# Multiple Imputation - Help Needed

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?

• 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. – Aleksandr Blekh Dec 19 '14 at 17:14