How to select predictor variables for linear mixed model?

Question

I have a linear mixed model with ~30 clinical/treatment variables and repeated outcome variables for patients. E.g. The outcome variable is Breast symptom scores, which were collected at different time points before and after treatment.

The aim of my modelling is to find variables associated with the endpoint - rather than for prediction purposes. E.g. Which variables are associated with worsening or decreasing breast symptoms (endpoint)? Patients are included as a random variable in my model because each patient reported breast symptom scores at 4 time points.

So far I have included all the predictor variables in the model to see which ones are significant - based on p value. However, I want to refine the list of predictor variables - I am not sure what kind of method is appropriate doing this. I've read numerous posts suggesting step-wise approach based on AIC is inappropriate. However, I am unsure on what other method to use. Since, the topic area about worsening breast symptoms is poorly understood, It may not be appropriate to select the appropriate predictor variables based on my knowledge/literature. What else can I do?

Below are the results. I used the lmerTest R package.

Fixed effects:
                       Estimate Std. Error         df t value Pr(>|t|)    
(Intercept)            32.96063    7.20278 1902.07183   4.576 5.04e-06 ***
age                    -0.17415    0.03504 1879.34386  -4.970 7.29e-07 ***
bmi                     0.31403    0.07700 1969.33699   4.078 4.72e-05 ***
smoking1                2.72097    0.64730 1872.91835   4.204 2.75e-05 ***
chemo1                 -4.19325    0.88424 1853.71145  -4.742 2.28e-06 ***
bed                    -0.14049    0.07950 1893.53615  -1.767 0.077338 .  
alcohol1               -0.02258    0.66668 1868.30786  -0.034 0.972983    
diabetes1               2.00570    2.96212 1793.26592   0.677 0.498419    
cvd1                    1.66621    1.27143 1859.70291   1.310 0.190189    
depression1             1.56981    1.92097 1895.40556   0.817 0.413918    
ra1                     2.01648    1.85537 1863.61027   1.087 0.277252    
ace_i1                  2.07307    1.38093 1874.34686   1.501 0.133470    
anti_diabetic1         -2.85922    3.26410 1836.86824  -0.876 0.381167    
analgesic1              4.18493    1.11017 1959.02745   3.770 0.000168 ***
anti_depressant1        1.43063    1.90994 1909.71400   0.749 0.453924    
statin1                -0.80427    1.02201 1904.96404  -0.787 0.431407    
surgery_type2           0.79662    0.97244 1847.94156   0.819 0.412781    
surgery_axilla_type1    2.01854    1.72102 1854.81912   1.173 0.240997    
surgery_axilla_type2    4.91054    2.15226 1844.93117   2.282 0.022628 *  
surgery_axilla_type3    3.98207    2.11948 1849.44602   1.879 0.060430 .  
imrt_type1             -0.69167    1.00083 1841.36311  -0.691 0.489593    
imrt_type2             -1.04521    1.15284 1863.99167  -0.907 0.364713    
rt_axilla1              1.08665    1.27481 1847.76952   0.852 0.394102    
rt_scf1                 0.24627    1.33754 1877.59482   0.184 0.853939    
hormonal_treatment1    -0.62619    0.87084 1895.21208  -0.719 0.472186    
breast                  0.11584    0.15604 1888.73815   0.742 0.457948    
bp1                    -1.69208    0.85946 1881.10264  -1.969 0.049125 *  
boost1                  3.85716    0.82329 1895.07486   4.685 3.00e-06 ***
non.white1              3.45889    1.43653 2123.07124   2.408 0.016133 *  
n_stage_max1           -1.82561    1.24045 1898.85195  -1.472 0.141258    
n_stage_max2           -5.73341    2.49696 1884.14608  -2.296 0.021777 *  
n_stage_max3           -2.84109    3.76984 1992.08783  -0.754 0.451156    
n_stage_maxx            1.78825    3.90495 1784.73440   0.458 0.647048    
t_stage_max1           -2.37050    1.50770 1854.04010  -1.572 0.116060    
t_stage_max2           -0.61233    1.67767 1862.83528  -0.365 0.715162    
t_stage_max3           -5.83685    3.90785 1903.32237  -1.494 0.135441    
t_stage_max4            2.52781    5.95680 1939.89062   0.424 0.671352    
t_stage_maxx          -10.66783    4.55709 1754.06351  -2.341 0.019347 *  
postop_haematoma1       4.79939    0.97454 1862.33932   4.925 9.19e-07 ***
postop_infection1       1.64284    1.57067 1920.76436   1.046 0.295718    
rthypo1                -4.07166    0.92510 1880.34087  -4.401 1.14e-05 ***

My model used the REML method.

Thanks in advance.

Answer 1

Are all your variables binary (0,1)? If some aren't really binary but you've made it so, please return them to factors. (i.e. n_stage, t_stage).

There are may strategies to perform a model. In this case, your brainstorming gives you an initial model that could be sufficient, by just looking at the most significant variables (three stars, which is p-value < 1%), such as:

$bsc = b_0 +b_1age+b_2bmi+b_3smoking1+b_4chemo1+b_5analgesic1 + b_6boost1 + b_7postophaematoma1 + b_8rthypo1$

However, the problem comes if you don't "like" this variable, believe that they shouldn't be here and/or believe that others should be there. According to your prior beliefs and knowledge, you may be right, but the statistics don't help much.

In addition to this model, you could try a second model without the variables already identified as significant. If some variables appear to be significant (at 1%), then perhaps they should've been included in the first model.

Be careful in two points: 1) Don't change the significance criteria (1%). 2) The inclusion of the significant variables of the second model to the first model can come with multicollinearity, among other statistical issues that you may need to address.