Exponential Competing Risk Step-Stress Model with Lagged Effect

Abstract

In many survival analysis studies, failure can come from one of several competing risks. Additionally, where survival times are lengthy, researchers can increase stress levels causing units to fail faster. One type of accelerated testing is a step-stress test where increases occur in quantum jumps at pre-determined time points. If the impact of the increase is not immediately attained an interim lag period is modeled. Although work has been done on stepstress models with competing risks and step-stress models with lagged effect, no known published works incorporate all three concepts. This paper proposes a two-competing risk step-stress model with lag period where each independent risk is exponentially distributed, the interim lag period is linear, and the attainment point is assumed known. We obtain the maximum likelihood estimators and Fisher information matrix and test our model via simulation. We construct confidence intervals and provide estimates of coverage probabilities using large sample theory, bootstrap, and bias-corrected accelerated (BCa) bootstrap methods. The results show that the model produces well-behaved estimators with small bias and MSE, and coverage probabilities close to nominal. In addition, we present an algorithm and results from a changepoint analysis using discrete optimization to estimate the unknown attainment point.