Real-time survival assessment in breast cancer with liver metastasis

Abstract

Background

The heterogeneity in outcomes of breast cancer liver metastasis (BCLM) complicates prognosis assessment. This study conducted conditional survival (CS) analysis and develop a CS-nomogram model for BCLM using SEER database data, providing individualized and adaptive prognostic predictions.

Methods

Data were extracted from the SEER 18 database, encompassing clinical records of BCLM patients diagnosed between 2010 and 2021. CS was calculated using the formula CS(t∣s) = S(t + s)/S(s), allowing for the dynamic assessment of survival probabilities. Annual hazard rate (AHR) analysis was performed to evaluate the risk of mortality at specific time intervals. A two-stage feature selection process was used to identify prognostic factors. We then developed a CS-nomogram, validated through calibration curves, time-dependent receiver operating characteristic curve (ROC) analysis, and decision curve analysis (DCA).

Results

The study cohort comprised 4,702 BCLM patients. The CS analysis and AHR analysis demonstrated that survival probabilities improved progressively for patients who survived beyond the high-risk period, particularly during the first year post-diagnosis. The CS-nomogram, developed using Cox regression, incorporated 14 variables, including patient characteristics, tumor features, and treatment information. It effectively predicted overall survival and CS at 3, 5, and 10 years. The model’s clinical utility was confirmed through calibrations, ROC with area under the curve values, and DCA, offering valuable insights for individualized treatment decisions.

Conclusion

By incorporating CS analysis, this study provided a dynamic, adaptable approach to predict prognosis for BCLMs. The CS-nomogram model transformed survival probabilities into a continuously adjustable process, supporting more precise clinical decision-making and offering hope to patients with a historically poor prognosis.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12672-025-02999-x.

Introduction

Breast cancer liver metastasis (BCLM) represents an advanced stage of breast cancer and is one of the most common sites of distant metastasis, alongside the bone, lung, and brain [1]. The liver serves as the first site of distant metastasis in nearly 30% of breast cancer patients, with malignant cells spreading to the liver, often following primary tumor progression or recurrence [2–4]. Clinically, BCLM exhibits highly aggressive biological behavior, characterized by rapid disease progression and resistance to systemic therapies. Despite the implementation of multimodal treatment strategies, including chemotherapy, targeted therapy, immunotherapy, and localized interventions such as hepatic resection or ablation, the median overall survival remains dismally low ranging from only 3 to 15 months [1, 5, 6]. And also, BCLM exhibits heterogeneity, with clinical outcomes influenced by factors such as age, tumor grade, ER and Her2 status, extrahepatic metastasis, performance status, and treatment choices [7]. These heterogeneities complicate prognosis assessment. Although several predictive tools have been developed to estimate the survival probability of BCLM [2, 6, 8–10], few are sufficiently sensitive, specific, or capable of real-time updates.

Traditional survival analysis, which estimate survival probabilities from the time of initial diagnosis, provide static and often overly pessimistic predictions that fail to account for the dynamic evolution of risk as patients survive longer [11]. This limitation highlights the necessity of adopting a more nuanced approach to prognostication—one that dynamically adjusts survival estimates based on elapsed survival time, thereby offering clinically actionable insights for patients who surpass early high-risk periods. Conditional survival (CS) analysis, defined as the probability of surviving an additional interval given that a patient has already survived a specific period, addresses the shortcomings of conventional survival models by incorporating time-dependent risk reassessment [11–13]. Moreover, the clinicopathological characteristics of patients significantly influence prognosis. Therefore, integrating CS into predictive tools such as nomograms, which account for prognostic weights based on patient characteristics, further enhances clinical utility by transforming complex survival dynamics into visually intuitive and individualized risk assessment tools [11, 14, 15].

In this study, we conducted a comprehensive CS analysis of BCLM patients and developed a CS-nomogram model using the Surveillance, Epidemiology, and End Results (SEER) database, a population-based registry renowned for its robust sample size and longitudinal follow-up data. This study not only validated the superiority of CS over traditional prognostic models but also provided a practical tool to guide personalized management in this high-risk population.

Methods

Data acquisition and study population

This population-based registry analysis utilized the SEER 18 registries (2000–2021) through SEER*Stat software (version 8.4.5) to extract clinical records of BCLM patients. Eligible participants met the following criteria: (1) histologically confirmed breast cancer with verified liver metastases; (2) initial diagnosis recorded between 2010 and 2021; (3) breast malignancy identified as the primary tumor. Exclusion criteria consisted of: (1) autopsy-confirmed cases; (2) unavailable survival duration data (lost to follow-up); (3) Incomplete documentation of clinicopathological characteristics or therapeutic interventions—including sociodemographic data (e.g., marital status), tumor features (e.g., T/N stage, metastasis, ER/PR/Her2 expression), and treatment details (e.g., surgical status)—was excluded from analysis. The detailed process can be found in Supplementary 1 (Flowchart). The data in the SEER database has undergone rigorous de-identification and ethical review, and the research is predominantly retrospective in nature. Therefore, using this data to publish SCI articles generally does not require additional ethical approval.

The included variables encompassed patient characteristics, tumor features, and treatment information. Owing to the inherent limitations of the SEER database, which lacks granular treatment details such as drug dosage, treatment duration, and therapeutic intent (curative vs. palliative), treatment modalities were categorized as binary variables (Yes/No). Primary site-directed surgical interventions and radiotherapy were identified and classified using standardized SEER-specific coding schemas. The clinical endpoint was overall survival (OS), estimated using the Kaplan-Meier method. Follow-up time was defined as the duration from the initial BCLM diagnosis to death from any cause.

Conditional survival and annual hazard rate analysis

CS is a dynamic statistical measure that estimates the probability of a patient surviving an additional period of time, given that they have already survived up to a specific time point. Mathematically, it is expressed as: CS(t∣s) = S(t + s)/S(s), where S(s) indicated the probability of surviving from diagnosis to time point s; CS(t∣s) indicated the probability of surviving an additional t years, conditional on having already survived s years [12]. This formulation enables the dynamic assessment of survival probabilities as patients progress through their disease course, providing a more refined understanding of prognosis over time.

Annual hazard rate (AHR) analysis calculates the risk of mortality at specific time intervals, typically on an annual basis. It is computed by dividing the number of deaths occurring in a given year by the number of patients at risk at the beginning of that year [16, 17].

Nomogram development and validation

Then all patients were subsequently stratified via computer-generated randomization into training and validation cohorts using a 7:3 allocation ratio for prognostic model construction and internal validation. A two-stage feature selection framework was implemented to enhance predictive accuracy while maintaining model simplicity. First, the Least Absolute Shrinkage and Selection Operator analysis (LASSO) with 10-fold cross-validation was applied to identify prognostic factors, reducing dimensionality and addressing multicollinearity. Additionally, variable selection was also performed using traditional Cox proportional hazards regression. The final set of predictors was determined by comparing Akaike Information Criterion (AIC) values from both analyses, with the model yielding the lowest AIC considered optimal [18, 19]. This approach effectively balanced model complexity and predictive performance. We further employed Integrated Discrimination Improvement (IDI) and Net Reclassification Improvement (NRI) to evaluate whether the inclusion of different variables led to an improvement in the predictive performance of the models. Finally, the resulting model was visualized as a nomogram, designed to provide individualized predictions for 3-year, 5-year, 10-year OS and 10-year CS rates.

The predictive accuracy and clinical utility of the nomogram were rigorously evaluated using the following methods: (1) Calibration curves: Graphical assessment of the agreement between predicted and observed survival probabilities, with 500 bootstrap resamples to correct for overfitting.

(2) Time-dependent receiver operating characteristic (ROC) curve analysis: Evaluation of the model’s discriminative ability at specific time points (3, 5, and 10 years) using area under the curve (AUC) metrics. (3) Decision curve analysis (DCA): Quantification of the net benefit of the nomogram across a range of threshold probabilities, comparing its clinical utility against alternative strategies.

Finally, we calculated each patient’s total risk score based on the variable assignments in the nomogram. We utilized the “surv_cutpoint” function from the “survminer” package to determine the optimal cutpoint for scores, based on the maximally selected rank statistics. Kaplan-Meier survival analysis was then performed to examine the relationship between risk scores and prognosis, evaluating whether the stratification effectively identified high-risk patients.

Statistical analyses were conducted using R (version 4.4.3), with a two-tailed test considering P < 0.05 statistically significant.

Results

The study cohort comprised 4,702 patients with BCLMs, divided into a training cohort (n = 3,291) and a validation cohort (n = 1,411) for model development and internal validation. Baseline demographic, clinicopathological, and treatment characteristics are summarized in Table 1. The majority of patients were aged 41–60 years (46.7%), single (51.3%), and had an annual household income below $80,000 (53.4%). Most tumors were high-grade (III/IV: 58.6%) and presented with advanced T (54.7% T3/4) and N (58.6% N+) stages. Other metastatic patterns included bone (58.2%), brain (8.5%), and lung (31.9%) involvement. Hormone receptor status analysis revealed ER positivity in 65.0%, PR positivity in 49.8%, and Her2 positivity in 41.6% of cases. Treatment modalities were heterogeneous, with 25.0% undergoing primary tumor resection, 26.5% receiving radiotherapy, and 76.3% administered chemotherapy. Further Chi-square tests revealed no significant differences between the groups, suggesting good comparability. Additionally, for these patient outcomes, the median survival was 25 months (95% CI: 23–26) for the entire cohort.

Table 1.

Basic information for all patients included in this study

Characteristics	Overall	Training	Validation	P
	(N = 4702)	(N = 3291)	(N = 1411)
Age				0.131
≤ 40	667 (14.2%)	470 (14.3%)	197 (14.0%)
41–60	2196 (46.7%)	1557 (47.3%)	639 (45.3%)
61–80	1558 (33.1%)	1058 (32.1%)	500 (35.4%)
> 80	281 (6.0%)	206 (6.3%)	75 (5.3%)
Marital status				0.426
Single	2411 (51.3%)	1700 (51.7%)	711 (50.4%)
Married	2291 (48.7%)	1591 (48.3%)	700 (49.6%)
Household income				0.284
< 80,000$	2510 (53.4%)	1740 (52.9%)	770 (54.6%)
≥ 80,000$	2192 (46.6%)	1551 (47.1%)	641 (45.4%)
Grade				0.734
I/II	1947 (41.4%)	1368 (41.6%)	579 (41.0%)
III/IV	2755 (58.6%)	1923 (58.4%)	832 (59.0%)
T stage				0.724
1/2	2131 (45.3%)	1486 (45.2%)	645 (45.7%)
3/4	2571 (54.7%)	1805 (54.8%)	766 (54.3%)
N stage				0.537
N0	1948 (41.4%)	1373 (41.7%)	575 (40.8%)
N+	2754 (58.6%)	1918 (58.3%)	836 (59.2%)
Bone metastasis				0.229
No	1964 (41.8%)	1356 (41.2%)	608 (43.1%)
Yes	2738 (58.2%)	1935 (58.8%)	803 (56.9%)
Brain metastasis				0.462
No	4304 (91.5%)	3006 (91.3%)	1298 (92.0%)
Yes	398 (8.5%)	285 (8.7%)	113 (8.0%)
Lung metastasis				0.198
No	3202 (68.1%)	2260 (68.7%)	942 (66.8%)
Yes	1500 (31.9%)	1031 (31.3%)	469 (33.2%)
ER				0.077
Negative	1648 (35.0%)	1180 (35.9%)	468 (33.2%)
Positive	3054 (65.0%)	2111 (64.1%)	943 (66.8%)
PR				0.438
Negative	2360 (50.2%)	1664 (50.6%)	696 (49.3%)
Positive	2342 (49.8%)	1627 (49.4%)	715 (50.7%)
Her2				0.107
Negative	2746 (58.4%)	1897 (57.6%)	849 (60.2%)
Positive	1956 (41.6%)	1394 (42.4%)	562 (39.8%)
Primary surgery				0.552
No	3526 (75.0%)	2476 (75.2%)	1050 (74.4%)
Yes	1176 (25.0%)	815 (24.8%)	361 (25.6%)
Radiotherapy				0.371
No	3457 (73.5%)	2432 (73.9%)	1025 (72.6%)
Yes	1245 (26.5%)	859 (26.1%)	386 (27.4%)
Chemotherapy				0.947
No	1116 (23.7%)	782 (23.8%)	334 (23.7%)
Yes	3586 (76.3%)	2509 (76.2%)	1077 (76.3%)
Median survival, months	25, 95%CI(23–26)	24, 95%CI(23–26)	26, 95%CI(23–29)

Conditional survival and annual hazard rate analyses

The CS and AHR analyses provided dynamic insights into survival trends over time. As shown in Fig. 1A, survival rates declined sharply within the first few years following diagnosis, but patients who survive longer exhibited improved survival probabilities. We further quantified this trend, demonstrating increasing survival probabilities conditional on having already survived a given number of years (Fig. 1B). Figure 1C highlighted the rising trend in CS, with 10-year CS improving progressively over time. Consistently, AHR analysis revealed a steep decline in AHR, with the highest mortality risk observed in the first year (31.99%), which subsequently decreased to 0.61% by year 10. These findings underscored the initially poor prognosis and the substantial improvement in survival for long-term survivors.

Fig. 1.

Conditional survival (CS) analysis of breast cancer liver metastasis. A and B Kaplan-Meier curves estimating real-time survival probabilities for patients who have survived 0–9 years, along with calculated results. C The CS (1|x) curve, representing the probability of surviving an additional year after x years since diagnosis, and the 10-year CS curve, showing the probability of surviving the 10th year after x years since diagnosis. D Annual hazard rate curve. CS, conditional survival

Condition survival nomogram development

We employed two analytical frameworks, LASSO and Cox regression, to identify the optimal combination of variables in training cohorts. Using the 1se criterion, LASSO selected 13 variables (Fig. 2A and B), while the traditional Cox regression model identified 14 variables, namely age, marital status, household income, tumor grade, T stage, bone metastasis, brain metastasis, lung metastasis, ER status, PR status, Her2 status, primary surgery, radiotherapy and chemotherapy (All P < 0.05, Fig. 2C). To further compare the performance of these two approaches, we assessed their goodness-of-fit using the AIC. The results indicated that the Cox regression model yielded a lower AIC value (LASSO, 30444.42 vs. Cox, 30440.13), suggesting that it provided a better fit to the data and exhibited superior predictive performance. We further compared the variable selection performance of the two methods using IDI and NRI metrics. The IDI value of 0.001 indicated only a minimal improvement in the model’s overall discriminative ability. Similarly, the NRI of 0.005 suggested a slight advantage when using variables selected by Cox regression compared to those selected by LASSO. Although the overall performance difference between the two methods was relatively small, these findings highlighted the relative advantage of Cox regression in this context and suggested that it may be more effective for identifying prognostic variables in survival analysis. Accordingly, we developed the final predictive model based on the variables selected through multivariate Cox regression.

Fig. 2.

Variable selection process. Variable selection was performed using both LASSO A and B and traditional Cox models C. LASSO, the Least Absolute Shrinkage and Selection Operator

To develop the CS-nomogram, we applied the CS formula to update the survival rates of patients at year 10, based on their survival from years 1 to 9 (Fig. 3). In using the CS-nomogram, only individualized parameters, quantified as risk scores by the model, were entered. The sum of these parameters was then used to calculate personalized OS and CS probabilities. Furthermore, we calculated the total risk score for each patient. Using the optimal cutoff value, we performed risk stratification. We found that applying the best cutoff point of 293 resulted in significant survival differences in both the training and validation cohorts (Fig. 4).

Fig. 3.

Conditional survival nomogram construction for predicting 3-, 5- and 10-year OS and 10-year CS. OS, overall survival; CS, conditional survival; RT, radiotherapy; CT, chemotherapy

Fig. 4.

Risk score calculation and stratification based on the nomogram. The optimal cutoff point of 293 was used to divide patients into high- and low-risk groups (A), with significant survival differences observed between the two groups (B and C)

Condition survival nomogram validation

The prognostic performance of the CS-nomogram was rigorously evaluated through calibration, discrimination, and clinical utility analyses in both training and validation groups. Calibration curves demonstrated excellent agreement between predicted and observed survival probabilities, with minimal deviations from the ideal 45-degree reference line across all timepoints (Fig. 5A–B). Time-dependent ROC analysis revealed robust discriminative capacity, yielding AUC values of 0.783 (95% CI: 0.765–0.801), 0.789 (95% CI: 0.765–0.812), and 0.868 (95% CI: 0.816–0.821) for 3-, 5-, and 10-year CS predictions in training cohort (Fig. 5C), and 0.779 (95% CI: 0.751–0.807), 0.777 (95% CI: 0.742–0.812), and 0.854 (95% CI: 0.767–0.942) in validation cohort (Fig. 5D). DCA further confirmed the clinical relevance of the nomogram, demonstrating superior net benefit compared to both “treat-none” and “treat-all” strategies across threshold probabilities in both training (Fig. 6A) and validation cohorts (Fig. 6B). These multi-dimensional validation metrics collectively affirmed the model’s reliability for individualized risk stratification and therapeutic decision-making in BCLM management.

Fig. 5.

Model evaluation and validation. A and B Calibration plots and C, D Receiver operating characteristic (ROC) curves with area under the curve (AUC) values in both the training group and the validation group

Fig. 6.

Model evaluation and validation. Decision curve analysis (DCA) curves in both the training group (A) and the validation group (B)

Discussion

The prognosis for BCLM is extremely poor, with median survival ranging from only 3 to 15 months and a 5-year survival rate as low as 8.5% [1, 5, 6]. Our study, leveraging CS analysis, revealed a previously underappreciated dynamic shift in survival outcomes over time. Notably, we observed that the 10-year survival probability increased substantially among patients who survived beyond the initial high-risk period, with the first post-diagnosis year marked by the steepest mortality decline (approximately 30% of deaths occurring within this window). Beyond this critical threshold, mortality rates diminished progressively, highlighting the inadequacy of static survival estimates. To address this temporal heterogeneity, we developed a CS-integrated nomogram model capable of dynamically recalibrating survival predictions based on accrued survivorship, thereby offering real-time, individualized prognostic stratification.

Traditional survival analyses, anchored to the time of diagnosis, inherently assume static risk profiles, failing to account for the evolving biological and clinical trajectories of survivors [20–22]. This approach systematically overestimates early mortality risks while underestimating long-term survival potential, particularly in malignancies like BCLM where prognosis improves with elapsed survival time. Our findings underscored the clinical necessity of dynamic prognostic tools: by quantifying how survival probabilities recalibrate annually, clinicians can tailor surveillance intensity, optimize therapeutic sequencing (e.g., transitioning from aggressive palliation to survivorship-focused care), and provide patients with updated, hope-infused prognostic narratives [22].

Our statistical findings have important clinical implications. The sharp drop in mortality after the first year suggested that key survival milestones (such as 1-year survival) could serve as crucial decision points. For instance, during the first year post-diagnosis, patients may require more aggressive treatment strategies and intensified surveillance to navigate the high-risk period. However, once they surpass this critical threshold, updated prognostic information can help refine treatment plans and tailored long-term management. Additionally, CS analysis enhanced prognostic clarity: a patient’s 5-year survival probability, when recalculated after surviving 3 years, may double compared to the initial estimate, fundamentally reshaping treatment goals and patient-clinician communication. This dynamic risk stratification aligns with the principles of precision oncology, recognizing that survival probabilities evolve over time and necessitate flexible, adaptive prognostic models.

Finally, by incorporating a multivariable feature selection strategy—including patient characteristics, tumor features (e.g., hormone receptor status), metastatic burden, and treatment approaches—our CS-based nomogram overcame the limitations of traditional survival evaluation. This model dynamically updated survival predictions based on accumulated survival time, allowing for more precise risk stratification. It helped distinguish patients who have a higher chance of long-term survival from those who remain at high risk. Clinically, this supports personalized resource allocation: high-risk patients may benefit from experimental treatments or clinical trials, while low-risk patients can transition to long-term survivorship programs. Additionally, the nomogram’s user-friendly visual design enables patients to take an active role in shared decision-making, promoting a treatment plan that is both realistic and hopeful. In our variable selection process, we also noted that socioeconomic factors significantly impacted the prognosis of BCLM, particularly marital status and income level. Numerous studies have highlighted the psychological and physiological benefits of marriage and higher income for cancer patients [23–25]. Married individuals tend to experience lower levels of distress, depression, and anxiety following a cancer diagnosis, largely due to the emotional and social support provided by a partner. Reduced depression is associated with better adherence to medical treatment, thereby improving survival outcomes [24]. From a physiological perspective, marriage has been associated with improved cardiovascular, endocrine, and immune function. Adequate social support may lower cortisol levels and positively influence immune responses, potentially enhancing cancer survival [24]. Similarly, household income is a key determinant of access to treatment and breast cancer care. It influences various aspects such as patient awareness, health literacy, insurance coverage, and even physician biases [26]. These socioeconomic disparities underscored the importance of incorporating such factors into prognostic models for more accurate and equitable outcome predictions.

While our study leveraged the robust, population-level data from the SEER database, several limitations must be acknowledged. First, as a retrospective dataset, SEER lacks granular details on systemic treatments (e.g., specific regimens, treatment responses) and molecular characteristics, which may impact the precision of survival estimates. Second, although CS analysis mitigated immortal time bias, some residual bias may persist in subgroups with varying treatment access. Third, in oncological research, reporting both OS and cancer-specific survival (CSS) provides a more comprehensive assessment of patient outcomes. While OS captures all-cause mortality and is straightforward to interpret, it lacks specificity. In populations with competing risks—such as elderly or advanced-stage patients—OS may not accurately reflect the benefit of cancer-directed therapies. Some treatments may improve CSS without affecting non-cancer mortality, leading OS to underestimate their efficacy. Conversely, if a treatment increases non-cancer-related deaths, OS may overstate its benefit. Moreover, OS-based models may overemphasize variables like age, which influence non-cancer mortality, thereby obscuring cancer-specific prognostic factors. Our study focused on OS and did not account for competing risks, which may introduce potential bias. Future research should clearly define endpoints when constructing prognostic models to enhance both interpretability and clinical relevance. Furthermore, the generalizability of our nomogram requires further validation in prospective cohorts to ensure broader applicability. Future studies should integrate multi-omics biomarkers and real-world treatment data to enhance dynamic prognostic models, ultimately bridging the gap between large-scale population statistics and personalized cancer care.

Conclusion

By redefining the prognosis of BCLM through CS analysis, this study challenged the pessimistic outlook on treatment and highlighted the dynamic relationship between survival time and remaining risk. Our CS-nomogram model translated evolving survival risks into a practical clinical tool, making survival probability not a fixed endpoint but a continuously adjustable process. This approach not only supports more precise clinical decision-making but also offers hope to patients facing an otherwise grim prognosis.

Supplementary 1. Flow charts of selected patients in this study.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Author contributions

SF and LQ designed the study and contributed to data analysis. SF wrote the initial draft of the manuscript; SF, GR, QL and LQ reviewed and edited the manuscript. All authors read and approved the manuscript.

Funding

None.

Data availability

The datasets generated during and/or analyzed during the current study are available in SEER database https://seer.cancer.gov/.

Declarations

Ethical approval

The SEER database is publicly available and contains only de-identified patient data; therefore, approval from an Institutional Review Board (IRB) was not required for this study.

Competing interests

The authors declare no competing interests.

Research involved in human and animal participate

Not applicable; This study used de-identified data from the SEER database, and no human subjects were directly involved. Therefore, ethics approval and informed consent were not required.

Consent to participate

The data used in this study are de-identified and publicly available from the SEER database; thus, no individual consent was required.

Consent publication

Not applicable.