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sim_results_tabls_sim1_sim2_v3.Rnw
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sim_results_tabls_sim1_sim2_v3.Rnw
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\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage{float}
\usepackage{subcaption}
\usepackage{amssymb,amsmath,amsfonts}
\usepackage[multiple]{footmisc}
\usepackage[utf8]{inputenc}
\usepackage{pdflscape}
\usepackage{booktabs}
\usepackage{ctable}
\usepackage{thumbpdf}
\begin{document}
<<include=FALSE, results='hide'>>=
library("Hmisc")
library("ggplot2")
library("data.table")
library("tikzDevice");
options(prompt = "R> ", continue = "+ ", useFancyQuotes = FALSE)
require("knitr"); require("simcausal"); require("tikzDevice");
# options(tikzDefaultEngine='xetex')
opts_chunk$set(fig.path = 'figure/plot-',fig.align = 'center',fig.show = 'hold')
knit_hooks$set(pdfcrop = hook_pdfcrop)
# to crop white space in output figures:
# knit_hooks$set(pdfcrop = hook_pdfcrop)
options(width=90) # make the printing fit on the page
# options(width=80) # make the printing fit on the page
set.seed(1121) # make the results repeatable
# est_levels = c("SDR", "DR Transform", "LTMLE", "GCOMP", "IPW")
est_levels = c("iTMLE", "DR Transform", "LTMLE", "Direct Plugin", "IPW")
scen_levels = c("Qc.gc", "Qi.gc", "Qc.gi", "Qi.gi", "QSDR.gSDR")
get_legend<-function(myggplot){
tmp <- ggplot_gtable(ggplot_build(myggplot))
leg <- which(sapply(tmp$grobs, function(x) x$name) == "guide-box")
legend <- tmp$grobs[[leg]]
return(legend)
}
# p <- ggplot(restab, aes(`Relative MSE`, Estimator))
# p + geom_point(aes(colour = Scenario, shape = Scenario), position = position_jitter(h = 0.1)) +
plotMSE <- function(restab, jitter = .1) {
ggplot(restab, aes(x = Scenario, y = `Relative MSE`)) +
# geom_point(aes(colour = Estimator, shape = Estimator), position = position_jitter(h = jitter)) +
geom_point(aes(colour = Estimator, shape = Estimator), position = position_dodge(jitter)) +
scale_colour_discrete(drop = FALSE) + scale_shape_discrete(drop = FALSE) +
scale_y_log10("Relative MSE", breaks = c(1, 2, 5, 10, 100)) +
# coord_flip() +
theme_bw()
}
plotBIAS <- function(restab, jitter = .2) {
ggplot(restab, aes(x = Scenario, y = `Relative Bias`)) +
# geom_point(aes(colour = Estimator, shape = Estimator), position = position_jitter(h = jitter)) +
geom_point(aes(colour = Estimator, shape = Estimator), position = position_dodge(jitter)) +
scale_colour_discrete(drop = FALSE) + scale_shape_discrete(drop = FALSE) +
scale_y_log10("Relative Absolute Bias") +
# coord_flip() +
theme_bw()
}
# p <- ggplot(restab, aes(`Coverage Probability`, Estimator))
# p + geom_point(aes(colour = Scenario, shape = Scenario), position = position_jitter(h = 0.15)) +
# geom_vline(xintercept = 0.95) +
# coord_flip() + theme_bw()
plotCI <- function(restab, jitter = .1, flip = TRUE) {
# setnames(restab,"Coverage prob.","Coverage Probability")
p <- ggplot(restab, aes(x = Scenario, `Coverage prob.`)) +
# geom_point(aes(colour = Estimator, shape = Estimator), position = position_jitter(h = jitter)) +
geom_point(aes(colour = Estimator, shape = Estimator), position = position_dodge(jitter)) +
scale_colour_discrete(drop = FALSE) + scale_shape_discrete(drop = FALSE) +
scale_y_continuous("Coverage Probability", breaks = c(.1, .3, .5, .7, .85, .95)) +
geom_hline(yintercept = 0.95)
if (flip) p <- p + coord_flip()
p + theme_bw()
}
plotCIlen <- function(restab, jitter = 0.35, flip = TRUE) {
ggplot(restab, aes(x = Scenario, y = y, ymin=ymin, ymax=ymax)) +
geom_point(aes(colour = Estimator, shape = Estimator), position = position_dodge(jitter)) +
geom_errorbar(aes(color = Estimator), alpha = 1, width = 0.3, size = 0.4, position = position_dodge(jitter)) +
scale_y_log10("Mean CI Length", breaks = c(.01, .1, 1)) +
scale_colour_discrete(drop = FALSE) +
scale_shape_discrete(drop = FALSE) +
# scale_linetype_discrete(drop = FALSE) +
theme_bw()
# +
# ylab("Mean CI Length")
}
genrestab <- function(restab, sim.name, est_levels, scen_levels) {
library("data.table")
scen.names <- rownames(restab)
restab <- data.table::data.table(restab, keep.rownames=TRUE)
restab[grep("ipw", scen.names), Estimator := "IPW"]
restab[grep("gcomp", scen.names), Estimator := "Direct Plugin"]
# restab[grep("br", scen.names), Estimator := "BR"]
restab[grep("tmle", scen.names), Estimator := "LTMLE"]
restab[grep("drtrans", scen.names), Estimator := "DR Transform"]
restab[grep("sdr", scen.names), Estimator := "iTMLE"]
restab[grep("Qc.gc", scen.names), Scenario := "Qc.gc"]
restab[grep("Qi.gc", scen.names), Scenario := "Qi.gc"]
restab[grep("Qc.gi", scen.names), Scenario := "Qc.gi"]
restab[grep("Qi.gi", scen.names), Scenario := "Qi.gi"]
restab[grep("QSDR.gSDR", scen.names), Scenario := "QSDR.gSDR"]
restab[, ("Estimator") := factor(restab[["Estimator"]], levels = est_levels)]
# restab[["Estimator"]] <- factor(restab[["Estimator"]], levels = est_levels)
# restab[["Estimator"]] <- factor(restab[["Estimator"]], levels = c("IPW", "GCOMP", "BR", "LTMLE", "DR Transform", "SDR"))
restab[, ("Scenario") := factor(restab[["Scenario"]], levels = scen_levels)]
# restab[["Scenario"]] <- factor(restab[["Scenario"]], levels = scen_levels)
restab[, ("sim") := sim.name]
return(restab)
}
@
\subsection{Proof-of-concept simulation. Simulation scenario 1 with 3 time-points.}
<<simscen.stats.t3, message=FALSE, warning=FALSE, echo=TRUE>>=
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim1_results_t2.Rd")
print(results[["res_name"]])
@
<<ggplot.MSE.t3, fig.pos="H", out.width=".7\\linewidth", message=FALSE, warning=FALSE, echo=FALSE, fig.width=8,fig.height=4.5, fig.cap="Relative MSE for $\\hat{Q}_1$ in simulation scenario 1 with 3 time points.">>=
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim1_results_t2.Rd")
restab <- results[["results_MSE"]]
rownames(restab) <- unlist(strsplit(rownames(restab), "_mse"))
restabMSE.t3 <- genrestab(restab, "Simulation 1", est_levels, scen_levels)
pMSEt3 <- plotMSE(restabMSE.t3) + ylab("simulation scenario 1")
pMSEt3
@
<<ggplot.bias.t3, fig.pos="H", out.width=".7\\linewidth", message=FALSE, warning=FALSE, echo=FALSE, fig.width=8,fig.height=4.5, fig.cap="Relative absolute bias for $\\hat{Q}_0$ in simulation scenario 1 with 3 time points.">>=
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim1_results_t2.Rd")
restab <- results[["results_bias"]]
rownames(restab) <- unlist(strsplit(rownames(restab), "_bias"))
restabBIAS.t3 <- genrestab(restab, "Simulation 1", est_levels, scen_levels)
pbiast3 <- plotBIAS(restabBIAS.t3) + ylab("simulation scenario 1")
pbiast3
@
% out.height = ".5\\linewidth",
<<ggplot.CIcov.CIlen.t3, fig.pos="H", out.width=".9\\linewidth", pdfcrop=TRUE, message=FALSE, warning=FALSE, echo=FALSE, fig.cap="Coverage (left panel) and mean length (right panel) of the two-sided 95\\% CIs for $Q_0$ in simulation scenario 1.">>=
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim1_results_t2.Rd")
restab <- results[["results_cov"]]
rownames(restab) <- unlist(strsplit(rownames(restab), "_cover"))
restabCIcov.t3 <- genrestab(restab, "Simulation 1", est_levels, scen_levels)
restabCIcov.t3 <- restabCIcov.t3[Estimator!= "Direct Plugin"]
pCIt3 <- plotCI(restabCIcov.t3, jitter =.25, flip = TRUE)
# pCIt3
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim1_results_t2.Rd")
library("Hmisc")
library("ggplot2")
library("data.table")
library("gridExtra")
restab <- results[["results_CIlen"]]
rownames(restab) <- unlist(strsplit(rownames(restab), "_CIlen"))
restabCIlen.t3 <- genrestab(restab, "Simulation 1", est_levels, scen_levels)
restabCIlen.t3 <- restabCIlen.t3[Estimator!= "Direct Plugin"]
restabCIlen.t3[, ("y") := 0]
# restabCIlen.t3[, ("ymin") := -`Mean CI length` / 2]
# restabCIlen.t3[, ("ymax") := +`Mean CI length` / 2]
restabCIlen.t3[, ("ymin") := 0]
restabCIlen.t3[, ("ymax") := `Mean CI length`]
pCIlent3 <- plotCIlen(restabCIlen.t3) + xlab("simulation scenario 1")
# pCIlent3
pCIlent3 <- pCIlent3 + theme(legend.position = "top")
legend.save <- get_legend(pCIlent3)
pCIt3 <- pCIt3 + theme(legend.position = "none", axis.title.x = element_text(size = 8), axis.title.y = element_blank())
pCIlent3 <- pCIlent3 + theme(legend.position = "none", axis.title.x = element_text(size = 8), axis.title.y = element_blank(), axis.text.y = element_blank()) + coord_flip()
grid.arrange(legend.save, pCIt3, pCIlent3,
nrow = 2, ncol = 2,
layout_matrix = rbind(c(1,1), c(2,3)),
widths = c(0.55,0.45),
heights = unit(c(0.5, 10), "cm")
# heights = c(0.005, 0.1)
)
@
<<ggplot.all.t3, fig.pos="H", message=FALSE, warning=FALSE, echo=FALSE,fig.cap="Simulation scenario 1 results. Top to bottom: MSE for estimation of $Q_1$, bias for estimation of $Q_0$ and 95\\% CI coverage for estimation of $Q_0$, over 3 time points and $n$=500.">>=
new_theme <- theme( # axis.title.x = element_blank(),
axis.title.y = element_text(size = 8),
axis.title.x = element_text(size = 8),
plot.margin = unit(c(0, 0, 0.5, 0), "lines"),
legend.position="top")
pMSEt3 <- pMSEt3 + new_theme
pbiast3 <- pbiast3 + new_theme
pCIt3 <- pCIt3 + new_theme
legend.save <- get_legend(pMSEt3)
pMSEt3 <- pMSEt3 + theme(legend.position = "none")
pbiast3 <- pbiast3 + theme(legend.position = "none")
pCIt3 <- pCIt3 + theme(legend.position = "none")
@
\clearpage
<<chunk.bias.t3, message=FALSE, warning=FALSE, echo=FALSE, results="asis">>=
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim1_results_t2.Rd")
library("Hmisc")
restab <- results[["results_bias"]]
rownames(restab) <- unlist(strsplit(rownames(restab), "_bias"))
cat("\n")
latex(restab, file = "", where = "H", caption.loc = 'bottom',
caption = "Simulation scenario 1. Relative absolute bias for estimation of $Q_0$, over 3 time points and $n$=500.",
label = 'tab1',booktabs = TRUE,landscape = FALSE,
#rowname = NULL,
col.just = c("l", "r"), size = "tiny")
@
<<chunk.MSE.t3, message=FALSE, warning=FALSE, echo=FALSE, results="asis">>=
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim1_results_t2.Rd")
library("Hmisc")
restab <- results[["results_MSE"]]
rownames(restab) <- unlist(strsplit(rownames(restab), "_mse"))
cat("\n")
latex(restab, file = "", where = "H", caption.loc = 'bottom',
caption = "Simulation scenario 1. Relative MSE for estimation of $Q_1$, over 3 time points and $n$=500.",
label = 'tab2',booktabs = TRUE,landscape = FALSE,
#rowname = NULL,
col.just = c("l", "r"), size = "tiny")
@
<<chunk.coverage.t3, message=FALSE, warning=FALSE, echo=FALSE, results="asis">>=
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim1_results_t2.Rd")
library("Hmisc")
restab <- results[["results_cov"]]
rownames(restab) <- unlist(strsplit(rownames(restab), "_cover"))
cat("\n")
latex(restab, file = "", where = "H", caption.loc = 'bottom',
caption = "Simulation scenario 1. Coverage of 95\\% CIs for $Q_0$, over 3 time points and $n$=500.",
booktabs = TRUE,landscape = FALSE,
#rowname = NULL,
col.just = c("l", "r"), size = "tiny")
@
\clearpage
Data generating distribution for simulation scenario 1.
<<chunk.simcode.t3, eval=FALSE>>=
require("simcausal")
D <- DAG.empty() +
node("L", t = 0, distr = "rnorm") +
node("A", t = 0, distr = "rbern", prob = plogis(L[0])) +
node("Y", t = 0, distr = "rconst", const = 0) +
node("L", t = 1, distr = "rnorm") +
node("A", t = 1, distr = "rbern", prob = plogis(L[1] + A[0])) +
node("Y", t = 1, distr = "rconst", const = 0) +
node("L", t = 2, distr = "rnorm", mean = L[0]*A[1] + A[0]*L[1] + L[1]*A[1]) +
node("A", t = 2, distr = "rbern", prob = plogis(L[2] + A[1])) +
node("Y", t = 2, distr = "rbern", prob = plogis(L[1]*A[2] + A[1]*L[2] + L[2]*A[2]))
@
Model specification for simulation scenario 1.
<<chunk.Qg.t3, eval=FALSE, echo=TRUE>>=
nsims <- 500
nsamp <- 500
tvals <- 2
## g model (same across all time-points):
gform.c <- "A ~ L + Atm1"
gform.i <- "A ~ L"
# Q models
Qforms.c <- c("Qkplus1 ~ L",
"Qkplus1 ~ A0L1 + L0A0 + L + A + Atm1 + Ltm1",
"Qkplus1 ~ A0L1 + L0A0 + L + A + Atm1 + Ltm1")
Qinteract.c <- list(c("A", "L"), c("A", "Ltm1"))
Qforms.i <- c("Qkplus1 ~ L", "Qkplus1 ~ Atm1", "Qkplus1 ~ Atm1")
Qinteract.i <- NULL
@
\clearpage
\subsection{Demonstrating SDR property. Simulation scenario 2 with 5 time-points.}
<<simscen.stats.t5, message=FALSE, warning=FALSE, echo=TRUE>>=
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim2_results_t4.Rd")
print(results[["res_name"]])
@
<<ggplot.MSE.t5, fig.pos="H", out.width=".7\\linewidth", message=FALSE, warning=FALSE, echo=FALSE, fig.width=8,fig.height=4.5, fig.cap="Relative MSE for $\\hat{Q}_1$ in simulation scenario 2 with 5 time points.">>=
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim2_results_t4.Rd")
restab <- results[["results_MSE"]]
rownames(restab) <- unlist(strsplit(rownames(restab), "_mse"))
restabMSE.t5 <- genrestab(restab, "Simulation 2", est_levels, scen_levels)
pMSEt5 <- plotMSE(restabMSE.t5) + ylab("simulation scenario 2")
pMSEt5
@
<<ggplot.bias.t5, fig.pos="H", out.width=".7\\linewidth", message=FALSE, warning=FALSE, echo=FALSE, fig.width=8,fig.height=4.5, fig.cap="Relative absolute bias for $\\hat{Q}_0$ in simulation scenario 2 with 5 time points.">>=
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim2_results_t4.Rd")
restab <- results[["results_bias"]]
# results[["results_bias_mean"]]
rownames(restab) <- unlist(strsplit(rownames(restab), "_bias"))
restabBIAS.t5 <- genrestab(restab, "Simulation 2", est_levels, scen_levels)
pbiast5 <- plotBIAS(restabBIAS.t5) + ylab("simulation scenario 2")
pbiast5
@
<<ggplot.CIcov.CIlen.t5, fig.pos="H", out.width=".9\\linewidth", pdfcrop=TRUE, message=FALSE, warning=FALSE, echo=FALSE, fig.cap="Coverage (left panel) and mean length (right panel) of the two-sided 95\\% CIs for $Q_0$ in simulation scenario 2.">>=
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim2_results_t4.Rd")
restab <- results[["results_cov"]]
rownames(restab) <- unlist(strsplit(rownames(restab), "_cover"))
restabCIcov.t5 <- genrestab(restab, "Simulation 2", est_levels, scen_levels)
restabCIcov.t5 <- restabCIcov.t5[Estimator!= "Direct Plugin"]
# pCIt5 <- plotCI(restabCIcov.t5, jitter =.25)
pCIt5 <- plotCI(restabCIcov.t5, jitter =.25, flip = TRUE)
# pCIt5
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim2_results_t4.Rd")
restab <- results[["results_CIlen"]]
rownames(restab) <- unlist(strsplit(rownames(restab), "_CIlen"))
restabCIlen.t5 <- genrestab(restab, "Simulation 2", est_levels, scen_levels)
restabCIlen.t5 <- restabCIlen.t5[Estimator!= "Direct Plugin"]
restabCIlen.t5[, ("y") := 0]
# restabCIlen.t5[, ("ymin") := -`Mean CI length` / 2]
# restabCIlen.t5[, ("ymax") := +`Mean CI length` / 2]
restabCIlen.t5[, ("ymin") := 0]
restabCIlen.t5[, ("ymax") := `Mean CI length`]
pCIlent5 <- plotCIlen(restabCIlen.t5) + xlab("simulation scenario 2")
# pCIlent5
pCIlent5 <- pCIlent5 + theme(legend.position = "top")
legend.save <- get_legend(pCIlent5)
pCIt5 <- pCIt5 + theme(legend.position = "none", axis.title.x = element_text(size = 8), axis.title.y = element_blank())
pCIlent5 <- pCIlent5 + theme(legend.position = "none", axis.title.x = element_text(size = 8), axis.title.y = element_blank(), axis.text.y = element_blank()) + coord_flip()
grid.arrange(legend.save, pCIt5, pCIlent5,
nrow = 2, ncol = 2,
layout_matrix = rbind(c(1,1), c(2,3)),
widths = c(0.55,0.45),
heights = unit(c(0.5, 10), "cm")
# heights = c(0.005, 0.1)
)
@
<<ggplot.all.t5, fig.pos="H", message=FALSE, warning=FALSE, echo=FALSE, fig.cap="Results for simulation scenario 2. Top to bottom: MSE for estimation of $Q_1$, bias for estimation of $Q_0$ and 95\\% CI coverage for estimation of $Q_0$, over 5 time points and $n$=5,000.">>=
new_theme <- theme( # axis.title.x = element_blank(),
axis.title.y = element_text(size = 8),
axis.title.x = element_text(size = 8),
plot.margin = unit(c(0, 0, 0.5, 0), "lines"),
legend.position="top")
pMSEt5 <- pMSEt5 + new_theme
pbiast5 <- pbiast5 + new_theme
pCIt5 <- pCIt5 + new_theme
legend.save <- get_legend(pMSEt5)
pMSEt5 <- pMSEt5 + theme(legend.position = "none")
pbiast5 <- pbiast5 + theme(legend.position = "none")
pCIt5 <- pCIt5 + theme(legend.position = "none")
@
\clearpage
<<chunk.bias.t5, fig.pos="H", message=FALSE, warning=FALSE, echo=FALSE, results="asis">>=
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim2_results_t4.Rd")
library("Hmisc")
restab <- results[["results_bias"]]
rownames(restab) <- unlist(strsplit(rownames(restab), "_bias"))
cat("\n")
latex(restab, file = "", where = "H", caption.loc = 'bottom',
caption = "Simulation scenario 2. Relative absolute bias for estimation of $Q_0$, over 5 time points and $n$=5,000.",
label = 'tab1',booktabs = TRUE,landscape = FALSE,
#rowname = NULL,
col.just = c("l", "r"), size = "tiny")
@
<<chunk.MSE.t5, fig.pos="H", message=FALSE, warning=FALSE, echo=FALSE, results="asis">>=
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim2_results_t4.Rd")
library("Hmisc")
restab <- results[["results_MSE"]]
rownames(restab) <- unlist(strsplit(rownames(restab), "_mse"))
cat("\n")
latex(restab, file = "", where = "H", caption.loc = 'bottom',
caption = "Simulation scenario 2. Relative MSE for estimation of $Q_1$, over 5 time points and $n$=5,000.",
label = 'tab2',booktabs = TRUE,landscape = FALSE,
#rowname = NULL,
col.just = c("l", "r"), size = "tiny")
@
<<chunk.coverage.t5, fig.pos="H", message=FALSE, warning=FALSE, echo=FALSE, results="asis">>=
load("/Users/olegsofrygin/GoogleDrive/Alex_SDR/sims/sims_final_04_20_17/sim2_results_t4.Rd")
library("Hmisc")
restab <- results[["results_cov"]]
rownames(restab) <- unlist(strsplit(rownames(restab), "_cover"))
cat("\n")
latex(restab, file = "", where = "H", caption.loc = 'bottom',
caption = "Simulation scenario 2. Coverage of 95\\% CIs for $Q_0$, over 5 time points and $n$=5,000.",
booktabs = TRUE,landscape = FALSE,
#rowname = NULL,
col.just = c("l", "r"), size = "tiny")
@
\clearpage
Data generating distribution for simulation scenario 2.
<<chunk.simcode.t5, eval=FALSE, echo=TRUE>>=
nsims <- 500
nsamp <- 5000
tvals <- 4
require("simcausal")
D <- DAG.empty() +
node("UL", t = 0, distr = "rnorm") +
node("W", t = 0, distr = "rnorm", mean = 0) +
node("L", t = 0, distr = "rconst", const = abs(UL[t])) +
node("phiRsk", t = 0, distr = "rconst", const = L[0]) +
node("hiRsk", t = 0, distr = "rconst", const = plogis(phiRsk[t]) > 0.8) +
node("A", t = 0, distr = "rbern", prob = plogis(L[0])) +
node("Y", t = 0, distr = "rconst", const = 0) +
node("UL",t = 1, distr = "rnorm") +
node("L", t = 1, distr = "rconst", const = abs(UL[t])) +
node("phiRsk", t = 1, distr = "rconst", const = -2 + 0.5*L[t-1] + 0.5*2*L[t]) +
node("hiRsk", t = 1, distr = "rconst", const = plogis(phiRsk[t]) > 0.9) +
node("A", t = 1, distr = "rbern", prob = A[t-1]*plogis(1.7 - 2.0*hiRsk[t])) +
node("Y", t = 1, distr = "rbern",
prob = plogis(-3 + 0.5*L[t-1]*A[t] + 0.5*A[t-1]*L[t] + 0.5*L[t]*A[t])) +
node("UL",t = 2, distr = "rnorm", mean = A[0]*L[1] + L[1]*A[1]) +
node("L", t = 2, distr = "rconst", const = abs(UL[t])) +
node("phiRsk", t = 2, distr = "rconst", const = -2 + 0.5*L[t-1] + 0.5*2*L[t]) +
node("hiRsk", t = 2, distr = "rconst", const = plogis(phiRsk[t]) > 0.85) +
node("A", t = 2, distr = "rbern", prob = A[t-1]*plogis(1.7 - 2.0*hiRsk[t])) +
node("Y", t = 2, distr = "rbern",
prob = plogis(-3*Y[t-1] + 0.5*L[t-1]*A[t] + 0.5*A[t-1]*L[t] + 0.5*L[t]*A[t])) +
node("UL",t = 3, distr = "rnorm", mean = L[1] * A[t-1] + A[1]*L[t-1] + L[t-1]*A[t-1]) +
node("L", t = 3, distr = "rconst", const = abs(UL[t])) +
node("phiRsk", t = 3, distr = "rconst", const = -2 + 0.5*L[t-1] + 0.5*2*L[t]) +
node("hiRsk", t = 3, distr = "rconst", const = plogis(phiRsk[t]) > 0.80) +
node("A", t = 3, distr = "rbern", prob = A[t-1]*plogis(1.7 - 2.0*hiRsk[t])) +
node("Y", t = 3, distr = "rbern",
prob = plogis(-3*Y[t-1] + 0.5*L[t-1]*A[t] + 0.5*A[t-1]*L[t] + 0.5*L[t]*A[t])) +
node("UL",t = 4, distr = "rnorm", mean = L[1] * A[t-1] + A[1]*L[t-1] + L[t-1]*A[t-1]) +
node("L", t = 4, distr = "rconst", const = abs(UL[t])) +
node("phiRsk", t = 4, distr = "rconst",
const = -1 + 0.25*L[t-1] + 0.25*2*L[t] - 0.1*L[t]*L[t-1] + 1.5*W[0]*L[t-1]) +
node("hiRsk", t = 4, distr = "rconst", const = plogis(phiRsk[t]) > 0.80) +
node("A", t = 4, distr = "rbern", prob = A[t-1]*plogis(2 - 2.0*hiRsk[t])) +
node("Y", t = 4, distr = "rbern",
prob = plogis(-1*Y[t-1] + A[t] + phiRsk[t]*A[t] + 0.20*A[t-1]*L[t]) )
@
\clearpage
Model specification for simulation scenario 2.
<<chunk.Qg.t5, eval=FALSE, echo=TRUE>>=
## g model (same across all time-points):
gform.c <- c(rep.int("A ~ hiRsk + L + Atm1 + Ytm1", tvals), "A ~ hiRsk + Atm1 + Ytm1")
gform.i <- "A ~ 1"
## Q models:
Qforms.c <- c("Qkplus1 ~ L + W",
"Qkplus1 ~ L + Ltm1 + A + Atm1 + Ytm1 + W",
"Qkplus1 ~ L + Ltm1 + Ltm2 + A + Atm1 + Atm2 + Ytm1 + W",
"Qkplus1 ~ L + Ltm1 + Ltm2 + A + Atm1 + Atm2 + Ytm1 + W",
"Qkplus1 ~ L + Ltm1 + A + Atm1 + Ytm1 + W"
)
Qinteract.c <- NULL
Qforms.i <- c("Qkplus1 ~ L + W",
"Qkplus1 ~ W",
"Qkplus1 ~ W",
"Qkplus1 ~ W",
"Qkplus1 ~ W")
Qinteract.i <- NULL
## g and Q model to demonstrate SDR property (only last g is correctly specified)
gform.SDR <- c(rep.int("A ~ 1", tvals-1), "A ~ 1", "A ~ hiRsk + Atm1 + Ytm1")
Qforms.SDR <- c("Qkplus1 ~ L + W",
"Qkplus1 ~ L + Ltm1 + A + Atm1 + Ytm1 + W",
"Qkplus1 ~ L + Ltm1 + A + Atm1 + Ytm1 + W",
"Qkplus1 ~ L + Ltm1 + A + Atm1 + Ytm1 + W",
"Qkplus1 ~ W")
Qinteract.SDR <- NULL
@
\clearpage
\subsection{Combined results for simulation scenarios 1 and 2.}
<<simres.all.MSE, out.width=".65\\linewidth", fig.pos="H", message=FALSE, warning=FALSE, echo=FALSE, fig.cap="Relative MSE for $\\hat{Q}_1$ for simulation scenario 1 (top panel) and simulation scenario 2 (bottom panel). Simulation 1 is based on longitudinal data with 3 time-points and $n$=500 observations. Simulation 2 is based on longitudinal data with 5 time-points and $n$=5,000 observations. The iTMLE and DR Transform typically outperform or perform comparably to both competitors.">>=
pMSE.combinet <- plotMSE(rbind(restabMSE.t3, restabMSE.t5), jitter = .2) +
facet_grid(sim ~ ., scales = "free") + # , labeller = label_parsed
theme( # axis.title.x = element_blank(),
axis.title.y = element_text(size = 8),
axis.title.x = element_text(size = 8),
plot.margin = unit(c(0, 0, 0, 0), "lines"),
legend.position="bottom")
pMSE.combinet
@
<<simres.all.BIAS, out.width=".65\\linewidth", fig.pos="H", message=FALSE, warning=FALSE, echo=FALSE, fig.cap="Relative absolute bias for $\\hat{Q}_0$ for simulation scenario 1 (top panel) and simulation scenario 2 (bottom panel). Simulation 1 is based on longitudinal data with 3 time-points and $n$=500 observations. Simulation 2 is based on longitudinal data with 5 time-points and $n$=5,000 observations. The performance of LTMLE, iTMLE, and DR Transform is similar. The only exception for Simulation 1 is under \\textit{Qi.gc}, where DR Transform outperforms other methods. The only exceptions for Simulation 2 are for \\textit{Qc.gi}, where DR Transform outperforms other methods, and \\textit{QSDR.gSDR}, where both SDR methods outperform LTMLE.">>=
pBIAS.combinet <- plotBIAS(rbind(restabBIAS.t3, restabBIAS.t5), jitter = .2) +
facet_grid(sim ~ ., scales = "free") + # , labeller = label_parsed
theme( # axis.title.x = element_blank(),
axis.title.y = element_text(size = 8),
axis.title.x = element_text(size = 8),
plot.margin = unit(c(0, 0, 0, 0), "lines"),
legend.position="bottom")
pBIAS.combinet
@
<<simres.all.coverCIlen, out.width=".9\\linewidth", fig.pos="H", pdfcrop=TRUE, message=FALSE, warning=FALSE, echo=FALSE, fig.cap="Coverage (left panels) and mean length (right panels) of the two-sided 95\\% CIs for $Q_0$ in simulation scenario 1 (top panels) and simulation scenario 2 (bottom panels). Confidence interval coverage and width appear to be comparable between the two SDR methods and the LTMLE. The only exception is for the \\textit{QSDR.gSDR} scenario, where the LTMLE has roughly 10\\% coverage, whereas the SDR approaches nearly achieve the nominal coverage level.">>=
pCIcov.combinet <- plotCI(rbind(restabCIcov.t3, restabCIcov.t5), jitter =.3) +
facet_grid(sim ~ ., scales = "free") + # , labeller = label_parsed
theme( # axis.title.x = element_blank(),
axis.title.y = element_text(size = 8),
axis.title.x = element_text(size = 8),
plot.margin = unit(c(0, 0, .5, 0), "lines"),
legend.position="bottom")
# pCIcov.combinet
pCIlen.combinet <- plotCIlen(rbind(restabCIlen.t3, restabCIlen.t5)) +
facet_grid(sim ~ ., scales = "free") + # , labeller = label_parsed
theme( # axis.title.x = element_blank(),
axis.title.y = element_text(size = 8),
axis.title.x = element_text(size = 8),
plot.margin = unit(c(0, 0, .5, 0), "lines"),
legend.position="bottom")
# pCIlen.combinet
pCIlen.combinet <- pCIlen.combinet + theme(legend.position = "bottom")
pCIcov.combinet <- pCIcov.combinet + theme(legend.position = "bottom")
legend.save <- get_legend(pCIlen.combinet)
pCIcov.combinet <- pCIcov.combinet + theme(legend.position = "none", axis.title.x = element_text(size = 8), axis.title.y = element_blank())
pCIlen.combinet <- pCIlen.combinet + theme(legend.position = "none", axis.title.x = element_text(size = 8), axis.title.y = element_blank(), axis.text.y = element_blank()) + coord_flip()
grid.arrange(pCIcov.combinet, pCIlen.combinet, legend.save,
nrow = 2, ncol = 2,
layout_matrix = rbind(c(1,2), c(3,3)),
widths = c(0.65,0.35),
heights = unit(c(12, 0.5), "cm"),
clip = "on"
# heights = c(0.005, 0.1)
)
@
\clearpage
<<ggplot.all, message=FALSE, warning=FALSE, echo=FALSE, fig.cap="Top to bottom: MSE for estimation of $Q_1$, bias for estimation of $Q_0$ and 95\\% CI coverage for estimation of $Q_0$. Left plot: simulation scenario 1. Right plot: simulation scenario 2.">>=
new_theme <- theme(axis.title.y = element_blank())
pMSEt5 <- pMSEt5 + new_theme
pbiast5 <- pbiast5 + new_theme
pCIt5 <- pCIt5 + new_theme
grid.arrange(legend.save, # legend.save,
pMSEt3, pMSEt5,
pbiast3, pbiast5,
pCIt3, pCIt5,
nrow = 4, ncol = 2,
heights = c(2.9, 2.9, 2.0, 0.40),
widths = c(0.48,0.52),
layout_matrix = rbind(c(2,3), c(4, 5), c(6, 7), c(1,1))
)
@
\end{document}