The Effect of Time-dependent Prognostic Factors on Survival of Non-Small Cell Lung Cancer using Bayesian Extended Cox Model

Lung cancer is one of the most common cancers around the world. The aim of this study was to use Extended Cox Model (ECM) with Bayesian approach to survey the behavior of potential time-varying prognostic factors of Non-small cell lung cancer.

Survival status of all 190 patients diagnosed with Non-Small Cell lung cancer referring to hospitals in Yazd were recorded from 2009 to 2013 by phone call. We fitted conventional Cox proportional hazards (Cox PH) as well as Bayesian ECM. Inference for estimated risk ratios was based on 90% credible intervals. Log pseudo marginal likelihood criteria (LMPL) was used for model comparison. Statistical computations were based on R language.

In this study, 190 patients with non-small cell lung cancer were followed, of whom 160 died because of the disease (84.2%). Median of survival time was 8 ± 0.076 month. After fitting the Cox PH Model, it was determined that the PH assumption was not satisfied for the type of treatment, the disease stage, and pathology status variables (p <0.001). LPML for Cox PH and Bayesian ECM was -431.593 and -401.01, respectively. Estimated hazard ratio curves based on Bayesian ECM showed that the risk ratio for these variables exhibited significant time varying behavior on hazard of lung cancer through follow up time.

Based on LMPL, Bayesian ECM was found to have a better fit than Cox PH Model which declares, results from Cox PH should be interpreted with care. Especially, from beginning of the study to about 20 month after, very high risk ratio was estimated for variables whose PH was not satisfying for them.