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Narrow dose interval.Rmd
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Narrow dose interval.Rmd
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---
output:
html_document:
theme: yeti
toc: true
toc_depth: 3
toc_float:
collapsed: false
title: "Narrow dose interval"
### Written by Edward Parker ([email protected]), 29 May 2018
---
## Full analysis
```{r, echo=FALSE, message=FALSE, warning=FALSE}
# Load packages required for meta-analysis
library(metafor)
library(forestplot)
library(ggplot2)
# Import data and plot settings
data = read.csv("Church_et_al_2018_metaregression_input.csv",header=TRUE, stringsAsFactors=FALSE)
settings = read.csv("Church_et_al_2018_plot_settings.csv",header=TRUE, stringsAsFactors=FALSE)
# Select intervention, then subset data
intervention = "Narrow dose interval"
data1 = subset(data, Intervention_category==intervention)
# Replace '--' with '-' characters in age column
data1$Age_formatted = gsub("--", "-", data1$Age_formatted)
# Set plotting parameters for selected intervention (axis limits, plot height, plot width, and footnote coordinates)
forest_x_min_main = settings[which(settings$intervention==intervention),"forest_x_min_main"]
forest_x_max_main = settings[which(settings$intervention==intervention),"forest_x_max_main"]
forest_x_min_polio = settings[which(settings$intervention==intervention),"forest_x_min_polio"]
forest_x_max_polio = settings[which(settings$intervention==intervention),"forest_x_max_polio"]
plot_width_main = settings[which(settings$intervention==intervention),"plot_width_main"]
plot_width_polio = settings[which(settings$intervention==intervention),"plot_width_polio"]
plot_height_main = settings[which(settings$intervention==intervention),"plot_height_main"]
plot_height_polio = settings[which(settings$intervention==intervention),"plot_height_polio"]
footnote_x_main = settings[which(settings$intervention==intervention),"footnote_x_main"]
footnote_y_main = settings[which(settings$intervention==intervention),"footnote_y_main"]
footnote_x_polio = settings[which(settings$intervention==intervention),"footnote_x_polio"]
footnote_y_polio = settings[which(settings$intervention==intervention),"footnote_y_polio"]
column_gap_main = settings[which(settings$intervention==intervention),"column_gap_main"]
# Create subsets of data for each vaccine target
input_cholera = subset(data1,Vaccine=="Cholera")
input_rota = subset(data1,Vaccine=="Rotavirus")
input_PV1 = subset(data1,Measure_of_SC=="OPV1 N-AB")
input_PV2 = subset(data1,Measure_of_SC=="OPV2 N-AB")
input_PV3 = subset(data1,Measure_of_SC=="OPV3 N-AB")
# Create two collated versions of dataset - one for CV, RV and PV3; one for all types of polio
input_all = rbind(input_cholera, input_rota, input_PV3)
input_PV_all = rbind(input_PV1, input_PV2, input_PV3)
# Set minimum study count for inclusion in meta-analysis
min = 2
```
```{r, echo=FALSE, message=FALSE, warning=FALSE}
# Calculate sums of N by vaccine
cholera_sum = sum(input_all$Total[input_all$Vaccine=="Cholera"])
rota_sum = sum(input_all$Total[input_all$Vaccine=="Rotavirus"])
polio_sum = sum(input_all$Total[input_all$Vaccine=="Polio"])
overall_sum = sum(input_all$Total)
# Calculate number of vaccines included in analysis
n_vaccines = as.numeric(cholera_sum>0) + as.numeric(rota_sum>0) + as.numeric(polio_sum>0)
# Calculate summary statistics for each subset
if (cholera_sum>0) { data_cholera = escalc(measure = "RR", ai = Int_SC_n, bi = Int_N-Int_SC_n, ci = Ctrl_SC_n, di = Ctrl_N-Ctrl_SC_n, data = input_cholera, append = TRUE) }
if (rota_sum>0) { data_rota = escalc(measure = "RR", ai = Int_SC_n, bi = Int_N-Int_SC_n, ci = Ctrl_SC_n, di = Ctrl_N-Ctrl_SC_n, data = input_rota, append = TRUE) }
if (polio_sum>0) { data_PV3 = escalc(measure = "RR", ai = Int_SC_n, bi = Int_N-Int_SC_n, ci = Ctrl_SC_n, di = Ctrl_N-Ctrl_SC_n, data = input_PV3, append = TRUE) }
data_all = escalc(measure = "RR", ai = Int_SC_n, bi = Int_N-Int_SC_n, ci = Ctrl_SC_n, di = Ctrl_N-Ctrl_SC_n, data = input_all, append = TRUE)
# Perform REML meta-analyses
if (cholera_sum>0) { meta_cholera = rma(yi, vi, data = data_cholera, method = "REML") }
if (rota_sum>0) { meta_rota = rma(yi, vi, data = data_rota, method = "REML") }
if (polio_sum>0) { meta_PV3 = rma(yi, vi, data = data_PV3, method = "REML") }
# Perform combined meta-analysis, including random effect on study ID if intervention is 'RVV separated from OPV' (to account for replication of infants for RVV and OPV outcomes)
if (intervention=="RVV separated from OPV") { meta_all = rma.mv(yi, vi, data = data_all, method = "REML", random = ~ 1 | Reference) }
if (intervention!="RVV separated from OPV") { meta_all = rma(yi, vi, data = data_all, method = "REML") }
# Perform mixed-effects meta-regression, including random effect on study ID for 'RVV separated from OPV'
if (nrow(data_all)>=min & n_vaccines>1 & intervention=="RVV separated from OPV") { mixed_all = rma.mv(yi, vi, mods = ~ Vaccine, data = data_all, method = "REML", random = ~ 1 | Reference) }
if (nrow(data_all)>=min & n_vaccines>1 & intervention!="RVV separated from OPV") { mixed_all = rma(yi, vi, mods = ~ Vaccine, data = data_all, method = "REML") }
if (n_vaccines==1) {
mixed_all = NA
mixed_all$QEp = mixed_all$QMp = 1 } # if there is only 1 vaccine type, assign arbitrary value of 1 to mixed_all p values so as to avoid errors in later logical operators
# Create function to extract RRs and CIs from individual studies in rma meta-analysis output
RR_CIs = function(x) {
paste0(formatC(round(exp(x$yi),2),format='f',digits=2)," (",formatC(round(exp(x$yi-1.96*sqrt(x$vi)),2),format='f',digits=2),"-",formatC(round(exp(x$yi+1.96*sqrt(x$vi)),2),format='f',digits=2),")")
}
# Create function to extract overall RRs and CIs from rma meta-analysis output
RR_summary = function(x) {
paste0(formatC(round(exp(x$b),2),format='f',digits=2)," (", formatC(round(exp(x$b-1.96*x$se),2),format='f',digits=2), "-", formatC(round(exp(x$b+1.96*x$se),2),format='f',digits=2),")")
}
# Create function to collate relevant data for each column of forest plot
table_column = function(column_title, ref) {
column = column_title # specify column title
if (nrow(input_cholera)>0) { column = c(column,NA,input_cholera[,ref]) } # add study-specific rows if there is at least one study
if (nrow(input_cholera)<min & nrow(input_cholera)>0) { column = c(column,NA) } # add gap if number of studies is <min
if (nrow(input_cholera)>=min) { column = c(column,NA,NA) } # add summary row if number of studies is >=min
if (nrow(input_rota)>0) { column = c(column,NA,input_rota[,ref]) }
if (nrow(input_rota)<min & nrow(input_rota)>0) { column = c(column,NA) }
if (nrow(input_rota)>=min) { column = c(column,NA,NA) }
if (nrow(input_PV3)>0) { column = c(column,NA,input_PV3[,ref]) }
if (nrow(input_PV3)<min & nrow(input_PV3)>0) { column = c(column,NA) }
if (nrow(input_PV3)>=min) { column = c(column,NA,NA) }
if (nrow(input_all)>=min & n_vaccines>1) { column = c(column,NA) }
if (nrow(input_all)>=min & n_vaccines==1) { column = column[-length(column)] }
return(column)
}
# Use function to create meta-data columns for forest plot
country = table_column(column_title="Country", ref="Country")
age = table_column(column_title="Age (m)", ref="Age_formatted")
vaccine = table_column(column_title="Vaccine", ref="Vaccine_formatted")
intervention_col = table_column(column_title="Intervention", ref="Intervention_formatted")
N_int = table_column(column_title="n/N (%)", ref="Int_SC_full")
control = table_column(column_title="Control", ref="Control_formatted")
N_ctrl = table_column(column_title="n/N (%)", ref="Ctrl_SC_full")
# Create first column composed of Study IDs and vaccine names
titles = "Study"
if (nrow(input_cholera)>0) { titles = c(titles,"Cholera",input_cholera$Reference) }
if (nrow(input_cholera)<min & nrow(input_cholera)>0) { titles = c(titles,NA) }
if (nrow(input_cholera)>=min) { titles = c(titles,"Summary",NA) }
if (nrow(input_rota)>0) { titles = c(titles,"Rotavirus",input_rota$Reference) }
if (nrow(input_rota)<min & nrow(input_rota)>0) { titles = c(titles,NA) }
if (nrow(input_rota)>=min) { titles = c(titles,"Summary",NA) }
if (nrow(input_PV3)>0) { titles = c(titles,"OPV3",input_PV3$Reference) }
if (nrow(input_PV3)<min & nrow(input_PV3)>0) { titles = c(titles,NA) }
if (nrow(input_PV3)>=min) { titles = c(titles,"Summary",NA) }
if (nrow(input_all)>=min & n_vaccines>1) { titles = c(titles, "Overall") }
if (nrow(input_all)>=min & n_vaccines==1) { titles = titles[-length(titles)] }
# Create final column composed of RRs and 95% CIs
RRs = "RR (95% CI)"
if (nrow(input_cholera)>0) { RRs = c(RRs,NA,RR_CIs(meta_cholera)) }
if (nrow(input_cholera)<min & nrow(input_cholera)>0) { RRs = c(RRs,NA) }
if (nrow(input_cholera)>=min) { RRs = c(RRs,RR_summary(meta_cholera),NA) }
if (nrow(input_rota)>0) { RRs = c(RRs,NA,RR_CIs(meta_rota)) }
if (nrow(input_rota)<min & nrow(input_rota)>0) { RRs = c(RRs,NA) }
if (nrow(input_rota)>=min) { RRs = c(RRs,RR_summary(meta_rota),NA) }
if (nrow(input_PV3)>0) { RRs = c(RRs,NA,RR_CIs(meta_PV3)) }
if (nrow(input_PV3)<min & nrow(input_PV3)>0) { RRs = c(RRs,NA) }
if (nrow(input_PV3)>=min) { RRs = c(RRs,RR_summary(meta_PV3),NA) }
if (nrow(input_all)>=min & n_vaccines>1) { RRs = c(RRs,RR_summary(meta_all)) }
if (nrow(input_all)>=min & n_vaccines==1) { RRs = RRs[-length(RRs)] }
# Collate forest plot text
tabletext = cbind(titles, country, age, vaccine, intervention_col, N_int, control, N_ctrl, RRs)
# Create variable composed of RRs
m = NA
if (nrow(input_cholera)>0) { m = c(m,NA,meta_cholera$yi) }
if (nrow(input_cholera)<min & nrow(input_cholera)>0) { m = c(m,NA) }
if (nrow(input_cholera)>=min) { m = c(m,meta_cholera$b,NA) }
if (nrow(input_rota)>0) { m = c(m,NA,meta_rota$yi) }
if (nrow(input_rota)<min & nrow(input_rota)>0) { m = c(m,NA) }
if (nrow(input_rota)>=min) { m = c(m,meta_rota$b,NA) }
if (nrow(input_PV3)>0) { m = c(m,NA,meta_PV3$yi) }
if (nrow(input_PV3)<min & nrow(input_PV3)>0) { m = c(m,NA) }
if (nrow(input_PV3)>=min) { m = c(m,meta_PV3$b,NA) }
if (nrow(input_all)>=min & n_vaccines>1) { m = c(m,meta_all$b) }
if (nrow(input_all)>=min & n_vaccines==1) { m = m[-length(m)] }
# Create variables for lower CI limits of RR estimates
l = NA
if (nrow(input_cholera)>0) { l = c(l,NA,meta_cholera$yi-sqrt(meta_cholera$vi)*1.96) }
if (nrow(input_cholera)<min & nrow(input_cholera)>0) { l = c(l,NA) }
if (nrow(input_cholera)>=min) { l = c(l,meta_cholera$b-meta_cholera$se*1.96,NA) }
if (nrow(input_rota)>0) { l = c(l,NA,meta_rota$yi-sqrt(meta_rota$vi)*1.96) }
if (nrow(input_rota)<min & nrow(input_rota)>0) { l = c(l,NA) }
if (nrow(input_rota)>=min) { l = c(l,meta_rota$b-meta_rota$se*1.96,NA) }
if (nrow(input_PV3)>0) { l = c(l,NA,meta_PV3$yi-sqrt(meta_PV3$vi)*1.96) }
if (nrow(input_PV3)<min & nrow(input_PV3)>0) { l = c(l,NA) }
if (nrow(input_PV3)>=min) { l = c(l,meta_PV3$b-meta_PV3$se*1.96,NA) }
if (nrow(input_all)>=min & n_vaccines>1) { l = c(l,meta_all$b-meta_all$se*1.96) }
if (nrow(input_all)>=min & n_vaccines==1) { l = l[-length(l)] }
# Create variables for upper CI limits of RR estimates
u = NA
if (nrow(input_cholera)>0) { u = c(u,NA,meta_cholera$yi+sqrt(meta_cholera$vi)*1.96) }
if (nrow(input_cholera)<min & nrow(input_cholera)>0) { u = c(u,NA) }
if (nrow(input_cholera)>=min) { u = c(u,meta_cholera$b+meta_cholera$se*1.96,NA) }
if (nrow(input_rota)>0) { u = c(u,NA,meta_rota$yi+sqrt(meta_rota$vi)*1.96) }
if (nrow(input_rota)<min & nrow(input_rota)>0) { u = c(u,NA) }
if (nrow(input_rota)>=min) { u = c(u,meta_rota$b+meta_rota$se*1.96,NA) }
if (nrow(input_PV3)>0) { u = c(u,NA,meta_PV3$yi+sqrt(meta_PV3$vi)*1.96) }
if (nrow(input_PV3)<min & nrow(input_PV3)>0) { u = c(u,NA) }
if (nrow(input_PV3)>=min) { u = c(u,meta_PV3$b+meta_PV3$se*1.96,NA) }
if (nrow(input_all)>=min & n_vaccines>1) { u = c(u,meta_all$b+meta_all$se*1.96) }
if (nrow(input_all)>=min & n_vaccines==1) { u = u[-length(u)] }
```
### Forest plot
```{r, echo=FALSE, message=FALSE, warning=FALSE, fig.width=plot_width_main, fig.height=plot_height_main}
# Create function to assign colours to meta-analysis boxes and lines
# Adapted from: https://stackoverflow.com/questions/46938910
fn <- local({
i = 0
b_clrs = vector()
if (nrow(input_cholera)>0) { b_clrs = rep("#90B11F", nrow(input_cholera)) }
if (nrow(input_rota)>0) { b_clrs = c(b_clrs, rep("#D43E55", nrow(input_rota))) }
if (nrow(input_PV3)>0) { b_clrs = c(b_clrs, rep("#F1A44F", nrow(input_PV3))) }
b_clrs = c(b_clrs, "black")
l_clrs = rep("grey", length(b_clrs))
# l_clrs = b_clrs # use this line instead of the line above to make lines the same colour as the boxes
function(..., clr.line, clr.marker){
i <<- i + 1
fpDrawNormalCI(..., clr.line = l_clrs[i], clr.marker = b_clrs[i])
}
})
# Create function to assign colours to meta-analysis summary diamonds
# Adapted from: https://stackoverflow.com/questions/46938910
fn_sum <- local({
i = 0
b_clrs_sum = vector()
if (nrow(input_cholera)>=min) { b_clrs_sum = "#90B11F" }
if (nrow(input_rota)>=min) { b_clrs_sum = c(b_clrs_sum, "#D43E55") }
if (nrow(input_PV3)>=min) { b_clrs_sum = c(b_clrs_sum, "#F1A44F") }
b_clrs_sum = c(b_clrs_sum, "black")
function(..., col){
i <<- i + 1
fpDrawSummaryCI(..., col = b_clrs_sum[i])
}
})
# Create forest plot
if (nrow(input_all)>=min) {
forestplot(tabletext,exp(m),exp(l),exp(u),zero=1,
is.summary=c(TRUE,TRUE,!is.na(tabletext[3:nrow(tabletext),1]) & (tabletext[3:nrow(tabletext),1]=="Summary" | tabletext[3:nrow(tabletext),1]=="Overall"| tabletext[3:nrow(tabletext),1]=="Cholera"| tabletext[3:nrow(tabletext),1]=="Rotavirus"| tabletext[3:nrow(tabletext),1]=="OPV3")),
clip=c(forest_x_min_main,forest_x_max_main), xlog=TRUE,
xticks=c(forest_x_min_main,1,forest_x_max_main),
fn.ci_norm=fn,
fn.ci_sum=fn_sum,
colgap=unit(column_gap_main,"mm"),
txt_gp = fpTxtGp(ticks = gpar(cex=0.8))
)
# Add footnote containing heterogeneity results
if (nrow(data_all)>=min & n_vaccines>1 & mixed_all$QEp>=0.0001) {
grid.text(paste0("Heterogeneity among vaccines (Qm ", formatC(round(mixed_all$QM,2),format='f',digits=2), ", df ", mixed_all$m, "), p = ", formatC(round(mixed_all$QMp,3),format='f',digits=3),
"; Residual heterogeneity (Qe ", formatC(round(mixed_all$QE,2),format='f',digits=2), ", df ", mixed_all$k-mixed_all$p, "), p = ", formatC(round(mixed_all$QEp,3),format='f',digits=3)),
footnote_x_main, footnote_y_main, gp = gpar(fontsize=12, font = "sans")) }
if (nrow(data_all)>=min & n_vaccines>1 & mixed_all$QEp<0.0001) {
grid.text(paste0("Heterogeneity among vaccines (Qm ", formatC(round(mixed_all$QM,2),format='f',digits=2), ", df ", mixed_all$m, "), p = ", formatC(round(mixed_all$QMp,3),format='f',digits=3),
"; Residual heterogeneity (Qe ", formatC(round(mixed_all$QE,2),format='f',digits=2), ", df ", mixed_all$k-mixed_all$p, "), p < 0.0001"),
footnote_x_main, footnote_y_main, gp = gpar(fontsize=12, font = "sans")) }
if (nrow(data_all)>=min & n_vaccines==1 & meta_all$QEp>=0.0001) {
grid.text(paste0("Heterogeneity (Q ", formatC(round(meta_all$QE,2),format='f',digits=2), ", df ", meta_all$k-meta_all$p, "), p = ", formatC(round(meta_all$QEp,3),format='f',digits=3)),
footnote_x_main, footnote_y_main, gp = gpar(fontsize=12, font = "sans")) }
if (nrow(data_all)>=min & n_vaccines==1 & meta_all$QEp<0.0001) {
grid.text(paste0("Heterogeneity (Q ", formatC(round(meta_all$QE,2),format='f',digits=2), ", df ", meta_all$k-meta_all$p, "), p < 0.0001"),
footnote_x_main, footnote_y_main, gp = gpar(fontsize=12, font = "sans")) }
} else { print("Insufficient studies (n<2)") }
```
### Funnel plot
```{r, echo=FALSE, message=FALSE, fig.height=3, fig.width=6}
# Draw funnel plot containing all results included in meta-analysis
overall_estimate = meta_all$b
funnel_input = data.frame(SE = sqrt(meta_all$vi), LogRR = meta_all$yi, Vaccine = input_all$Vaccine, N = input_all$Total)
ggplot(funnel_input, aes(y=SE, x=LogRR)) + geom_point(aes(color = Vaccine), size=3.5, alpha=0.7) +
geom_vline(xintercept=overall_estimate, color='grey', linetype='dashed') + theme_minimal() +
ylab('SE (log RR)') + xlab('log RR') + scale_y_reverse() + xlim(-2,2) +
scale_color_manual(values = c("Cholera" = "#90B11F", "Polio" = "#F1A44F" , "Rotavirus" = "#D43E55")) +
theme(legend.title=element_blank(), legend.position="right")
```
### Egger's test
```{r, echo=FALSE, message=FALSE, warning=FALSE}
# Perform Egger's test; for 'RVV separated from OPV', this should be stratified by vaccine type to account for replication of infants for RVV and OPV outcomes
if (nrow(data_all)<3) { print("Insufficient studies (n<3)") }
if (nrow(data_all)>=3 & intervention!="RVV separated from OPV" & mixed_all$QMp>=0.05) {
print("No replication of infants across vaccines or significant vaccine effect, therefore combined test performed")
regtest(meta_all, predictor="sei") }
if (nrow(data_all)>=3 & (intervention=="RVV separated from OPV" | mixed_all$QMp<0.05)) {
print("Infants replicated across vaccines or vaccine effect significant, therefore separate tests performed")
print("Cholera:")
if (nrow(input_cholera)>=3) { print(regtest(meta_cholera, predictor="sei")) } else { print("Insufficient studies (n<3)")}
print("Rotavirus:")
if (nrow(input_rota)>=3) { print(regtest(meta_rota, predictor="sei")) } else { print("Insufficient studies (n<3)")}
print("OPV3:")
if (nrow(input_PV3)>=3) { print(regtest(meta_PV3, predictor="sei")) } else { print("Insufficient studies (n<3)")}
}
```
### Meta-analysis output
```{r, echo=FALSE, message=FALSE, warning=FALSE}
if (nrow(input_all)>=min) { summary(meta_all) } else { print("Insufficient studies (n<2)") }
```
### Meta-regression output
```{r, echo=FALSE, message=FALSE, warning=FALSE}
# If more than one type of vaccine included in analysis, print meta-regression results
if (nrow(data_all)>=min & n_vaccines>1) { mixed_all } else { print("Insufficient studies for meta-regression (either <2 studies or only 1 vaccine type)") }
```
### Intervention-specific outputs
#### Summary of cholera studies
```{r, echo=FALSE, message=FALSE, warning=FALSE}
if (nrow(input_cholera)>=min) { summary(meta_cholera) } else { print("Insufficient studies (n<2)")}
```
#### Summary of rotavirus studies
```{r, echo=FALSE, message=FALSE, warning=FALSE}
if (nrow(input_rota)>=min) { summary(meta_rota) } else { print("Insufficient studies (n<2)")}
```
#### Summary of PV3 studies
```{r, echo=FALSE, message=FALSE, warning=FALSE}
if (nrow(input_PV3)>=min) { summary(meta_PV3) } else { print("Insufficient studies (n<2)")}
```
### Meta-regression: secondary moderators
#### Age group
```{r, echo=FALSE, message=FALSE, warning=FALSE}
if (nrow(data_all)>=min & n_vaccines>1) { QEp = mixed_all$QEp }
if (nrow(data_all)>=min & n_vaccines==1) { QEp = meta_all$QEp }
if (QEp>0.05) { print("Residual heterogeneity not significant (p>0.05)")
} else if (nlevels(factor(data_all$Age_group))==1) { print("No variation in moderator among studies")
} else if (nlevels(factor(data_all$Age_group))==nrow(data_all)) { print("Insufficient studies (n studies == n moderators)")
} else if (intervention=="RVV separated from OPV") {
print("Rotavirus-specific analysis performed owing to absence of significant residual heterogeneity for OPV studies")
print(table(data_rota$Age_group))
meteregression_age = rma.mv(yi, vi, mods = ~ factor(Age_group), data = data_rota, method = "REML")
meteregression_age
} else if (intervention!="RVV separated from OPV") {
print(table(data_all$Age_group))
meteregression_age = rma(yi, vi, mods = ~ factor(Age_group), data = data_all, method = "REML")
meteregression_age
}
```
#### Income setting
```{r, echo=FALSE, message=FALSE, warning=FALSE}
if (QEp>0.05) { print("Residual heterogeneity not significant (p>0.05)")
} else if (nlevels(factor(data_all$Income_group))==1) { print("No variation in moderator among studies")
} else if (nlevels(factor(data_all$Income_group))==nrow(data_all)) { print("Insufficient studies (n studies == n moderators)")
} else if (intervention=="RVV separated from OPV") {
print("Rotavirus-specific analysis performed owing to absence of significant residual heterogeneity for OPV studies")
print(table(data_rota$Income_group))
meteregression_setting = rma.mv(yi, vi, mods = ~ factor(Income_group), data = data_rota, method = "REML")
meteregression_setting
} else if (intervention!="RVV separated from OPV") {
print(table(data_all$Income_group))
meteregression_setting = rma(yi, vi, mods = ~ factor(Income_group), data = data_all, method = "REML")
meteregression_setting
}
```
#### Background immunogenicity (seroconversion rate in the control group)
```{r, echo=FALSE, message=FALSE, warning=FALSE}
if (QEp>0.05) { print("Residual heterogeneity not significant (p>0.05)")
} else if (intervention=="RVV separated from OPV") {
print("Rotavirus-specific analysis performed owing to absence of significant residual heterogeneity for OPV studies")
meteregression_baseline = rma.mv(yi, vi, mods = ~ asin(sqrt(Baseline_seroconversion)), data = data_rota, method = "REML")
meteregression_baseline
} else if (intervention!="RVV separated from OPV") {
meteregression_baseline = rma(yi, vi, mods = ~ asin(sqrt(Baseline_seroconversion)), data = data_all, method = "REML")
meteregression_baseline
}
```
## OPV-specific analysis
```{r, echo=FALSE, message=FALSE, warning=FALSE}
# Calculate sums of N by vaccine
PV1_sum = sum(input_PV_all$Total[input_PV_all$Measure_of_SC=="OPV1 N-AB"])
PV2_sum = sum(input_PV_all$Total[input_PV_all$Measure_of_SC=="OPV2 N-AB"])
PV3_sum = sum(input_PV_all$Total[input_PV_all$Measure_of_SC=="OPV3 N-AB"])
overall_PV_sum = sum(input_PV_all$Total)
# Calculate number of vaccines included in analysis
n_PV_vaccines = as.numeric(PV1_sum>0) + as.numeric(PV2_sum>0) + as.numeric(PV3_sum>0)
# Calculate summary statistics for each subset
if (PV1_sum>0) {data_PV1 = escalc(measure = "RR", ai = Int_SC_n, bi = Int_N-Int_SC_n, ci = Ctrl_SC_n, di = Ctrl_N-Ctrl_SC_n, data = input_PV1, append = TRUE) }
if (PV2_sum>0) {data_PV2 = escalc(measure = "RR", ai = Int_SC_n, bi = Int_N-Int_SC_n, ci = Ctrl_SC_n, di = Ctrl_N-Ctrl_SC_n, data = input_PV2, append = TRUE) }
if (PV3_sum>0) {data_PV3 = escalc(measure = "RR", ai = Int_SC_n, bi = Int_N-Int_SC_n, ci = Ctrl_SC_n, di = Ctrl_N-Ctrl_SC_n, data = input_PV3, append = TRUE) }
if (overall_PV_sum>0) {data_PV_all = escalc(measure = "RR", ai = Int_SC_n, bi = Int_N-Int_SC_n, ci = Ctrl_SC_n, di = Ctrl_N-Ctrl_SC_n, data = input_PV_all, append = TRUE) }
# Perform REML meta-analyses
if (PV1_sum>0) { meta_PV1 = rma(yi, vi, data = data_PV1, method = "REML") }
if (PV2_sum>0) { meta_PV2 = rma(yi, vi, data = data_PV2, method = "REML") }
if (PV3_sum>0) { meta_PV3 = rma(yi, vi, data = data_PV3, method = "REML") }
# Perform combined meta-analysis, including random effect on study ID
if (overall_PV_sum>0) { meta_PV_all = rma.mv(yi, vi, data = data_PV_all, method = "REML", random = ~ 1 | Reference) }
# Perform mixed-effects meta-regression, including random effect on study ID
if (nrow(input_PV_all)>=min & n_PV_vaccines>1) { mixed_PV_all = rma.mv(yi, vi, mods = ~ Measure_of_SC, data = data_PV_all, method = "REML", random = ~ 1 | Reference) }
if (n_PV_vaccines==1) {
mixed_PV_all = NA
mixed_PV_all$QEp = mixed_PV_all$QMp = 1 } # if there is only 1 vaccine type, assign arbitrary value of 1 to mixed_all p values so as to avoid errors in later logical operators
# Create function to collate relevant data for each column of PV-specific forest plot
table_column_PV = function(column_title, ref) {
column = column_title # specify column title
if (nrow(input_PV1)>0) { column = c(column,NA,input_PV1[,ref]) } # add study-specific rows if there is at least one study
if (nrow(input_PV1)<min & nrow(input_PV1)>0) { column = c(column,NA) } # add gap if number of studies is <min
if (nrow(input_PV1)>=min) { column = c(column,NA,NA) } # add summary row if number of studies is >=min
if (nrow(input_PV2)>0) { column = c(column,NA,input_PV2[,ref]) }
if (nrow(input_PV2)<min & nrow(input_PV2)>0) { column = c(column,NA) }
if (nrow(input_PV2)>=min) { column = c(column,NA,NA) }
if (nrow(input_PV3)>0) { column = c(column,NA,input_PV3[,ref]) }
if (nrow(input_PV3)<min & nrow(input_PV3)>0) { column = c(column,NA) }
if (nrow(input_PV3)>=min) { column = c(column,NA,NA) }
if (nrow(input_PV_all)>=min & n_PV_vaccines>1) { column = c(column,NA) }
if (nrow(input_PV_all)>=min & n_PV_vaccines==1) { column = column[-length(column)] }
return(column)
}
# Use function to create meta-data columns for forest plot
country = table_column_PV(column_title="Country", ref="Country")
age = table_column_PV(column_title="Age (m)", ref="Age_formatted")
vaccine = table_column_PV(column_title="Vaccine", ref="Vaccine_formatted")
intervention_col = table_column_PV(column_title="Intervention", ref="Intervention_formatted")
N_int = table_column_PV(column_title="n/N (%)", ref="Int_SC_full")
control = table_column_PV(column_title="Control", ref="Control_formatted")
N_ctrl = table_column_PV(column_title="n/N (%)", ref="Ctrl_SC_full")
# Create first column composed of Study IDs and vaccine names
titles = "Study"
if (nrow(input_PV1)>0) { titles = c(titles,"OPV1",input_PV1$Reference) }
if (nrow(input_PV1)<min & nrow(input_PV1)>0) { titles = c(titles,NA) }
if (nrow(input_PV1)>=min) { titles = c(titles,"Summary",NA) }
if (nrow(input_PV2)>0) { titles = c(titles,"OPV2",input_PV2$Reference) }
if (nrow(input_PV2)<min & nrow(input_PV2)>0) { titles = c(titles,NA) }
if (nrow(input_PV2)>=min) { titles = c(titles,"Summary",NA) }
if (nrow(input_PV3)>0) { titles = c(titles,"OPV3",input_PV3$Reference) }
if (nrow(input_PV3)<min & nrow(input_PV3)>0) { titles = c(titles,NA) }
if (nrow(input_PV3)>=min) { titles = c(titles,"Summary",NA) }
if (nrow(input_PV_all)>=min & n_PV_vaccines>1) { titles = c(titles, "Overall") }
if (nrow(input_PV_all)>=min & n_PV_vaccines==1) { titles = titles[-length(titles)] }
# Create final column composed of RRs and 95% CIs
RRs = "RR (95% CI)"
if (nrow(input_PV1)>0) { RRs = c(RRs,NA,RR_CIs(meta_PV1)) }
if (nrow(input_PV1)<min & nrow(input_PV1)>0) { RRs = c(RRs,NA) }
if (nrow(input_PV1)>=min) { RRs = c(RRs,RR_summary(meta_PV1),NA) }
if (nrow(input_PV2)>0) { RRs = c(RRs,NA,RR_CIs(meta_PV2)) }
if (nrow(input_PV2)<min & nrow(input_PV2)>0) { RRs = c(RRs,NA) }
if (nrow(input_PV2)>=min) { RRs = c(RRs,RR_summary(meta_PV2),NA) }
if (nrow(input_PV3)>0) { RRs = c(RRs,NA,RR_CIs(meta_PV3)) }
if (nrow(input_PV3)<min & nrow(input_PV3)>0) { RRs = c(RRs,NA) }
if (nrow(input_PV3)>=min) { RRs = c(RRs,RR_summary(meta_PV3),NA) }
if (nrow(input_PV_all)>=min & n_PV_vaccines>1) { RRs = c(RRs,RR_summary(meta_PV_all)) }
if (nrow(input_PV_all)>=min & n_PV_vaccines==1) { RRs = RRs[-length(RRs)] }
# Collate forest plot text
tabletext = cbind(titles, country, age, vaccine, intervention_col, N_int, control, N_ctrl, RRs)
# Create variable composed of RRs
m = NA
if (nrow(input_PV1)>0) { m = c(m,NA,meta_PV1$yi) }
if (nrow(input_PV1)<min & nrow(input_PV1)>0) { m = c(m,NA) }
if (nrow(input_PV1)>=min) { m = c(m,meta_PV1$b,NA) }
if (nrow(input_PV2)>0) { m = c(m,NA,meta_PV2$yi) }
if (nrow(input_PV2)<min & nrow(input_PV2)>0) { m = c(m,NA) }
if (nrow(input_PV2)>=min) { m = c(m,meta_PV2$b,NA) }
if (nrow(input_PV3)>0) { m = c(m,NA,meta_PV3$yi) }
if (nrow(input_PV3)<min & nrow(input_PV3)>0) { m = c(m,NA) }
if (nrow(input_PV3)>=min) { m = c(m,meta_PV3$b,NA) }
if (nrow(input_PV_all)>=min & n_PV_vaccines>1) { m = c(m,meta_PV_all$b) }
if (nrow(input_PV_all)>=min & n_PV_vaccines==1) { m = m[-length(m)] }
# Create variables for lower CI limits of RR estimates
l = NA
if (nrow(input_PV1)>0) { l = c(l,NA,meta_PV1$yi-sqrt(meta_PV1$vi)*1.96) }
if (nrow(input_PV1)<min & nrow(input_PV1)>0) { l = c(l,NA) }
if (nrow(input_PV1)>=min) { l = c(l,meta_PV1$b-meta_PV1$se*1.96,NA) }
if (nrow(input_PV2)>0) { l = c(l,NA,meta_PV2$yi-sqrt(meta_PV2$vi)*1.96) }
if (nrow(input_PV2)<min & nrow(input_PV2)>0) { l = c(l,NA) }
if (nrow(input_PV2)>=min) { l = c(l,meta_PV2$b-meta_PV2$se*1.96,NA) }
if (nrow(input_PV3)>0) { l = c(l,NA,meta_PV3$yi-sqrt(meta_PV3$vi)*1.96) }
if (nrow(input_PV3)<min & nrow(input_PV3)>0) { l = c(l,NA) }
if (nrow(input_PV3)>=min) { l = c(l,meta_PV3$b-meta_PV3$se*1.96,NA) }
if (nrow(input_PV_all)>=min & n_PV_vaccines>1) { l = c(l,meta_PV_all$b-meta_PV_all$se*1.96) }
if (nrow(input_PV_all)>=min & n_PV_vaccines==1) { l = l[-length(l)] }
# Create variables for upper CI limits of RR estimates
u = NA
if (nrow(input_PV1)>0) { u = c(u,NA,meta_PV1$yi+sqrt(meta_PV1$vi)*1.96) }
if (nrow(input_PV1)<min & nrow(input_PV1)>0) { u = c(u,NA) }
if (nrow(input_PV1)>=min) { u = c(u,meta_PV1$b+meta_PV1$se*1.96,NA) }
if (nrow(input_PV2)>0) { u = c(u,NA,meta_PV2$yi+sqrt(meta_PV2$vi)*1.96) }
if (nrow(input_PV2)<min & nrow(input_PV2)>0) { u = c(u,NA) }
if (nrow(input_PV2)>=min) { u = c(u,meta_PV2$b+meta_PV2$se*1.96,NA) }
if (nrow(input_PV3)>0) { u = c(u,NA,meta_PV3$yi+sqrt(meta_PV3$vi)*1.96) }
if (nrow(input_PV3)<min & nrow(input_PV3)>0) { u = c(u,NA) }
if (nrow(input_PV3)>=min) { u = c(u,meta_PV3$b+meta_PV3$se*1.96,NA) }
if (nrow(input_PV_all)>=min & n_PV_vaccines>1) { u = c(u,meta_PV_all$b+meta_PV_all$se*1.96) }
if (nrow(input_PV_all)>=min & n_PV_vaccines==1) { u = u[-length(u)] }
```
### Forest plot
```{r, echo=FALSE, message=FALSE, warning=FALSE, fig.width=plot_width_polio, fig.height=plot_height_polio}
# Create function to assign colours to meta-analysis boxes and lines
# Adapted from: https://stackoverflow.com/questions/46938910
fn <- local({
i = 0
b_clrs = vector()
if (nrow(input_PV1)>0) { b_clrs = rep("#f1cd4f", nrow(input_PV1)) }
if (nrow(input_PV2)>0) { b_clrs = c(b_clrs, rep("#734109", nrow(input_PV2))) }
if (nrow(input_PV3)>0) { b_clrs = c(b_clrs, rep("#F1A44F", nrow(input_PV3))) }
b_clrs = c(b_clrs, "black")
l_clrs = rep("grey", length(b_clrs))
# l_clrs = b_clrs # use this line instead of the line above to make lines the same colour as the boxes
function(..., clr.line, clr.marker){
i <<- i + 1
fpDrawNormalCI(..., clr.line = l_clrs[i], clr.marker = b_clrs[i])
}
})
# Create function to assign colours to meta-analysis summary diamonds
# Adapted from: https://stackoverflow.com/questions/46938910
fn_sum <- local({
i = 0
b_clrs_sum = vector()
if (nrow(input_PV1)>=min) { b_clrs_sum = "#f1cd4f" }
if (nrow(input_PV2)>=min) { b_clrs_sum = c(b_clrs_sum, "#734109") }
if (nrow(input_PV3)>=min) { b_clrs_sum = c(b_clrs_sum, "#F1A44F") }
b_clrs_sum = c(b_clrs_sum, "black")
function(..., col){
i <<- i + 1
fpDrawSummaryCI(..., col = b_clrs_sum[i])
}
})
# Create forest plot
if (nrow(input_PV_all)>=min) {
forestplot(tabletext,exp(m),exp(l),exp(u),zero=1,
is.summary=c(TRUE,TRUE,!is.na(tabletext[3:nrow(tabletext),1]) & (tabletext[3:nrow(tabletext),1]=="Summary" | tabletext[3:nrow(tabletext),1]=="Overall"| tabletext[3:nrow(tabletext),1]=="OPV1"| tabletext[3:nrow(tabletext),1]=="OPV2"| tabletext[3:nrow(tabletext),1]=="OPV3")),
clip=c(forest_x_min_polio,forest_x_max_polio), xlog=TRUE,
xticks=c(forest_x_min_polio,1,forest_x_max_polio),
fn.ci_norm=fn,
fn.ci_sum=fn_sum,
colgap=unit(5,"mm"),
txt_gp = fpTxtGp(ticks = gpar(cex=0.8))
)
# Add footnote containing heterogeneity results
if (nrow(input_PV_all)>=min & n_PV_vaccines>1 & mixed_PV_all$QEp>=0.0001) {
grid.text(paste0("Heterogeneity among vaccines (Qm ", formatC(round(mixed_PV_all$QM,2),format='f',digits=2), ", df ", mixed_PV_all$m, "), p = ", formatC(round(mixed_PV_all$QMp,3),format='f',digits=3),
"; Residual heterogeneity (Qe ", formatC(round(mixed_PV_all$QE,2),format='f',digits=2), ", df ", mixed_PV_all$k-mixed_PV_all$p, "), p = ", formatC(round(mixed_PV_all$QEp,3),format='f',digits=3)),
footnote_x_polio, footnote_y_polio, gp = gpar(fontsize=12, font = "sans")) }
if (nrow(input_PV_all)>=min & n_PV_vaccines>1 & mixed_PV_all$QEp<0.0001) {
grid.text(paste0("Heterogeneity among vaccines (Qm ", formatC(round(mixed_PV_all$QM,2),format='f',digits=2), ", df ", mixed_PV_all$m, "), p = ", formatC(round(mixed_PV_all$QMp,3),format='f',digits=3),
"; Residual heterogeneity (Qe ", formatC(round(mixed_PV_all$QE,2),format='f',digits=2), ", df ", mixed_PV_all$k-mixed_PV_all$p, "), p < 0.0001"),
footnote_x_polio, footnote_y_polio, gp = gpar(fontsize=12, font = "sans")) }
if (nrow(input_PV_all)>=min & n_PV_vaccines==1 & meta_PV_all$QEp>=0.0001) {
grid.text(paste0("Heterogeneity (Q ", formatC(round(meta_PV_all$QE,2),format='f',digits=2), ", df ", meta_PV_all$k-meta_PV_all$p, "), p = ", formatC(round(meta_PV_all$QEp,3),format='f',digits=3)),
0.1, footnote_y_polio, gp = gpar(fontsize=12, font = "sans")) }
if (nrow(input_PV_all)>=min & n_PV_vaccines==1 & meta_PV_all$QEp<0.0001) {
grid.text(paste0("Heterogeneity (Q ", formatC(round(meta_PV_all$QE,2),format='f',digits=2), ", df ", meta_PV_all$k-meta_PV_all$p, "), p < 0.0001"),
0.1, footnote_y_polio, gp = gpar(fontsize=12, font = "sans")) }
} else { print("Insufficient studies (n<2)")}
```
### Funnel plot
```{r, echo=FALSE, message=FALSE, warning=FALSE, fig.height=3, fig.width=6}
# Draw funnel plot containing all results included in meta-analysis
if (overall_PV_sum>0) {
overall_estimate = meta_PV_all$b
funnel_input = data.frame(SE = sqrt(meta_PV_all$vi), LogRR = meta_PV_all$yi,
Vaccine = substr(input_PV_all$Measure_of_SC,0,4), N = input_PV_all$Total, Study = input_PV_all$Reference)
ggplot(funnel_input, aes(y=SE, x=LogRR)) + geom_point(aes(color = Vaccine), size=3.5, alpha=0.7) +
geom_vline(xintercept=overall_estimate, color='grey', linetype='dashed') + theme_minimal() +
ylab('SE (log RR)') + xlab('log RR') + scale_y_reverse() + xlim(-2,2) +
scale_color_manual(values = c("OPV1" = "#f1cd4f", "OPV2" = "#734109" , "OPV3" = "#F1A44F")) +
theme(legend.title=element_blank(), legend.position="right")
} else { print("Insufficient studies (n<2)")}
```
### Egger's test
Infants replicated across vaccines, therefore separate tests performed
```{r, echo=FALSE, message=FALSE, warning=FALSE}
# Perform Egger's test; this should be stratified by vaccine type to account for replication of infants across PV serotypes
print("OPV1:")
if (nrow(input_PV1)>=3) { print(regtest(meta_PV1, predictor="sei")) } else { print("Insufficient studies (n<3)")}
print("OPV2:")
if (nrow(input_PV2)>=3) { print(regtest(meta_PV2, predictor="sei")) } else { print("Insufficient studies (n<3)")}
print("OPV3:")
if (nrow(input_PV3)>=3) { print(regtest(meta_PV3, predictor="sei")) } else { print("Insufficient studies (n<3)")}
```
### Meta-analysis output
```{r, echo=FALSE, message=TRUE, warning=TRUE}
if (nrow(input_PV_all)>=min) { summary(meta_PV_all) } else { print("Insufficient studies (n<2)")}
```
### Meta-regression output
```{r, echo=FALSE, message=FALSE, warning=FALSE}
# If more than one type of vaccine included in analysis, print meta-regression results
if (nrow(input_PV_all)>=min & n_PV_vaccines>1) { mixed_PV_all } else { print("Insufficient studies for meta-regression (either <2 studies or only 1 vaccine type)") }
```
### Serotype-specific outputs
#### Summary of PV1 studies
```{r, echo=FALSE, message=FALSE, warning=FALSE}
if (nrow(input_PV1)>=min) { summary(meta_PV1) } else { print("Insufficient studies (n<2)")}
```
#### Summary of PV2 studies
```{r, echo=FALSE, message=FALSE, warning=FALSE}
if (nrow(input_PV2)>=min) { summary(meta_PV2) } else { print("Insufficient studies (n<2)")}
```
#### Summary of PV3 studies
```{r, echo=FALSE, message=FALSE, warning=FALSE}
if (nrow(input_PV3)>=min) { summary(meta_PV3) } else { print("Insufficient studies (n<2)")}
```