
==== Front
Breast
Breast
The Breast : Official Journal of the European Society of Mastology
0960-9776
1532-3080
Elsevier

S0960-9776(24)00119-X
10.1016/j.breast.2024.103788
103788
Original Article
Estimating the risk of major adverse cardiac events following radiotherapy for left breast cancer using a modified generalized Lyman normal-tissue complication probability model
Lai Tzu-Yu abc
Hu Yu-Wen ab
Wang Ti-Hao def
Chen Jui-Pin a
Shiau Cheng-Ying a
Huang Pin-I ab
Lai I-Chun ab
Liu Yu-Ming ab
Huang Chi-Cheng gh
Tseng Ling-Ming bg
Huang Nicole ci
Liu Chia-Jen chiajenliu@gmail.com
bcjk⁎
a Department of Heavy Particles & Radiation Oncology, Taipei Veterans General Hospital, Taipei, Taiwan, R.O.C
b School of Medicine, National Yang Ming Chiao Tung University, Taipei, Taiwan, R.O.C
c Institute of Public Health, National Yang Ming Chiao Tung University, Taipei, Taiwan, R.O.C
d Department of Radiation Oncology, China Medical University Hospital, Taichung, Taiwan, R.O.C
e Department of Medicine, China Medical University, Taichung, Taiwan, R.O.C
f Everfortune.AI, Taichung, Taiwan, R.O.C
g Comprehensive Breast Health Center & Division of Breast Surgery, Department of Surgery, Taipei Veterans General Hospital, Taipei, Taiwan, R.O.C
h Institute of Epidemiology and Preventive Medicine, College of Public Health, National Taiwan University, Taipei, Taiwan, R.O.C
i Institute of Hospital and Health Care Administration, National Yang Ming Chiao Tung University, Taipei, Taiwan, R.O.C
j Division of Transfusion Medicine, Department of Medicine, Taipei Veterans General Hospital, Taipei, Taiwan, R.O.C
k Institute of Emergency and Critical Care Medicine, National Yang Ming Chiao Tung University, Taipei, Taiwan, R.O.C
⁎ Corresponding author. Division of Transfusion Medicine, Department of Medicine, Taipei Veterans General Hospital, Taipei, Taiwan No.201, Sec. 2, Shipai Rd., Beitou District, Taipei City, Taiwan, 11217, R.O.C. chiajenliu@gmail.com
12 8 2024
10 2024
12 8 2024
77 10378827 6 2024
31 7 2024
9 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Background

We introduced an adapted Lyman normal-tissue complication probability (NTCP) model, incorporating clinical risk factors and censored time-to-event data, to estimate the risk of major adverse cardiac events (MACE) following left breast cancer radiotherapy (RT).

Materials and methods

Clinical characteristics and MACE data of 1100 women with left-side breast cancer receiving postoperative RT from 2005 to 2017 were retrospectively collected. A modified generalized Lyman NTCP model based on the individual left ventricle (LV) equivalent uniform dose (EUD), accounting for clinical risk factors and censored data, was developed using maximum likelihood estimation. Subgroup analysis was performed for low-comorbidity and high-comorbidity groups.

Results

Over a median follow-up 7.8 years, 64 patients experienced MACE, with higher mean LV dose in affected individuals (4.1 Gy vs. 2.9 Gy). The full model accounting for clinical factors identified D50 = 43.3 Gy, m = 0.59, and n = 0.78 as the best-fit parameters. The threshold dose causing a 50 % probability of MACE was lower in the high-comorbidity group (D50 = 30 Gy) compared to the low-comorbidity group (D50 = 45 Gy). Predictions indicated that restricting LV EUD below 5 Gy yielded a 10-year relative MACE risk less than 1.3 and 1.5 for high-comorbidity and low-comorbidity groups, respectively.

Conclusion

Patients with comorbidities are more susceptible to cardiac events following breast RT. The proposed modified generalized Lyman model considers nondosimetric risk factors and addresses incomplete follow-up for late complications, offering comprehensive and individualized MACE risk estimates post-RT.

Highlights

• We retrospectively investigated major adverse cardiac events (MACE) for left breast cancer patients post-RT.

• A total of 64 MACE developed in 1100 patients with median follow-up 7.8 years.

• We proposed a Lyman NTCP model based on patient's left ventricle DVH, incorporating clinical risk factors and time-to-event data.

• The best-fit values for the proposed Lyman NTCP model parameters are D50 = 43.3 Gy, m = 0.59, and n = 0.78.

• Patients with comorbidities are more susceptible to cardiac injury following breast RT.

Keywords

Breast cancer
Ischemic heart disease
Lyman model
Major adverse cardiac event
Normal-tissue complication probability model
Radiotherapy
==== Body
pmc1 Introduction

Radiation-associated cardiac events are recognized complications for patients with breast cancer receiving radiotherapy (RT) [[1], [2], [3], [4], [5]]. Understanding how the heart responds to radiation and ascertaining its tolerance dose for cardiotoxicities is the fundamental goal in the clinical practice of RT. However, the optimal model for risk prediction is yet to be determined. Modeling the risk of cardiac events following breast cancer RT has been challenging due to several factors, including the rarity and long-term nature of the complication, the significant influence of the patient's baseline cardiovascular risk factors, and the complexity of heart substructures with the associated morbidities [[6], [7], [8]].

The Lyman model is the most widely used mathematical model for predicting normal-tissue complication probability (NTCP) in RT [9]. It is simple and considers all the information of a dose-volume histogram (DVH) with the equivalent uniform dose (EUD) in the DVH-reduction scheme [10]. NTCP models predicting various endpoints of toxicities for an organ-at-risk (OAR) based on the Lyman model have been proposed [[11], [12], [13], [14], [15]], while few studies have focused on cardiac events [16,17], Several issues must be considered when modeling cardiac events using the Lyman model. First, the Lyman model overlooks baseline risk factors crucial for heart disease development, limiting its utility. Another feature of the Lyman model is that it categorizes patients into binary outcomes as “with” or “without” the endpoint, without considering the effect of time-to-event. However, cardiac events typically manifest years after RT [3,[18], [19], [20]]. Patients are lost to follow-up or die of other causes during the study period. Therefore, accounting for censored data is necessary to obtain a valid estimation for NTCP.

Several extensions of the standard Lyman model have been suggested to address the limitations mentioned above, including incorporating dose-modifying factors (DMF) or multivariable logistic regression to account for the effect of clinical factors [13,21], and using the mixture model for latent times modeling [22,23], but few studies have delved into these two issues simultaneously. Our study aims to evaluate the risk of major adverse cardiac events (MACE) following breast cancer RT based on the Lyman NTCP model. We propose a modified generalized Lyman model to account for the influence of both clinical risk factors and censored data to estimate the risk of MACE individually.

2 Materials and methods

2.1 Study population and radiotherapy

This retrospective cohort study at Taipei Veterans General Hospital involved 2428 women with newly diagnosed invasive breast cancer or breast carcinoma in situ receiving breast cancer RT between January 2005 and December 2017. After excluding those with right-side disease (n = 1160), bilateral breast cancer (n = 55), metastatic or recurrent diseases (n = 57), prior cancer history (n = 53), and those lacking RT dosimetry data (n = 3), the final analysis included 1100 patients with left-side disease.

Details of the regimen and practice of RT have been presented in our prior work [24]. Briefly, the whole breast or chest wall was predominantly irradiated using three-dimensional conformal radiotherapy with a field-in-field technique. Intensity-modulated radiation therapy was reserved for patients with challenging anatomies (n = 50). The dose was 45–50.4 Gy to the whole breast or the chest wall, with or without a boost dose of 10–16 Gy to the primary tumor surgical bed via either a simultaneous integrated boost technique or a sequential boost method within 25–28 fractions. Regional nodal irradiation (RNI) was at the discretion of the physician, typically covering ipsilateral infraclavicular and supraclavicular regions for elective RNI. Internal mammary chain (IMC) irradiation was delivered only for patients with radiological or pathological positive lymph nodes in the IMC region (n = 8). For left-side breast cancer, the routine use of the deep inspiration breath hold technique was standard. Patients with right-side disease were treated using diaphragmatic breathing.

The contours of the heart and cardiac substructures were generated via an in-house deep learning-trained auto-segmentation model, followed by independent review by two radiation oncologists using a validated heart atlas [25]. The descriptive analysis of the dosimetric data for cardiac substructures, including left ventricle (LV), right ventricle, left atrium, right atrium, left anterior descending coronary artery, right coronary artery, and left circumflex coronary artery has been described previously [24]. In this study, the dose of LV was used for modeling, given its relevance in cardiac injury following breast RT [4,24,26,27]. The RT doses and structures of the LV were exported from the treatment planning system (Eclipse, version 13.6, Varian Medical Systems, Inc., Palo Alto, CA, USA). The grid size for dose calculation was 2.5 mm. We converted the dose to an equivalent dose in 2-Gy fractions (EQD2) by voxel and calculated differential DVHs with 0.01 Gy bin sizes. The EQD2 = nd[(d + α/β)/(2 + α/β)], where n is the number of fractions, d is the dose per fraction, and α/β is taken as 3 Gy for the breast and the late effect of the heart.

2.2 Study endpoint and follow-up

The primary endpoint was a MACE occurring after RT initiation, defined as acute myocardial infarction (International Classification of Diseases, 10th Revision, ICD-10, I21–I24), unstable angina (ICD-10, I20), coronary revascularization, coronary artery bypass grafting surgery, heart failure with hospitalization or death from cardiac disease. Events were identified using the ICD codes and in-depth medical records review. Pre-existing heart disease is defined as a history of ischemic heart disease (ICD-10, I20–I25) or heart failure ((ICD-10, I50). Patients with baseline heart disease were determined to have a MACE if the event was of a different category or more severe than previous episodes [28].

Clinical data including body mass index (BMI), smoking, cancer stage (based on the 8th edition of the American Joint Committee on Cancer Staging), comorbidities, type of surgery received (lumpectomy or mastectomy), hormone therapy, trastuzumab treatment, and anthracycline-based chemotherapy were obtained. Comorbidities included heart disease, diabetes, hypertension, hyperlipidemia, and chronic kidney disease (CKD), which were defined as diagnoses documented during any outpatient visits or inpatient care before the diagnosis of breast cancer. The ICD-10 codes used to define comorbidities are listed in Supplementary Table 1. We followed up on the patients until MACE occurrence, loss of follow-up, death, or the end of 2022. The study was approved by the Institutional Review Board in Taipei Veterans General Hospital (2023-07-018BCE).

2.3 The Lyman model

The standard Lyman model describes NTCP as the function of a subvolume of an OAR irradiated by a uniform dose [9]. Because the dose distribution is heterogeneous in clinical treatment, a DVH-reduction method with the concept of EUD is typically employed [10]. EUD represents a single uniform dose value equivalent to the biological effect of the non-uniform dose distribution delivered to an organ or tumor.(1) NTCP=1/2π∫−∞te−x2/2dxwitht=EUD−D50m·D50EUD=(∑iviDi1n)n

where vi is the relative volume receiving the corresponding ith dose bin with the dose Di of a differential DVH. The parameter D50 is the dose that corresponds to a 50 % probability of complication, m is the slope of the NTCP curve, and n represents the volume dependency of the risk of complications [21].

2.4 Incorporating clinical factors into the Lyman model

To account for both dose and patient baseline conditions in estimating the risk of complications for an OAR, we corrected the NTCP estimated from the standard Lyman model (NTCPLyman) according to clinical factors. We adopted the method suggested by Appelt et al., incorporating the odds ratio (OR) of clinical factors to adjust the risk estimated from the Lyman model [29,30]. It assumes that the effect of clinical factors on NTCP is independent of dose. By using logistic regression, the odds of the modified NTCP (NTCPm) can be defined as(2) OddsofNTCPm=OddsofNTCPLyman·OR

(3) OddsofNTCPm=NTCPLyman1−NTCPLyman·exp(β1x1+β2x2+…+βkxk)

where OR represents the odds ratio of a set of clinical variables with values x1, x2, …xk, and β1, β2, …βk are the corresponding regression coefficients. Therefore, the NTCPm incorporating clinical factors can be described as(4) NTCPm=OddsofNTCPm1+OddsofNTCPm=NTCPLyman·ORNTCPLyman·(OR−1)+1

2.5 The modified generalized Lyman model

The above NTCPm model estimates the probability that complications will eventually occur with an infinite follow-up time. To address censored data, we applied the concept of the generalized Lyman model, also known as the mixture Lyman model, incorporating a time-to-event distribution formula into the NTCPm model [22,23]. We used the observed time-to-event distribution based on our cohort, with corrections. At each event-time point, a weighting was assigned using the ratio of number of events to the number at risk (i.e., the number of patients still under follow-up) at that time point to obtain a distribution that simulates a cohort without any loss of follow-up. Let f(τ) represent the corrected density function for event-time, and F(τ) be the corresponding cumulative distribution function. Then the cumulative incidence of complication at time τ can be calculated as(5) NTCPm(τ)=NTCPm·F(τ)

Eq. (5) is the proposed modified generalized Lyman model considering clinical factors and time-to-event distribution.

As presented in detail elsewhere [22], the likelihood of a patient developing complications at time τ is NTCPm ∙ f(τ), while the likelihood of a patient not developing complications with follow-up to time τ can be described as 1 - NTCPm ∙ F(τ).

2.6 Maximum likelihood analysis

The modified generalized Lyman model was fitted to our data by maximum likelihood estimation (MLE) to obtain the optimal fit value for the parameters (D50, m, n) and the regression coefficient of clinical factors. The log-likelihood (LLH) function is(6) LLH=∑yi=1ln(NTCPm·f(τ))+∑yi=0ln(1−NTCPm·F(τ))

where yi represents the binary outcome of MACE for the patient. The DVH information of the LV was used for modeling. Clinical factors were subsequently fitted in a separate modified generalized Lyman model, with those having P value < 0.05 included in the full model. In the MLE analysis, age and BMI values were centralized to the median, whereas other clinical factors were dichotomized (yes or no). We compared the C-index of each model to assess their discrimination ability. A higher C-index value reflects better discriminatory power to distinguish between patients who experience the event of interest and those who do not. We performed sensitivity analyses by removing one clinical factor at a time from the full model to assess the model's robustness by comparing the resulting C-index.

The subgroup analysis divided the cohort into low- and high-comorbidity groups, where patients without any comorbidities were classified as the low-comorbidity group and those with one or more of the comorbidities as the high-comorbidity. Age and BMI were factors considered in the subgroup analysis. Optimal fits for D50, m, and n parameters were estimated for subgroups.

2.7 Statistical analysis

Demographic characteristics and clinical factors between groups were compared using Fisher's exact test and the Wilcoxon rank-sum test for categorical and continuous variables, respectively. The cumulative incidence of MACE was estimated using the Kaplan–Meier method and compared using a log-rank test. Patients were stratified based on quartiles of LV EUD to correlate their observed MACE risk with the predicted risk. MLE was conducted using the minimize function in Python, version 3.9.7 (Python Software Foundation). Statistical analyses were performed using R software version 4.1.0 (R Foundation for Statistical Computing, Vienna, Austria). P values for D50, m, and n parameters were calculated using the likelihood ratio test, and the 95 % confidence intervals (CI) were estimated using the profile likelihood method. A P value < 0.05 was considered significant.

3 Results

The characteristics of the 1100 patients are presented in Table 1. The median follow-up time was 7.8 years (interquartile range [IQR], 5.6–10.8 years), during which 64 patients developed MACE, with a median time to event 4.9 years (IQR, 2.3–8.0 years). Those who experienced MACE were older, with higher BMI, underwent more mastectomies, and had more comorbidities. The five-year and 10-year cumulative incidence rates of MACE were 3.3 % (95 % CI, 2.2%–4.4 %) and 6.8 % (95 % CI, 4.9%–8.6 %), respectively (Fig. 1).Table 1 Patient characteristics stratified by the development of MACE.

Table 1Characteristics	Total (n = 1100)	No MACE (n = 1036)	MACE (n = 64)	P value	
No. (%)	No. (%)	No. (%)	
Age (years; median [IQR])	51.0 [45.0, 60.0]	51.0 [45.0, 59.0]	57.50 [52.0, 67.3]	<0.001	
BMI (kg/m2; median [IQR])	23.5 [21.0, 26.0]	23.3 [20.9, 25.9]	24.4 [22.1, 27.3]	0.010	
Smoking	43 (3.9)	39 (3.8)	4 (6.2)	0.309	
Heart disease	55 (5.0)	47 (4.5)	8 (12.5)	0.012	
Diabetes	102 (9.3)	87 (8.4)	15 (23.4)	<0.001	
Hypertension	266 (24.2)	238 (23.0)	28 (43.8)	<0.001	
Hyperlipidemia	103 (9.4)	85 (8.2)	18 (28.1)	<0.001	
CKD	21 (1.9)	17 (1.6)	4 (6.2)	0.030	
Pathological T stage				0.689	
 T0 (carcinoma in situ)	152 (13.8)	139 (13.4)	13 (20.3)		
 T1	509 (46.3)	486 (46.9)	23 (35.9)		
 T2	363 (33.0)	345 (33.3)	18 (28.1)		
 T3	52 (4.7)	45 (4.3)	7 (10.9)		
 T4	24 (2.2)	21 (2.0)	3 (4.7)		
Pathological N stage				0.894	
 N0	676 (61.5)	637 (61.5)	39 (60.9)		
 N1	202 (18.4)	189 (18.2)	13 (20.3)		
 N2	127 (11.5)	118 (11.4)	9 (14.1)		
 N3	95 (8.6)	92 (8.9)	3 (4.7)		
Mastectomy	283 (25.7)	257 (24.8)	26 (40.6)	0.008	
Hormone therapy	888 (80.7)	840 (81.1)	48 (75.0)	0.252	
Trastuzumab	180 (16.4)	171 (16.5)	9 (14.1)	0.729	
Chemotherapy				0.702	
 No or other regimens	541 (49.2)	508 (49.0)	33 (51.6)		
 Anthracycline-based	559 (50.8)	528 (51.0)	31 (48.4)		
MHD (Gy, EQD2; median [IQR])	1.87 [1.15, 3.22]	1.86 [1.15, 3.17]	2.55 [1.37, 4.27]	0.023	
Mean LV dose (Gy, EQD2; median [IQR])	2.94 [1.64, 5.33]	2.88 [1.63, 5.21]	4.05 [1.98, 6.73]	0.009	
IQR, interquartile range; BMI, body mass index; CKD, chronic kidney disease; MHD, mean heart dose; EQD2, 2-Gy equivalent dose; LV, left ventricle.

Fig. 1 Cumulative incidence of major adverse cardiac events (MACE) of the study cohort. RT, radiotherapy.

Fig. 1

The adjusted distribution of time-to-MACE in our cohort is shown in Supplementary Fig. 1. The curve was plotted to 16 years after RT, the longest event-time observed in our data. The values of cumulative distribution function F(τ) at 5, 10, and 15 years are listed in Supplementary Table 2.

The MLE results for parameters in the modified generalized Lyman model based on LV DVH and clinical factors are shown in Table 2. The best fit for the standard Lyman model parameters was D50 = 30 Gy (95 % CI, 20.9–52.0), m = 0.71 (95 % CI, 0.63–0.81), and n = 0.74 (95 % CI, 0.5–1.78). Including clinical factors in the model generally increased the C-index. Incorporating individual clinical factor in separated models showed that age, diabetes, hypertension, heart disease, hyperlipidemia, and CKD significantly improve the fit, while smoking, mastectomy, hormone therapy, trastuzumab, and anthracycline chemotherapy did not. The full model, based on the LV DVH and significant clinical factors, yielded the best-fit values of D50 = 43.3 Gy (95 % CI, 27.9–92.3), m = 0.59 (95 % CI, 0.53–0.65), and n = 0.78 (95 % CI, 0.48–8.4). In the sensitivity analyses, the C-index values for models with one clinical factor removed at a time were similar to that of the full model (Supplementary Table 3), indicating the robustness of our model.Table 2 Results of maximum likelihood analysis for the modified generalized Lyman NTCP model.

Table 2Models with only one clinical factor included	
Clinical variables	D50	m	n	LLH	OR (95 % CI)	P value	C-index	
No (Lyman model)	30.0 (20.9–52.0)	0.71 (0.63–0.81)	0.74 (0.50–1.78)	-376.39	–	–	0.591	
Agea	42.9 (27.7–92.5)	0.65 (0.58–0.74)	0.68 (0.42–3.34)	-360.15	1.08 (1.05–1.11)	<0.001	0.698	
BMIa	32.0 (21.6–60.7)	0.72 (0.63–0.82)	0.75 (0.49–2.49)	-373.72	1.06 (1.01–1.12)	0.021	0.640	
Smoking	29.7 (22.4–48.9)	0.69 (0.61–0.79)	0.75 (0.51–1.76)	-375.71	2.14 (0.58–6.82)	0.245	0.592	
Diabetes	33.4 (23.5–56.7)	0.65 (0.58–0.74)	0.68 (0.46–1.38)	-369.96	4.17 (2.05–8.50)	<0.001	0.652	
Hypertension	29.9 (20.6–53.5)	0.63 (0.57–0.71)	0.93 (0.60–5.69)	-368.62	3.31 (2.05–5.26)	<0.001	0.669	
Heart disease	30.0 (21.0–51.8)	0.68 (0.61–0.77)	0.76 (0.51–1.83)	-372.88	4.10 (1.52–11.36)	0.008	0.633	
Hyperlipidemia	29.8 (21.0–51.1)	0.64 (0.58–0.72)	0.82 (0.55–2.10)	-366.14	5.56 (2.89–10.91)	<0.001	0.654	
CKD	30.1 (21.1–52.2)	0.69 (0.61–0.79)	0.75 (0.50–1.82)	-373.99	5.47 (1.23–34.12)	0.029	0.600	
Mastectomy	37.5 (24.2–81.4)	0.69 (0.62–0.78)	0.81 (0.49–NAb)	-374.53	1.81 (1.13–2.83)	0.054	0.608	
Hormone therapy	25.5 (17.7–45.9)	0.82 (0.71–0.97)	0.75 (0.50–2.07)	-375.52	0.64 (0.46–0.86)	0.187	0.596	
Trastuzumab	29.1 (21.8–49.9)	0.71 (0.63–0.81)	0.74 (0.50–1.70)	-376.23	0.80 (0.36–1.58)	0.573	0.585	
Anthracycline	27.0 (19.2–45.5)	0.73 (0.64–0.85)	0.74 (0.51–1.64)	-375.96	0.77 (0.51–1.13)	0.355	0.582	
Full model	
Clinical variables	D50	m	n	LLH	OR (95 % CI)	P value	C-index	
Full model	43.3 (27.9–92.3)	0.59 (0.53–0.65)	0.78 (0.48–8.4)	-350.26	–	–	0.744	
Agea	–	–	–	–	1.07 (1.04–1.09)	<0.001	–	
BMIa	–	–	–	–	1.03 (0.98–1.08)	0.315	–	
Diabetes	–	–	–	–	1.64 (0.76–3.60)	0.303	–	
Hypertension	–	–	–	–	1.46 (0.86–2.46)	0.307	–	
Heart disease	–	–	–	–	1.61 (0.52–5.47)	0.454	–	
Hyperlipidemia	–	–	–	–	2.43 (1.17–5.21)	0.055	–	
CKD	–	–	–	–	4.07 (0.83–23.57)	0.090	–	
NTCP, normal-tissue complication probability; LLH, log-likelihood; OR, odds ratio; CI, confidence interval; BMI, body mass index; CKD, chronic kidney disease.

a Age and BMI are centralized to the median value.

b The value is not available.

The predicted five-year and 10-year cumulative incidence of MACE as the function of LV EUD, along with the observed risks of MACE, is illustrated in Fig. 2A. It shows that the observation was graphically concordant with the predicted curve. In Fig. 2B, patients are grouped based on estimated values of modified NTCP (NTCPm; Eq. (4)) into <5 % (n = 346), 5–10 % (n = 320), and >10 % (n = 434), with cumulative incidence of MACE plotted accordingly.Fig. 2 Predicted and observed risk of major adverse cardiac events.

(A) Predicted five-year and 10-year cumulative incidence of major adverse cardiac events (MACE), computed from the fit of the full model. The observed incidence is plotted for patients grouped by quartile of left ventricle equivalent uniform dose (EUD), represented by the symbols positioned at the mean EUD for each group. Symbols with a triangle shape represent a five-year risk, and symbols with a dot shape indicate a 10-year risk. The vertical error bars indicate a 95 % confidence interval of the observation. (B) Cumulative incidence of MACE for patient groups defined by the modified normal-tissue complication probability (NTCP; Eq. (4)), calculated using the parameters estimates in the full model from Table 2. RT, radiotherapy.

Fig. 2

In the subgroup analysis, 361 patients (32.8 %) with pre-existing comorbidities were included in the high-comorbidity group. MACE developed in 35 and 29 patients in the high-comorbidity and the low-comorbidity groups, respectively. Patients in the high-comorbidity group were older (median [IQR], years, 58 [50–65] vs. 50 [44–56], P < 0.001) and had a higher BMI (median [IQR], kg/m2, 24.5 [22.0–27.1] vs. 22.9 [20.5–25.4], P < 0.001) than those in the low-comorbidity group. However, there were no significant differences in mean heart dose (median [IQR], Gy in EQD2, 2.09 [1.19–3.27] vs. 1.80 [1.14–3.18]) and mean LV dose (median [IQR], Gy in EQD2, 3.13 [1.74–5.36] vs. 2.86 [1.56–5.31]) between groups. The cumulative incidence of MACE was significantly higher in the high-comorbidity group than in the low-comorbidity group, with a 10-year cumulative incidence of 11.8 % vs. 4.4 % (P < 0.001; Fig. 3). The estimated parameters (D50, m, and n) for the low-comorbidity and high-comorbidity groups were 45, 0.56, 0.5 and 30, 0.81, 1.7, respectively (Supplementary Table 4). The predicted 10-year cumulative incidence of MACE based on these parameters is plotted in Fig. 4. It shows that when the LV EUD increases from 0 Gy to 5 Gy, the relative risk of MACE approximately increases 50 % in the low-comorbidity group (0 Gy 2.4 % vs. 5 Gy 3.6 %) and 30 % in the high-comorbidity group (0 Gy 10.3 % vs. 5 Gy 13.6 %).Fig. 3 Cumulative incidence of major adverse cardiac events (MACE) of subgroups defined by the comorbidity status. RT, radiotherapy.

Fig. 3

Fig. 4 Predicted 10-year cumulative incidence of major adverse cardiac events (MACE) for subgroups. This figure is computed from the fits of the low-comorbidity and the high-comorbidity groups. EUD, equivalent uniform dose.

Fig. 4

4 Discussion

This is the first and the most extensive study based on the Lyman NTCP model to assess the risk of MACE following breast cancer RT. The proposed modified generalized Lyman NTCP model incorporates clinical factors and addresses the effect of censoring. This approach increases the generalizability of the Lyman model, allowing its application to a broader context of NTCP modeling.

Unlike other RT-related normal tissue complications, the risk of cardiac events largely depends on the patient's baseline risk factors [1,4,31,32]. The fact is that even for patients not receiving thoracic RT, heart disease can occur. Therefore, the influence of nondosimetric factors must be taken into consideration. Under the presumption that the contribution of clinical factors on the risk of cardiac events is independent of the heart dose, we applied the method suggested by Appelt et al. [29,30]. With this approach, the influence of both dosimetric and nondosimetric factors on NTCP can be readily estimated.

Although cardiac events can happen early within first five years post-RT [1], their latent onset typically extends beyond this timeframe. The standard Lyman model neglects time-to-event dynamics, resulting in biased risk estimates. The generalized Lyman model combines the NTCP and latent time component, to address incomplete follow-up. Previous studies modeled the latent time component by a log-normal distribution [22,23]. However, the risk for cardiac events extends up to and beyond 15 years post-RT [3,[18], [19], [20]], indicating a different distribution. Therefore, we modeled the latency component based on the time-to-event distribution in our study. Further long-term MACE assessment of the cohort is necessary. Clinicians can utilize the proposed model to calculate NTCP and guide radiotherapy planning, as demonstrated in the supplement (Supplementary Example).

Currently, only a few studies have explored the risk of cardiac events following RT from the aspect of NTCP models, and most of them have used outdated RT techniques or focused on patient population with Hodgkin lymphoma [17,[33], [34], [35]]. We built the model based on left breast cancer population because the dose distribution was typically differs from that of Hodgkin lymphoma. In addition, we used the LV instead of the whole heart as the target OAR for the endpoint of MACE, because previous studies have suggested that the volume irradiated or the dose received by the LV serves as a representative measure for cardiac ischemia [4,24,26,27,36]. Given that the heart is a complex organ with intricate anatomical structures and physiologic functions, future studies should explore NTCP for specific cardiac substructures like coronary arteries, considering their complexities and related comorbidities.

Patients with different baseline characteristics may respond differently to radiation exposure. In the subgroup analysis, the value of D50 was lower in the high-comorbidity group than in the low-comorbidity group, indicating that patients with cardiovascular risk factors were more susceptible to radiation exposure with a lower threshold dose. Therefore, it is advisable to apply stricter dose constraints for high-risk patients. Individuals with high comorbidity demonstrate a higher baseline risk of MACE, emphasizing the importance of pre-existing risk factors. However, the extent to which the modification of the baseline comorbidities can reduce the RT-related heart disease risk remains uncertain and merits future investigation [37,38]. Additionally, limiting the LV EUD to below 5 Gy results in a modest decrease in the relative 10-year cumulative incidence of MACE, underscoring the need for validation of this dose constraint for RT treatment planning.

This study has several limitations due to its retrospective design. The events were retrospectively collected using a hospital-based database with limited follow-up lengths. The limited sample size and event numbers resulted in wide confidence intervals for model parameters. Currently, we are unable to validate our results using an external dataset. Due to the small number of events, it was not feasible to split the cohort into separate training and test sets. This constraint hindered our ability to perform internal validation techniques such as cross-validation. However, our study provides estimates for Lyman model parameters to evaluate MACE following breast RT, which have not been explored before. The generalizability of our findings may be limited due to variations in treatment planning practices and the increasing adoption of hypofractionated whole breast RT. In addition, we recognize that a recent study by the Danish Breast Cancer Group did not demonstrate a significant difference in the risk of heart disease post-modern RT between left-side and right-side breast cancer [39,40]. While the heart dose is decreasing with the evolution of RT techniques, risk assessment for certain high-risk patient groups remains necessary. Further validation studies for our model in external population are warranted. Strengths of our study include the construction of an NTCP model using individual DVH data based on modern RT techniques and comprehensive adjustment for baseline characteristics, comorbidities, and cancer treatments. By incorporating these factors, our study addresses potential confounders and time-to-event data that can better inform clinical decision-making and personalized treatment planning.

In conclusion, our modified generalized Lyman NTCP model incorporates clinical risk factors and accounts for censored data, enhancing the capabilities of the EUD-based Lyman model. This allows for a more individualized and comprehensive assessment of MACE, aiding in the evaluation of different RT treatment plans.

Funding

This study was supported by grants from the National Science and Technology Council (NSTC 112-2314-B-075-082 -).

Ethical approval

The study was approved by the Institutional Review Board in Taipei Veterans General Hospital (2023-07-018BCE).

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

CRediT authorship contribution statement

Tzu-Yu Lai: Writing – original draft, Funding acquisition, Formal analysis, Conceptualization. Yu-Wen Hu: Writing – review & editing, Software, Methodology. Ti-Hao Wang: Software. Jui-Pin Chen: Formal analysis. Cheng-Ying Shiau: Resources. Pin-I Huang: Resources. I-Chun Lai: Resources. Yu-Ming Liu: Resources. Chi-Cheng Huang: Resources. Ling-Ming Tseng: Resources. Nicole Huang: Supervision. Chia-Jen Liu: Writing – review & editing, Supervision.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A Supplementary data

The following is the Supplementary data to this article:Multimedia component 1

Multimedia component 1

Acknowledgment

We recognize that a portion of the study data is based on the Cancer Registry Database at Taipei Veterans General Hospital.

Appendix A Supplementary data to this article can be found online at https://doi.org/10.1016/j.breast.2024.103788.
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