Background
Methods
Study population
Female (n=6300) | Male (n=6641) | Total (n=12941) | |
---|---|---|---|
Age | |||
Age\(\le\)50 | 2138 (33.9%) | 2007 (30.2%) | 4145 (32.0%) |
50<Age\(\le\)65 | 1530 (24.3%) | 2061 (31.0%) | 3591 (27.7%) |
Age>65 | 2632 (41.8%) | 2573 (38.7%) | 5205 (40.2%) |
Race | |||
White, non-Hispanic | 3610 (57.3%) | 3961 (59.6%) | 7571 (58.5%) |
Black, non-Hispanic | 820 (13.0%) | 698 (10.5%) | 1518 (11.7%) |
Asian, non-Hispanic | 213 (3.4%) | 251 (3.8%) | 464 (3.6%) |
Hispanic | 1317 (20.9%) | 1341 (20.2%) | 2658 (20.5%) |
Other/Unknown | 340 (5.4%) | 390 (5.9%) | 730 (5.6%) |
BMI | |||
Normal (BMI<25) | 1368 (21.7%) | 1341 (20.2%) | 2709 (20.9%) |
Overweight (25\(\le\)BMI<30) | 1528 (24.3%) | 2050 (30.9%) | 3578 (27.6%) |
Obese (BMI\(\ge\)30) | 2502 (39.7%) | 2132 (32.1%) | 4634 (35.8%) |
Missing | 902 (14.3%) | 1118 (16.8%) | 2020 (15.6%) |
Deaths | |||
Number of deaths | 488 (7.7%) | 710 (10.7%) | 1198 (9.3%) |
Time (days) to death | 10.5 (5, 16) | 11 (6, 18) | 11 (6, 17) |
Time (days) in hospital | |||
Overall | 5 (3, 9) | 5 (3, 10) | 5 (3, 10) |
For dead within 30 days | 8 (4, 13) | 8 (5, 15) | 8 (4, 14) |
For alive and discharged within 30 days | 5 (3, 8) | 5 (3, 8) | 5 (3, 8) |
For alive and still in hospital after 30 days | 38.5 (33, 46.25) | 41 (34, 54) | 39.5 (34, 52.5) |
Data pre-processing
Statistical analysis
fdapace
package in R [26]. Based on the cumulative percentage of variance explained, we determined the number of FPCs (M) to adopt, resulting in \(K\times M\) exposure variables. Missing FPC scores were imputed using MICE
based on the FPC scores of all other biomarkers [27].SGL
package in R, we performed Cox SGL regression with the \(K\times M\) FPC scores as the exposure variables, while adjusting for J demographic characteristics \(Y_{ij}\) including race/ethnicity, age (indicator for \(>50\) years), and BMI (orthogonal polynomials of degree 2):MICE
package in R [27]. Analyses were again stratified by sex and adjusted for race/ethnicity, age, and BMI while accounting for the pathophysiological groupings of biomarkers.Simulation studies
\(\varvec{\alpha }_{\varvec{1}}\) | \(\varvec{\alpha }_{\varvec{2}}\) | \(\varvec{\alpha }_{\varvec{3}}\) | \(\varvec{\alpha }_{\varvec{4}}\) | |
---|---|---|---|---|
Model 1 (LME with a linear time trend) | ||||
Scenario 1 (low correlation) | 1 | 1 | 0 | 0 |
Scenario 2 (high correlation) | 0 | 0 | 1 | 1 |
Scenario 3 (both groups) | 1 | 1 | 1 | 1 |
Scenario 4 (null case) | 0 | 0 | 0 | 0 |
Scenario 5a (complete null case) | 0 | 0 | 0 | 0 |
Model 2 (LME with a quadratic term for time) | ||||
Scenario 1 (low correlation) | 1 | 1 | 0 | 0 |
Scenario 2 (high correlation) | 0 | 0 | 1 | 1 |
Scenario 3 (both groups) | 0.5 | 0.5 | 0.5 | 0.5 |
Scenario 4 (null case) | 0 | 0 | 0 | 0 |
Scenario 5a (complete null case) | 0 | 0 | 0 | 0 |
Model 3 (LME with a 3-knot spline function for time) | ||||
Scenario 1 (low correlation) | 1 | 1 | 0 | 0 |
Scenario 2 (high correlation) | 0 | 0 | 1 | 1 |
Scenario 3 (both groups) | 1 | 1 | 1 | 1 |
Scenario 4 (null case) | 0 | 0 | 0 | 0 |
Scenario 5a (complete null case) | 0 | 0 | 0 | 0 |
Results
Application using MGB cohort
Simulation studies
Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | |||
---|---|---|---|---|---|---|
TPR | FPR | TPR | FPR | TPR | FPR | |
A. Model 1 (LME with a linear time trend) | ||||||
A.1 Using baseline measures | ||||||
Group 1 | ||||||
Biomarker 1 | 100.0% | N/A | N/A | 10.0% | 100.0% | 14.0% |
Biomarker 2 | 100.0% | N/A | N/A | 10.0% | 100.0% | 14.5% |
Group 2 | ||||||
Biomarker 3 | N/A | 6.5% | 100.0% | N/A | 100.0% | 15.0% |
Biomarker 4 | N/A | 6.5% | 100.0% | N/A | 100.0% | 16.0% |
A.2 Using peak measures | ||||||
Group 1 | ||||||
Biomarker 1 | 100.0% | N/A | N/A | 5.0% | 100.0% | 18.0% |
Biomarker 2 | 100.0% | N/A | N/A | 5.0% | 100.0% | 17.5% |
Group 2 | ||||||
Biomarker 3 | N/A | 12.0% | 100.0% | N/A | 100.0% | 17.0% |
Biomarker 4 | N/A | 12.0% | 100.0% | N/A | 100.0% | 17.0% |
A.3 Using FPC scores | ||||||
Group 1 | ||||||
Biomarker 1 FPC1 | 100.0% | N/A | N/A | 0.0% | 100.0% | 9.0% |
Biomarker 1 FPC2 | 94.0% | N/A | N/A | 0.0% | 92.0% | 9.0% |
Biomarker 1 FPC3 | 90.5% | N/A | N/A | 0.0% | 92.5% | 9.0% |
Biomarker 2 FPC1 | 100.0% | N/A | N/A | 0.0% | 100.0% | 8.5% |
Biomarker 2 FPC2 | 93.5% | N/A | N/A | 0.0% | 93.5% | 9.0% |
Biomarker 2 FPC3 | 90.5% | N/A | N/A | 0.0% | 88.0% | 9.0% |
Group 2 | ||||||
Biomarker 3 FPC1 | N/A | 3.5% | 100.0% | N/A | 100.0% | 5.5% |
Biomarker 3 FPC2 | N/A | 3.0% | 92.5% | N/A | 91.5% | 5.5% |
Biomarker 3 FPC3 | N/A | 3.5% | 91.0% | N/A | 93.0% | 5.5% |
Biomarker 4 FPC1 | N/A | 3.5% | 100.0% | N/A | 100.0% | 5.5% |
Biomarker 4 FPC2 | N/A | 3.5% | 89.5% | N/A | 93.0% | 5.5% |
Biomarker 4 FPC3 | N/A | 3.5% | 91.5% | N/A | 87.0% | 5.5% |
B. Model 2 (LME with a quadratic term for time) | ||||||
B.1 Using baseline measures | ||||||
Group 1 | ||||||
Biomarker 1 | 100.0% | N/A | N/A | 21.0% | 99.0% | 15.5% |
Biomarker 2 | 100.0% | N/A | N/A | 21.0% | 99.0% | 15.5% |
Group 2 | ||||||
Biomarker 3 | N/A | 18.0% | 100.0% | N/A | 100.0% | 17.0% |
Biomarker 4 | N/A | 18.0% | 100.0% | N/A | 100.0% | 17.5% |
B.2 Using peak measures | ||||||
Group 1 | ||||||
Biomarker 1 | 100.0% | N/A | N/A | 22.0% | 98.0% | 14.0% |
Biomarker 2 | 100.0% | N/A | N/A | 22.0% | 98.0% | 13.5% |
Group 2 | ||||||
Biomarker 3 | N/A | 17.0% | 100.0% | N/A | 100.0% | 17.5% |
Biomarker 4 | N/A | 17.0% | 100.0% | N/A | 100.0% | 18.0% |
B.3 Using FPC scores | ||||||
Group 1 | ||||||
Biomarker 1 FPC1 | 100.0% | N/A | N/A | 0.0% | 98.5% | 12.0% |
Biomarker 1 FPC2 | 98.0% | N/A | N/A | 0.0% | 95.0% | 12.0% |
Biomarker 1 FPC3 | 90.0% | N/A | N/A | 0.0% | 87.5% | 11.5% |
Biomarker 2 FPC1 | 100.0% | N/A | N/A | 0.0% | 98.5% | 12.0% |
Biomarker 2 FPC2 | 96.0% | N/A | N/A | 0.0% | 89.5% | 12.0% |
Biomarker 2 FPC3 | 87.5% | N/A | N/A | 0.0% | 87.0% | 11.5% |
Group 2 | ||||||
Biomarker 3 FPC1 | N/A | 0.5% | 100.0% | N/A | 100.0% | 10.5% |
Biomarker 3 FPC2 | N/A | 0.5% | 97.0% | N/A | 95.0% | 10.5% |
Biomarker 3 FPC3 | N/A | 0.5% | 90.0% | N/A | 90.0% | 10.5% |
Biomarker 4 FPC1 | N/A | 0.5% | 100.0% | N/A | 100.0% | 10.5% |
Biomarker 4 FPC2 | N/A | 0.5% | 97.0% | N/A | 90.5% | 10.0% |
Biomarker 4 FPC3 | N/A | 0.5% | 89.0% | N/A | 92.5% | 10.5% |
C. Model 3 (LME with a 3-knot spline function for time) | ||||||
C.1 Using baseline measures | ||||||
Group 1 | ||||||
Biomarker 1 | 100.0% | N/A | N/A | 5.5% | 98.5% | 16.5% |
Biomarker 2 | 100.0% | N/A | N/A | 5.5% | 98.5% | 17.5% |
Group 2 | ||||||
Biomarker 3 | N/A | 5.5% | 100.0% | N/A | 100.0% | 16.0% |
Biomarker 4 | N/A | 5.5% | 100.0% | N/A | 100.0% | 16.0% |
C.2 Using peak measures | ||||||
Group 1 | ||||||
Biomarker 1 | 100.0% | N/A | N/A | 5.0% | 99.5% | 41.5% |
Biomarker 2 | 100.0% | N/A | N/A | 5.0% | 99.5% | 40.5% |
Group 2 | ||||||
Biomarker 3 | N/A | 10.0% | 100.0% | N/A | 100.0% | 40.5% |
Biomarker 4 | N/A | 10.0% | 100.0% | N/A | 100.0% | 40.5% |
C.3 Using FPC scores | ||||||
Group 1 | ||||||
Biomarker 1 FPC1 | 100.0% | N/A | N/A | 0.0% | 99.0% | 9.0% |
Biomarker 1 FPC2 | 95.0% | N/A | N/A | 0.0% | 89.5% | 8.5% |
Biomarker 1 FPC3 | 91.0% | N/A | N/A | 0.0% | 89.0% | 8.5% |
Biomarker 2 FPC1 | 100.0% | N/A | N/A | 0.0% | 99.0% | 8.5% |
Biomarker 2 FPC2 | 94.0% | N/A | N/A | 0.0% | 93.5% | 8.5% |
Biomarker 2 FPC3 | 95.5% | N/A | N/A | 0.0% | 90.5% | 8.5% |
Group 2 | ||||||
Biomarker 3 FPC1 | N/A | 3.5% | 100.0% | N/A | 100.0% | 8.0% |
Biomarker 3 FPC2 | N/A | 4.0% | 94.5% | N/A | 93.5% | 8.0% |
Biomarker 3 FPC3 | N/A | 4.0% | 88.5% | N/A | 88.5% | 8.0% |
Biomarker 4 FPC1 | N/A | 4.0% | 100.0% | N/A | 100.0% | 8.0% |
Biomarker 4 FPC2 | N/A | 4.0% | 96.5% | N/A | 92.5% | 7.5% |
Biomarker 4 FPC3 | N/A | 4.0% | 88.0% | N/A | 88.5% | 7.5% |