SVM Survival 072524
Karl Brown
2024-07-25
Table 1
|
BA (n=2341)
|
WA (n=1697)
|
|||
|---|---|---|---|---|
| Mean | SD | Mean | SD | |
| Age | 68.2 | 3.5 | 69.7 | 4.2 |
| % male | 94.3 |
|
95.9 |
|
| SVM risk score | -0.56 | 0.41 | -0.49 | 0.38 |
| % dementia incidence | 4.9 |
|
2.9 |
|
| % censored and alive | 78.3 |
|
77.2 |
|
| % censored and dead | 16.8 |
|
20.0 |
|
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
6-month outcome summaries
## # A tibble: 2 × 2
## Race overall
## <chr> <int>
## 1 AA 1300
## 2 EA 876## # A tibble: 6 × 5
## # Groups: Race [2]
## Race event_status2 total overall proportion
## <chr> <fct> <int> <int> <dbl>
## 1 AA censored 1038 1300 79.8
## 2 AA dementia 64 1300 4.92
## 3 AA death 198 1300 15.2
## 4 EA censored 678 876 77.4
## 5 EA dementia 28 876 3.20
## 6 EA death 170 876 19.4
1-year outcome summaries
## # A tibble: 2 × 2
## Race overall
## <chr> <int>
## 1 AA 2341
## 2 EA 1697## # A tibble: 6 × 5
## # Groups: Race [2]
## Race event_status2 total overall proportion
## <chr> <fct> <int> <int> <dbl>
## 1 AA censored 1834 2341 78.3
## 2 AA dementia 114 2341 4.87
## 3 AA death 393 2341 16.8
## 4 EA censored 1310 1697 77.2
## 5 EA dementia 50 1697 2.95
## 6 EA death 337 1697 19.9
Competing risks analysis (score quintiles)
6-month data
## Call:
## coxph(formula = Surv(time_to_event, event_status2) ~ score_group,
## data = surv_6m, id = X)
##
## n= 2176, number of events= 460
##
## coef exp(coef) se(coef) robust se z Pr(>|z|)
## score_group2_1:2 0.4779 1.6126 0.3852 0.3841 1.244 0.21346
## score_group3_1:2 0.1258 1.1340 0.4629 0.4624 0.272 0.78562
## score_group4_1:2 1.3188 3.7390 0.3485 0.3479 3.791 0.00015 ***
## score_group5_1:2 1.9354 6.9271 0.3128 0.3113 6.218 5.03e-10 ***
## score_group2_1:3 0.2641 1.3023 0.1752 0.1744 1.515 0.12981
## score_group3_1:3 0.7533 2.1241 0.1645 0.1648 4.571 4.85e-06 ***
## score_group4_1:3 0.6941 2.0020 0.1735 0.1734 4.003 6.25e-05 ***
## score_group5_1:3 1.2235 3.3990 0.1510 0.1505 8.128 4.36e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## score_group2_1:2 1.613 0.6201 0.7596 3.424
## score_group3_1:2 1.134 0.8818 0.4582 2.807
## score_group4_1:2 3.739 0.2675 1.8907 7.394
## score_group5_1:2 6.927 0.1444 3.7637 12.750
## score_group2_1:3 1.302 0.7679 0.9253 1.833
## score_group3_1:3 2.124 0.4708 1.5378 2.934
## score_group4_1:3 2.002 0.4995 1.4252 2.812
## score_group5_1:3 3.399 0.2942 2.5306 4.565
##
## Concordance= 0.64 (se = 0.013 )
## Likelihood ratio test= 131.3 on 8 df, p=<2e-16
## Wald test = 132.5 on 8 df, p=<2e-16
## Score (logrank) test = 151.4 on 8 df, p=<2e-16, Robust = 102.5 p=<2e-16
##
## (Note: the likelihood ratio and score tests assume independence of
## observations within a cluster, the Wald and robust score tests do not).## Warning: Removed 40 rows containing missing values (`geom_line()`).## Warning: Removed 368 rows containing missing values (`geom_point()`).## Warning: Removed 40 rows containing missing values (`geom_line()`).
## Removed 40 rows containing missing values (`geom_line()`).
## Removed 40 rows containing missing values (`geom_line()`).## Warning: Removed 92 rows containing missing values (`geom_point()`).## Warning: Removed 40 rows containing missing values (`geom_line()`).
## Removed 40 rows containing missing values (`geom_line()`).
1-year data
## Call:
## coxph(formula = Surv(time_to_event, event_status2) ~ score_group,
## data = surv_1y, id = X)
##
## n= 4038, number of events= 894
##
## coef exp(coef) se(coef) robust se z Pr(>|z|)
## score_group2_1:2 0.30579 1.35770 0.29518 0.29493 1.037 0.2998
## score_group3_1:2 -0.09707 0.90749 0.36411 0.36363 -0.267 0.7895
## score_group4_1:2 1.19695 3.31002 0.26505 0.26402 4.534 5.80e-06 ***
## score_group5_1:2 1.99864 7.37903 0.23584 0.23496 8.506 < 2e-16 ***
## score_group2_1:3 0.25681 1.29280 0.12759 0.12696 2.023 0.0431 *
## score_group3_1:3 0.63809 1.89287 0.12433 0.12440 5.129 2.91e-07 ***
## score_group4_1:3 0.92488 2.52157 0.11958 0.11914 7.763 8.29e-15 ***
## score_group5_1:3 1.32238 3.75235 0.11161 0.11142 11.869 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## score_group2_1:2 1.3577 0.7365 0.7617 2.420
## score_group3_1:2 0.9075 1.1019 0.4450 1.851
## score_group4_1:2 3.3100 0.3021 1.9729 5.553
## score_group5_1:2 7.3790 0.1355 4.6558 11.695
## score_group2_1:3 1.2928 0.7735 1.0080 1.658
## score_group3_1:3 1.8929 0.5283 1.4833 2.416
## score_group4_1:3 2.5216 0.3966 1.9965 3.185
## score_group5_1:3 3.7524 0.2665 3.0162 4.668
##
## Concordance= 0.649 (se = 0.009 )
## Likelihood ratio test= 289.2 on 8 df, p=<2e-16
## Wald test = 290.4 on 8 df, p=<2e-16
## Score (logrank) test = 341.8 on 8 df, p=<2e-16, Robust = 220.1 p=<2e-16
##
## (Note: the likelihood ratio and score tests assume independence of
## observations within a cluster, the Wald and robust score tests do not).
Competing risks analysis (continuous risk scores)
6-month data
## Call:
## coxph(formula = Surv(time_to_event, event_status2) ~ Score, data = surv_6m,
## id = X)
##
## n= 2176, number of events= 460
##
## coef exp(coef) se(coef) robust se z Pr(>|z|)
## Score_1:2 1.6831 5.3823 0.1953 0.1867 9.017 <2e-16 ***
## Score_1:3 0.9965 2.7088 0.1100 0.1051 9.481 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score_1:2 5.382 0.1858 3.733 7.760
## Score_1:3 2.709 0.3692 2.205 3.328
##
## Concordance= 0.645 (se = 0.013 )
## Likelihood ratio test= 132.7 on 2 df, p=<2e-16
## Wald test = 164.7 on 2 df, p=<2e-16
## Score (logrank) test = 161.8 on 2 df, p=<2e-16, Robust = 93.36 p=<2e-16
##
## (Note: the likelihood ratio and score tests assume independence of
## observations within a cluster, the Wald and robust score tests do not).## Warning: Removed 40 rows containing missing values (`geom_line()`).## Warning: Removed 368 rows containing missing values (`geom_point()`).## Warning: Removed 40 rows containing missing values (`geom_line()`).
## Removed 40 rows containing missing values (`geom_line()`).
## Removed 40 rows containing missing values (`geom_line()`).## Warning: Removed 92 rows containing missing values (`geom_point()`).## Warning: Removed 40 rows containing missing values (`geom_line()`).
## Removed 40 rows containing missing values (`geom_line()`).
1-year data
## Call:
## coxph(formula = Surv(time_to_event, event_status2) ~ Score, data = surv_1y,
## id = X)
##
## n= 4038, number of events= 894
##
## coef exp(coef) se(coef) robust se z Pr(>|z|)
## Score_1:2 1.74250 5.71161 0.14606 0.14178 12.29 <2e-16 ***
## Score_1:3 1.07789 2.93848 0.07768 0.07562 14.25 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score_1:2 5.712 0.1751 4.326 7.541
## Score_1:3 2.938 0.3403 2.534 3.408
##
## Concordance= 0.651 (se = 0.01 )
## Likelihood ratio test= 281.8 on 2 df, p=<2e-16
## Wald test = 337.2 on 2 df, p=<2e-16
## Score (logrank) test = 347.5 on 2 df, p=<2e-16, Robust = 188.4 p=<2e-16
##
## (Note: the likelihood ratio and score tests assume independence of
## observations within a cluster, the Wald and robust score tests do not).
Dementia only analysis
6-month data
## Call:
## coxph(formula = Surv(time_to_event, event_status) ~ score_group,
## data = surv_6m_demonly, id = X)
##
## n= 2176, number of events= 92
##
## coef exp(coef) se(coef) z Pr(>|z|)
## score_group2 0.4779 1.6126 0.3852 1.241 0.214733
## score_group3 0.1258 1.1340 0.4629 0.272 0.785867
## score_group4 1.3188 3.7390 0.3485 3.784 0.000154 ***
## score_group5 1.9354 6.9271 0.3128 6.187 6.12e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## score_group2 1.613 0.6201 0.7580 3.431
## score_group3 1.134 0.8818 0.4577 2.810
## score_group4 3.739 0.2675 1.8885 7.403
## score_group5 6.927 0.1444 3.7522 12.789
##
## Concordance= 0.707 (se = 0.028 )
## Likelihood ratio test= 56.37 on 4 df, p=2e-11
## Wald test = 55.64 on 4 df, p=2e-11
## Score (logrank) test = 69.6 on 4 df, p=3e-14
1-year data
## Call:
## coxph(formula = Surv(time_to_event2, event_status2) ~ score_group,
## data = surv_1y_demonly, id = X)
##
## n= 4038, number of events= 163
##
## coef exp(coef) se(coef) z Pr(>|z|)
## score_group2 0.32537 1.38455 0.29517 1.102 0.270
## score_group3 -0.09433 0.90999 0.36412 -0.259 0.796
## score_group4 1.20397 3.33333 0.26505 4.542 5.56e-06 ***
## score_group5 1.98396 7.27150 0.23623 8.398 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## score_group2 1.385 0.7223 0.7764 2.469
## score_group3 0.910 1.0989 0.4458 1.858
## score_group4 3.333 0.3000 1.9827 5.604
## score_group5 7.272 0.1375 4.5766 11.553
##
## Concordance= 0.718 (se = 0.021 )
## Likelihood ratio test= 112.8 on 4 df, p=<2e-16
## Wald test = 113 on 4 df, p=<2e-16
## Score (logrank) test = 145.7 on 4 df, p=<2e-16## Call:
## coxph(formula = Surv(time_to_event2, event_status2) ~ ScoreIQR +
## Race, data = surv_1y_demonly, id = X)
##
## n= 4038, number of events= 163
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ScoreIQR 0.78917 2.20156 0.06643 11.880 < 2e-16 ***
## RaceEA -0.55743 0.57268 0.16990 -3.281 0.00103 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ScoreIQR 2.2016 0.4542 1.9328 2.508
## RaceEA 0.5727 1.7462 0.4105 0.799
##
## Concordance= 0.733 (se = 0.021 )
## Likelihood ratio test= 122.9 on 2 df, p=<2e-16
## Wald test = 150.3 on 2 df, p=<2e-16
## Score (logrank) test = 161.8 on 2 df, p=<2e-16## Call:
## coxph(formula = Surv(time_to_event2, event_status2) ~ ScoreIQR +
## Race_flipped, data = surv_1y_demonly, id = X)
##
## n= 4038, number of events= 163
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ScoreIQR 0.78917 2.20156 0.06643 11.880 < 2e-16 ***
## Race_flippedAA 0.55743 1.74618 0.16990 3.281 0.00103 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ScoreIQR 2.202 0.4542 1.933 2.508
## Race_flippedAA 1.746 0.5727 1.252 2.436
##
## Concordance= 0.733 (se = 0.021 )
## Likelihood ratio test= 122.9 on 2 df, p=<2e-16
## Wald test = 150.3 on 2 df, p=<2e-16
## Score (logrank) test = 161.8 on 2 df, p=<2e-16## chisq df p
## ScoreIQR 2.454 1 0.12
## Race 0.654 1 0.42
## GLOBAL 3.072 2 0.22
Death and dementia as the same outcome analysis
6-month data
## Call:
## coxph(formula = Surv(time_to_event, event_status) ~ score_group,
## data = surv_6m_both, id = X)
##
## n= 2161, number of events= 454
##
## coef exp(coef) se(coef) z Pr(>|z|)
## score_group2 0.2873 1.3328 0.1600 1.796 0.0726 .
## score_group3 0.6500 1.9156 0.1552 4.187 2.83e-05 ***
## score_group4 0.8312 2.2961 0.1542 5.391 7.02e-08 ***
## score_group5 1.3500 3.8576 0.1354 9.970 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## score_group2 1.333 0.7503 0.974 1.824
## score_group3 1.916 0.5220 1.413 2.597
## score_group4 2.296 0.4355 1.697 3.106
## score_group5 3.858 0.2592 2.958 5.030
##
## Concordance= 0.636 (se = 0.013 )
## Likelihood ratio test= 113.2 on 4 df, p=<2e-16
## Wald test = 115.8 on 4 df, p=<2e-16
## Score (logrank) test = 127.8 on 4 df, p=<2e-16
1-year data
## Call:
## coxph(formula = Surv(time_to_event, event_status) ~ score_group,
## data = surv_1y_both, id = X)
##
## n= 4038, number of events= 893
##
## coef exp(coef) se(coef) z Pr(>|z|)
## score_group2 0.2646 1.3029 0.1171 2.260 0.0238 *
## score_group3 0.5553 1.7425 0.1169 4.751 2.02e-06 ***
## score_group4 0.9718 2.6428 0.1089 8.926 < 2e-16 ***
## score_group5 1.4556 4.2871 0.1002 14.527 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## score_group2 1.303 0.7675 1.036 1.639
## score_group3 1.743 0.5739 1.386 2.191
## score_group4 2.643 0.3784 2.135 3.271
## score_group5 4.287 0.2333 3.523 5.217
##
## Concordance= 0.647 (se = 0.009 )
## Likelihood ratio test= 263.5 on 4 df, p=<2e-16
## Wald test = 270.8 on 4 df, p=<2e-16
## Score (logrank) test = 303.4 on 4 df, p=<2e-16## chisq df p
## score_group 7.29 4 0.12
## GLOBAL 7.29 4 0.12
Setting all those who died to the maximum censoring time
6-month data
## Call:
## coxph(formula = Surv(time_to_event, event_status) ~ score_group,
## data = surv_6m_deathmax, id = X)
##
## n= 2161, number of events= 92
##
## coef exp(coef) se(coef) z Pr(>|z|)
## score_group2 0.47204 1.60326 0.38517 1.226 0.220370
## score_group3 0.03814 1.03887 0.46292 0.082 0.934344
## score_group4 1.24946 3.48847 0.34847 3.586 0.000336 ***
## score_group5 1.77152 5.87978 0.31266 5.666 1.46e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## score_group2 1.603 0.6237 0.7536 3.411
## score_group3 1.039 0.9626 0.4193 2.574
## score_group4 3.488 0.2867 1.7620 6.906
## score_group5 5.880 0.1701 3.1858 10.852
##
## Concordance= 0.696 (se = 0.028 )
## Likelihood ratio test= 48.89 on 4 df, p=6e-10
## Wald test = 47.47 on 4 df, p=1e-09
## Score (logrank) test = 57.58 on 4 df, p=9e-12
1-year data
## Call:
## coxph(formula = Surv(time_to_event, event_status) ~ score_group,
## data = surv_1y_deathmax, id = X)
##
## n= 4038, number of events= 164
##
## coef exp(coef) se(coef) z Pr(>|z|)
## score_group2 0.3039 1.3552 0.2952 1.030 0.303
## score_group3 -0.1637 0.8490 0.3641 -0.450 0.653
## score_group4 1.0981 2.9986 0.2650 4.143 3.42e-05 ***
## score_group5 1.7979 6.0368 0.2357 7.627 2.40e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## score_group2 1.355 0.7379 0.7599 2.417
## score_group3 0.849 1.1779 0.4159 1.733
## score_group4 2.999 0.3335 1.7837 5.041
## score_group5 6.037 0.1657 3.8033 9.582
##
## Concordance= 0.705 (se = 0.021 )
## Likelihood ratio test= 96.64 on 4 df, p=<2e-16
## Wald test = 95.25 on 4 df, p=<2e-16
## Score (logrank) test = 118.2 on 4 df, p=<2e-16Summarizing
Censoring date = most recent visit before 09/12/23
## Analysis Data Estimate Lower.CI Upper.CI Estimate.2 Lower.CI2
## 1 Competing risks 6m 5.263 3.658 7.573 2.672 2.17568336809375
## 2 Competing risks 1y 5.602 4.247 7.390 2.901 2.50215717257962
## 3 Dementia only 6m 5.382 3.671 7.892 - -
## 4 Dementia only 1y 5.627 4.220 7.503 - -
## 5 Dementia/death 6m 3.120 2.583 3.770 - -
## 6 Dementia/death 1y 3.345 2.925 3.826 - -
## 7 Deaths as max 6m 4.433 3.063 6.415 - -
## 8 Deaths as max 1y 4.440 3.374 5.843 - -
## Upper.CI2
## 1 3.28
## 2 3.364
## 3 -
## 4 -
## 5 -
## 6 -
## 7 -
## 8 -
Worse case sensitivity analyses
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Race as an effect modifier or confounder
## Call:
## coxph(formula = Surv(time_to_event2, event_status2) ~ Score +
## Race + Score:Race, data = surv_1y_demonly, id = X)
##
## n= 4038, number of events= 163
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Score 1.6170 5.0380 0.1734 9.324 < 2e-16 ***
## RaceEA -0.4961 0.6089 0.1777 -2.792 0.00524 **
## Score:RaceEA 0.3501 1.4192 0.3137 1.116 0.26440
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score 5.0380 0.1985 3.5862 7.0776
## RaceEA 0.6089 1.6423 0.4298 0.8626
## Score:RaceEA 1.4192 0.7046 0.7674 2.6248
##
## Concordance= 0.735 (se = 0.02 )
## Likelihood ratio test= 124.1 on 3 df, p=<2e-16
## Wald test = 147.1 on 3 df, p=<2e-16
## Score (logrank) test = 163.1 on 3 df, p=<2e-16## Analysis of Deviance Table
## Cox model: response is Surv(time_to_event2, event_status2)
## Terms added sequentially (first to last)
##
## loglik Chisq Df Pr(>|Chi|)
## NULL -1316.5
## Score -1260.8 111.4418 1 < 2.2e-16 ***
## Race -1255.1 11.4423 1 0.0007179 ***
## Score:Race -1254.5 1.2278 1 0.2678312
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Call:
## coxph(formula = Surv(time_to_event2, event_status2) ~ Score +
## Race, data = surv_1y_demonly, id = X)
##
## n= 4038, number of events= 163
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Score 1.7197 5.5828 0.1448 11.880 < 2e-16 ***
## RaceEA -0.5574 0.5727 0.1699 -3.281 0.00103 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score 5.5828 0.1791 4.2037 7.414
## RaceEA 0.5727 1.7462 0.4105 0.799
##
## Concordance= 0.733 (se = 0.021 )
## Likelihood ratio test= 122.9 on 2 df, p=<2e-16
## Wald test = 150.3 on 2 df, p=<2e-16
## Score (logrank) test = 161.8 on 2 df, p=<2e-16## Call:
## coxph(formula = Surv(time_to_event2, event_status2) ~ quintile_new +
## Race + quintile_new:Race, data = surv_1y_demonly, id = X)
##
## n= 4038, number of events= 163
##
## coef exp(coef) se(coef) z Pr(>|z|)
## quintile_new2 0.2060 1.2287 0.3780 0.545 0.58575
## quintile_new3 0.1459 1.1570 0.3934 0.371 0.71079
## quintile_new4 0.9139 2.4940 0.3390 2.696 0.00702 **
## quintile_new5 1.7535 5.7747 0.3025 5.797 6.74e-09 ***
## RaceEA -1.0204 0.3604 0.7559 -1.350 0.17705
## quintile_new2:RaceEA -0.1745 0.8398 0.9880 -0.177 0.85978
## quintile_new3:RaceEA 0.6701 1.9544 0.8931 0.750 0.45309
## quintile_new4:RaceEA 0.0298 1.0303 0.8602 0.035 0.97236
## quintile_new5:RaceEA 0.7240 2.0627 0.7904 0.916 0.35967
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## quintile_new2 1.2287 0.8138 0.58578 2.577
## quintile_new3 1.1571 0.8643 0.53516 2.502
## quintile_new4 2.4940 0.4010 1.28335 4.847
## quintile_new5 5.7747 0.1732 3.19206 10.447
## RaceEA 0.3604 2.7744 0.08192 1.586
## quintile_new2:RaceEA 0.8398 1.1907 0.12111 5.824
## quintile_new3:RaceEA 1.9544 0.5117 0.33947 11.252
## quintile_new4:RaceEA 1.0303 0.9706 0.19088 5.561
## quintile_new5:RaceEA 2.0627 0.4848 0.43815 9.711
##
## Concordance= 0.723 (se = 0.02 )
## Likelihood ratio test= 111.5 on 9 df, p=<2e-16
## Wald test = 104.7 on 9 df, p=<2e-16
## Score (logrank) test = 137 on 9 df, p=<2e-16## Analysis of Deviance Table
## Cox model: response is Surv(time_to_event2, event_status2)
## Terms added sequentially (first to last)
##
## loglik Chisq Df Pr(>|Chi|)
## NULL -1316.5
## quintile_new -1268.6 95.9265 4 < 2.2e-16 ***
## Race -1262.8 11.4329 1 0.0007216 ***
## quintile_new:Race -1260.8 4.1854 4 0.3814943
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Call:
## coxph(formula = Surv(time_to_event2, event_status2) ~ quintile_new,
## data = surv_1y_demonly[surv_1y_demonly$Race == "AA", ], id = X)
##
## n= 2341, number of events= 113
##
## coef exp(coef) se(coef) z Pr(>|z|)
## quintile_new2 0.2068 1.2297 0.3780 0.547 0.58430
## quintile_new3 0.1465 1.1578 0.3934 0.373 0.70952
## quintile_new4 0.9146 2.4958 0.3390 2.698 0.00697 **
## quintile_new5 1.7572 5.7964 0.3025 5.809 6.28e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## quintile_new2 1.230 0.8132 0.5862 2.580
## quintile_new3 1.158 0.8637 0.5355 2.503
## quintile_new4 2.496 0.4007 1.2843 4.850
## quintile_new5 5.796 0.1725 3.2038 10.487
##
## Concordance= 0.688 (se = 0.026 )
## Likelihood ratio test= 58.44 on 4 df, p=6e-12
## Wald test = 60.3 on 4 df, p=3e-12
## Score (logrank) test = 72.91 on 4 df, p=6e-15## Call:
## coxph(formula = Surv(time_to_event2, event_status2) ~ quintile_new,
## data = surv_1y_demonly[surv_1y_demonly$Race == "EA", ], id = X)
##
## n= 1697, number of events= 50
##
## coef exp(coef) se(coef) z Pr(>|z|)
## quintile_new2 0.03149 1.03199 0.91288 0.034 0.972485
## quintile_new3 0.81552 2.26035 0.80179 1.017 0.309091
## quintile_new4 0.94234 2.56599 0.79059 1.192 0.233280
## quintile_new5 2.46875 11.80768 0.73041 3.380 0.000725 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## quintile_new2 1.032 0.96900 0.1724 6.176
## quintile_new3 2.260 0.44241 0.4696 10.881
## quintile_new4 2.566 0.38971 0.5449 12.084
## quintile_new5 11.808 0.08469 2.8212 49.418
##
## Concordance= 0.743 (se = 0.034 )
## Likelihood ratio test= 45.01 on 4 df, p=4e-09
## Wald test = 41.75 on 4 df, p=2e-08
## Score (logrank) test = 57.95 on 4 df, p=8e-12
Grace period analysis
6-month data
## Call:
## coxph(formula = Surv(time_to_event_grace, event_status) ~ Score,
## data = surv_6m_demonly_grace, id = X)
##
## n= 2164, number of events= 92
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Score 1.6809 5.3702 0.1951 8.617 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score 5.37 0.1862 3.664 7.871
##
## Concordance= 0.713 (se = 0.029 )
## Likelihood ratio test= 60.94 on 1 df, p=6e-15
## Wald test = 74.26 on 1 df, p=<2e-16
## Score (logrank) test = 78.71 on 1 df, p=<2e-16
1-year data
## Call:
## coxph(formula = Surv(time_to_event_grace, event_status) ~ Score,
## data = surv_1y_demonly_grace, id = X)
##
## n= 3981, number of events= 163
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Score 1.735 5.669 0.147 11.8 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score 5.669 0.1764 4.25 7.562
##
## Concordance= 0.715 (se = 0.022 )
## Likelihood ratio test= 113.6 on 1 df, p=<2e-16
## Wald test = 139.3 on 1 df, p=<2e-16
## Score (logrank) test = 148.7 on 1 df, p=<2e-16
## Analysis Data Estimate Lower.CI Upper.CI
## 1 Dementia only 6m 5.382 3.671 7.892
## 2 Dementia only 1y 5.627 4.220 7.503
## 3 Grace period 6m 5.370 3.664 7.871
## 4 Grace period 1y 5.669 4.250 7.562Assessing nonlinearity
surv_1y_demonly$Score2 <- surv_1y_demonly$Score^2
surv_1y_demonly$Score3 <- surv_1y_demonly$Score^3
ggcoxfunctional(Surv(time_to_event2, event_status2) ~ Score + Score2 + Score3, id = X, data = surv_1y_demonly)## Warning: arguments formula is deprecated; will be removed in the next version;
## please use fit instead.
summary(surv_1y_demonly$Score)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -1.5608 -0.8060 -0.6073 -0.5320 -0.3471 1.6023
## Call:
## coxph(formula = Surv(time_to_event2, event_status) ~ Score +
## Score2, data = surv_6m, id = X)
##
## n= 2176, number of events= 460
##
## coef exp(coef) se(coef) robust se z Pr(>|z|)
## Score_1:2 1.6235 5.0707 0.2105 0.2038 7.966 1.64e-15 ***
## Score2_1:2 -0.2846 0.7523 0.3421 0.3497 -0.814 0.4158
## Score_1:3 0.8145 2.2580 0.1458 0.1562 5.216 1.83e-07 ***
## Score2_1:3 -0.4319 0.6493 0.2005 0.2227 -1.939 0.0525 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score_1:2 5.0707 0.1972 3.4009 7.560
## Score2_1:2 0.7523 1.3292 0.3791 1.493
## Score_1:3 2.2580 0.4429 1.6627 3.067
## Score2_1:3 0.6493 1.5402 0.4196 1.005
##
## Concordance= 0.646 (se = 0.013 )
## Likelihood ratio test= 136.3 on 4 df, p=<2e-16
## Wald test = 143.3 on 4 df, p=<2e-16
## Score (logrank) test = 174.1 on 4 df, p=<2e-16, Robust = 103.2 p=<2e-16
##
## (Note: the likelihood ratio and score tests assume independence of
## observations within a cluster, the Wald and robust score tests do not).## Call:
## coxph(formula = Surv(time_to_event2, event_status) ~ Score +
## Score2, data = surv_1y, id = X)
##
## n= 4038, number of events= 894
##
## coef exp(coef) se(coef) robust se z Pr(>|z|)
## Score_1:2 1.69494 5.44634 0.15567 0.15340 11.049 <2e-16 ***
## Score2_1:2 -0.29406 0.74523 0.26266 0.27193 -1.081 0.2795
## Score_1:3 0.97530 2.65196 0.09375 0.09671 10.085 <2e-16 ***
## Score2_1:3 -0.27995 0.75582 0.13588 0.15123 -1.851 0.0642 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score_1:2 5.4463 0.1836 4.0321 7.357
## Score2_1:2 0.7452 1.3419 0.4373 1.270
## Score_1:3 2.6520 0.3771 2.1941 3.205
## Score2_1:3 0.7558 1.3231 0.5619 1.017
##
## Concordance= 0.652 (se = 0.01 )
## Likelihood ratio test= 283.4 on 4 df, p=<2e-16
## Wald test = 293.8 on 4 df, p=<2e-16
## Score (logrank) test = 379.4 on 4 df, p=<2e-16, Robust = 201.7 p=<2e-16
##
## (Note: the likelihood ratio and score tests assume independence of
## observations within a cluster, the Wald and robust score tests do not).## Call:
## coxph(formula = Surv(time_to_event, event_status) ~ Score + Score2,
## data = surv_6m_demonly, id = X)
##
## n= 2176, number of events= 92
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Score 1.6495 5.2041 0.2105 7.837 4.62e-15 ***
## Score2 -0.2582 0.7724 0.3406 -0.758 0.448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score 5.2041 0.1922 3.4450 7.861
## Score2 0.7724 1.2947 0.3962 1.506
##
## Concordance= 0.714 (se = 0.029 )
## Likelihood ratio test= 61.59 on 2 df, p=4e-14
## Wald test = 68.47 on 2 df, p=1e-15
## Score (logrank) test = 95.42 on 2 df, p=<2e-16## Call:
## coxph(formula = Surv(time_to_event, event_status) ~ Score + Score2,
## data = surv_1y_demonly, id = X)
##
## n= 4038, number of events= 163
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Score 1.6998 5.4728 0.1568 10.843 <2e-16 ***
## Score2 -0.2728 0.7612 0.2635 -1.035 0.3
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score 5.4728 0.1827 4.0251 7.441
## Score2 0.7612 1.3137 0.4541 1.276
##
## Concordance= 0.715 (se = 0.023 )
## Likelihood ratio test= 113.9 on 2 df, p=<2e-16
## Wald test = 127.6 on 2 df, p=<2e-16
## Score (logrank) test = 180.4 on 2 df, p=<2e-16## Call:
## coxph(formula = Surv(time_to_event, event_status) ~ Score + Score2,
## data = surv_6m_both, id = X)
##
## n= 2161, number of events= 454
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Score 1.0292 2.7989 0.1194 8.620 <2e-16 ***
## Score2 -0.3254 0.7222 0.1706 -1.908 0.0565 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score 2.7989 0.3573 2.2149 3.537
## Score2 0.7222 1.3846 0.5169 1.009
##
## Concordance= 0.644 (se = 0.013 )
## Likelihood ratio test= 123.6 on 2 df, p=<2e-16
## Wald test = 128.6 on 2 df, p=<2e-16
## Score (logrank) test = 145.8 on 2 df, p=<2e-16## Call:
## coxph(formula = Surv(time_to_event, event_status) ~ Score + Score2,
## data = surv_1y_both, id = X)
##
## n= 4038, number of events= 893
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Score 1.14445 3.14070 0.07925 14.441 <2e-16 ***
## Score2 -0.23112 0.79364 0.11886 -1.944 0.0518 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score 3.1407 0.3184 2.6889 3.668
## Score2 0.7936 1.2600 0.6287 1.002
##
## Concordance= 0.651 (se = 0.01 )
## Likelihood ratio test= 268.1 on 2 df, p=<2e-16
## Wald test = 291.2 on 2 df, p=<2e-16
## Score (logrank) test = 339.8 on 2 df, p=<2e-16## Call:
## coxph(formula = Surv(time_to_event, event_status) ~ Score + Score2,
## data = surv_6m_deathmax, id = X)
##
## n= 2161, number of events= 92
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Score 1.4708 4.3528 0.2064 7.126 1.03e-12 ***
## Score2 -0.3356 0.7149 0.3081 -1.089 0.276
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score 4.3528 0.2297 2.9046 6.523
## Score2 0.7149 1.3988 0.3909 1.308
##
## Concordance= 0.701 (se = 0.029 )
## Likelihood ratio test= 51.87 on 2 df, p=5e-12
## Wald test = 55.36 on 2 df, p=1e-12
## Score (logrank) test = 72.74 on 2 df, p=<2e-16## Call:
## coxph(formula = Surv(time_to_event, event_status) ~ Score + Score2,
## data = surv_1y_deathmax, id = X)
##
## n= 4038, number of events= 164
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Score 1.4816 4.3998 0.1535 9.655 <2e-16 ***
## Score2 -0.3953 0.6735 0.2395 -1.651 0.0988 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score 4.3998 0.2273 3.2570 5.944
## Score2 0.6735 1.4849 0.4212 1.077
##
## Concordance= 0.7 (se = 0.023 )
## Likelihood ratio test= 94.56 on 2 df, p=<2e-16
## Wald test = 99.86 on 2 df, p=<2e-16
## Score (logrank) test = 131.1 on 2 df, p=<2e-16
## Call:
## coxph(formula = Surv(time_to_event, event_status) ~ Score + Score2,
## data = surv_1y_demonly_ba, id = X)
##
## n= 2341, number of events= 113
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Score 1.6015 4.9603 0.1896 8.449 <2e-16 ***
## Score2 -0.2015 0.8175 0.3063 -0.658 0.511
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score 4.9603 0.2016 3.4210 7.192
## Score2 0.8175 1.2232 0.4485 1.490
##
## Concordance= 0.704 (se = 0.027 )
## Likelihood ratio test= 72.76 on 2 df, p=<2e-16
## Wald test = 82.66 on 2 df, p=<2e-16
## Score (logrank) test = 113.9 on 2 df, p=<2e-16## Call:
## coxph(formula = Surv(time_to_event, event_status) ~ Score + Score2,
## data = surv_1y_demonly_wa, id = X)
##
## n= 1697, number of events= 50
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Score 2.0120 7.4781 0.3004 6.697 2.12e-11 ***
## Score2 -0.8579 0.4241 0.5560 -1.543 0.123
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Score 7.4781 0.1337 4.1503 13.474
## Score2 0.4241 2.3582 0.1426 1.261
##
## Concordance= 0.763 (se = 0.036 )
## Likelihood ratio test= 47.96 on 2 df, p=4e-11
## Wald test = 46.98 on 2 df, p=6e-11
## Score (logrank) test = 71.69 on 2 df, p=3e-16