1) Univariate statistics
1.1 Nonparametric survival analysis
The median topography-specific survival time in cancer patients with BM, or the time when the survival probability, S(t), decreased by 50%, was 17.9 months in tumors originating from the testis (95%CI[15.2,26.9];p < 0.0001). Patients with BM from nodal NHLs had a median survival of 13.6 months (95%CI[10.6,20.3];p < 0.0001), prostate metastases reached a S(t) of 15.8 months (95%CI[12.7,18.3];p < 0.0001) while patients with BM originating from breast had a S(t) of 10.7 months (95%CI[10.2,11.5];p < 0.0001), as shown in Figure 1. The topographies with the lowest median survival times were lung(other type), S(t) = 1.8 months (95%CI[1.74,1.84];p < 0.0001), pancreas, S(t) = 2.3 months (95%CI[2.20,2.60];p < 0.0001), urinary tracts, S(t) = 2.4 months (95%CI[1.87,3.30];p < 0.0001) and liver, S(t) = 2.6 months (95%CI[2.10,3.06];p < 0.0001). The Kaplan-Meier estimates of systemic malignancy topography on patient survival are demonstrated in Figures 1 and 2. When comparing the most common origin sites of BM, as previously reported in the literature,1-6 there is a continuous survival advantage among patients with prostate cancer by a 14-month median overall increase in the survival probability.
The median morphology-specific survival time was highest, or 18.4 months (95%CI[13.2,25.4]; p < 0.0001), in patients with infiltrating duct and lobular carcinoma. BM originating from acinar cell carcinomas had a median survival of 16.3 months (95%CI[12.6,18.6];p < 0.0001), while patients with malignant struma ovarii metastatic to the brain achieved an S(t) of 15.2 months (95%CI[13.7,19.3];p < 0.0001). BM originating from malignant neoplasms (ICD-O-3, #8000/3) had the lowest median survival of 1.3 months (95%CI[1.25,1.38];p < 0.0001), followed by spindle cell carcinomas not otherwise specified, S(t) = 2.4 months (95%CI[2.10,3.61];p < 0.0001) and hepatocellular carcinomas, S(t) = 2.7 months (95%CI[2.14,3.19];p < 0.0001).
1.2 Cox regression analysis
The regression beta coefficients along with the hazard ratios (HR) and variable significance based on the topography and morphology of systemic disease were calculated for the variables of interest. Each predictor was assessed through separate Cox regression analysis followed by stratified Cox. The PH assumption was frankly violated for multiple covariates in the NCDB population, and proportionality was unable to be achieved after multiple stratification attempts (supplement).
All the following primary topography types: pancreas, liver, biliary, urinary tracts, lung(other) were associated with poorer survival in patients with BM (Figure3). Tumors originating from testis, nodal NHL, extra-nodal NHL, and prostate were associated with improved survival. Furthermore, BM originating from extra-nodal NHLs reduced the hazard factor by 32% (HR= 0.68, 95%CI[0.52,0.88];p < 0.0001), followed by BM from testis with a HR decrease by 31% (HR= 0.69, 95%CI[0.59,0.81];p < 0.0001) when compared with metastases from prostate cancer (Figure3).
In the univariate Cox regression, choriocarcinomas showed the best overall survival benefit among all morphology groups. Spindle cell carcinomas not otherwise specified (HR= 9.21, 95%CI[0.39,0.75]; p < 0.0001), hepatocellular carcinomas (HR= 8.21, 95%CI[4.72,14.28]; p < 0.0001), and malignant neoplasms (ICD-O-3 code #8000/3) were poor morphology prognostics in cancer patients with BM (supplement).
2) Multiple regression analysis
2.1 Feature selection
Feature selection started from a full, or saturated, survival model including all 91 variables in the study (supplement). The optimal regression model was the one that minimized the AIC using stepwise backward elimination. The best model to describe the data was the one featuring the seventeen covariates demonstrated in Table2.
2.2 Semiparametric vs parametric survival analysis
We fit a Cox model using all the significant covariates from feature selection. The HRs for each respective covariate can be seen in the supplement. The Schoenfeld residuals test was significant for multiple covariates in the model. The non-proportionality was further supported by graphical diagnostics given the log(- log(S(t))) plots did not demonstrate any parallelism (supplement). We were unable to correct for nonproportionality in the Cox model after multiple stratification attempts. We concluded that the estimates derived from utilizing Cox regression in the study should not be generalized, as semiparametric regression led to incorrect inferences. AFT models are especially important under such circumstances, given their parametric distribution for the survival times AFT models can make statistical inference accurate and lead to a proper model fitting.16
2.3 Parametric model fit and results
Relative to other parametric distribution results, the log-logistic distribution achieved the lowest AIC and likelihood ratio tests indicating a more parsimonious model able to better describe the NCDB population survival pattern (Figure4). The log-logistic distribution has a non-monotonic arc-shaped decreasing hazard rate. The absolute parametric model goodness of fit for validity was assessed through Q-Q graphical plots, which demonstrated linearity in a function of time for the loglogistic model. Next, we fit a loglogistic AFT model using all the significant variables from feature selection.
2.3.1 Topography and morphology
We identified the topography “prostate” as the best overall prognostic among sites of origin in patients with BM (Table2). The median life expectancy for metastatic liver cancer was 10.1 times less (PO= 10.1, 95%CI[6.14,16.5];p < 0.0001) that of BM from prostate. BM from the biliary tree (PO= 8.14, 95%CI[5.37,12.3];p < 0.0001), pancreas (PO= 7.52, 95%CI[6.12,9.24];p < 0.0001), and gallbladder (PO= 7.17, 95%CI[4.67,11.0];p < 0.0001) were associated with poor survival. Similarly, ovarian (PO= 8.48,95%CI[6.09,11.8];p< 0.0001), uterine (PO= 8.49, 95%CI[6.61,10.9];p < 0.0001), and cervical (PO= 8.68, 95%CI[6.65,11.3];p < 0.0001) cancers were poor prognostics. In contrast, patients with BM originating from breast (PO= 3.44, 95%CI[2.81,4.22]; p < 0.0001), bone/joints (PO= 3.22, 95%CI[1.63,6.34];p < 0.0001), and testis (PO= 3.27, 95%CI[1.65,6.45];p < 0.0001) had an improved overall survival second only to that of prostate cancer.
The histology “choriocarcinoma” has been reported as a potential favorable prognostic in BM,17 therefore it was utilized as the morphology reference group in the model. Similarly, the histopathology choriocarcinoma was among the best overall morphology prognostics along with mature B-cell lymphomas (Table2). Other good prognostics were carcinoid tumor (PO= 2.72, 95%CI[1.11,6.68];p < 0.0001) and papillary adenocarcinoma (PO= 4.12, 95%CI[1.77,9.58];p < 0.0001). The combined morphology category cystic mucinous and serous carcinomas (ICD-O-3 codes #844-849) was associated with increased survival. In contrast, the median life expectancy for metastatic spindle cell carcinoma was 19.4 times less (PO= 19.4, 95%CI[7.77,48.4];p < 0.0001) that of choriocarcinoma. Hemangiosarcoma was also among the worse prognostics (PO= 18.6, 95%CI[7.3,47.2];p < 0.0001). The remaining morphology groups associated with poor survival were carcinoma undifferentiated (PO= 14.6, 95%CI[5.88,36.4];p < 0.0001), Ewing sarcoma (PO= 14.0, 95%CI[4.55,43.3];p < 0.0001), malignant neoplasm (PO= 15.9, 95%CI[6.91,36.7];p < 0.0001), pseudosarcomatous carcinoma (PO= 13.8, 95%CI[5.92,32.2];p < 0.0001), renal cell carcinoma/sarcomatoid (PO= 14.0, 95%CI[5.81,33.9];p < 0.0001), signet ring cell carcinoma (PO= 12.2, 95%CI[5.22,28.6];p < 0.0001), spindle cell sarcoma (PO= 14.5, 95%CI[5.34,39.2];p < 0.0001) and squamous cell carcinoma from spindle cells (PO= 13.5, 95%CI[4.97,36.5];p < 0.0001). Tumors in the combined morphology category osseous and chondromatous neoplasms (ICD-O-3 codes #918-924) were poor prognostics (Table2).
2.3.2 Demographics and patient specific factors
The median survival for males was 1.24 times less that of females when adjusting for other covariates in the model (PO= 1.24, 95%CI[1.22,1.27];p < 0.0001). Increasing patient age, White race, and American Indians or Eskimos were bad prognostics (Table2). Asian race demonstrated a protective effect as the survival was accelerated by a factor of 1.3 (AF= 1.3, 95%CI[1.25,1.36];p < 0.0001) when compared to Black patients. Increasing Charlson-Deyo comorbidity score (CDScore) was associated with poor survival, while patients with a CDscore of 3 had the worse overall prognosis (PO= 1.52, 95%CI[1.45,1.59];p < 0.0001) among other CDscore groups. The median patient income and level of education did not achieve significance in the model. In patients with coexisting liver metastatic disease the median life expectancy was decreased by half (PO= 1.99, 95%CI[1.95,2.04];p < 0.0001).
2.3.3 Type of treatment
Patients with BM who underwent surgery of the primary site with no residual tumor margins had 2.07 times increased overall survival (AF= 2.07, 95%CI[1.72,2.49];p < 0.0001). Failure of administering chemotherapy, despite being part of first course treatment, decreased the median survival by 4.31 (PO= 4.31, 95%CI[4.13,4.49];p < 0.0001). Similarly, no administration of radiotherapy (PO= 1.59, 95%CI[1.5,1.68];p < 0.0001), immunotherapy (PO= 2.01, 95%CI[1.66,2.44]; p < 0.0001) and hormone therapy (PO= 2.53, 95%CI[2.34,2.74];p < 0.0001) were all associated with shorter survival times.