Bootstrap design document; method 1 for non parametric bootstrap added

design/Bootstrap_design.Rmd

@@ -1 +1,203 @@
+---
+title: "Bootstrap design"
+output:
+ html_document:
+ code_folding: hide
+ theme: spacelab 
+ toc: true
+ number_sections: true
+---
 
+
+<style type="text/css">
+
+body{ /* Normal */
+ font-size: 14px;
+ }
+td { /* Table */
+ font-size: 14px;
+}
+h1.title {
+ font-size: 28px;
+ color: DarkRed;
+}
+h1 { /* Header 1 */
+ font-size: 22px;
+ color: DarkBlue;
+}
+h2 { /* Header 2 */
+ font-size: 18px;
+ color: DarkBlue;
+}
+h3 { /* Header 3 */
+ font-size: 18px;
+ color: DarkBlue;
+}
+
+h4 { /* Header 4 */
+ font-size: 18px;
+ color: DarkBlue;
+}
+
+code.r{ /* Code block */
+ font-size: 12px;
+}
+pre { /* Code block - determines code spacing between lines */
+ font-size: 14px;
+}
+</style>
+
+
+
+# Method 1 
+
+## Steps
+- Create bootstrap_HR() function to get the bootstrap weighted hazard ratios.
+- The bootstrap weighted hazard ratios will then be used as an input of the standard boot() function in order to obtain the
+bootstrap confidence interval of the weighted HR. 
+- The boot() function will be included in the maic_tte_unanchor() function of the maic_tte_unanchored.R file so that we can get 
+the results of all the different approaches (i.e., sandwich estimator, non-parametric bootstrap, posson approximation) for the unanchored cases
+of time to event endpoints. 
+- Add additional input parameter in the maic_tte_unanchor() function to meet the requirements for the boot() function
+- Report bootstrap results 
+
+
+
+## Bootstrapping for MAIC weighted hazard ratios 
+
+The bootstrap_HR() function will be created to get the bootstrap weighted hazard ratios.
+This function will include the following input parameters:
+
+- *intervention_data:* A data frame containing individual patient data from the internal IPD study including
+columns (treatment, time, status, centered baseline characteristics)
+- *centered_colnames:* 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 the boot() function.
+- *model:* A model formula in the form 'Surv(time, status == 1) ~ treatment '. 
+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
+including columns (time, event, weight=1, scaled_weight=1).
+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.
+- *trt_ext:* A character giving the name of the comparator treatment to be used as reference
+
+
+Note: The bootstrap_HR() 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() function and returning a 
+weighted hazard ratio (HR) from a Cox proportional hazards model. This is used as the 'statistic' argument in
+the boot function.
+
+From the bootstrap_HR() function we will export the HR as a numeric value. 
+
+
+### Example code 
+
+```{r}`r ''`
+bootstrap_HR <- function(intervention_data, centered_colnames, i, model, comparator_data, min_weight = 0.0001, trt_ext) {
+ # create a visible binding for R CMD check
+ wt <- NULL
+
+ # Samples the data
+ bootstrap_data <- intervention_data[i, ]
+
+ # Estimates weights
+ perform_wt <- estimate_weights(data = bootstrap_data, centered_colnames = centered_colnames)
+
+
+ # Give comparator data weights of 1
+ comparator_data_wts <- comparator_data %>% dplyr::mutate(weights = 1, scaled_weights = 1)
+
+ # Add the comparator data
+ combined_data <- dplyr::bind_rows(perform_wt$data, comparator_data_wts)
+ combined_data$treatment <- stats::relevel(as.factor(combined_data$treatment), ref = trt_ext)
+
+ # set weights that are below min_weight to min_weight to avoid issues with 0 values
+ combined_data$wt <- ifelse(combined_data$weights < min_weight, min_weight, combined_data$weights)
+
+ # survival data stat
+ cox_model <- survival::coxph(model, data = combined_data, weights = wt)
+ HR <- exp(cox_model$coefficients)
+} 
+
+```
+
+## Bootstrap the confidence interval of the weighted HR 
+ 
+The boot() function will include the following in the same format as defined in the bootstrap_HR() function: 
+
+- Intervention data
+- The statistic to be bootsrapped; i.e. bootstap_HR
+- Number of bootstrap sampes
+- Comparator pseudo data
+- Matching variables
+- Model to fit 
+
+
+ 
+### Example code
+
+```{r}`r ''`
+HR_bootstraps <- boot(
+ data = dat_centered, # intervention data
+ statistic = bootstrap_HR, # bootstrap the HR 
+ R = 1000, # number of bootstrap samples
+ comparator_data = dat_ext, # comparator pseudo data
+ centered_colnames = grep("_CENTERED$", names(dat_centered)), # matching variables
+ model = Surv(time, status == 1) ~ treatment # model to fit
+ )
+
+```
+
+
+## Additional input parameter in the maic_tte_unanchor() function
+
+In the maic_tte_unanchor() function of the maic_tte_unanchored.R file we need to add an additional input parameter as this function will
+use the boot() function. Specifically, the dat_centered which is the intervention data as defined in the bootstrap_HR() function will be added. 
+
+
+## Reporting bootstrap results 
+
+Report the following: 
+
+- Summarize bootstrap estimates in a histogram
+- Median of the bootstrap samples
+- Percentile CIs (This method takes the 2.5th and 97.5th percentiles)
+- Bias-corrected and accelerated (BCa) CI (This method attempts to correct for any bias and skewness in the distribution of bootstrap estimates)
+
+Add section 'Report 4: Bootstrapping' in the maic_tte_unanchor() function of the maic_tte_unanchored.R file
+
+
+### Example code
+
+```{r}`r ''`
+
+ # ==> Report 4: Bootstrapping
+
+ ## 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")
+
+ res[["boot_hist"]] <- grDevices::recordPlot()
+ res[["HR_median"]] <- HR_median
+ res[["boot_ci_HR"]] <- boot_ci_HR
+ res[["boot_ci_HR_BCA"]] <- boot_ci_HR_BCA`
+
+```
+
+
+# Method 2 
+
+Mike to complete.