Cox Regression Models with Time-Varying Covariates Applied to Survival Success of Young Firms 1(*)

Headnote

ABSTRACT

The most widely used model in multivariate analysis of survival data is proportional hazards model proposed by Cox. While it is easy to get and interpret the results of the model, the basic assumption of proportional hazards model is that independent variables assumed to remain constant throughout the observation period. Model can give biased results in cases which this assumption is violated. One of the methods used modelling the hazard ratio in the cases that the proportional hazard assumption is not met is to add a time-dependent variable showing the interaction between the predictor variable and a parametric function of time. In this study, we investigate the factors that affect the survival time of the firms and the time dependence of these factors using Cox regression considering time-varying variables. The firm data comes from Business Development Centers (ISGEM) which is a prominent business incubation center operating in Turkey.

Jel Code: C41, C24, M13

KEYWORDS

Survival Analysis, Cox Regression Model, Proportional Hazard Assumption, New Firms

ARTICLE HISTORY

Submitted:22 Jun 2012

Resubmitted:03 January 2013

Accepted:25 March 2013

(ProQuest: ... denotes formulae omitted.)

Introduction

Survival analysis deals with the probability of occurrence of a given event at a set of particular points in a time interval (Cox and Oakes, 1984; Sertkaya, Ata and Sözer, 2005) - In the small business and entrepreneurship literature, survival analysis has been used to track the start-ups over the years. The typical survival anaylsis may include the reports of hazard rates, ratios and survival curves while relating a likely set of independent variables to a specific event. A survival curve of a cohort of newly established firms reports what percentage of the cohort continue to survive since its inception over time, indicating whether some of the firms are failed over the years (Karaöz and Albeni, 2011). In many survival studies, it has been examined whether some variables or risk factors are effective on survival or not. Cox proportional hazards (PH) model is the most preferred model in order to investigate the effect of variables on survival time. The key assumption of Cox model is that hazard rate related to different levels of the factors is constant throughout the follow-up period (Ba§ar, 2006) . Violation of the PH assumption requires additional...