0.1 Raw data description

## ------------------------------------------------------------------------- 
## Describe database[-c(1, 2)] (tbl_df, tbl, data.frame):
## 
## data.frame:  423 obs. of  7 variables
## 
##   Nr  ColName       Class      NAs       Levels         Label       
##   1   Death         factor     .         (2): 1-0, 2-1  Death       
##   2   Age           numeric    .                        Age (years) 
##   3   Neutrophiles  numeric    3 (0.7%)                 Neutrophiles
##                                                         (#/μl)      
##   4   Creatinine    numeric    .                        Creatinine  
##                                                         (mg/dl)     
##   5   Leucocytes    numeric    2 (0.5%)                 Leucocytes  
##                                                         (#/μl)      
##   6   TI            character  .                        ICU stay    
##   7   ICU           factor     .         (2): 1-0, 2-1  ICU         
## 
## 
## ------------------------------------------------------------------------- 
## 1 - Death (factor - dichotomous) :
##   Death
## 
## 
##   length      n    NAs unique
##      423    423      0      2
##          100.0%   0.0%       
## 
##    freq   perc  lci.95  uci.95'
## 0   394  93.1%   90.3%   95.2%
## 1    29   6.9%    4.8%    9.7%
## 
## ' 95%-CI Wilson

## ------------------------------------------------------------------------- 
## 2 - Age (numeric) :
##   Age (years)
## 
## 
##   length       n    NAs  unique     0s   mean  meanCI
##      423     423      0      31      0  75.70   75.03
##           100.0%   0.0%           0.0%          76.38
##                                                      
##      .05     .10    .25  median    .75    .90     .95
##    66.00   67.00  70.00   76.00  80.00  86.00   88.00
##                                                      
##    range      sd  vcoef     mad    IQR   skew    kurt
##    36.00    7.07   0.09    8.90  10.00   0.45   -0.45
##                                                      
## lowest : 65.0 (18), 66.0 (14), 67.0 (25), 68.0 (21), 69.0 (23)
## highest: 91.0, 92.0 (2), 93.0 (3), 94.0 (2), 101.0

## ------------------------------------------------------------------------- 
## 3 - Neutrophiles (numeric) :
##   Neutrophiles (#/μl)
## 
## 
##   length      n    NAs  unique     0s   mean  meanCI
##      423    420      3     266      0  75.90   73.96
##           99.3%   0.7%           0.0%          77.84
##                                                     
##      .05    .10    .25  median    .75    .90     .95
##    49.99  57.29  65.57   76.85  85.00  91.00   92.61
##                                                     
##    range     sd  vcoef     mad    IQR   skew    kurt
##   260.00  20.22   0.27   13.94  19.43   4.39   38.78
##                                                     
## lowest : 12.0, 20.76, 38.2, 38.4, 38.5
## highest: 97.0, 153.0, 227.0, 246.0, 272.0

## ------------------------------------------------------------------------- 
## 4 - Creatinine (numeric) :
##   Creatinine (mg/dl)
## 
## 
##   length       n    NAs  unique    0s  mean  meanCI
##      423     423      0     155     3  1.21    1.13
##           100.0%   0.0%          0.7%          1.29
##                                                    
##      .05     .10    .25  median   .75   .90     .95
##     0.59    0.66   0.80    0.98  1.30  1.91    2.47
##                                                    
##    range      sd  vcoef     mad   IQR  skew    kurt
##     7.41    0.84   0.69    0.33  0.50  3.73   18.43
##                                                    
## lowest : 0.0 (3), 0.28, 0.37, 0.4, 0.42
## highest: 5.4, 5.91, 6.15, 6.79, 7.41

## ------------------------------------------------------------------------- 
## 5 - Leucocytes (numeric) :
##   Leucocytes (#/μl)
## 
## 
##   length      n    NAs  unique     0s   mean  meanCI
##      423    421      2     352      0  10.62    9.41
##           99.5%   0.5%           0.0%          11.82
##                                                     
##      .05    .10    .25  median    .75    .90     .95
##     3.75   4.60   6.29    8.53  11.98  16.29   19.19
##                                                     
##    range     sd  vcoef     mad    IQR   skew    kurt
##   177.06  12.56   1.18    3.85   5.69   9.46  109.43
##                                                     
## lowest : 1.1, 1.67, 2.04 (2), 2.15, 2.27
## highest: 42.64, 53.98, 92.0, 146.44, 178.16

## ------------------------------------------------------------------------- 
## 6 - TI (character - dichotomous) :
##   ICU stay
## 
## 
##   length      n    NAs unique
##      423    423      0      2
##          100.0%   0.0%       
## 
##      freq   perc  lci.95  uci.95'
## no    391  92.4%   89.5%   94.6%
## yes    32   7.6%    5.4%   10.5%
## 
## ' 95%-CI Wilson

## ------------------------------------------------------------------------- 
## 7 - ICU (factor - dichotomous) :
##   ICU
## 
## 
##   length      n    NAs unique
##      423    423      0      2
##          100.0%   0.0%       
## 
##    freq   perc  lci.95  uci.95'
## 0   391  92.4%   89.5%   94.6%
## 1    32   7.6%    5.4%   10.5%
## 
## ' 95%-CI Wilson

## ------------------------------------------------------------------------- 
## Age ~ Death
## 
## Summary: 
## n pairs: 423, valid: 423 (100.0%), missings: 0 (0.0%), groups: 2
## 
##                         
##               0        1
## mean     75.536   77.966
## median   75.000   78.000
## sd        7.067    6.869
## IQR      10.000   11.000
## n           394       29
## np      93.144%   6.856%
## NAs           0        0
## 0s            0        0
## 
## Kruskal-Wallis rank sum test:
##   Kruskal-Wallis chi-squared = 3, df = 1, p-value = 0.07

## ------------------------------------------------------------------------- 
## Neutrophiles ~ Death
## 
## Summary: 
## n pairs: 423, valid: 420 (99.3%), missings: 3 (0.7%), groups: 2
## 
##                         
##               0        1
## mean     75.332   83.610
## median   76.100   89.200
## sd       20.555   12.834
## IQR      19.150   12.900
## n           391       29
## np      93.095%   6.905%
## NAs           3        0
## 0s            0        0
## 
## Kruskal-Wallis rank sum test:
##   Kruskal-Wallis chi-squared = 19, df = 1, p-value = 0.00001

## ------------------------------------------------------------------------- 
## Creatinine ~ Death
## 
## Summary: 
## n pairs: 423, valid: 423 (100.0%), missings: 0 (0.0%), groups: 2
## 
##                         
##               0        1
## mean      1.148    2.097
## median    0.970    1.560
## sd        0.680    1.817
## IQR       0.490    1.250
## n           394       29
## np      93.144%   6.856%
## NAs           0        0
## 0s            3        0
## 
## Kruskal-Wallis rank sum test:
##   Kruskal-Wallis chi-squared = 14, df = 1, p-value = 0.0002

## ------------------------------------------------------------------------- 
## Leucocytes ~ Death
## 
## Summary: 
## n pairs: 423, valid: 421 (99.5%), missings: 2 (0.5%), groups: 2
## 
##                         
##               0        1
## mean     10.244   15.625
## median    8.225   13.700
## sd       12.681    9.635
## IQR       5.490    9.690
## n           392       29
## np      93.112%   6.888%
## NAs           2        0
## 0s            0        0
## 
## Kruskal-Wallis rank sum test:
##   Kruskal-Wallis chi-squared = 22, df = 1, p-value = 0.000003

## ------------------------------------------------------------------------- 
## TI ~ Death
## 
## 
## Summary: 
## n: 423, rows: 2, columns: 2
## 
## Pearson's Chi-squared test (cont. adj):
##   X-squared = 141, df = 1, p-value <0.0000000000000002
## Fisher's exact test p-value <0.0000000000000002
## McNemar's chi-squared = 0.2, df = 1, p-value = 0.7
## 
## Warning message:
##   Exp. counts < 5: Chi-squared approx. may be incorrect!!
## 
## 
##                     estimate   lwr.ci   upr.ci'
##                                               
## odds ratio           55.6846  21.6563 143.1814
## rel. risk (col1)      2.3986   1.5773   3.6475
## rel. risk (col2)      0.0431   0.0219   0.0847
## 
## 
## Phi-Coefficient        0.595
## Contingency Coeff.     0.511
## Cramer's V             0.595
## 
##                                 
##       Death      0      1    Sum
## TI                              
##                                 
## no    freq     381     10    391
##       perc   90.1%   2.4%  92.4%
##       p.row  97.4%   2.6%      .
##       p.col  96.7%  34.5%      .
##                                 
## yes   freq      13     19     32
##       perc    3.1%   4.5%   7.6%
##       p.row  40.6%  59.4%      .
##       p.col   3.3%  65.5%      .
##                                 
## Sum   freq     394     29    423
##       perc   93.1%   6.9% 100.0%
##       p.row      .      .      .
##       p.col      .      .      .
##                                 
## 
## ----------
## ' 95% conf. level

## ------------------------------------------------------------------------- 
## ICU ~ Death
## 
## 
## Summary: 
## n: 423, rows: 2, columns: 2
## 
## Pearson's Chi-squared test (cont. adj):
##   X-squared = 141, df = 1, p-value <0.0000000000000002
## Fisher's exact test p-value <0.0000000000000002
## McNemar's chi-squared = 0.2, df = 1, p-value = 0.7
## 
## Warning message:
##   Exp. counts < 5: Chi-squared approx. may be incorrect!!
## 
## 
##                     estimate   lwr.ci   upr.ci'
##                                               
## odds ratio           55.6846  21.6563 143.1814
## rel. risk (col1)      2.3986   1.5773   3.6475
## rel. risk (col2)      0.0431   0.0219   0.0847
## 
## 
## Phi-Coefficient        0.595
## Contingency Coeff.     0.511
## Cramer's V             0.595
## 
##                                 
##       Death      0      1    Sum
## ICU                             
##                                 
## 0     freq     381     10    391
##       perc   90.1%   2.4%  92.4%
##       p.row  97.4%   2.6%      .
##       p.col  96.7%  34.5%      .
##                                 
## 1     freq      13     19     32
##       perc    3.1%   4.5%   7.6%
##       p.row  40.6%  59.4%      .
##       p.col   3.3%  65.5%      .
##                                 
## Sum   freq     394     29    423
##       perc   93.1%   6.9% 100.0%
##       p.row      .      .      .
##       p.col      .      .      .
##                                 
## 
## ----------
## ' 95% conf. level

0.2 Full model: Death~Neutrophiles+Creatinine+Leucocytes+Age+ICU

Dependent: Death

alive (0)

dead (1)

OR

OR-adj

Neutrophiles (#/μl)

75.3 (20.6)

83.6 (12.8)

1.01 (1.00-1.03, p=0.050)

1.01 (0.98-1.02, p=0.419)

Creatinine (mg/dl)

1.1 (0.7)

2.1 (1.8)

1.97 (1.47-2.68, p<0.001)

1.60 (1.04-2.47, p=0.036)

Leucocytes (#/μl)

10.2 (12.7)

15.6 (9.6)

1.02 (1.00-1.03, p=0.064)

1.01 (0.96-1.04, p=0.529)

Age (years)

75.5 (7.1)

78.0 (6.9)

1.05 (0.99-1.10, p=0.076)

0.98 (0.91-1.05, p=0.516)

ICU stay: no

381 (96.7)

10 (34.5)

-

-

- yes

13 (3.3)

19 (65.5)

55.68 (22.32-149.41, p<0.001)

43.49 (15.74-132.11, p<0.001)

Number in dataframe = 423, Number in model = 420, Missing = 3, AIC = 142.1, C-statistic = 0.84, H&L = Chi-sq(8) 8.16 (p=0.418)

Values are Means (SD), # (%), or OR (95% CI, p-values).

0.3 Other models

  Full Full (Box-Cox) Only creatinine Only creatinine (Box-Cox)
Predictors Odds Ratios p Odds Ratios p Odds Ratios p Odds Ratios p
(Intercept) 0.04 (0.00 – 6.70) 0.216 Inf (Inf – Inf) <0.001 0.03 (0.01 – 0.05) <0.001 0.05 (0.03 – 0.08) <0.001
Neutrophiles(#/μl) 1.01 (0.99 – 1.03) 0.419 2.66 (0.14 – 51.06) 0.516
Creatinine(mg/dl) 1.60 (1.03 – 2.49) 0.036 2.22 (0.94 – 5.25) 0.070 1.97 (1.46 – 2.64) <0.001 4.43 (2.28 – 8.62) <0.001
Leucocytes(#/μl) 1.01 (0.98 – 1.05) 0.529 4.86 (0.83 – 28.52) 0.080
Age(years) 0.98 (0.91 – 1.05) 0.516 0.00 (0.00 – 0.00) <0.001
TIyes 43.49 (15.17 – 124.68) <0.001
ICU 1 34.30 (11.77 – 99.99) <0.001
Observations 420 420 423 423
Tjur’s R2 0.394 0.402 0.086 0.072
Deviance 130.129 127.380 191.816 192.891
AIC 142.129 139.380 195.816 196.891
log-Likelihood -65.064 -63.690 -95.908 -96.446