Residuals for proportional hazards models with interval-censored survival data

We develop diagnostic tools for use with proportional hazards models for in terval-censored survival data. We propose counterparts to the Cox-Snell, La gakos (or martingale), deviance, and Schoenfeld residuals. Many of the prop erties of these residuals carry over to the interval-censored case. In part icular, the interval-censored versions of the Lagakos and Schoenfeld residu als may be derived as components of suitable score statistics. The Lagakos residuals may be used to check regression relationships, while the Schoenfe ld residuals can help to detect nonproportional hazards in semiparametric m odels. The methods apply to parametric models and to the semiparametric mod el with discrete observation times.