Modeling Continuous Prognostic Factors in Survival Analysis: Implications for Tumor Staging and Assessing Chemotherapy Effect in Osteosarcoma
Extent of response to neoadjuvant chemotherapy, tumor size, and patient age are important prognostic variables for patients with osteosarcoma, but applying information from these continuous variables in survival models is difficult. Dichotomization is usually inappropriate and alternative statistical techniques should be considered instead. Nonlinear multivariable regression methods (restricted cubic splines and fractional polynomials) were applied to data from the National Cancer Database to model continuous prognostic factors for overall survival from localized, high-grade osteosarcoma of the appendicular and nonspinal skeleton following neoadjuvant chemotherapy and surgical resection (N=2493). The assumption that log hazard ratios were linear in relation to these continuous prognostic factors was tested using likelihood ratio tests of model deviance and Wald tests of spline coefficients. Log hazard ratios for increasing patient age were linear over the range of 4 to 80 years, but showed evidence for variation in the coefficient over elapsed follow-up time. Tumor size also showed a linear relationship with log hazard over the range of 1 to 30 cm. Hazard ratios for chemotherapy effect profoundly deviated from log-linear (P<0.004), with significantly decreased hazard for death from baseline for patients with ≥90% tumor necrosis (hazard ratio, 0.32; 95% confidence interval, 0.20-0.52; P<0.0001). Important implications of these results include: (1) ≥90% tumor necrosis defines good chemotherapy response in a clinically useful manner; (2) staging osteosarcoma by dichotomizing tumor size is inappropriate; and (3) patient age can be modeled as a linear effect on the log hazard ratio in prognostic models with the caveat that risk may change over duration of the analysis.