Hello,

I think this question might be more a statistics understanding than a code troubleshooting. Still, I am posting here because there are more R-users with a better knowledge of biological applications.

I want to understand some differences to represent the allele presence/absence with lm() function in R. As a dependent variable, I have ICU_days period, which I am trying to relate to HLA-B alleles. So, as an independent variable, I have HLA-B alleles adjusted for Age.

The first representation would be a dataset containing all alleles present in my sample as lm_designmatrix2:

id ICU_days Age allele
1         49  74   B*35
2         45  73   B*07
3         20  63   B*07
4         52  55   B*08
5         29  46   B*07
6         66  77   B*38
7         44  76   B*08
8         76  65   B*08
9         47  34   B*14
10        25  58   B*13
11        30  57   B*35
12         7  80   B*07
13        30  27   B*15
14        28  79   B*40
15         2  68   B*07
16        20  56   B*07
17        20  85   B*07
18        24  58   B*35
19        31  47   B*44
20        11  58   B*07

The linear model:

summary(lm(ICU_days ~ allele + Age, data = lm_designmatrix2))

Call:
lm(formula = ICU_days ~ allele + Age, data = lm_designmatrix2)

Residuals:
    Min      1Q  Median      3Q     Max 
-29.627 -11.032  -2.047   7.942  63.348 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)   
(Intercept)  18.37896    7.75141   2.371   0.0190 * 
alleleB*08    7.79160    6.49281   1.200   0.2321   
alleleB*13   20.30319    7.62279   2.663   0.0086 **
alleleB*14   10.58582    7.56816   1.399   0.1640   
alleleB*15   13.78044    6.81690   2.022   0.0450 * 
alleleB*18    7.68169    7.56604   1.015   0.3116   
alleleB*27  -17.64699   13.32670  -1.324   0.1875   
alleleB*35    8.23656    5.62620   1.464   0.1453   
alleleB*37   35.60011   18.31386   1.944   0.0538 . 
alleleB*38   25.62458    9.83688   2.605   0.0101 * 
[...] etc

Age           0.05827    0.10997   0.530   0.5970   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 17.8 on 147 degrees of freedom
Multiple R-squared:  0.1607,    Adjusted R-squared:  0.02362 
F-statistic: 1.172 on 24 and 147 DF,  p-value: 0.2766

However, even though I know that is a dumb question, I didn't realize the difference between the above model with a dataset with dummy variables for each allele:

ICU_days   Age `B*07` `B*08` `B*13` `B*14`
      <int> <int>  <int>  <int>  <int>  <int>
 1       30    27      0      0      0      0
 2       47    34      0      0      0      1
 3       21    35      0      0      0      0
 4       22    37      1      0      0      0
 5        3    39      0      0      0      0
 6       14    39      1      1      0      0
 7       49    39      0      0      0      1
 8       84    39      1      0      1      0
 9       30    40      0      0      0      0
10       32    40      0      0      0      0

And it performs linear modeling for each allele separately, like this:

summary(lm(ICU_days ~ Age + `B*13`, data = lm_designmatrix))

Call:
lm(formula = ICU_days ~ Age + `B*13`, data = lm_designmatrix)

Residuals:
   Min     1Q Median     3Q    Max 
-27.29 -14.72  -3.76  10.74  47.00 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept) 22.70441    8.70438   2.608   0.0108 *
Age          0.09689    0.14743   0.657   0.5129  
`B*13`      14.02777    6.68684   2.098   0.0390 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 17.8 on 83 degrees of freedom
Multiple R-squared:  0.05161,   Adjusted R-squared:  0.02876 
F-statistic: 2.258 on 2 and 83 DF,  p-value: 0.1109

Could anyone explain how to interpret these different representations?