Submitted:
01 April 2025
Posted:
02 April 2025
You are already at the latest version
Abstract
Keywords:
1. Introduction
2. Methods
2.1. Dataset and Patients
2.2. Recurrence
2.3. Deep Learning Predictive Modeling
Discrete Time-to-Event Data

Experiments
3. Results
3.1. Patient Characteristics
3.2. Predictive Modeling of Recurrence-Free Survival
4. Discussion
5. Conclusions
Institutional Review Board Statement
Acknowledgments
References
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| Algorithm 1: ALGORITHM TO INFER PATIENT'S RECURRENCE | |||||
|---|---|---|---|---|---|
|
Input:Window_after_completion_of_adjuvant_therapy=4 Month 2nd_Mal_Neop_BC_dx=19881 SRG=["8511","8512","850","8519","8520","8521","8522","8523","8525","8591","860d1", "8533","8534", "8535","8536","4022","4023","4029","403","4050","4051","8541","8542","8543","8544","8545","8546","8547","8548] PR=["9221","9222","9223","9224","9225","9226","9227","9228","9229","9230","9231","9232","9233","9239","9241"] TR=["G9829","1","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17","18","19","20", "21","22", "23","24","25","26","27","28","29","30","31","32","33","34","35","36","37","38","39","40","41","42","43","44","45","46"] |
|||||
|
Output:For Each Patient: Infer her/his Rec_flag and the corresponding Rec_Date |
|||||
|
1 2 |
Initialization: New_Chem_Hor_Bio_Rad_List=[], Mal_Neop_List=[], New_Contralat_List=[], No_Rec_Date←“2050-01-01” |
||||
| 3 | For Each Patient | ||||
|
4 5 6 7 8 9 10 |
Rec_flag← 0, Rec_Date← No_Rec_Date Identify: Date_1st_Chem, Date_1st Hor, Date_1st Bio, Date_1st Rad, Date_1st_Sur, Date_1st_Course_Tr Date_Init_Adj_Therapy←Max{Date_1st_Chem, Date_1st Hor, Date_1st Bio, Date_1st Rad, Date_1st_Sur, Date_1st_Course_Tr } Order visits in ascending order of Visit_Date |
||||
| 11 | For Each Visit | ||||
| 12 | For Each Entry within this Visit | ||||
|
13 14 |
If ( (Visit_Date-Date_Init_Adj_Therapy) >=4mon) And (Sur OR Bio OR Hor OR Rad) |
||||
| 15 | Rec_flag← 1 | ||||
|
16 17 |
Rec_Date ← VisitDate Break |
||||
| 18 | If (Rec_flag = 1) | ||||
|
19 20 21 |
Append this Patient to New_Chem_Hor_Bio_Rad_List Rec_flag ← 0, Rec_Date ← No_Rec_Date |
||||
| 22 | For Each Visit | ||||
| 23 | For Each Entry within this Visit | ||||
| 24 | If (dx_code=2nd_Mal_Neop_BC_dx) | ||||
| 25 | Rec_flag← 1 | ||||
| 26 | If ( (Rec_flag =1 & (Visit_Date < Rec_Date) ) | ||||
| 27 | Rec_Date← Visit_Date | ||||
| 28 | If (Rec_flag = 1) | ||||
|
29 30 31 |
Append this Patient to Mal_Neop_List Rec_flag ← 0, Rec_Date ← No_Rec_Date |
||||
| 32 | For Each of the Ten Recorded Diagnoses | ||||
| 33 | If Diagnosis =1 | ||||
|
34 35 36 |
Prev_Laterality=Current_Laterality Rec_flag← 0 Date_of_Prev_diagnosis ← No_Rec_Date |
||||
|
37 38 |
If ( ((Current_Laterality).isin(2,4,5,9)) & (Prev_Laterality)=1)) OR ((Current_Laterality).isin(1,4,5,9)) & (Prev_Laterality)=2)) ) |
||||
|
39 40 |
Rec_flag1← 1 If (Date_of_this_Diagnosis < Date_of_Prev_Diagnosis) |
||||
| 41 | Rec_Date← Date_of_this_Diagnosis | ||||
| 42 | Date_of_Prev_Diagnosis← Date_of_this_Diagnosis | ||||
| 43 | If (Rec_flag = 1) | ||||
|
44 45 46 |
Append this Patient to New_Contralat_List Rec_flag← 0, Rec_Date← No_Rec_Date |
||||
| 47 | If (patient isin New_Chem_Hor_Bio_Rad_List OR isin Mal_Neop_List OR isin New_Contralat_List)) | ||||
|
48 49 50 |
Rec_flag← 0, Rec_Date← Min{Patient’s Rec_Date in New_Chem_Hor_Bio_Rad_List, Patient’s Rec_Date in Mal_Neop_List, Patient’s Rec_Date in New_Contralat_List} |
||||
| All Patients | All patients with Anxiety/Depression | |||||||
|---|---|---|---|---|---|---|---|---|
| Number (%) | Age + SD | Comorbidity at Dx + SD | Number (%) | p (chi sq) | Age + SD | Comorbidity at Dx + SD | Mos, Dx-Dep/anx Avg+ SD |
|
| Total Patients | 239,288 (100) | 75.2 + 7.2 | 0.6 + 1.5 | 86,745 (100) (36.3% of all) | 75.4 + 7.0 | 0.7 + 1.7 | 31.4 + 48.0 | |
| ER+/PR+ | 154,730 (64.7) | 75.1 + 7.1 | 0.7 + 1.5 | 55,681 (64.2) | n.s. | 75.3 + 7.0 | 0.8 + 1.7 | 29.9 + 46.6 |
| ER+/PR- | 29,278 (12.2) | 75.6 + 7.3 | 0.6 + 1.5 | 10,775 (12.4) | 75.7 + 7.1 | 0.7 + 1.6 | 31.8 + 47.6 | |
| ER-/PR- | 32,400 (13.5) | 74.8 + 7.2 | 0.6 + 1.5 | 11,505 (13.3) | 75.0 + 7.1 | 0.7 + 1.7 | 28.3 + 46.3 | |
| Stage I | 134,598 (56.2) | 74.7 + 6.8 | 0.6 + 1.4 | 49,628 (57.2) | n.s. | 75.0 + 6.7 | 0.7 + 1.6 | 34.5 + 50.2 |
| Stage II | 76,928 (32.1) | 75.8 + 7.6 | 0.7 + 1.6 | 28,098 (32.4) | 76.0 + 7.4 | 0.8 + 1.8 | 28.8 + 46.0 | |
| Stage III | 27,762 (11.6) | 76.0 + 7.7 | 0.6 + 1.6 | 9,019 (10.4) | 76.1 + 7.5 | 0.8 + 1.7 | 22.8 + 39.8 | |
| Race–W | 210,108 (87.8) | 75.3 + 7.2 | 0.6 + 1.5 | 79,239 (91.3) | p = 0 | 75.5 + 7.0 | 0.7 + 1.6 | 31.7 + 48.2 |
| Race–AA | 16,887 (7.1) | 74.8 + 7.2 | 0.8 + 1.7 | 4,781 (5.5) | 75.3 + 7.2 | 1.0 + 2.0 | 27.4 + 44.4 | |
| Race–Other | 12,293 (5.1) | 73.7 + 6.7 | 0.7 + 1.5 | 2,725 (3.1) | 74.2 + 6.6 | 0.9 + 1.8 | 31.3 + 48.3 | |
| Hispanic | 12,603 (5.3) | 4,486 (5.2) | p=0 | |||||
| Non-Recurrent Patients | Recurrent Patients | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Number (%) | Age + SD | Comorb. at Dx + SD | Number (%) | p (chi sq.) | Age + SD | Comorb. at Dx + SD | Mos, Dx-Recr + SD | Comorb. at recur. + SD | |
| Total Patients | 202,339 (100) (84.6% of all) | 75.2 + 7.2 | 0.6 + 1.5 | 36,949 (100) (15.4% of all) | 74.6 + 6.9 | 0.5 + 1.4 | 37.5 + 44.6 | 2.9 + 3.5 | |
| ER+/PR+ | 133,560 (66.0) | 75.2 + 7.2 | 0.7 + 1.6 | 21,170 (57.3) | p = 0 | 74.5 + 6.8 | 0.6 + 1.4 | 39.7 + 45.6 | 3.2 + 3.5 |
| ER+/PR- | 24,280 (12.0) | 75.7 + 7.3 | 0.6 + 1.5 | 4,998 (13.5) | 75.0 + 7.0 | 0.5 + 1.4 | 36.2 + 41.5 | 3.0 + 3.5 | |
| ER-/PR- | 25,762 (12.7) | 74.9 + 7.3 | 0.6 + 1.5 | 6,638 (18.0) | 74.2 + 6.8 | 0.5 + 1.3 | 28.6 + 37.6 | 2.6 + 3.3 | |
| Stage I | 120,231 (59.4) | 74.7 + 6.8 | 0.6 + 1.4 | 14,367 (38.9) | p = 0 | 74.4 + 6.6 | 0.5 + 1.4 | 46.0 + 50.3 | 3.3 + 3.6 |
| Stage II | 63,363 (31.3) | 76.0 + 7.6 | 0.7 + 1.6 | 13,565 (36.7) | 74.6 + 7.0 | 0.5 + 1.4 | 36.1 + 42.9 | 2.9 + 3.5 | |
| Stage III | 18,745 (9.3) | 76.6 + 7.9 | 0.6 + 1.5 | 9,017 (24.4) | 74.7 + 7.1 | 0.5 + 1.3 | 26.2 + 33.6 | 2.3 + 3.3 | |
| Race–W | 177,554 (87.8) | 75.4 + 7.3 | 0.6 + 1.5 | 32,554 (88.1) | p = 0 | 74.7 + 6.9 | 0.5 + 1.3 | 38.4 + 45.3 | 2.9 + 3.5 |
| Race–AA | 14,189 (7.0) | 74.9 + 7.3 | 0.9 + 1.8 | 2,698 (7.3) | 73.9 + 6.9 | 0.5 + 1.4 | 28.6 + 35.8 | 2.9 + 3.6 | |
| Race–Other | 10,596 (5.2) | 73.8 + 6.7 | 0.0 + 0.3 | 1,697 (4.6) | 73.1 + 6.5 | 0.6 + 1.4 | 35.3 + 43.0 | 3.1 + 3.4 | |
| Hispanic | 10,789 (5.3) | 1,814 (4.9) | p = 0 | ||||||
| Recurrent patients without anxiety/depression | Recurrent patients with anxiety/depression | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Number (%) | Age + SD | Mos, Dx- Recr + (SD) | Comorb. at recur. + SD | Number (%) | p (chi sq.) | Age + SD | Mos, Dx-Recr + (SD) p (t-test) |
Comorb.at recur. + SD p (t-test) |
Mos, Dx-Dep /Anx + SD |
|
| Tot. Pts. |
21,412 (100) 14.0% of pts. without anx/dep | 74.5 + 7.0 | 36.3 + 43.6 | 2.4 + 3.1 | 15,537 (100) 17.9% of pts with anx/dep | p= 0 | 74.6 + 6.7 | 39.3 + 46.0 p=0 |
3.6 + 3.8 p=0 |
32.9 + 48.8 |
| ER+/PR+ | 12,101 (56.5) | 74.5 + 7.0 | 38.6 + 44.8 | 2.7 + 3.2 | 9,069 (58.4) | p=0 | 746 + 6.7 | 41.1 + 46.6 p=0 |
3.9 + 3.9 p=0 |
32.7 + 48.0 |
| ER+/PR- | 2,875 (13.4) | 75.1 + 7.1 | 34.9 + 40.1 | 2.5 + 3.1 | 2,123 (13.7) | 74.9 + 7.0 | 38.0 + 43.2 p=0.009 |
3.7 + 3.8 p= |
32.4 + 48.2 | |
| ER-/PR- | 3,976 (18.6) | 74.0 + 6.9 | 27.9 + 37.2 | 2.0 + 2.9 | 2,662 (17.1) | 74.4 + 6.8 | 29.8 + 38.3 p=0.044 |
3.3 + 3.7 p=0 |
25.6 + 42.6 | |
| Stage I | 7,900 (36.9) | 74.4 + 6.7 | 44.6 + 49.4 | 2.8 + 3.2 | 6,467 (41.6) | p=0 | 74.4 + 6.5 | 47.8 + 51.3 p=0 |
3.9.+ 3.9 p=0 |
38.0 + 53.1 |
| Stage II | 7,737 (36.1) | 74.6 + 7.1 | 36.0 + 42.5 | 2.4 + 3.1 | 5,828 (37.5) | 74.7 + 6.9 | 36.2 + 43.3 n.s. |
3.6 + 3.8 p=0 |
32.0 + 48.8 | |
| Stage III | 5,775 (27.0) | 74.6 + 7.2 | 25.3 + 32.8 | 1.8 + 2.8 | 3,242 (20.9) | 74.9 + 7.0 | 27.7 + 34.9 p=0.001 |
3.2 + 3.7 p=0 |
24.3 + 38.8 | |
| Race–W | 18,399 (85.9) | 74.7 + 7.0 | 37.3 + 44.4 | 2.4 + 3.1 | 14,155 (91.1) | p=0 | 74.7 + 6.8 | 39.9 + 46.4 p=0 |
3.6 + 3.8 p=0 |
32.9 + 48.8 |
| Race–AA | 1,799 (8.4) | 73.8 + 7.0 | 27.8 + 35.6 | 2.4 + 3.2 | 899 (5.8) | 74.2 + 6.7 | 30.2 + 36.1 n.s. |
3.9.+ 4.0 p=0 |
30.6 + 46.5 | |
| Race–Oth | 1,214 (5.7) | 73.0 + 6.5 | 34.0 + 41.4 | 2.8 + 3.2 | 583 (3.1) | 73.5 + 6.4 | 38.4 + 46.8 p=0.044 |
3.8 + 3.8 p=0 |
35.9 + 51.9 | |
| Hispanic | 957 (4.5) | 857 (5.5) | p=0 | |||||||
| Model | ER+/PR+ | ER-PR- | ||
|---|---|---|---|---|
| Time-dependent Concordance (C-Index) Avg. + SD | Integrated Brier Score (IBS) Avg. + SD | Time-dependent Concordance (C-Index) Avg. + SD | Integrated Brier Score (IBS) Avg. + SD | |
| Stage I | ||||
| CoxTime | 0.989 + 0.001 | 0.031 + 0.007 | 0.983 + 0.001 | 0.028 + 0.007 |
| DeepHit | 0.983 + 0.001 | 0.036 + 0.003 | 0.972 + 0.004 | 0.018 + 0.004 |
| DeepSurv | 0.987 + 0.001 | 0.027 + 0.001 | 0.984 + 0.001 | 0.024 + 0.001 |
|
Nnet-Survival (Logistic Hazard) |
0.982 + 0.001 | 0.026 + 0.001 | 0.969 + 0.001 | 0.055 + 0.002 |
| Stage II | ||||
| CoxTime | 0.981 + 0.001 | 0.056 + 0.022 | 0.972 + 0.001 | 0.055 + 0.018 |
| DeepHit | 0.981 + 0.001 | 0.009 + 0.001 | 0.970 + 0.001 | 0.021 + 0.002 |
| DeepSurv | 0.970 + 0.001 | 0.052 + 0.002 | 0.967 + 0.006 | 0.035 + 0.006 |
|
Nnet-Survival (Logistic Hazard) |
0.982 + 0.001 | 0.026 + 0.001 | 0.966 + 0.001 | 0.045 + 0.003 |
| Stage III | ||||
| CoxTime | 0.968 + 0.001 | 0.024 + 0.009 | 0.955 + 0.002 | 0.028 + 0.025 |
| DeepHit | 0.948 + 0.002 | 0.012 + 0.001 | 0.945 + 0.001 | 0.091 + 0.002 |
| DeepSurv | 0.972 + 0.002 | 0.019 + 0.001 | 0.961 + 0.001 | 0.021 + 0.001 |
|
Nnet-Survival (Logistic Hazard) |
0.965 + 0.002 | 0.039 + 0.002 | 0.928 + 0.003 | 0.030 + 0.002 |
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