Partial likelihood

Key Points

• To develop and formalize the concept of partial likelihood, providing a rigorous mathematical foundation for estimating primary parameters without fully specifying nuisance baseline functions.
• Constructed a general likelihood factorization separating information into conditional and marginal components to isolate parameters of interest.
• Derived the asymptotic sampling distribution and properties of the partial score function and information matrix.
• Demonstrated that maximum partial likelihood estimators maintain standard maximum likelihood properties, including consistency and asymptotic normality.
• Established the theoretical validity of statistical inference in proportional hazards regression models with unspecified baseline hazards.