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Table 3 ARMAX model input variables and regression coefficients by cluster for the calibration dataset

From: Integrating data from randomized controlled trials and observational studies to predict the response to pregabalin in patients with painful diabetic peripheral neuropathy

ARMAX model input variables

Final ARMAX output regression coefficients, by clustera

1

2

3

4

5

6

y-intercepts for regression models, not variables

−0.0409

−0.1447

−0.0604

−0.0826

0.0789

−0.2732

Age cohort (×10)

–

–

–

–

0.0465

–

Gender (×9)

–

–

–

–

−0.0496

–

Pregabalin monotherapy (×8)

–

–

–

–

−0.1107

–

pDPN duration (years) (×11)

0.0179

–

–

–

–

–

Insulin use (×7)

–

–

–

–

–

0.0276

Pain score (t-1)b (×1)

0.7180

0.8749

0.7865

0.8341

0.9011

0.8919

Pain score (t-2)c (×2)

0.0436

0.0196

0.0164

0.0451

0.0107

−0.0103

Sleep interference score (t-1)b (×3)

0.0949

–

0.0374

–

–

–

Dose (t)d (×4)

–

−0.0006

–

–

−0.0011

–

Dose (t-1)b (×5)

−0.0012

−0.0007

−0.0009

−0.0012

–

−0.0004

Dose (t-2)c (×6)

0.0015

0.0015

0.0012

0.0017

0.0012

0.0007

General feeling: full of energy (t-1)b (×13)

–

0.0250

0.0425

–

–

–

General feeling: calm and relaxed (t-1)b (×12)

–

–

–

−0.0109

–

0.0655

Model performance measures applied

Performance, by cluster

1

2

3

4

5

6

Likelihood ratio P value

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

R 2

0.86

0.89

0.85

0.87

0.91

0.89

Root mean square error

0.54

0.55

0.55

0.53

0.53

0.57

Observed vs. estimated responder level (Student’s t test P value)e

0.95

1.00

0.95

0.97

0.92

0.96

  1. Abbreviations: ARMAX autoregressive moving average model, pDPN painful diabetic peripheral neuropathy
  2. aThe first number in each column is the regression intercept value. Blank spaces in columns indicate that the associated row variable was not a predictor in the final model for that cluster
  3. b(t-1) indicates one week before prediction
  4. c(t-2) indicates two weeks before prediction
  5. d(t) indicates the same week of the prediction
  6. Given the time series of pain scores, ARMAX is essentially a linear regression model for understanding future values of pain scores in the series. The ARMAX model inputs were assigned unique variable names, x1x13, and are represented in the cluster-specific ARMAX equations below
  7. Equations for the ARMAX models (where ‘y’ is pain score, treated as a continuous variable)
  8. CLUSTER 1: y = −0.0409 + 0.7180 × 1 + 0.0436 × 2 + 0.0949 × 3–0.0012 × 5 + 0.0015 × 6 + 0.0179 × 11
  9. CLUSTER 2: y = −0.1447 + 0.8749 × 1 + 0.0196 × 2–0.0006 × 4–0.0007 × 5 + 0.0015 × 6 + 0.0250 × 13
  10. CLUSTER 3: y = −0.0604 + 0.7865 × 1 + 0.0164 × 2 + 0.0374 × 3–0.0009 × 5 + 0.0012 × 6 + 0.0425 × 13
  11. CLUSTER 4: y = −0.0826 + 0.8341 × 1 + 0.0451 × 2–0.0012 × 5 + 0.0017 × 6–0.0109 × 12
  12. CLUSTER 5: y = 0.0789 + 0.9011 × 1 + 0.0107 × 2–0.0011 × 4 + 0.0012 × 6–0.1107 × 8–0.0496 × 9 + 0.0465 × 10
  13. CLUSTER 6: y = −0.2732 + 0.8919 × 1–0.0103 × 2–0.0004 × 5 + 0.0007 × 6 + 0.0276 × 7 + 0.0655 × 12
  14. eThe ARMAXs estimate pain score, but we also want to be able to identify whether that patient is a responder at different thresholds (e.g., 50% reduction in pain or 30% reduction in pain). Hence, we sought to confirm estimation of responder level based on the ARMAXs for pain score
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BMC Medical Research Methodology

ISSN: 1471-2288

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