Cox proportional-hazard survival models

The primary endpoint for this study was overall survival, and in order to identify CTC-based genes associated with mortality, we performed univariate Cox regression analysis in CTC positive patients for each of the measured genes [35]. The Halabi nomogram was utilized to account for baseline clinicopathologic variables, including ECOG performance status, disease site, opioid analgesic use, albumin, hemoglobin, alkaline phosphatase, and PSA in a multivariate Cox model. We obtained 18-month survival probabilities from https://www.cancer.duke.edu/Nomogram/firstlinechemotherapy.html. We subtract this probability from one to define a ‘Halabi’ score so that hazard ratios above one indicate increased risk of death. Cox bivariate regression analyses were then performed for each gene, adjusting for Halabi score, to identify genes associated with mortality independent of measureable clinical factors.

Cox regression was performed for 78 genes, after removing endogenous controls (ACTB, HMBS, TUBA-1B), epithelial markers (CD326, CDH1, CDH2, DSG2, EGFR, KRT8, KRT18, KRT19), blood-cell markers (CD20, CD45), artificial RNAs used in assay development (Spike1, Spike4, Spike7), alternate primers for SChLAP1, and SPANXB2. Log-transformed normalized expression values for each gene were rescaled by the interquartile range in order to make hazard ratios easier to interpret. Models were fit using the R function coxph in the survival package [36]. Genes were ranked using p-values from bivariate proportional hazards models with a single gene and the Halabi score as predictors. These p-values were transformed to FDR q-values using the Benjamini-Hochberg method [37]. The three genes significant at <10% FDR in the CTC positive cohort, AURKA, BMP7, and WNT5A, were selected for further analysis. Cox regression and Kaplan-Meir analysis was performed to assess whether CTC positive or negative status was associated with survival within the cohort. To aid in the interpretation of hazard ratios, we repeated the analysis using CTC probability based on our epithelial score as a continuous variable. This probability “p” was scaled using the transform: 2*(p-0.5), so that one unit change can be thought of as going from p=0.25 to p=0.75.