Data was obtained from the most current publication of the SEER 18 registry database, which had been made available in November 2018. The SEER 18 database owned by the National Cancer Institute provided the largest source of registry data on tumor incidences as well as survival rates between 2010 and 2016, which would be appropriate for this study. However, data on metastatic bone, brain and liver sites were not documented until 2010, so we included patients diagnosed with SCLC after 2010. Because the data from the SEER database were publicly accessible and de-identified, ethical approval and the need for informed consents were waived.

The inclusion criteria for this study were (1): Between 2010 and 2016, cytology or biopsy samples were used to establish pathologic diagnosis under a microscope. Patients who had been diagnosed before 2010 were not included (2). SCLC diagnosis was based on the International Classification of Diseases for Oncology, 3rd Edition (ICD-3) histology codes 8041, 8042, 8043, 8044, and 8045 (3). Site as well as morphology were recoded as ICD-O-3/WHO 2008: lung and bronchus

Exclusion criteria were (1): death certificate or autopsy did not confirm SCLC and (2) incomplete follow-up information ( Figure 1 ).

Relevant variables were extracted from each patient’s data. Age, sex, race, and survival time (months) were included. Pathological variables were the tumor number, primary site, tumor size, T stage, laterality, N stage and grade. In addition, clinical characteristics, including radiation sequence with surgery, surgery, radiation, and chemotherapy, were collected from the SEER database. The specific variable information is shown in Table 1 .

In order to get all of the raw data for this study from the SEER website (https://seer.cancer.gov/data), we submitted an access request, agreement, and signed the SEER research.

The OS outcome was determined as the survival interval from diagnosis to death of patients with SCLC with BM, while CSS was from diagnosis to death due to cancer.

Descriptive statistics were generated and are expressed as frequency (percentage) for categorical variables. The Pearson’s chi-square test was used to compare categorical variables. Multivariable logistic regression models were used to evaluate the risk variables for BM in SCLC. Time-to-event data (OS, CSS) are expressed as Kaplan-Meier estimates, and log-rank tests were used to compare the differences in survival curves. Clinically important baseline variables or those that exhibited univariate relationships with the outcome were included in multivariate in order to assess the relationship between OS (CSS) outcomes and prognostic factors, a Cox proportional hazards regression model was used. Based on the number of available events, the included variables were prudently selected, to guarantee parsimony of final models. Using the marginal Cox model, lesion-level multivariate models were adjusted for patient effects, and insignificant variables were dropped through backward selection. The SEER*Stat software was used to retrieve data for the years 2010 to 2016. Kaplan-Meier and Log-rank analyses were carried out using GraphPad Prism 8.0 (GraphPad Software). SPSS software version 26.0 (15) was used for the statistical analyses, and a P-value of 0.05 was considered significant. Patients were randomly assigned to two cohorts (training and validation cohorts) with a 7:3 ratio. Nomograms were created using “rms” in R (version 3.6.1; http://www.r-project.org/) and evaluated using the Harrell’s C-index, receiver operating curve (ROC), calibration curve, and decision curve analysis based on the outcomes of the multivariate Cox proportional hazards regression model (DCA). For deep learning purposes, we performed Recursive partitioning analysis (RPA) to construct a decision tree model for risk stratification using the R package ‘rpart’. Patients were allocated into 3 groups: high-, intermediate- and low-risk groups for survival analysis and forest plot presentation.

We identified 4201 patients diagnosed with SCLC between 2010 and 2016. Baseline data for all patients were selected from the SEER program dataset. Patient demographics, tumor characteristics, and treatment information are provided in Table 1 . Based on age distribution, two groups were assigned for the patients: <65 years (34.02%) and ≥65 years (65.92%). The proportion of women (52.44%) was slightly higher than that of men (47.55%). Based on patients’ racial characteristics, 3747 (89.19%) were white patients, 265(6.31%) were black patients, and 189 were other race patients (4.50%). The ICD-O-3 histology code was used to classify the tumor histology. Patients were grouped into five groups: SCLC, fusiform cell, oat cell carcinoma, intermediate cell, and combined small cell carcinoma, the latter constituting the largest proportion (91.95%). Moreover, single tumor site was more common (74.67% of patients) than multiple sites of the lung tumor. The grades were predominantly classified as I, II, III, and IV in 0.62%, 1.37%, 36.78%, and 61.82%, respectively, with the proportion being notably higher in grade IV. The compositions of patients with tumor sizes (in cm) 0≤x<3 3≤x<5, 5≤x<7, 7≤x<10, and ≥10 was 27.99%, 21.33%, 20.30%, 17.81%, and 7.81%, respectively. Based on recommendations for tumor nodule metastasis (TNM) staging from the American Joint Committee on Cancer (AJCC), T4 and N2 patients had the biggest proportion based on the T and N stage (31.54% and 49.68%, respectively). Most patients (85.43%, 77.31%) had accompanying brain and/or liver metastases. A significant number of patients were treated with surgery (90.15%) or chemotherapy (71.44%). As for radiation, there was a slight radiotherapy predominance (51.13%) versus no radiation (48.87%) in the radiation distribution.

After the exclusion of patients with unknown BM information, 780 (18.57%) were reported to exhibit BM. Table 1 presents the results obtained from the univariate analysis between clinicopathological variables and incidence of BM. We found that sex (χ2 = 15.081, P<0.001), histologic type (χ2 = 12.772, P=0.012), tumor number (χ2 = 17.274, P<0.001), tumor size (χ2 = 45.297, P<0.001), T stage (χ2 = 60.658, P<0.001), liver metastasis (χ2 = 79.240, P<0.001), N stage (χ2 = 154.467, P<0.001), brain metastasis (χ2 = 15.043, P<0.001), radiation sequence with surgery (χ2 = 49.181, P<0.001), surgery (χ2 = 508.699, P<0.001), and radiation (χ2 = 18.496, P<0.001) all showed significant correlation with the incidence of BM. Thus, we included the abovementioned variables in the multivariate analysis, appropriately relaxed the criteria in combination with clinical significance, and included chemotherapy (χ2 = 3.668, P=0.055).

The following clinicopathological characteristics were discovered to be BM risk factors that were statistically significant: female sex (OR=0.766, 95% CI=0.645–0.909, P=0.002), N1 (OR=0.507, 95% CI =0.268–0.957, P<0.001), and surgery (OR=0.766, 95% CI=0.645–0.909, P<0.001). These factors were significantly associated with lower BM risk, and patients with T2 and T3 had lower BM risk compared with patients with T0. In contrast, brain metastasis (OR=1.353, 95% CI=1.071–1.709, P=0.011), liver metastasis (OR=4.915, 95% CI=4.103–5.887, P<0.001), and chemotherapy (OR=1.362, 95% CI=1.108–1.674, P=0.003) were significantly correlated with higher BM risk, and patients with larger tumor size (5≤x<7 cm: OR=1.476, 95% CI=1.035–2.105, P=0.031; 7≤x<10 cm: OR=1.660, 95% CI=1.166–2.364, P=0.005) were highly associated with BM than those with smaller tumor size. Detailed data are shown in Table 2 .

Figure 2A shows the OS results for SCLC patients who had vs. who did not have BM. Patients with SCLC with BM had a shorter median survival time (MST) for OS (MST=6 months, 95% CI=5.441–6.559 months) than patients with SCLC without BM (MST=10 months, 95% CI=9.507–10.493 months). To calculate OS, Kaplan-Meier survival curves were utilized in different subgroups based on prognostic factors. Age, sex, liver metastasis, radiation, and chemotherapy were significantly associated with OS ( Figures 2B–F ). The results showed that SCLC patients with BM younger than 65 years old, female, without liver metastasis, receiving radiotherapy and chemotherapy have a better OS. Long rank tests and Kaplan-Meier survival curves were significant (P<0.05), while other variables did not exert significant effects on OS (P>0.05).

To determine prognostic indicators for OS and CSS, univariate and multivariate Cox proportional risk regression models were conducted, as shown in Tables 3 , 4 . Age ≥65 (HR=1.248, 95% CI=1.042–1.495, P=0.015), female (HR=0.749, 95% CI=0.627–0.895, P=0.001), tumor size between 7≤X<10 (HR=1.606, 95% CI=1.219–2.117, P=0.001), N2-3 (HR=1.391, 95% CI=1.239–1.411, P=0.039; HR=1.485, 95% CI=1.291–1.573, P=0.007), liver metastasis (HR=1.392, 95% CI=1.166–1.652, P=0.001), radiotherapy (HR=0.805, 95% CI=0.661–0.979, P=0.03) as well as chemotherapy (HR=0.200, 95% CI=0.161–0.249, P=0.001) were independent prognostic factors affecting OS. Meanwhile, Age ≥65 (HR=1.320, 95% CI=1.081–1.613, P=0.006), female (HR=0.719, 95% CI=0.588–0.878, P=0.001), white race (HR=1.792, 95% CI=1.174–2.735, P=0.006), tumor number >1 (HR=0.049, 95% CI=0.021–0.111, P=0.001), tumor size between 7≤X<10 (HR=1.673, 95% CI=1.231–2.274, P=0.001), N3 (HR=1.570, 95% CI=1.075–2.293, P=0.019), liver metastasis (HR=1.351, 95% CI=1.107–1.649, P=0.003), radiotherapy (HR=0.769, 95% CI=0.614–0.964, P=0.022) and chemotherapy (HR=0.178, 95% CI=0.138–0.230, P=0.001) were independent prognostic factors for CSS.

We applied the nomogram model to further predict OS and CSS ( Figures 3 , 4 ) in SCLC patients with BM. Gender, race, tumor size, age, N stage, brain metastasis, liver metastasis, radiation as well as chemotherapy were included in the nomogram for OS and CSS. C-indices for validation of OS as well as CSS predictions were 0.715 (95% CI, 0.702-0.728) and 0.769 (95% CI, 0.70-0.783), respectively. The 3-month, 6-month and 12-month OS and CSS calibration curves ( Figure 5 ) revealed that the actual and predicted survival probabilities were in strong accordance with validation as well as training cohorts. Meanwhile, area under the curve (AUC) and ROC curves were developed through time. Overall, the values of AUCs for OS and CSS ( Figure 6A–D ) at different time points were around 0.7 in the training as well as validation cohorts, indicating that the OS and CSS nomograms were accurate and valid at different time points. Clinical applications were evaluated with DCA, and the DCA curves at different time points had greater net benefit in training as well as validation cohorts for the OS ( Figure 8 ) and the CSS ( Figure 7 ).

To create decision rules influencing SCLC patients with BM, decision tree analysis incorporated every variable in the OS nomogram ( Figure 8 ). First, chemotherapy was the most vital determinant because it was the 1^st level split of two initial branches of the classification tree. Gender and radiotherapy were the most vital determinants for 2^nd and 3^rd level splits, respectively. Furthermore, we classified SCLC patients with BM into three risk groups based on the decision tree results: high, intermediate, and low, with marked differences in survival analysis among the three risk groups. Forest plots represented the final Cox results. We used the same method for decision tree analysis of CSS ( Figure 9 ). The results showed that the tumor number was the best determinant of CSS. Further analysis according to the guidelines revealed that a higher proportion of patients with tumor number >1 was older than 65 years ( Table 5 ), leading to the possibility that patients with high tumor number were included in the low-risk group population. In addition, the survival time increased sequentially in high, intermediate as well as low risk groups. Cox results were represented as forest plots.