediator variance between level 2 units (intervention clusters) in the treatment group.

rho3_trt

Proportion of unconditional outcome variance between level 3 units (second intervention clusters) in the treatment group.

rho2_trt

Proportion of unconditional outcome variance between level 2 units (first intervention clusters) in the treatment group.

rho_trt

Proportion of unconditional outcome variance between level 2 units (intervention clusters) in the control group.

r2m1_ctrl

Proportion of variance in the mediator explained by level 1 covariates in the control group.

r2m2_ctrl

Proportion of variance in the aggregate mediator explained by level 2 covariates in the control group.

r2m1_trt

Proportion of variance in the level 1 mediator explained by level 1 covariates in the treatment group

r2m2_trt

Proportion of variance in the aggregate mediator (at level 2) explained by level 2 covariates in the treatment group.

r2m3_trt

Proportion of variance in the aggregate mediator (at level 3) explained by level 3 covariates in the treatment group.

r2y1z_trt

Proportion of variance in the level 1 outcome explained by level 1 covariates in the treatment group.

r2y2z_trt

Proportion of variance in the aggregate outcome (at level 2) explained by level 2 covariates in the treatment group.

r2y3z_trt

Proportion of variance in the aggregate outcome (at level 3) explained by level 3 covariates in the treatment group.

r2y1_trt

Proportion of variance in the level 1 outcome explained by level 1 predictors (including mediator) in the treatment group.

r2y2_trt

Proportion of variance in the aggregate outcome (level 2) explained by level 2 predictors (including aggregate mediator) in the treatment group.

r2y3_trt

Proportion of variance in the aggregate outcome (level 3) explained by level 3 predictors (including aggregate mediator) in the treatment group.

g1_ctrl

Number of covariates introduced at level 1 in the control group.

g2_ctrl

Number of covariates introduced at level 2 (intervention clusters) in the control group.

n_ctrl

Total number of subjects for two/one mediation. Number of subjects per level 2 unit (intervention cluster) in the control group for Three/One and Three/Two mediation.

J_ctrl

Number of level 2 units (intervention clusters) in the control group.

g2_trt

Number of covariates introduced at level 2 (intervention clusters) in the treatment group.

g3_trt

Number of covariates introduced at level 3 (second intervention clusters) in the treatment group.

n_trt

Number of subjects per level 2 unit (first intervention cluster).

J_trt

Number of level 2 units per level 3 unit (second intervention cluster.)

K_trt

Number of level 3 units (second intervention clusters).

mc

logical; TRUE for monte carlo simulation based power.

nsims

number of replications, if mc = TRUE.

ndraws

number of draws from the distribution of the path coefficients for each replication, if mc = TRUE.

Value

fun

function name.

parms

list of parameters used in power calculation.

df

degrees of freedom.

ncp

noncentrality parameter.

power

statistical power \((1-\beta)\).

References

Kelcey, B., Bai, F., \& Xie, Y. (2020). Statistical power in partially nested designs probing multilevel mediation. Psychotherapy Research. Advance online publication. 10.1080/10503307.2020.1717012

Examples

# NOT RUN {
# Two/One partially nested design
power.med_pn21(esa = .40, esB = .40, esb1 = .40,
               two.tailed = TRUE, alpha = .05,
               rhom_trt = .20, rho_trt = .20,
               r2m1_ctrl = .60, r2m1_trt = .60, r2m2_trt = .60,
               r2y1_trt = .50, r2y2_trt = .50,
               n_ctrl = 50, n_trt =  6, J_trt = 50)

# Three/One partially nested design
power.med_pn31(esa = .50, esB = .50, esb1 = .10, esb2 = .10,
               rhom3_trt = .10, rhom2_trt = .20, rho3_trt = .10, rho2_trt = .20,
               r2m1_ctrl = .20, r2m1_trt = .20, r2m2_trt = .20, r2m3_trt = .20,
               r2y1_trt = .20, r2y2_trt = .20, r2y3_trt = .20,
               n_ctrl = 60, n_trt =  20, J_trt = 10, K_trt = 60)

# Three/Two partially nested design
power.med_pn32(esa = .50, esB = .50, esb1 = .10, esb2 = .10,
               rhom2_ctrl = .20, rhom3_trt = .10, rhom2_trt = .20,
               rho3_trt = .10, rho2_trt = .20,
               r2m1_ctrl = .20, r2m2_ctrl = .20,
               r2m1_trt = .20, r2m2_trt = .20, r2m3_trt = .20,
               r2y1_trt = .20, r2y2_trt = .20, r2y3_trt = .20,
               n_ctrl = 24, n_trt =  24, J_trt = 12, J_ctrl = 60, K_trt = 60)
# }