Development and validation of nomograms to predict brain metastasis-free survival in lung and breast cancer.

Introduction
Brain metastases (BMs) commonly occur in patients with advanced solid tumors worldwide. BMs are approximately ten times more common than primary malignant brain tumors according to epidemiological data published in 2021 [1]. The incidence of BM is difficult to quantify and varies significantly in different types of primary cancers [2]. Patients with lung cancer or breast cancer are most likely to develop BM later in life. Lung cancer has the highest incidence in males and the third highest incidence in females, while breast cancer has exceeded lung cancer as the top cause of cancer incidence for females [3]. Lung cancer, accounting for approximately half of BMs, is the most prone to BMs among all malignant tumors [4], followed by breast cancer, accounting for approximately 10%-30% [5]. Moreover, for those patients, the main cause of death is not the primary tumor but BM. The occurrence of BM often predicts poor prognosis, decreased quality of life, limited treatment, and significantly shortened overall survival, which has become one of the hot topics of concern for clinicians. However, to date, there are neither screening guidelines for early detection of BM nor treatment guidelines for preventing BM in patients with primary tumors.
Currently, numerous studies have reported prognostic factors in lung cancer or breast cancer with BM. Available studies have shown that risk factors affecting the prognosis of patients with BM from lung cancer are female sex, higher T stage, higher N grade, poorly differentiated grade, presence of lung, liver, and bone metastases, and adenocarcinoma histology [6, 7]. Age, race, breast subtype, tumor size, tumor grade, liver metastases, surgery, and chemotherapy are independent prognostic factors for BM from breast cancer [8, 9]. Subsequently, the relevant nomograms were also constructed based on these factors [10–13]. However, few studies have focused on the factors that influence non-BM survival, i.e., the factors that influence the development of BM from primary tumors. Accordingly, there are few studies on the construction of nomograms of factors influencing non-BM survival.
With the burgeoning medical technology, there is a growing interest in developing predictive tools to guide disease treatment strategies and predict survival or prognosis. In recent years, nomograms have been increasingly used in medicine, especially in oncology. Nomograms are an important component of modern medical decision-making and consist of graphical representations of complex mathematical formulas. Their main merit is the ability to estimate individualized risk based on patient and disease characteristics [14].
In the present research, the occurrence of BM was regarded as the main end event of the study. We aimed to construct nomograms predicting non-BM survival in primary lung cancer and breast cancer based on clinical features, which were simple, intuitive, and efficient to apply. In this way, patients with lung or breast cancer at high risk of BM can be quickly screened, which could aid physicians in recommending more aggressive treatment for them.

Materials and methods

Study population
We conducted a retrospective cohort study of adult patients diagnosed with primary lung cancer or breast cancer at Harbin Medical University Cancer Hospital and Xiamen Cardiovascular Hospital of Xiamen University from January 1, 2016, to December 31, 2023, and followed them for subsequent development of BM to analyze the risk factors for BM. The inclusion criteria were as follows: (1) age at diagnosis ≥ 18 years; (2) patients whose only primary site tumor was pathologically diagnosed as lung cancer or breast cancer; (3) diagnosis was not made based on a death certificate or autopsy; (4) patients with BM diagnosed by pathological confirmation of imaging evidence; and (5) clear information about whether or not brain metastases were present at the time of initial diagnosis of lung or breast cancer. The study’s primary endpoint was non-BM survival, defined as the time interval from the date of primary diagnosis to the date of BM (TPDBM). TPDBM was defined as 0 if BM was present at the time of primary cancer diagnosis. Ultimately, 1739 patients with primary lung cancer and 1150 patients with breast cancer were screened for inclusion in the study. All data for this study were obtained from the patients’ medical records (with signed written informed consent) and were analyzed anonymously.

Ethics statement
The present study was performed in accordance with the Declaration of Helsinki (as revised in 2013) of the World Medical Association and was ethically approved by the Ethics Committee of Harbin Medical University Cancer Hospital and Xiamen Cardiovascular Hospital of Xiamen University (#KY2021-42).

Lung cancer study cohort
Demographic data included sex and age, while clinical data included the histological subtypes of primary lung cancer (adenocarcinoma, squamous lung cancer, adenosquamous carcinoma, large cell lung cancer, small cell lung cancer, and others), tumor tissue stage (T1 to T4), regional lymph node stage (N0 to N3), tumor distant metastatic stage (M0 or M1), clinical stage (stage I to stage IV), targeted therapy, chemotherapy, surgery, radiotherapy, and epidermal growth factor receptor (EGFR) mutations. We randomly assigned 1447 of these patients to the training set in a 5:1 ratio and used them to develop a robust nomogram to predict the incidence of brain metastases at 1, 2, and 3 years. A total of 292 patients were assigned to the independent validation set, which was used to validate the model. The baseline characteristics of these patients are summarized in Supplementary Table S1.

Breast cancer study cohort
The baseline data of primary breast cancer included age at diagnosis, estrogen receptor (ER), progereceptor (PR), human epidermal growth factor receptor 2 (HER2) status, molecular subtypes, tumor T stage (Tis to T4), regional lymph node stage (N0 to N3), tumor distant metastasis stage (M0 or M1), clinical stage (stage I to stage IV), targeted therapy, chemotherapy, neoadjuvant therapy, endocrine therapy, radiotherapy, surgery, and Ki-67 index. Breast cancer molecular subtypes include luminal A (high ER/PR expression; usually HER2-; low Ki-67), luminal B (lower ER/PR expression; usually HER2-; high Ki-67), HER2+ (HER2-positive; ER/PR negative or positive), and triple-negative breast cancer (TNBC) (ER-/PR-/HER2-) [15]. We used a computer to randomly assign 958 of these patients to the training set in a 5:1 ratio and used them to develop a robust nomogram to predict the incidence of brain metastases at 3, 5, and 7 years; 192 patients were assigned to the independent validation set and used to validate the model. The baseline characteristics of these patients are summarized in Supplementary Table S3.

Statistical analysis
This study adhered to the TRIPOD reporting guidelines for transparent reporting of prediction model studies. The sample size adequacy was assessed using the events-per-variable (EPV) criterion, which recommends at least 10 events per predictor variable to ensure model stability. In the breast cancer training cohort, 177 brain metastasis events were observed. The final multivariate Cox model incorporated 5 predictor variables, resulting in an EPV of 35.4, which substantially exceeds the recommended threshold. Similarly, the lung cancer model also met this criterion.
Nomograms were created in the training set and validated in the validation set. Descriptive statistics were applied to summarize the baseline data characteristics of patients between the BM and non-BM groups. For missing data in key variables, we employed a complete-case analysis approach. The proportion of missing values for each variable was less than 5%, which is considered acceptable for predictive modeling. No imputation was performed due to the low missing rate and the retrospective nature of the study. The independent-sample T test was used for continuous variables. Categorical variables were expressed as numbers with frequency percentages using the chi-square test or Fisher’s exact test. Univariate Cox regression analysis was performed to identify factors that may be associated with the development of BM in primary lung cancer or breast cancer. Then, factors with P ≤ 0.10 in the univariate Cox regression analysis were included in the multivariate Cox regression analysis to obtain independent risk factors for BM in primary lung cancer or breast cancer. Each factor was converted to a different score from 0 to 100 based on its contribution to non-BM survival [16]. Finally, the scores were converted into a functional relationship with non-BM survival by R software, and a nomogram model was developed to predict non-BM survival in patients with primary lung cancer or breast cancer.
The nomogram’s predictive performance was assessed visually through discrimination performance and calibration plots. Discrimination is defined as the ability to distinguish between patients with primary tumors with BM and those without BM. The differentiation of the nomogram of non-BM survival was assessed by the concordance index (C-index) [17]. The larger the C-index is, the more accurate the prediction. A C-index of 0.5 indicates complete inconsistency, indicating that the model has no predictive effect; a C-index of 1 indicates a perfect predictive model [18]. Overfitting bias was reduced with calibration and bootstrap methods. The X-axis of the calibration plot represents the predicted value calculated using the nomogram, and the Y-axis represents the individual’s actual risk odds [18]. The 45-degree line represents the ideal performance of the nomogram; that is, the predicted results are exactly in agreement with the actual results [19]. Decision curve analysis (DCA) was performed by stdca.R to evaluate the clinical utility of the nomogram by quantifying the net benefits at different threshold probabilities.
All statistical analyses for this study were performed using the Statistical Package for the Social Sciences (SPSS) version 23.0 and the R software “RMS”, “Survival”, and “Nomogram Ex” packages. Statistical significance was set at p < 0.05 (two-tailed).

Results

Patient characteristics

Lung cancer patient characteristics
A flowchart summarizing the screening, inclusion, and randomization of patients for model construction and validation is shown in Fig. 1. A total of 1739 eligible LC patients were enrolled in this study. The dataset was randomly divided into a training set (4/5, n = 1447) and a validation set (1/5, n = 292) using a computer-generated random seed. We compared the baseline characteristics between the training and validation cohorts, including sex ratio, age, pathological type, and the proportions of patients with and without brain metastases. No statistically significant differences were observed (Supplementary Table S2). The median follow-up time for lung cancer patients without brain metastasis was 19.2 months (IQR, 10.7–33.9 months). In the training set, 548 patients (37.9%) developed BM. The median non-BM survival was 5.1 months (interquartile range [IQR], 0.6–13.1). Among them, the incidence of BM was 22.8%, 11.7%, 2.7%, and 0.6% for lung adenocarcinoma (LUAD), small cell lung cancer (SCLC), lung squamous cell carcinoma (LUSC), and other types of lung cancer, respectively. Compared to the non-BM group, a higher proportion of patients in the BM group were diagnosed with clinical stage IV disease (p < 0.001). Regarding follow-up treatment, the BM group rarely opted for targeted therapy (11.9%) and more often opted for adjuvant chemotherapy (32.1%). However, there was no significant difference in age (p = 0.087) or sex (p = 0.694) between the BM and non-BM groups (Table 1). An overview of the patient’s basic characteristics is provided in Table 1.

Breast cancer patient characteristics
A total of 1150 eligible patients (1148 females, 2 males) were enrolled in this study and randomized in a 5:1 ratio into a training set (n = 958) and a validation set (n = 192). No statistically significant baseline characteristic differences were observed between training and validation cohorts (Supplementary Table S4). In the training set, the median follow-up time for breast cancer patients without brain metastasis was 22.6 months (IQR, 7.1–48.2 months). 177 patients, accounting for 18.5% of the entire cohort, developed BM with a median non-BM survival of 47 (IQR, 29-81.5) months. BM was more common in HER-2-positive patients (6.4%) and less common in luminal B patients (2.3%). In the BM group, the mean age at diagnosis of primary breast cancer was 46.6 years. The T stage (p < 0.001), N stage (p < 0.001), clinical stage (p < 0.001), and Ki-67 index (p < 0.001) differed between the two groups. Regarding treatment, more chemotherapy (16%), mastectomy (13.5%), and radiotherapy (10.4%) and less targeted therapy (5.4%), neoadjuvant (4%), and endocrine therapy (6.7%) were administered to the BM patients (Table 2). Basic patient information is shown in Table 2.

Independent risk factors for non-BM survival
As shown in Table 3, univariate Cox regression analysis showed that nine factors, including pathology classification (p < 0.001), age (p = 0.018), T stage (p = 0.007), N stage (p < 0.001), M stage (p < 0.001), clinical stage (p < 0.001), targeted therapy (p < 0.001), chemotherapy (p < 0.001), and surgical treatment (p < 0.001), were significantly associated with non-BM survival in lung cancer patients. These factors were then included in a multivariate Cox regression analysis, which ultimately identified SCLC (HR = 2.133, p < 0.001), N0 (HR = 0.370, p < 0.001), not receiving targeted therapy (HR = 1.753, p < 0.001), and receiving chemotherapy treatment (HR = 0.233, p < 0.001) as independent factors for non-BM survival in lung cancer patients.

The results of the univariate and multivariate Cox regression analyses of non-BM survival in breast cancer patients are shown in Table 4. Univariate regression analysis showed that the risk factors significantly associated with non-BM survival were age (p = 0.002), molecular type (p = 0.001), ER (p < 0.001), Ki-67 index (p < 0.001), T stage (p = 0.004), N stage (p < 0.001), clinical stage (p = 0.012), targeted therapy (p < 0.001), endocrine therapy (p < 0.036), radiotherapy (p < 0.001), and surgery (p < 0.001). In the multivariate Cox regression analysis, TNBC molecular subtype (HR = 2.632, p = 0.001), high Ki-67 index (HR = 7.344, p < 0.001), and mastectomy (HR = 8.701, p < 0.001) were independent risk factors for non-BM survival in breast cancer patients. In contrast, the absence of targeted therapy (HR = 0.452, p < 0.015) or radiotherapy (HR = 0.494, p = 0.002) was an independent protective factor.

Clinical stage is determined by both TNM classification and tumor size; therefore, it has a certain degree of overlap with the TNM stage. We also compared models that included only the clinical stage or only the TNM stage, and the results of the multivariate analyses were consistent, indicating that this overlap did not affect the final conclusions.

Nomogram construction and validation

Construction and validation of a nomogram to predict lung cancer brain metastases
We established a nomogram (Fig. 2A) to predict the development of BM in lung cancer based on independent risk factors selected from a multivariate Cox regression analysis of non-BM survival. By inputting the corresponding prediction information of patients, the probability of developing BM in lung cancer patients at 1, 2, and 3 years was evaluated. According to this model, we could calculate the total points by drawing a vertical line from each predictor axis to the points’ axis. Then, we drew a vertical line from the total points scale to the non-BM survival scale to estimate the probability of BM at 1, 2, and 3 years for each patient. In Fig. 2B, calibration plots are shown for validation using bootstrapping resampling. For the nomogram, the C-index was 0.786 (95% confidence interval (CI): 0.773-0.800). This result indicates that the nomogram prediction is in good agreement with the actual observations.

In the validation set, we used the same parameters as in the training set to test the nomogram prognostic model. As the calibration chart in Fig. 2C shows that there is excellent agreement between predictions and actual observations in terms of probabilities at 1, 2, and 3 years. Its C-index was 0.809 (95% CI: 0.783–0.836). The clinical utility of the nomogram was further evaluated using decision curve analysis (DCA). For lung cancer, at the 1-, 2-, and 3-year prediction time points, the DCA in both the training and validation cohorts demonstrated that the nomogram provided superior overall net benefits across a range of clinically reasonable threshold probabilities, compared to the “treat all” or “treat none” strategies, as well as to each individual predictor (Supplementary Figure S1A-F). These results showed that the predictive effect was appreciable in an independent dataset, and therefore, the model was exportable.

Construction and validation of a nomogram to predict breast cancer brain metastases
Figure 3A shows the predictive nomogram of all significant independent factors according to the multivariate analysis results of non-BM survival in breast cancer patients shown in Table 3. The C-index for the prediction of BM was 0.783 (95% CI: 0.763–0.804). An examination of the validation set confirmed the favorable discrimination of the nomogram (C-index = 0.843, 95% CI: 0.814–0.872). In both the training and validation sets, the calibration curves verified based on bootstrap resampling were well standardized; that is, the points were close to the 45-degree line (Fig. 3B and C). Similarly, for breast cancer at the 3-, 5-, and 7-year prediction time points, the DCA in both cohorts confirmed that the nomogram had superior overall net benefits compared to the “treat all” or “treat none” strategies and to each independent predictor (Supplementary Figure S1G-L).This result shows excellent agreement between forecasts and observations at 3-, 5- and 7-year probabilities.

Discussion
This study was a retrospective study that analyzed the clinical characteristics and risk factors for BMs in 1739 patients with primary lung cancer and 1150 patients with primary breast cancer. Robust nomograms were developed and validated to predict BM in patients with primary lung cancer and breast cancer. By corresponding each variable to the nomogram, a more accurate prediction of patients at high risk of BM was achieved.
Our results showed that the incidence of BM among patients with primary lung cancer was 37.9%, which is consistent with previous studies [20–22]. Our model suggested that BM is more likely to occur in patients with primary lung cancer with the following characteristics: small cell lung cancer, advanced N stage, and absence of chemotherapy or targeted therapy. It is worth noting that previous studies revealed that older patients and males are more likely to develop BM [23–25]. However, based on these aspects, no significant differences in the occurrence of BM were observed among patients in our study. In addition, some studies have suggested that a higher T stage is an independent risk factor for brain metastasis in lung cancer patients [26–28]. However, our analysis failed to support T staging as a risk factor, a result that is consistent with the findings of several recent studies [29–31]. More comprehensive research is needed to determine the reasons underlying this difference.
Our study demonstrated an 18.5% incidence of BM from primary breast cancer, in accordance with previous studies. These are some interesting conclusions based on the nomogram. We demonstrate a higher risk of BM in primary breast cancer patients with TNBC, a high Ki-67 index, mastectomy, targeted therapy, and radiation therapy. This study that TNBC patients had the highest risk of BM, followed by luminal A, HER2+, and luminal B patients. Some previous studies have discussed the relationship between molecular subtypes of breast cancer and BM, which is consistent with our findings [32, 33]. In our model, targeted therapy or radiotherapy was associated with a higher risk of BM, which may appear counterintuitive. This observation may be attributed to confounding by indication, wherein these treatments are more frequently administered to patients with aggressive tumor biology or advanced disease, which are inherently associated with a higher propensity for BM [34]. Thus, the treatments may serve as proxies for tumor virulence rather than direct causative factors of BM. Additionally, the relationship between age and BM has not been established, with some studies indicating that younger patients are more likely to develop BM and others reporting that older people are more likely to develop BM. Our study did not find a significant correlation between age and BM. The reasons underlying this phenomenon require further research.
Compared with recently published nomograms focusing on single cancer types or specific metastatic scenarios, our dual-cancer model demonstrates competitive predictive performance. For instance, Rong et al. developed a nomogram predicting cancer-specific survival in small cell lung cancer patients with brain metastasis, reporting a C-index of 0.71 [35]. Our model, which predicts the occurrence of BM in a broader lung cancer population, achieved a superior C-index of 0.786. Similarly, Zhang et al. built a conditional survival nomogram for predicting real-time prognosis in patients after breast cancer brain metastasis was diagnosed (C-index: 0.73) [36]. In contrast, our nomogram is designed to predict the risk of developing BM in breast cancer patients at an earlier stage, yet still achieved a comparable C-index of 0.783. The strength of our study lies not only in its competitive predictive accuracy but also in its proactive dual-cancer approach, providing a unified pre-screening tool for two major BM-prone malignancies, which may facilitate broader clinical applicability.
The most common primary tumors that metastasize to the brain are lung cancer, breast cancer, and melanoma. Lung cancer and breast cancer were selected for inclusion in this study based on the incidence of primary tumors at our institution. The results of this study showed that the progression period of non-BM in lung cancer was significantly shorter than that in breast cancer. The reason for this discrepancy is unclear and needs to be further investigated in future clinical studies.
Our study focused on the subsequent treatment of primary lung or breast cancer and demonstrated that the choice of treatment after diagnosis of primary lung or breast cancer may influence the development of BM, which has implications for clinicians in choosing treatment options. The treatment of BM has always been a difficult clinical challenge, with the ultimate focus of treatment being the primary tumor; thus, attention to follow-up treatment of the primary tumor is the key to delaying the occurrence of BM.
The current National Comprehensive Cancer Network (NCCN) guidelines do not yet recommend screening for BMs in patients with asymptomatic lung or breast cancer [10, 37]. However, BMs have become a major hurdle in the treatment of lung or breast cancer. Therefore, predicting which patients are at higher risk of developing BM to prevent or delay the onset of BM has become a key research question for clinicians.
To screen for BM in appropriate populations, we have developed and validated an easy-to-use nomogram based on our institutional data that can quantify individual risk. For each lung or breast cancer patient, all of these variables are readily available in the clinic, helping clinicians to select patients at high risk of BM and to identify more effective treatments to prolong non-BM survival and improve patients’ quality of life. It also demonstrates the usefulness of this nomogram as a predictive tool.
Our nomograms offer a straightforward clinical tool for risk stratification in outpatient settings. By integrating readily available clinical variables, clinicians can identify high-risk patients who may benefit from intensified surveillance, such as more frequent MRI screenings, or consider enrollment in clinical trials for preventive strategies like prophylactic cranial irradiation (PCI). This proactive approach could potentially delay BM onset and improve overall survival in selected populations.
In addition, this study has some limitations. First, the nomogram was developed based on a limited sample of patients and was not validated by an external cohort. Second, there are no patient data on smoking history, menopausal history, or driver gene status; these should be potential risk factors. Third, the study only collected data from China, and further research is needed to determine whether the nomogram can be generalized to other countries. Although major clinicopathological variables were included, detailed treatment regimens (e.g., specific targeted agents or histological grading for breast cancer) were not uniformly available in our database, which may have affected the model’s comprehensiveness.
Future research will focus on integrating radiomic features from primary tumor imaging to enhance the predictive accuracy of the model. Additionally, multi-institutional external validation will be conducted to assess the generalizability and robustness of the nomograms across diverse populations and clinical settings. These efforts aim to translate our predictive tool into a more comprehensive and widely applicable clinical resource.
Our study used Cox proportional hazards regression combined with nomograms to construct a robust model for predicting the development of BM in patients with primary lung or breast cancer. It was found that in lung cancer, the independent predictors of BM were pathological classification, advanced N stage, targeted therapy, and chemotherapy, while in breast cancer, the independent predictors were TNBC molecular subtype, high Ki-67 index, mastectomy, targeted therapy, and radiotherapy.
The two models were based on a combination of clinical characteristics of patients with primary lung or breast cancer that should be readily available to clinicians and may help us to identify subgroups of patients who are more susceptible to developing BM, tailor treatment for such patients, and further improve their clinical outcome.

Supplementary Information
Below is the link to the electronic supplementary material.