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These multiple imputation results relate to data I have previously described and shown here - Skewed Distributions for Logistic Regression

Three variables I am using have missing data. Their names, descriptions and % missing are shown below.

inctoCran - Time from head injury to craniotomy in minutes = 0-2880 (After 2880 minutes is defined as a separate diagnosis) - 58% missing
GCS - Glasgow Coma Scale = 3-15 - 37% missing
rcteyemi - Pupil reactivity (1 = neither, 2 = one, 3 = both) - 56% missing

I have been using mutliple imputation to model the missing data above following advice in a previous post here - Describing Results from Logistic Regression with Restricted Cubic Splines Using rms in R

Given this is a longitudinal analysis, a key variable of importance is the year of the treatment so we can investigate how our patient management has improved. The variable in question, Yeardecimal is highly significant in univariate analysis:

> rcs.ASDH<-lrm(formula = Survive ~ Yeardecimalc, data = ASDH_Paper1.1)
> 
> rcs.ASDH

Logistic Regression Model

lrm(formula = Survive ~ Yeardecimalc, data = ASDH_Paper1.1)

                      Model Likelihood     Discrimination    Rank Discrim.    
                         Ratio Test            Indexes          Indexes       
Obs          5998    LR chi2      91.47    R2       0.023    C       0.572    
 0           1281    d.f.             1    g        0.309    Dxy     0.143    
 1           4717    Pr(> chi2) <0.0001    gr       1.362    gamma   0.146    
max |deriv| 3e-12                          gp       0.054    tau-a   0.048    
                                           Brier    0.165                     

             Coef   S.E.   Wald Z Pr(>|Z|)
Intercept    0.8696 0.0530 16.42  <0.0001 
Yeardecimalc 0.0551 0.0057  9.70  <0.0001 

To deal with missingness, I used aregImpute and fit.mult.impute to conduct multiple imputation prior to multivariate logisic regression. When including Yeardecimal, the results were as follows:

> a <- aregImpute(~ I(Outcome30) + Age + GCS + I(Other) + ISS + inctoCran + I(rcteyemi) + I(neuroFirst) + I(neuroYN) + Mechanism + LOS + Yeardecimalc, nk=4, data = ASDH_Paper1.1, n.impute=10)
Iteration 13 
> 
> a

Multiple Imputation using Bootstrap and PMM

aregImpute(formula = ~I(Outcome30) + Age + GCS + I(Other) + ISS + 
    inctoCran + I(rcteyemi) + I(neuroFirst) + I(neuroYN) + Mechanism + 
    LOS + Yeardecimalc, data = ASDH_Paper1.1, n.impute = 10, 
    nk = 4)

n: 5998     p: 12   Imputations: 10     nk: 4 

Number of NAs:
   Outcome30          Age          GCS        Other          ISS    inctoCran     rcteyemi   neuroFirst      neuroYN 
           0            0         2242            0            0         3500         3376            0            0 
   Mechanism          LOS Yeardecimalc 
           0            0            0 

             type d.f.
Outcome30       c    1
Age             s    3
GCS             s    3
Other           c    1
ISS             s    3
inctoCran       s    3
rcteyemi        l    1
neuroFirst      l    1
neuroYN         l    1
Mechanism       c    4
LOS             s    3
Yeardecimalc    s    3

Transformation of Target Variables Forced to be Linear

R-squares for Predicting Non-Missing Values for Each Variable
Using Last Imputations of Predictors
      GCS inctoCran  rcteyemi 
    0.421     0.181     0.358 

> rcs.ASDH <- fit.mult.impute(Survive ~ rcs(Age) + GCS + Mechanism + rcs(ISS) + neuroFirst + rcs(inctoCrand) + inctoCranYN + rcs(Yeardecimalc) + Sex + Other + rcteyemi,lrm,a,data=ASDH_Paper1.1)

> rcs.ASDH

Logistic Regression Model

fit.mult.impute(formula = Survive ~ rcs(Age) + GCS + Mechanism + 
    rcs(ISS) + neuroFirst + rcs(inctoCrand) + inctoCranYN + rcs(Yeardecimalc) + 
    Sex + Other + rcteyemi, fitter = lrm, xtrans = a, data = ASDH_Paper1.1)

                      Model Likelihood     Discrimination    Rank Discrim.    
                         Ratio Test            Indexes          Indexes       
Obs          5998    LR chi2    1609.98    R2       0.365    C       0.836    
 0           1281    d.f.            25    g        1.584    Dxy     0.672    
 1           4717    Pr(> chi2) <0.0001    gr       4.875    gamma   0.674    
max |deriv| 0.001                          gp       0.222    tau-a   0.226    
                                           Brier    0.121                     

                              Coef    S.E.    Wald Z Pr(>|Z|)
Intercept                     21.3339 67.4400  0.32  0.7517  
Age                           -0.0088  0.0132 -0.67  0.5052  
Age'                          -0.0294  0.0643 -0.46  0.6471  
Age''                         -0.0134  0.2479 -0.05  0.9570  
Age'''                         0.2588  0.3534  0.73  0.4639  
GCS                            0.1100  0.0145  7.61  <0.0001 
Mechanism=Fall > 2m           -0.0651  0.1162 -0.56  0.5754  
Mechanism=Other                0.2285  0.1338  1.71  0.0876  
Mechanism=RTC                  0.0449  0.1332  0.34  0.7360  
Mechanism=Shooting / Stabbing  2.1150  1.1142  1.90  0.0577  
ISS                           -0.1069  0.0318 -3.36  0.0008  
ISS'                          -0.0359  0.1306 -0.27  0.7835  
ISS''                          1.8296  1.9259  0.95  0.3421  
neuroFirst                    -0.3483  0.0973 -3.58  0.0003  
inctoCrand                     0.0001  0.0053  0.02  0.9872  
inctoCrand'                   -0.0745  0.3060 -0.24  0.8077  
inctoCrand''                   0.1696  0.5901  0.29  0.7738  
inctoCrand'''                 -0.1167  0.3150 -0.37  0.7110  
inctoCranYN                   -0.2814  0.6165 -0.46  0.6480  
Yeardecimalc                  -0.0101  0.0337 -0.30  0.7641  
Yeardecimalc'                  0.0386  0.0651  0.59  0.5536  
Yeardecimalc''                -0.7417  0.8210 -0.90  0.3663  
Yeardecimalc'''                7.0367  4.9344  1.43  0.1539  
Sex=Male                       0.0668  0.0891  0.75  0.4534  
Other=1                        0.3238  0.1611  2.01  0.0445  
rcteyemi                       1.1589  0.1050 11.04  <0.0001 


> anova(rcs.ASDH)
                Wald Statistics          Response: Survive 

 Factor          Chi-Square d.f. P     
 Age              83.07      4   <.0001
  Nonlinear        5.97      3   0.1131
 GCS              57.89      1   <.0001
 Mechanism         8.14      4   0.0867
 ISS              77.31      3   <.0001
  Nonlinear       35.04      2   <.0001
 neuroFirst       12.81      1   0.0003
 inctoCrand        2.32      4   0.6777
  Nonlinear        2.29      3   0.5149
 inctoCranYN       0.21      1   0.6480
 Yeardecimalc      4.19      4   0.3807
  Nonlinear        3.77      3   0.2874
 Sex               0.56      1   0.4534
 Other             4.04      1   0.0445
 rcteyemi        121.80      1   <.0001
 TOTAL NONLINEAR  47.27     11   <.0001
 TOTAL           679.09     25   <.0001
> 

Yeardecimal is no longer significant. However, if I exclude Yeardecimal from aregImpute only, I have the alternative result below:

> a <- aregImpute(~ I(Outcome30) + Age + GCS + I(Other) + ISS + inctoCran + I(rcteyemi) + I(neuroFirst) + I(neuroYN) + Mechanism + LOS, nk=4, data = ASDH_Paper1.1, n.impute=10)
Iteration 13 
> 
> a

Multiple Imputation using Bootstrap and PMM

aregImpute(formula = ~I(Outcome30) + Age + GCS + I(Other) + ISS + 
    inctoCran + I(rcteyemi) + I(neuroFirst) + I(neuroYN) + Mechanism + 
    LOS, data = ASDH_Paper1.1, n.impute = 10, nk = 4)

n: 5998     p: 11   Imputations: 10     nk: 4 

Number of NAs:
 Outcome30        Age        GCS      Other        ISS  inctoCran   rcteyemi neuroFirst    neuroYN  Mechanism        LOS 
         0          0       2242          0          0       3500       3376          0          0          0          0 

           type d.f.
Outcome30     c    1
Age           s    3
GCS           s    3
Other         c    1
ISS           s    3
inctoCran     s    3
rcteyemi      l    1
neuroFirst    l    1
neuroYN       l    1
Mechanism     c    4
LOS           s    3

Transformation of Target Variables Forced to be Linear

R-squares for Predicting Non-Missing Values for Each Variable
Using Last Imputations of Predictors
      GCS inctoCran  rcteyemi 
    0.407     0.194     0.320 
> 

> rcs.ASDH <- fit.mult.impute(Survive ~ rcs(Age) + GCS + Mechanism + rcs(ISS) + neuroFirst + rcs(inctoCrand) + inctoCranYN + rcs(Yeardecimalc) + Sex + Other + rcteyemi,lrm,a,data=ASDH_Paper1.1)
> rcs.ASDH

Logistic Regression Model

fit.mult.impute(formula = Survive ~ rcs(Age) + GCS + Mechanism + 
    rcs(ISS) + neuroFirst + rcs(inctoCrand) + inctoCranYN + rcs(Yeardecimalc) + 
    Sex + Other + rcteyemi, fitter = lrm, xtrans = a, data = ASDH_Paper1.1)

                      Model Likelihood     Discrimination    Rank Discrim.    
                         Ratio Test            Indexes          Indexes       
Obs          5998    LR chi2    1607.92    R2       0.364    C       0.834    
 0           1281    d.f.            25    g        1.578    Dxy     0.667    
 1           4717    Pr(> chi2) <0.0001    gr       4.846    gamma   0.669    
max |deriv| 0.003                          gp       0.221    tau-a   0.224    
                                           Brier    0.120                     

                              Coef     S.E.    Wald Z Pr(>|Z|)
Intercept                     -55.6574 58.3464 -0.95  0.3401  
Age                            -0.0084  0.0128 -0.66  0.5105  
Age'                           -0.0335  0.0612 -0.55  0.5838  
Age''                           0.0050  0.2365  0.02  0.9830  
Age'''                          0.2321  0.3387  0.69  0.4930  
GCS                             0.1099  0.0124  8.88  <0.0001 
Mechanism=Fall > 2m            -0.0631  0.1138 -0.55  0.5793  
Mechanism=Other                 0.2354  0.1381  1.70  0.0883  
Mechanism=RTC                   0.0315  0.1319  0.24  0.8114  
Mechanism=Shooting / Stabbing   1.9297  1.0930  1.77  0.0775  
ISS                            -0.1012  0.0335 -3.02  0.0025  
ISS'                           -0.0599  0.1366 -0.44  0.6613  
ISS''                           2.1581  2.0120  1.07  0.2834  
neuroFirst                     -0.3753  0.0888 -4.23  <0.0001 
inctoCrand                     -0.0007  0.0054 -0.13  0.9002  
inctoCrand'                    -0.0496  0.3116 -0.16  0.8734  
inctoCrand''                    0.1316  0.6021  0.22  0.8270  
inctoCrand'''                  -0.1078  0.3224 -0.33  0.7381  
inctoCranYN                    -0.1697  0.6172 -0.27  0.7834  
Yeardecimalc                    0.0281  0.0291  0.96  0.3349  
Yeardecimalc'                   0.0682  0.0600  1.14  0.2553  
Yeardecimalc''                 -1.4037  0.7685 -1.83  0.0678  
Yeardecimalc'''                10.2513  4.8156  2.13  0.0333  
Sex=Male                        0.0595  0.0890  0.67  0.5037  
Other=1                         0.3579  0.1641  2.18  0.0292  
rcteyemi                        1.1862  0.0799 14.85  <0.0001 


> anova(rcs.ASDH)
                Wald Statistics          Response: Survive 

 Factor          Chi-Square d.f. P     
 Age              78.39      4   <.0001
  Nonlinear        6.23      3   0.1011
 GCS              78.86      1   <.0001
 Mechanism         7.53      4   0.1104
 ISS              76.46      3   <.0001
  Nonlinear       31.16      2   <.0001
 neuroFirst       17.87      1   <.0001
 inctoCrand        3.22      4   0.5214
  Nonlinear        3.19      3   0.3630
 inctoCranYN       0.08      1   0.7834
 Yeardecimalc     44.83      4   <.0001
  Nonlinear        4.67      3   0.1979
 Sex               0.45      1   0.5037
 Other             4.76      1   0.0292
 rcteyemi        220.51      1   <.0001
 TOTAL NONLINEAR  45.39     11   <.0001
 TOTAL           715.22     25   <.0001
> 

Can anyone help me understand why the statistical results for Yeardecimal are so starkly different?

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  • 1
    $\begingroup$ I can't answer your direct question. However, I suggest you to consider trying to reproduce your analysis, using mice for multiple imputation. See my earlier answer, especially pay attention to the mentioned sections in the referenced paper. $\endgroup$ – Aleksandr Blekh Dec 19 '14 at 17:14

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