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.
Figure 2.1: 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_perform
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_perform(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 selection
res
## $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
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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_perform
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_perform(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
res
## $stats_val
## Orig Apparent Test Optimism Corrected
## AUC 0.8871000 0.9001200 0.8740600 0.02606000 0.8610400
## R2 0.5605521 0.6012708 0.5231900 0.07808081 0.4824713
## Brier Scaled 0.4514569 0.5105213 0.4331223 0.07739902 0.3740579
## 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
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_perform
function including FW, FW 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_perform(pool_lr, val_method = "MI_boot", nboot = 5, p.crit=0.05, direction = "FW")
##
## Boot 1
## Entered at Step 1 is - Pain
## Entered at Step 2 is - factor(Satisfaction)
## Entered at Step 3 is - rcs(Tampascale,3)
##
## Selection correctly terminated,
## No new variables entered the model
##
## Boot 2
## Entered at Step 1 is - Pain
## Entered at Step 2 is - factor(Satisfaction)
##
## Selection correctly terminated,
## No new variables entered the model
##
## Boot 3
## Entered at Step 1 is - rcs(Tampascale,3)
## Entered at Step 2 is - Pain
## Entered at Step 3 is - factor(Satisfaction)
##
## Selection correctly terminated,
## No new variables entered the model
##
## Boot 4
## Entered at Step 1 is - Pain
## Entered at Step 2 is - factor(Satisfaction)
##
## Selection correctly terminated,
## No new variables entered the model
##
## Boot 5
## Entered at Step 1 is - Pain
## Entered at Step 2 is - factor(Satisfaction)
##
## Selection correctly terminated,
## No new variables entered the model
res
## $stats_val
## Orig Apparent Test Optimism Corrected
## AUC 0.8871000 0.9024200 0.6622000 0.240220 0.6468800
## R2 0.5605521 0.6061594 0.2127155 0.393444 0.1671082
## Brier Scaled 0.4514569 0.5153547 -0.7659031 1.281258 -0.8298009
## Slope 1.0000000 1.0000000 -0.3117138 1.311714 -0.3117138
##
## $intercept_test
## intercept
## -4.969914
##
## $res_boot
## ROC_app ROC_test R2_app R2_test Brier_sc_app Brier_sc_test
## Boot 1 0.8680 0.8170 0.5132543 0.34548078 0.3997598 -0.7666667
## Boot 2 0.8941 0.7290 0.5801429 0.25446803 0.4867631 -0.7665664
## Boot 3 0.9415 0.5627 0.7076212 0.02626783 0.6200654 -0.7666667
## Boot 4 0.9156 0.7940 0.6410638 0.39033595 0.5565305 -0.7666581
## Boot 5 0.8929 0.4083 0.5887150 0.04702472 0.5136547 -0.7629576
## intercept Slope
## Boot 1 -5.389639 -0.14785309
## Boot 2 -5.887225 -0.52051344
## Boot 3 -3.596809 -0.07416648
## Boot 4 -7.748762 -0.55147565
## Boot 5 -2.227136 -0.26456015
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