Use of progression-free survival in the evaluation of clinical interventions is hampered by a variety of issues, including censoring patterns not addressed in the usual methods for survival analysis. Progression can be right-censored before survival or interval-censored between inspection times. Current practice calls for imputing events to their time of detection. Such an approach is prone to bias, underestimates standard errors and makes inefficient use of the data at hand. Moreover a composite outcome prevents inference about the actual treatment effect on the risk of progression. This thesis develops semiparametric and sieve maximum likelihood estimators to more formally analyze progression-related endpoints. For the special case where death rarely precedes progression, a Cox-Aalen model is proposed for regression analysis of time-to-progression under intermittent inspection. The general setting considering both progression and survival is examined with a Markov Cox-type illness-death model under various censoring schemes. All of the resulting estimators globally converge to the truth slower than the parametric rate, but their finite-dimensional components are asymptotically efficient. Numerical studies suggest that the new methods perform better than their imputation-based alternatives under moderate to large samples having higher rates of censoring.