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Abstract:
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This paper introduces a general framework for survival analysis based on ordinary differential equations (ODE). Many existing models, such as proportional hazards models, linear transformation models, accelerated failure time models, and time-varying coefficient models, can all be viewed as special cases under this framework. This unified framework provides a novel perspective on modeling censored data and offers opportunities for designing new and more flexible model structures. Further, based on well-established numerical solvers and sensitivity analysis tools for ODEs, we propose a general estimation procedure applicable to a wide range of models under the proposed framework, which is scalable and easy to implement. Specifically, we develop a sieve maximum likelihood estimator for a general semi-parametric class of ODE models as an illustrative example. We also establish a general sieve M-theorem for bundled parameters and show that the proposed sieve estimator is consistent and asymptotically normal, and achieves the semi-parametric efficiency bound. Finite sample performances of the proposed estimator are examined in simulation studies and a data example.
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