The package provides functions to apply pooling, backward and forward selection of linear, logistic and Cox regression models across multiply imputed data sets using Rubin’s Rules (RR). The D1, D2, D3, D4 and the median p-values method can be used to pool the significance of categorical variables (multiparameter test). The model can contain continuous, dichotomous, categorical and restricted cubic spline predictors and interaction terms between all these type of variables. Variables can also be forced in the model during selection.
Validation of the prediction models can be performed with cross-validation or bootstrapping across multiply imputed data sets and pooled model performance measures as AUC value, Reclassification, R-square, Hosmer and Lemeshow test, scaled Brier score and calibration plots are generated. Also a function to externally validate logistic prediction models across multiple imputed data sets is available and a function to compare models in multiply imputed data.
Installation
You can install the released version of psfmi with:
install.packages("psfmi")And the development version from GitHub with:
# install.packages("devtools")
devtools::install_github("mwheymans/psfmi")Examples
This example shows you how to pool a logistic regression model across 5 multiply imputed datasets and that includes two restricted cubic spline variables and a categorical, continuous and dichotomous variable. The pooling method that is used is method D1.
library(psfmi)
pool_lr <- psfmi_lr(data=lbpmilr, formula = Chronic ~ rcs(Pain, 3) +
JobDemands + rcs(Tampascale, 3) + factor(Satisfaction) +
Smoking, nimp=5, impvar="Impnr", method="D1")
pool_lr$RR_model
#> $`Step 1 - no variables removed -`
#> term estimate std.error statistic df
#> 1 (Intercept) -21.374498123 7.96491209 -2.6835824 65.71094
#> 2 JobDemands -0.007500147 0.05525835 -0.1357288 38.94021
#> 3 Smoking 0.072207184 0.51097303 0.1413131 47.98415
#> 4 factor(Satisfaction)2 -0.506544055 0.56499941 -0.8965391 139.35335
#> 5 factor(Satisfaction)3 -2.580503376 0.77963853 -3.3098715 100.66273
#> 6 rcs(Pain, 3)Pain -0.090675006 0.50510774 -0.1795162 26.92182
#> 7 rcs(Pain, 3)Pain' 1.183787048 0.55697046 2.1254036 94.79276
#> 8 rcs(Tampascale, 3)Tampascale 0.583697990 0.22707747 2.5704796 77.83368
#> 9 rcs(Tampascale, 3)Tampascale' -0.602128298 0.29484065 -2.0422160 31.45559
#> p.value OR lower.EXP upper.EXP
#> 1 0.009206677 5.214029e-10 6.460344e-17 0.00420815
#> 2 0.892734942 9.925279e-01 8.875626e-01 1.10990663
#> 3 0.888214212 1.074878e+00 3.847422e-01 3.00295282
#> 4 0.371511077 6.025744e-01 1.971829e-01 1.84141687
#> 5 0.001296125 7.573587e-02 1.612863e-02 0.35563604
#> 6 0.858876729 9.133145e-01 3.239353e-01 2.57503035
#> 7 0.036152843 3.266722e+00 1.081155e+00 9.87043962
#> 8 0.012063538 1.792655e+00 1.140659e+00 2.81733025
#> 9 0.049589266 5.476448e-01 3.002599e-01 0.99885104
pool_lr$multiparm
#> $`Step 1 - no variables removed -`
#> p-values D1 F-statistic
#> JobDemands 0.892487763 0.01842230
#> Smoking 0.887968553 0.01996939
#> factor(Satisfaction) 0.002611518 6.04422205
#> rcs(Pain,3) 0.014630986 4.84409246
#> rcs(Tampascale,3) 0.130741167 2.24870192This example shows you how to apply forward selection of the above model using a p-value of 0.05.
library(psfmi)
pool_lr <- psfmi_lr(data=lbpmilr, formula = Chronic ~ rcs(Pain, 3) +
JobDemands + rcs(Tampascale, 3) + factor(Satisfaction) +
Smoking, p.crit = 0.05, direction="FW",
nimp=5, impvar="Impnr", method="D1")
#> Entered at Step 1 is - rcs(Pain,3)
#> Entered at Step 2 is - factor(Satisfaction)
#>
#> Selection correctly terminated,
#> No new variables entered the model
pool_lr$RR_model_final
#> $`Final model`
#> term estimate std.error statistic df p.value
#> 1 (Intercept) -3.6027668 1.5427414 -2.3353018 60.25659 0.022875170
#> 2 factor(Satisfaction)2 -0.4725289 0.5164342 -0.9149838 145.03888 0.361718841
#> 3 factor(Satisfaction)3 -2.3328994 0.7317131 -3.1882707 122.95905 0.001815476
#> 4 rcs(Pain, 3)Pain 0.6514983 0.4028728 1.6171315 51.09308 0.112008088
#> 5 rcs(Pain, 3)Pain' 0.4703811 0.4596490 1.0233483 75.29317 0.309419924
#> OR lower.EXP upper.EXP
#> 1 0.02724823 0.001245225 0.5962503
#> 2 0.62342367 0.224644070 1.7301016
#> 3 0.09701406 0.022793375 0.4129150
#> 4 1.91841309 0.854476033 4.3070942
#> 5 1.60060402 0.640677978 3.9987846
pool_lr$multiparm
#> $`Step 0 - selected - rcs(Pain,3)`
#> p-value D1
#> JobDemands 7.777737e-01
#> Smoking 9.371529e-01
#> factor(Satisfaction) 9.271071e-01
#> rcs(Pain,3) 3.282999e-07
#> rcs(Tampascale,3) 2.780012e-06
#>
#> $`Step 1 - selected - factor(Satisfaction)`
#> p-value D1
#> JobDemands 0.952900908
#> Smoking 0.769394518
#> factor(Satisfaction) 0.004738608
#> rcs(Tampascale,3) 0.125280292More examples for logistic, linear and Cox regression models as well as internal and external validation of prediction models can be found on the package website or in the online book Applied Missing Data Analysis.