## knitr configuration: http://yihui.name/knitr/options#chunk_options library(knitr) showMessage <- FALSE showWarning <- TRUE set_alias(w = "fig.width", h = "fig.height", res = "results") opts_chunk$set(comment = "##", error= TRUE, warning = showWarning, message = showMessage, tidy = FALSE, cache = FALSE, echo = TRUE, fig.width = 7, fig.height = 7, fig.path = "man/figures")
Since there is no gold standard to verify our extended formulas incorporating effect modifications, we use bootstrap to check the point estimates and standard errors given in one single run of regmedint()
. The original estimation for standard errors uses delta method, which agrees with bootstrap asymptotically.
We use simulated data, and present the estimates from 5000 times of boostrap. For the purpose of demonstration, we include all three effect modification terms (i.e. $A\times C$ in mediator model, $A\times C$ in outcome model, and $M\times C$ in outcome model). Due to the long computational time, the code chunks are commented out and only the summary tables are shown. Readers are free to run the code on their side to replicate the results.
library(regmedint) library(tidyverse) expit <- function(x){exp(x)/(1 + exp(x))}
library(parallel) library(MASS) numCores <- detectCores() numCores
# Number of bootstrap trials <- 1:5000 seed <- 3104
# Model 1: M linear, Y linear datamaker.s4.m1 <- function(n, k){ C <- matrix(rnorm(n*1, 0, 2), ncol = 1) A <- rbinom(n, 1, expit(C + C^2)) M <- 0.2 + 0.4*A + 0.5*C + 0.2*A*C + rnorm(n, 0, 0.5) Y <- 0.5 + 0.3*A + 0.2*M + 0.5*A*M + 0.2*A*C + k*M*C + rnorm(n, 0, 0.5) list(C = C, A = A, M = M, Y = Y) } # Model 2: M logistic, Y linear datamaker.s4.m2 <- function(n, k){ C <- matrix(rnorm(n*1, 0, 2), ncol = 1) A <- rbinom(n, 1, expit(C + C^2)) M <- rbinom(n, 1, expit(0.2 + 0.4*A + 0.5*C + 0.2*A*C)) Y <- 0.5 + 0.3*A + 0.2*M + 0.5*A*M + 0.2*A*C + k*M*C + rnorm(n, 0, 0.5) list(C = C, A = A, M = M, Y = Y) } # Model 3: M linear, Y logistic datamaker.s4.m3 <- function(n, k){ C <- matrix(rnorm(n*1, 0, 2), ncol = 1) A <- rbinom(n, 1, expit(C + C^2)) M <- (0.2 + 0.4*A + 0.5*C + 0.2*A*C + rnorm(n, 0, 0.5)/5) Y <- rbinom(n, 1, expit((0.5 + 0.3*A + 0.6*M + 0.4*C + 0.5*A*M + 0.2*A*C + k*M*C))) list(C = C, A = A, M = M, Y = Y) } # Model 4: M logistic, Y logistic datamaker.s4.m4 <- function(n, k){ C <- matrix(rnorm(n*1, 0, 2), ncol = 1) A <- rbinom(n, 1, expit(C + C^2)) M <- rbinom(n, 1, expit(0.2 + 0.4*A + 0.5*C + 0.2*A*C)) Y <- rbinom(n, 1, expit(0.5 + 0.3*A + 0.2*M + 0.1*C + 0.5*A*M + 0.2*A*C + k*M*C)) list(C = C, A = A, M = M, Y = Y) }
set.seed(seed) dat_linear_M_linear_Y <- as.data.frame(datamaker.s4.m1(n = 5000, k = 0.3)) dat_logistic_M_linear_Y <- as.data.frame(datamaker.s4.m2(n = 5000, k = 0.3)) dat_linear_M_logistic_Y <- as.data.frame(datamaker.s4.m3(n = 5000, k = 0.7)) dat_logistic_M_logistic_Y <- as.data.frame(datamaker.s4.m4(n = 5000, k = 0.3))
regmedint1 <- regmedint(data = dat_linear_M_linear_Y, yvar = "Y", avar = "A", mvar = "M", cvar = c("C"), emm_ac_mreg = c("C"), emm_ac_yreg = c("C"), emm_mc_yreg = c("C"), eventvar = NULL, a0 = 0, a1 = 1, m_cde = 0.5012509, c_cond = -0.0434094, mreg = "linear", yreg = "linear", interaction = TRUE, casecontrol = FALSE, na_omit = FALSE) summary(regmedint1)
data1 <- dat_linear_M_linear_Y boot1 <- function(trials){ ind <- sample(5000, 5000, replace = TRUE) dat <- data1[ind,] regmedint1 <- regmedint(data = dat, yvar = "Y", avar = "A", mvar = "M", cvar = c("C"), emm_ac_mreg = c("C"), emm_ac_yreg = c("C"), emm_mc_yreg = c("C"), eventvar = NULL, a0 = 0, a1 = 1, m_cde = 0.5012509, c_cond = -0.0434094, mreg = "linear", yreg = "linear", interaction = TRUE, casecontrol = FALSE, na_omit = FALSE) out <- summary(regmedint1) cde.est.boot <- out$summary_myreg[1,1] pnde.est.boot <- out$summary_myreg[2,1] tnie.est.boot <- out$summary_myreg[3,1] tnde.est.boot <- out$summary_myreg[4,1] pnie.est.boot <- out$summary_myreg[5,1] te.est.boot <- out$summary_myreg[6,1] pm.est.boot <- out$summary_myreg[7,1] return(c(cde.est.boot, pnde.est.boot, tnie.est.boot, tnde.est.boot, pnie.est.boot, te.est.boot, pm.est.boot)) } set.seed(seed) system.time({ results1 <- mclapply(trials, boot1, mc.cores = numCores) }) results1.df <- as.data.frame(do.call(rbind, results1)) apply(results1.df, 2, mean) apply(results1.df, 2, sd)
regmedint2 <- regmedint(data = dat_logistic_M_linear_Y, yvar = "Y", avar = "A", mvar = "M", cvar = c("C"), emm_ac_mreg = c("C"), emm_ac_yreg = c("C"), emm_mc_yreg = c("C"), eventvar = NULL, a0 = 0, a1 = 1, m_cde = 0, c_cond = -0.0434094, mreg = "logistic", yreg = "linear", interaction = TRUE, casecontrol = FALSE, na_omit = FALSE) summary(regmedint2)
data2 <- dat_logistic_M_linear_Y boot2 <- function(trials){ ind <- sample(5000, 5000, replace = TRUE) dat <- data2[ind,] regmedint2 <- regmedint(data = dat, yvar = "Y", avar = "A", mvar = "M", cvar = c("C"), emm_ac_mreg = c("C"), emm_ac_yreg = c("C"), emm_mc_yreg = c("C"), eventvar = NULL, a0 = 0, a1 = 1, m_cde = 0, c_cond = -0.0434094, mreg = "logistic", yreg = "linear", interaction = TRUE, casecontrol = FALSE, na_omit = FALSE) out <- summary(regmedint2) cde.est.boot <- out$summary_myreg[1,1] pnde.est.boot <- out$summary_myreg[2,1] tnie.est.boot <- out$summary_myreg[3,1] tnde.est.boot <- out$summary_myreg[4,1] pnie.est.boot <- out$summary_myreg[5,1] te.est.boot <- out$summary_myreg[6,1] pm.est.boot <- out$summary_myreg[7,1] return(c(cde.est.boot, pnde.est.boot, tnie.est.boot, tnde.est.boot, pnie.est.boot, te.est.boot, pm.est.boot)) } set.seed(seed) system.time({ results2 <- mclapply(1:100, boot2, mc.cores = numCores) }) results2.df <- as.data.frame(do.call(rbind, results2)) apply(results2.df, 2, mean) apply(results2.df, 2, sd)
regmedint3 <- regmedint(data = dat_linear_M_logistic_Y, yvar = "Y", avar = "A", mvar = "M", cvar = c("C"), emm_ac_mreg = c("C"), emm_ac_yreg = c("C"), emm_mc_yreg = c("C"), eventvar = NULL, a0 = 0, a1 = 1, m_cde = 0.5012509, c_cond = 0.5, mreg = "linear", yreg = "logistic", interaction = TRUE, casecontrol = FALSE, na_omit = FALSE) summary(regmedint3)
data3 <- dat_linear_M_logistic_Y boot3 <- function(trials){ ind <- sample(5000, 5000, replace = TRUE) dat <- data3[ind,] regmedint3 <- regmedint(data = dat, yvar = "Y", avar = "A", mvar = "M", cvar = c("C"), emm_ac_mreg = c("C"), emm_ac_yreg = c("C"), emm_mc_yreg = c("C"), eventvar = NULL, a0 = 0, a1 = 1, m_cde = 0.5012509, c_cond = 0.5, mreg = "linear", yreg = "logistic", interaction = TRUE, casecontrol = FALSE, na_omit = FALSE) out <- summary(regmedint3) cde.est.boot <- out$summary_myreg[1,1] pnde.est.boot <- out$summary_myreg[2,1] tnie.est.boot <- out$summary_myreg[3,1] tnde.est.boot <- out$summary_myreg[4,1] pnie.est.boot <- out$summary_myreg[5,1] te.est.boot <- out$summary_myreg[6,1] pm.est.boot <- out$summary_myreg[7,1] return(c(cde.est.boot, pnde.est.boot, tnie.est.boot, tnde.est.boot, pnie.est.boot, te.est.boot, pm.est.boot)) } set.seed(seed) system.time({ results3 <- mclapply(trials, boot3, mc.cores = numCores) }) results3.df <- as.data.frame(do.call(rbind, results3)) apply(results3.df, 2, mean) apply(results3.df, 2, sd)
regmedint4 <- regmedint(data = dat_logistic_M_logistic_Y, yvar = "Y", avar = "A", mvar = "M", cvar = c("C"), emm_ac_mreg = c("C"), emm_ac_yreg = c("C"), emm_mc_yreg = c("C"), eventvar = NULL, a0 = 0, a1 = 1, m_cde = 0, c_cond = -0.0434094, mreg = "logistic", yreg = "logistic", interaction = TRUE, casecontrol = FALSE, na_omit = FALSE) summary(regmedint4)
data4 <- dat_logistic_M_logistic_Y boot4 <- function(trials){ ind <- sample(5000, 5000, replace = TRUE) dat <- data4[ind,] regmedint4 <- regmedint(data = dat, yvar = "Y", avar = "A", mvar = "M", cvar = c("C"), emm_ac_mreg = c("C"), emm_ac_yreg = c("C"), emm_mc_yreg = c("C"), eventvar = NULL, a0 = 0, a1 = 1, m_cde = 0, c_cond = -0.0434094, mreg = "logistic", yreg = "logistic", interaction = TRUE, casecontrol = FALSE, na_omit = FALSE) out <- summary(regmedint4) cde.est.boot <- out$summary_myreg[1,1] pnde.est.boot <- out$summary_myreg[2,1] tnie.est.boot <- out$summary_myreg[3,1] tnde.est.boot <- out$summary_myreg[4,1] pnie.est.boot <- out$summary_myreg[5,1] te.est.boot <- out$summary_myreg[6,1] pm.est.boot <- out$summary_myreg[7,1] return(c(cde.est.boot, pnde.est.boot, tnie.est.boot, tnde.est.boot, pnie.est.boot, te.est.boot, pm.est.boot)) } set.seed(seed) system.time({ results4 <- mclapply(trials, boot4, mc.cores = numCores) }) results4.df <- as.data.frame(do.call(rbind, results4)) apply(results4.df, 2, mean) apply(results4.df, 2, sd)
The following tables shows the point estimates and standard errors from one single run of regmedint()
and bootstrap.
m_lin_y_lin <- cbind.data.frame(c(0.54832158, 0.37202753, 0.28120386, 0.58513575, 0.06809564, 0.65323139, 0.43048124), c(0.02201021, 0.02273628, 0.01480052, 0.02334807, 0.01196713, 0.02075177, 0.02380022), c(0.5476528, 0.3719104, 0.2807417, 0.5843535, 0.0682987, 0.6526522, 0.4304126), c(0.02170323, 0.02241993, 0.01490996, 0.02312960, 0.01233101, 0.02123155, 0.02344534)) row.names(m_lin_y_lin) <- c("CDE", "PNDE", "TNIE", "TNDE", "PNIE", "TE", "PM") colnames(m_lin_y_lin) <- c(rep(c("Point Estimate", "Standard Error"), 2)) m_log_y_lin <- cbind.data.frame(c(0.2674768, 0.5532311, 0.0869584, 0.6227790, 0.0174105, 0.6401895, 0.1358323), c(0.02753958, 0.02144037, 0.01342216, 0.02032353, 0.00459631, 0.02035298, 0.02033647), c(0.27144584, 0.55465628, 0.08809824, 0.62500131, 0.01775321, 0.64275452, 0.13703290), c(0.02890304, 0.02129513, 0.01480665, 0.01874403, 0.00467464, 0.01879988, 0.02272391)) m_lin_y_log <- cbind.data.frame(c(0.9731831, 1.0001259, 0.6608177, 0.6089993, 1.0519444, 1.6609436, 0.5969717), c(0.2696701, 0.2838602, 0.2557117, 0.3558141, 0.3044409, 0.1614044, 0.1616112), c(0.9779244, 1.0044763, 0.6606327, 0.6078226, 1.0572864, 1.6651091, 0.5776469), c(0.2712117, 0.2857491, 0.2528156, 0.3542694, 0.3059525, 0.1599455, 0.1685690)) m_log_y_log <- cbind.data.frame(c(0.20341749, 0.76137841, 0.06535229, 0.82960632, -0.00287562, 0.82673070, 0.11246227), c(0.11831758, 0.08613598, 0.01561403, 0.08759429, 0.01138042, 0.08688896, 0.02606395), c(0.20089667, 0.76132524, 0.06497380, 0.82951442, -0.00321537, 0.82629904, 0.11228721), c(0.12168979, 0.08675318, 0.01562340, 0.08783860, 0.01164672, 0.08757983, 0.02634418)) row_name <- c("CDE", "PNDE", "TNIE", "TNDE", "PNIE", "TE", "PM") col_name <- c(rep(c("Point Estimate", "Standard Error"), 2)) row.names(m_lin_y_lin) <- row.names(m_log_y_lin) <- row.names(m_lin_y_log) <- row.names(m_log_y_log) <- row_name colnames(m_lin_y_lin) <- colnames(m_log_y_lin) <- colnames(m_lin_y_log) <- colnames(m_log_y_log) <- col_name
# output table library(kableExtra) library(formattable) kbl1 <- knitr::kable(m_lin_y_lin, align = "cccc", col.names = col_name, digits = 8) kbl2 <- knitr::kable(m_log_y_lin, align = "cccc", col.names = col_name, digits = 8) kbl3 <- knitr::kable(m_lin_y_log, align = "cccc", col.names = col_name, digits = 8) kbl4 <- knitr::kable(m_log_y_log, align = "cccc", col.names = col_name, digits = 8) # formatting: # https://haozhu233.github.io/kableExtra/awesome_table_in_html.html
kbl1 %>% kable_classic(html_font = "Garamond") %>% add_header_above(c(" " = 1, "Non-bootstrap" = 2, "Bootstrap" = 2))
kbl2 %>% kable_classic(html_font = "Garamond") %>% add_header_above(c(" " = 1, "Non-bootstrap" = 2, "Bootstrap" = 2))
kbl3 %>% kable_classic(html_font = "Garamond") %>% add_header_above(c(" " = 1, "Non-bootstrap" = 2, "Bootstrap" = 2))
kbl4 %>% kable_classic(html_font = "Garamond") %>% add_header_above(c(" " = 1, "Non-bootstrap" = 2, "Bootstrap" = 2))
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