bootstrap_HR: Bootstrapping for MAIC weighted hazard ratios

In Roche/MAIC: Package to Perform Matched-adjusted Indirect Comparisons

Bootstrapping for MAIC weighted hazard ratios

Description

Bootstrapping for MAIC weighted hazard ratios

Usage

bootstrap_HR(
  intervention_data,
  matching,
  i,
  model,
  comparator_data,
  min_weight = 1e-04
)

Arguments

intervention_data	A data frame containing individual patient data from the intervention study.
matching	A character vector giving the names of the covariates to use in matching. These names must match the column names in intervention_data.
i	Index used to select a sample within boot.
model	A model formula in the form 'Surv(Time, Event==1) ~ ARM'. Variable names need to match the corresponding columns in intervention_data.
comparator_data	A data frame containing pseudo individual patient data from the comparator study needed to derive the relative treatment effect. The outcome variables names must match intervention_data.
min_weight	A numeric value that defines the minimum weight allowed. This value (default 0.0001) will replace weights estimated at 0 in a sample.

Details

This function is intended to be used in conjunction with the boot function to return the statistic to be bootstrapped. In this case by performing MAIC weighting using estimate_weights and returning a weighted hazard ratio (HR) from a Cox proportional hazards model. This is used as the 'statistic' argument in the boot function.

Value

The HR as a numeric value.

See Also

estimate_weights, boot

Examples

# This example code combines weighted individual patient data for 'intervention'
# and pseudo individual patient data for 'comparator' and performs analyses for
# two endpoints: overall survival (a time to event outcome) and objective
# response (a binary outcome)

library(dplyr)
library(boot)
library(survival)
library(MAIC)
library(ggplot2)
library(survminer)
library(flextable)
library(officer)

# load intervention data with weights saved in est_weights
data(est_weights, package = "MAIC")

# Combine data -----------------------------------------------------------------

# Combine the the comparator pseudo data with the analysis data, outputted from
# the estimate_weights function

# Read in digitised pseudo survival data for the comparator
comparator_surv <- read.csv(system.file("extdata", "psuedo_IPD.csv",
                                        package = "MAIC", mustWork = TRUE)) %>%
                            rename(Time=Time, Event=Event)


# Simulate response data based on the known proportion of responders
comparator_n <- nrow(comparator_surv) # total number of patients in the comparator data
comparator_prop_events <- 0.4 # proportion of responders
# Calculate number with event
# Use round() to ensure we end up with a whole number of people
# number without an event = Total N - number with event to ensure we keep the
# same number of patients
n_with_event <- round(comparator_n*comparator_prop_events, digits = 0)
comparator_binary <- data.frame("response"= c(rep(1, n_with_event), rep(0, comparator_n - n_with_event)))


# Join survival and response comparator data
# Note the rows do not represent observations from a particular patient
# i.e. there is no relationship between the survival time and response status
# for a given row since this is simulated data
# In a real data set this relationship would be present
comparator_input <- cbind(comparator_surv, comparator_binary) %>%
  mutate(wt=1, wt_rs=1, ARM="Comparator") # All patients have weight = 1
head(comparator_input)

# Join comparator data with the intervention data (naming of variables should be
# consistent between both datasets)
# Set factor levels to ensure "Comparator" is the reference treatment
combined_data <-  bind_rows(est_weights$analysis_data, comparator_input)
combined_data$ARM <- relevel(as.factor(combined_data$ARM), ref="Comparator")


#### Estimating the relative effect --------------------------------------------

### Example for survival data --------------------------------------------------

## Kaplan-Meier plot

# Unweighted intervention data
KM_int <- survfit(formula = Surv(Time, Event==1) ~ 1 ,
                  data = est_weights$analysis_data,
                  type="kaplan-meier")

# Weighted intervention data
KM_int_wtd <- survfit(formula = Surv(Time, Event==1) ~ 1 ,
                      data = est_weights$analysis_data,
                      weights = wt,
                      type="kaplan-meier")

# Comparator data
KM_comp <- survfit(formula = Surv(Time, Event==1) ~ 1 ,
                   data = comparator_input,
                   type="kaplan-meier")

# Combine the survfit objects ready for ggsurvplot
KM_list <- list(Intervention = KM_int,
                Intervention_weighted = KM_int_wtd,
                Comparator = KM_comp)

#Produce the Kaplan-Meier plot
KM_plot <- ggsurvplot(KM_list,
                      combine = TRUE,
                      risk.table=TRUE, # numbers at risk displayed on the plot
                      break.x.by=50,
                      xlab="Time (days)",
                      censor=FALSE,
                      legend.title = "Treatment",
                      title = "Kaplan-Meier plot of overall survival",
                      legend.labs=c("Intervention",
                                    "Intervention weighted",
                                    "Comparator"),
                      font.legend = list(size = 10)) +
  guides(colour=guide_legend(nrow = 2))


## Estimating the hazard ratio (HR)

# Fit a Cox model without weights to estimate the unweighted HR
unweighted_cox <- coxph(Surv(Time, Event==1) ~ ARM, data = combined_data)

HR_CI_cox <- summary(unweighted_cox)$conf.int %>%
  as.data.frame() %>%
  transmute("HR" = `exp(coef)`,
            "HR_low_CI" = `lower .95`,
            "HR_upp_CI" = `upper .95`)

# Fit a Cox model with weights to estimate the weighted HR
weighted_cox <- coxph(Surv(Time, Event==1) ~ ARM,
                      data = combined_data,
                      weights = wt)

HR_CI_cox_wtd <- summary(weighted_cox)$conf.int %>%
  as.data.frame() %>%
  transmute("HR" = `exp(coef)`,
            "HR_low_CI" = `lower .95`,
            "HR_upp_CI" = `upper .95`)

## Bootstrap the confidence interval of the weighted HR

HR_bootstraps <- boot(data = est_weights$analysis_data, # intervention data
                      statistic = bootstrap_HR, # bootstrap the HR (defined in the MAIC package)
                      R=1000, # number of bootstrap samples
                      comparator_data = comparator_input, # comparator pseudo data
                      matching = est_weights$matching_vars, # matching variables
                      model = Surv(Time, Event==1) ~ ARM # model to fit
  )

## Bootstrapping diagnostics
# Summarize bootstrap estimates in a histogram
# Vertical lines indicate the median and upper and lower CIs
hist(HR_bootstraps$t, main = "", xlab = "Boostrapped HR")
abline(v= quantile(HR_bootstraps$t, probs = c(0.025, 0.5, 0.975)), lty=2)

# Median of the bootstrap samples
HR_median <- median(HR_bootstraps$t)

# Bootstrap CI - Percentile CI
boot_ci_HR <- boot.ci(boot.out = HR_bootstraps, index=1, type="perc")

# Bootstrap CI - BCa CI
boot_ci_HR_BCA <- boot.ci(boot.out = HR_bootstraps, index=1, type="bca")

## Summary

# Produce a summary of HRs and CIs
HR_summ <-  rbind(HR_CI_cox, HR_CI_cox_wtd) %>% # Unweighted and weighted HRs and CIs from Cox models
  mutate(Method = c("HR (95% CI) from unadjusted Cox model",
                    "HR (95% CI) from weighted Cox model")) %>%

  # Median bootstrapped HR and 95% percentile CI
  rbind(data.frame("HR" = HR_median,
                   "HR_low_CI" = boot_ci_HR$percent[4],
                   "HR_upp_CI" = boot_ci_HR$percent[5],
                   "Method"="Bootstrap median HR (95% percentile CI)")) %>%

  # Median bootstrapped HR and 95% bias-corrected and accelerated bootstrap CI
  rbind(data.frame("HR" = HR_median,
                   "HR_low_CI" = boot_ci_HR_BCA$bca[4],
                   "HR_upp_CI" = boot_ci_HR_BCA$bca[5],
                   "Method"="Bootstrap median HR (95% BCa CI)")) %>%
  #apply rounding for numeric columns
  mutate_if(.predicate = is.numeric, sprintf, fmt = "%.3f") %>%
  #format for output
  transmute(Method, HR_95_CI = paste0(HR, " (", HR_low_CI, " to ", HR_upp_CI, ")"))

# Summarize the results in a table suitable for word/ powerpoint
HR_table <- HR_summ %>%
    regulartable() %>% #make it a flextable object
    set_header_labels(Method = "Method",  HR_95_CI = "Hazard ratio (95% CI)") %>%
    font(font = 'Arial', part = 'all') %>%
    fontsize(size = 14, part = 'all') %>%
    bold(part = 'header') %>%
    align(align = 'center', part = 'all') %>%
    align(j = 1, align = 'left', part = 'all') %>%
    border_outer(border = fp_border()) %>%
    border_inner_h(border = fp_border()) %>%
    border_inner_v(border = fp_border()) %>%
    autofit(add_w = 0.2, add_h = 2)


### Example for response data --------------------------------------------------

## Estimating the odds ratio (OR)

# Fit a logistic regression model without weights to estimate the unweighted OR
unweighted_OR <- glm(formula = response~ARM,
                     family = binomial(link="logit"),
                     data = combined_data)

# Log odds ratio
log_OR_CI_logit <- cbind(coef(unweighted_OR), confint.default(unweighted_OR, level = 0.95))[2,]

# Exponentiate to get Odds ratio
OR_CI_logit <- exp(log_OR_CI_logit)
#tidy up naming
names(OR_CI_logit) <- c("OR", "OR_low_CI", "OR_upp_CI")

# Fit a logistic regression model with weights to estimate the weighted OR
weighted_OR <- suppressWarnings(glm(formula = response~ARM,
                                    family = binomial(link="logit"),
                                    data = combined_data,
                                    weight = wt))

# Weighted log odds ratio
log_OR_CI_logit_wtd <- cbind(coef(weighted_OR), confint.default(weighted_OR, level = 0.95))[2,]

# Exponentiate to get weighted odds ratio
OR_CI_logit_wtd <- exp(log_OR_CI_logit_wtd)
#tidy up naming
names(OR_CI_logit_wtd) <- c("OR", "OR_low_CI", "OR_upp_CI")

## Bootstrap the confidence interval of the weighted OR
OR_bootstraps <- boot(data = est_weights$analysis_data, # intervention data
                      statistic = bootstrap_OR, # bootstrap the OR
                      R = 1000, # number of bootstrap samples
                      comparator_data = comparator_input, # comparator pseudo data
                      matching = est_weights$matching_vars, # matching variables
                      model = 'response ~ ARM' # model to fit
                      )

## Bootstrapping diagnostics
# Summarize bootstrap estimates in a histogram
# Vertical lines indicate the median and upper and lower CIs
hist(OR_bootstraps$t, main = "", xlab = "Boostrapped OR")
abline(v= quantile(OR_bootstraps$t, probs = c(0.025,0.5,0.975)), lty=2)

# Median of the bootstrap samples
OR_median <- median(OR_bootstraps$t)

# Bootstrap CI - Percentile CI
boot_ci_OR <- boot.ci(boot.out = OR_bootstraps, index=1, type="perc")

# Bootstrap CI - BCa CI
boot_ci_OR_BCA <- boot.ci(boot.out = OR_bootstraps, index=1, type="bca")

## Summary
# Produce a summary of ORs and CIs
OR_summ <- rbind(OR_CI_logit, OR_CI_logit_wtd) %>% # Unweighted and weighted ORs and CIs
  as.data.frame() %>%
  mutate(Method = c("OR (95% CI) from unadjusted logistic regression model",
                    "OR (95% CI) from weighted logistic regression model")) %>%

  # Median bootstrapped HR and 95% percentile CI
  rbind(data.frame("OR" = OR_median,
                   "OR_low_CI" = boot_ci_OR$percent[4],
                   "OR_upp_CI" = boot_ci_OR$percent[5],
                   "Method"="Bootstrap median HR (95% percentile CI)")) %>%

  # Median bootstrapped HR and 95% bias-corrected and accelerated bootstrap CI
  rbind(data.frame("OR" = OR_median,
                   "OR_low_CI" = boot_ci_OR_BCA$bca[4],
                   "OR_upp_CI" = boot_ci_OR_BCA$bca[5],
                   "Method"="Bootstrap median HR (95% BCa CI)")) %>%
  #apply rounding for numeric columns
  mutate_if(.predicate = is.numeric, sprintf, fmt = "%.3f") %>%
  #format for output
  transmute(Method, OR_95_CI = paste0(OR, " (", OR_low_CI, " to ", OR_upp_CI, ")"))

# turns the results to a table suitable for word/ powerpoint
OR_table <- OR_summ %>%
            regulartable() %>% #make it a flextable object
            set_header_labels(Method = "Method",  OR_95_CI = "Odds ratio (95% CI)")  %>%
            font(font = 'Arial', part = 'all') %>%
            fontsize(size = 14, part = 'all') %>%
            bold(part = 'header') %>%
            align(align = 'center', part = 'all') %>%
            align(j = 1, align = 'left', part = 'all') %>%
            border_outer(border = fp_border()) %>%
            border_inner_h(border = fp_border()) %>%
            border_inner_v(border = fp_border()) %>%
            autofit(add_w = 0.2)

Roche/MAIC documentation built on Nov. 9, 2024, 5:21 p.m.