This page contains information of the MI_boot method that is implemented in the psfmi package and that combines Multiple Imputation with bootstrapping for the validation of logistic regression / prediction models. Internal validation is always done of the last model that is selected by the function psfmi_lr. An explanation and examples of how to use the methods can be found below.
With this method bootstrap samples are drawn from each multiply imputed dataset. The same cases are drawn in each imputed dataset. The pooled model is analyzed in the each bootstrap training data and subsequently tested in original multiply imputed data. The method can be performed in combination with backward or forward selection.
How these steps work is visualized in the Figure below.
Schematic overview of the boot_MI method
internal validation is done of the last model that is selected by the function psfmi_lr. In the example below, psfmi_lr is used with p.crit set at 1. This setting is also used in the psfmi_validate function. This means that first the full model is pooled and subsequently interval validation is done of the full model.
library(psfmi)
pool_lr <- psfmi_lr(data=lbpmilr, formula = Chronic ~ Pain + JobDemands + rcs(Tampascale, 3) +
factor(Satisfaction) + Smoking, p.crit = 1, direction="FW",
nimp=5, impvar="Impnr", method="D1")
set.seed(200)
res <- psfmi_validate(pool_lr, val_method = "MI_boot", nboot = 5, p.crit=1)##
## Boot 1##
## Boot 2##
## Boot 3##
## Boot 4##
## Boot 5##
## p.crit = 1, validation is done without variable selectionres## $stats_val
## Orig Apparent Test Optimism Corrected
## AUC 0.8871000 0.9131800 0.8786800 0.0345000 0.8526000
## R2 0.5605521 0.6354404 0.5332539 0.1021865 0.4583656
## Brier Scaled 0.4514569 0.5382256 0.4128859 0.1253397 0.3261172
## Slope 1.0000000 1.0000000 0.7449554 0.2550446 0.7449554
##
## $intercept_test
## intercept
## -0.1683646
##
## $res_boot
## ROC_app ROC_test R2_app R2_test Brier_sc_app Brier_sc_test
## Boot 1 0.8708 0.8767 0.5261128 0.5275393 0.4123378 0.4042778
## Boot 2 0.9099 0.8813 0.6249260 0.5439424 0.5238909 0.4342868
## Boot 3 0.9447 0.8793 0.7183270 0.5353093 0.6457725 0.4158834
## Boot 4 0.9225 0.8714 0.6620081 0.5166176 0.5715999 0.4284101
## Boot 5 0.9180 0.8847 0.6458284 0.5428610 0.5375269 0.3815714
## intercept Slope
## Boot 1 -0.153194405 0.9741632
## Boot 2 -0.008403925 0.7697086
## Boot 3 -0.121148496 0.5440115
## Boot 4 -0.074413523 0.6987898
## Boot 5 -0.484662668 0.7381040
##
## $predictors_selected
## Pain JobDemands Smoking factor(Satisfaction) rcs(Tampascale,3)
## Boot 1 1 1 1 1 1
## Boot 2 1 1 1 1 1
## Boot 3 1 1 1 1 1
## Boot 4 1 1 1 1 1
## Boot 5 1 1 1 1 1
##
## $model_orig
## Chronic ~ Pain + JobDemands + Smoking + factor(Satisfaction) +
## rcs(Tampascale, 3)
## <environment: 0x000000002cce1810>Back to Examples
Internal validation is done of the last model that is selected by the function psfmi_lr. In the example below, psfmi_lr is used with p.crit set at 1, and pooling is than done without variable selection, i.e. the full model is pooled. When subsequently interval validation is done with the psfmi_validate function including BW, BW is applied in each bootstrap sample from the full model.
library(psfmi)
pool_lr <- psfmi_lr(data=lbpmilr, formula = Chronic ~ Pain + JobDemands + rcs(Tampascale, 3) +
factor(Satisfaction) + Smoking, p.crit = 1, direction="FW",
nimp=5, impvar="Impnr", method="D1")
set.seed(200)
res <- psfmi_validate(pool_lr, val_method = "MI_boot", nboot = 5, p.crit=0.05, direction = "BW")##
## Boot 1## Removed at Step 1 is - Smoking## Removed at Step 2 is - JobDemands##
## Selection correctly terminated,
## No more variables removed from the model##
## Boot 2## Removed at Step 1 is - JobDemands## Removed at Step 2 is - Smoking## Removed at Step 3 is - rcs(Tampascale,3)##
## Selection correctly terminated,
## No more variables removed from the model##
## Boot 3## Removed at Step 1 is - Smoking## Removed at Step 2 is - rcs(Tampascale,3)## Removed at Step 3 is - JobDemands##
## Selection correctly terminated,
## No more variables removed from the model##
## Boot 4## Removed at Step 1 is - rcs(Tampascale,3)## Removed at Step 2 is - Smoking## Removed at Step 3 is - JobDemands##
## Selection correctly terminated,
## No more variables removed from the model##
## Boot 5## Removed at Step 1 is - Smoking## Removed at Step 2 is - JobDemands## Removed at Step 3 is - rcs(Tampascale,3)##
## Selection correctly terminated,
## No more variables removed from the model## Removed at Step 1 is - Smoking## Removed at Step 2 is - JobDemands## Removed at Step 3 is - rcs(Tampascale,3)##
## Selection correctly terminated,
## No more variables removed from the modelres## $stats_val
## Orig Apparent Test Optimism Corrected
## AUC 0.8730000 0.9001200 0.8740600 0.02606000 0.8469400
## R2 0.5244014 0.6012708 0.5231900 0.07808081 0.4463206
## Brier Scaled 0.4384749 0.5105213 0.4331223 0.07739902 0.3610759
## Slope 1.0000000 1.0000000 0.8603053 0.13969467 0.8603053
##
## $intercept_test
## intercept
## -0.06307424
##
## $res_boot
## ROC_app ROC_test R2_app R2_test Brier_sc_app Brier_sc_test
## Boot 1 0.8680 0.8783 0.5132543 0.5362514 0.3997598 0.4122129
## Boot 2 0.8941 0.8730 0.5801429 0.5236584 0.4867631 0.4385677
## Boot 3 0.9300 0.8730 0.6831782 0.5173532 0.5958985 0.4446954
## Boot 4 0.9156 0.8730 0.6410638 0.5169447 0.5565305 0.4441806
## Boot 5 0.8929 0.8730 0.5887150 0.5217423 0.5136547 0.4259549
## intercept Slope
## Boot 1 -0.181845909 1.0237503
## Boot 2 -0.066031545 0.8350387
## Boot 3 0.057587096 0.7083871
## Boot 4 -0.009979645 0.7793790
## Boot 5 -0.115101220 0.9549715
##
## $predictors_selected
## Pain JobDemands Smoking factor(Satisfaction) rcs(Tampascale,3)
## Boot 1 1 0 0 1 1
## Boot 2 1 0 0 1 0
## Boot 3 1 0 0 1 0
## Boot 4 1 0 0 1 0
## Boot 5 1 0 0 1 0
##
## $model_orig
## Chronic ~ Pain + factor(Satisfaction)
## <environment: 0x000000002aebf020>Back to Examples