This thesis considers the econometric problem of endogeneity in an accelerated life regression model. The proposed instrumental variables inference, based on inverting a pivotal statistic, is exact regardless of instrument quality. A (i) least squares statistic and (ii) distribution-free linear rank statistic allowing censoring are provided. A simulation confirms that the quality of exogenous variation determines an instrument’s informative content. We provide an empirical illustration with an original prospectively collected ob- servational data set, in which, the trauma status of a pediatric critical care patient instruments a possibly confounded illness severity index in a length of stay regression for a specific pediatric intensive care population. Results suggest a clinically relevant bias correction for routinely collected patient risk indices that is meaningful for informing policy in the health care setting.