# Stability analysis after Multiple Imputation

#### Martijn W Heymans

#### 2021-09-23

# Stability analysis

The psfmi package contains a function to conduct stability analyses of logistic, Cox and Mixed models. With this function the stability of models selected and the bootstrap inclusion frequency can be evaluated. For logistic and Cox regression models bootstrapping is than used and for Multilevel models cluster bootstrapping.

# Examples

- Stability analysis of Logistic regression model
- Stability analysis of Cox regression model

## Stability analysis of Logistic regression model

      library(psfmi)
      psfmi_res <- psfmi_lr(data=lbpmilr, nimp=5, impvar="Impnr", Outcome="Chronic",
                          predictors=c("Gender", "Smoking", "JobControl", "Age", "Duration",
                             "JobDemands", "SocialSupport"), p.crit =0.157, method="MPR",
                          cat.predictors = "Satisfaction", int.predictors = c("Gender:JobControl"),
                          direction = "BW")
    #> Removed at Step 1 is - Smoking
    #> Removed at Step 2 is - Duration
    #> Removed at Step 3 is - JobDemands
    #> Removed at Step 4 is - factor(Satisfaction)
    #> Removed at Step 5 is - Gender*JobControl
    #> Removed at Step 6 is - JobControl
    #> Removed at Step 7 is - SocialSupport
    #> Removed at Step 8 is - Age
    #>
    #> Selection correctly terminated,
    #> No more variables removed from the model
       stab_res <- psfmi_stab(psfmi_res, direction="FW", start_model = TRUE,
          boot_method = "single", nboot=20, p.crit=0.05)
    #>
    #> Boot 1
    #> Entered at Step 1 is - Age
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 2
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 3
    #> Entered at Step 1 is - Gender
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 4
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 5
    #> Entered at Step 1 is - Age
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 6
    #> Entered at Step 1 is - Age
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 7
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 8
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 9
    #> Entered at Step 1 is - Gender
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 10
    #> Entered at Step 1 is - Gender
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 11
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 12
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 13
    #> Entered at Step 1 is - Age
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 14
    #> Entered at Step 1 is - Gender
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 15
    #> Entered at Step 1 is - Age
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 16
    #> Entered at Step 1 is - Duration
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 17
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 18
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 19
    #> Entered at Step 1 is - Age
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 20
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
       stab_res$bif
    #>         Gender Smoking JobControl Age Duration JobDemands SocialSupport
    #> boot 1       0       0          0   1        0          0             0
    #> boot 2       0       0          0   0        0          0             0
    #> boot 3       1       0          0   0        0          0             0
    #> boot 4       0       0          0   0        0          0             0
    #> boot 5       0       0          0   1        0          0             0
    #> boot 6       0       0          0   1        0          0             0
    #> boot 7       0       0          0   0        0          0             0
    #> boot 8       0       0          0   0        0          0             0
    #> boot 9       1       0          0   0        0          0             0
    #> boot 10      1       0          0   0        0          0             0
    #> boot 11      0       0          0   0        0          0             0
    #> boot 12      0       0          0   0        0          0             0
    #> boot 13      0       0          0   1        0          0             0
    #> boot 14      1       0          0   0        0          0             0
    #> boot 15      0       0          0   1        0          0             0
    #> boot 16      0       0          0   0        1          0             0
    #> boot 17      0       0          0   0        0          0             0
    #> boot 18      0       0          0   0        0          0             0
    #> boot 19      0       0          0   1        0          0             0
    #> boot 20      0       0          0   0        0          0             0
    #>         factor(Satisfaction) Gender*JobControl
    #> boot 1                     0                 0
    #> boot 2                     0                 0
    #> boot 3                     0                 0
    #> boot 4                     0                 0
    #> boot 5                     0                 0
    #> boot 6                     0                 0
    #> boot 7                     0                 0
    #> boot 8                     0                 0
    #> boot 9                     0                 0
    #> boot 10                    0                 0
    #> boot 11                    0                 0
    #> boot 12                    0                 0
    #> boot 13                    0                 0
    #> boot 14                    0                 0
    #> boot 15                    0                 0
    #> boot 16                    0                 0
    #> boot 17                    0                 0
    #> boot 18                    0                 0
    #> boot 19                    0                 0
    #> boot 20                    0                 0
      stab_res$bif_perc
    #>               Gender              Smoking           JobControl
    #>                   20                    0                    0
    #>                  Age             Duration           JobDemands
    #>                   30                    5                    0
    #>        SocialSupport factor(Satisfaction)    Gender*JobControl
    #>                    0                    0                    0
      stab_res$model_stab
    #>   Gender Smoking JobControl Age Duration JobDemands SocialSupport
    #> 1      0       0          0   0        0          0             0
    #> 2      0       0          0   1        0          0             0
    #> 3      1       0          0   0        0          0             0
    #> 4      0       0          0   0        1          0             0
    #>   factor(Satisfaction) Gender*JobControl freq bif_pat_perc
    #> 1                    0                 0    9           45
    #> 2                    0                 0    6           30
    #> 3                    0                 0    4           20
    #> 4                    0                 0    1            5

Back to Examples

### Stability analysis of Cox regression model

      library(psfmi)
      pool_lr <- psfmi_coxr(formula = Surv(Time, Status) ~ Pain + factor(Satisfaction) + rcs(Tampascale,3) +
                            Radiation + Radiation*factor(Satisfaction) + Age + Duration + Previous +
                            Radiation*rcs(Tampascale, 3), data=lbpmicox, p.crit = 0.157, direction="FW",
                            nimp=5, impvar="Impnr", keep.predictors = NULL, method="D1")
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #> Entered at Step 1 is - Pain
    #> Entered at Step 2 is - Duration
    #> Entered at Step 3 is - rcs(Tampascale,3)
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
      pool_lr$RR_Model
    #> NULL
      pool_lr$multiparm
    #> $`Step 0 - selected - Pain`
    #>                                 p-value D1
    #> Pain                           0.002972173
    #> Radiation                      0.181042842
    #> Age                            0.351345242
    #> Duration                       0.044028841
    #> Previous                       0.714681296
    #> factor(Satisfaction)           0.708284253
    #> rcs(Tampascale,3)              0.032223680
    #> factor(Satisfaction)*Radiation 0.712860014
    #> rcs(Tampascale,3)*Radiation    0.452891382
    #>
    #> $`Step 1 - selected - Duration`
    #>                                p-value D1
    #> Radiation                      0.31938607
    #> Age                            0.22333023
    #> Duration                       0.04853205
    #> Previous                       0.54425893
    #> factor(Satisfaction)           0.76439993
    #> rcs(Tampascale,3)              0.07594972
    #> factor(Satisfaction)*Radiation 0.66328781
    #> rcs(Tampascale,3)*Radiation    0.44642240
    #>
    #> $`Step 2 - selected - rcs(Tampascale,3)`
    #>                                p-value D1
    #> Radiation                      0.32679294
    #> Age                            0.40528789
    #> Previous                       0.44216497
    #> factor(Satisfaction)           0.81050733
    #> rcs(Tampascale,3)              0.06066281
    #> factor(Satisfaction)*Radiation 0.70440131
    #> rcs(Tampascale,3)*Radiation    0.35955920
      stab_res <- psfmi_stab(pool_lr, direction="FW", start_model = TRUE,
          boot_method = "single", nboot=20, p.crit=0.05)
    #>
    #> Boot 1
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 2
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #> Entered at Step 1 is - Pain
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 3
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #> Entered at Step 1 is - Pain
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 4
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #> Entered at Step 1 is - Pain
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 5
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #> Entered at Step 1 is - Pain
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 6
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 7
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #> Entered at Step 1 is - Pain
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 8
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 9
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 10
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #> Entered at Step 1 is - Pain
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 11
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #> Entered at Step 1 is - Pain
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 12
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 13
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 14
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #> Entered at Step 1 is - Duration
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 15
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #> Entered at Step 1 is - Pain
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 16
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 17
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 18
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 19
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
    #>
    #> Boot 20
    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.

    #> Warning in mitml::testModels(fit1, fit0, method = method): The 'model' and
    #> 'null.model' arguments appear to include objects of different classes. Results
    #> may not be trustworthy.
    #> Entered at Step 1 is - Pain
    #>
    #> Selection correctly terminated,
    #> No new variables entered the model
      stab_res$bif
    #>         Pain Radiation Age Duration Previous factor(Satisfaction)
    #> boot 1     0         0   0        0        0                    0
    #> boot 2     1         0   0        0        0                    0
    #> boot 3     1         0   0        0        0                    0
    #> boot 4     1         0   0        0        0                    0
    #> boot 5     1         0   0        0        0                    0
    #> boot 6     0         0   0        0        0                    0
    #> boot 7     1         0   0        0        0                    0
    #> boot 8     0         0   0        0        0                    0
    #> boot 9     0         0   0        0        0                    0
    #> boot 10    1         0   0        0        0                    0
    #> boot 11    1         0   0        0        0                    0
    #> boot 12    0         0   0        0        0                    0
    #> boot 13    0         0   0        0        0                    0
    #> boot 14    0         0   0        1        0                    0
    #> boot 15    1         0   0        0        0                    0
    #> boot 16    0         0   0        0        0                    0
    #> boot 17    0         0   0        0        0                    0
    #> boot 18    0         0   0        0        0                    0
    #> boot 19    0         0   0        0        0                    0
    #> boot 20    1         0   0        0        0                    0
    #>         rcs(Tampascale,3) factor(Satisfaction)*Radiation
    #> boot 1                  0                              0
    #> boot 2                  0                              0
    #> boot 3                  0                              0
    #> boot 4                  0                              0
    #> boot 5                  0                              0
    #> boot 6                  0                              0
    #> boot 7                  0                              0
    #> boot 8                  0                              0
    #> boot 9                  0                              0
    #> boot 10                 0                              0
    #> boot 11                 0                              0
    #> boot 12                 0                              0
    #> boot 13                 0                              0
    #> boot 14                 0                              0
    #> boot 15                 0                              0
    #> boot 16                 0                              0
    #> boot 17                 0                              0
    #> boot 18                 0                              0
    #> boot 19                 0                              0
    #> boot 20                 0                              0
    #>         rcs(Tampascale,3)*Radiation
    #> boot 1                            0
    #> boot 2                            0
    #> boot 3                            0
    #> boot 4                            0
    #> boot 5                            0
    #> boot 6                            0
    #> boot 7                            0
    #> boot 8                            0
    #> boot 9                            0
    #> boot 10                           0
    #> boot 11                           0
    #> boot 12                           0
    #> boot 13                           0
    #> boot 14                           0
    #> boot 15                           0
    #> boot 16                           0
    #> boot 17                           0
    #> boot 18                           0
    #> boot 19                           0
    #> boot 20                           0
      stab_res$bif_perc
    #>                           Pain                      Radiation
    #>                             45                              0
    #>                            Age                       Duration
    #>                              0                              5
    #>                       Previous           factor(Satisfaction)
    #>                              0                              0
    #>              rcs(Tampascale,3) factor(Satisfaction)*Radiation
    #>                              0                              0
    #>    rcs(Tampascale,3)*Radiation
    #>                              0
      stab_res$model_stab
    #>   Pain Radiation Age Duration Previous factor(Satisfaction) rcs(Tampascale,3)
    #> 1    0         0   0        0        0                    0                 0
    #> 2    1         0   0        0        0                    0                 0
    #> 3    0         0   0        1        0                    0                 0
    #>   factor(Satisfaction)*Radiation rcs(Tampascale,3)*Radiation freq bif_pat_perc
    #> 1                              0                           0   10           50
    #> 2                              0                           0    9           45
    #> 3                              0                           0    1            5

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