Background
Methods
The study data
Outcome measures
Candidate predictors
Missing data
Variable selection, model fitting, performance and validation
Variable selection and model fitting via the lasso
Model performance: discrimination and calibration
Validation
Software
R
statistical software, version 2.15.2 [26]. The mice package [21] was used to perform MI. Variable selection and model fitting was performed using the glmnet [27] and caret [28], packages. Additional routines were developed to perform the bootstrap resampling procedure in the presence of multiply imputed data (See Additional file 1).Results
Covariates | Best model parameters | 3% tolerance model parameters | ||||
---|---|---|---|---|---|---|
Number
|
Uncalibrated β
|
Re-calibrated β
|
Number
|
Uncalibrated β
|
Re-calibrated β
| |
Intercept | 10 | 1.038638 | 0.880085 | 10 | 1.30578 | 0.862149 |
Anxiety medication | 10 | -0.04399 | -0.04534 | 1 | -0.00066 | -0.00075 |
Cardiovascular medication | 10 | -0.01752 | -0.01774 | 0 | ||
Pulmonary medication | 10 | -0.01454 | -0.01486 | 0 | ||
Use of long acting beta agonists | 3 | -0.00143 | -0.00129 | 0 | ||
Influenza vaccination | 10 | -0.04283 | -0.04365 | 0 | ||
Renal:chronic kidney disease | 10 | -0.06797 | -0.06939 | 0 | ||
Lung function | 6 | 0.000162 | 0.00018 | 0 | ||
HADS depression score | 8 | -0.00372 | -0.00403 | 7 | -0.00274 | -0.00311 |
Physical activity score | 10 | 0.02788 | 0.028764 | 6 | 0.005337 | 0.006068 |
Self-efficacy 2 | 3 | 0.01409 | 0.014715 | 3 | 0.006139 | 0.006978 |
Self-efficacy 3 | 1 | 0.000367 | 0.000384 | 0 | ||
Sit to stand test | 10 | 0.001774 | 0.001901 | 10 | 0.001518 | 0.001632 |
crqdyspnea | 10 | 0.654104 | 0.682812 | 10 | 0.60923 | 0.690902 |
crqfatigue | 10 | 0.109821 | 0.114304 | 10 | 0.089453 | 0.100929 |
crqmastery | 6 | 0.010376 | 0.010272 | 1 | 0.001909 | 0.002171 |
crqemotional | 3 | 0.00078 | 0.00089 | 2 | 0.00134 | 0.001523 |
Feeling thermometer change score | 10 | -0.04587 | -0.04658 | 0 | ||
HADS depression change score | 10 | 0.039783 | 0.040061 | 0 | ||
crqdyspnea change score | 10 | -0.1582 | -0.16403 | 10 | -0.04866 | -0.05207 |
MSE0= 2.4183 | Averaged best model 0.9047 | Averaged 3% tolerance 0.9672 | ||||||
---|---|---|---|---|---|---|---|---|
Apparent MSE
X
|
Appr 1
|
Appr 2
|
Appr 3
|
Appr 4
|
Appr 1
|
Appr 2
|
Appr 3
|
App 4
|
Optimism | -0.1162 | -0.0127 | -0.0988 | -0.1452 | -0.0656 | -0.0081 | -0.0537 | -0.0781 |
Optimism corrected MSE
X
| 1.0209 | 0.9174 | 1.0035 | 1.0499 | 1.0328 | 0.9753 | 1.0209 | 1.0453 |
1.0443 | 1.0552 | 1.0361 | 1.0498 | 1.1368 | 1.1257 | 1.1136 | 1.1297 |