{Truncation is a well-known phenomenon that may be present in observational studies of time-to-event data. For example, autopsy-confirmed survival studies of neurodegenerative diseases are subject to selection bias due to the simultaneous presence of left and right truncation, also known as double truncation. While many methods exist to adjust for either left or right truncation, there are very few methods that adjust for double truncation. When time-to-event data is doubly truncated, the regression coefficient estimators from the standard Cox regression model will be biased. In this dissertation, we develop two novel methods to adjust for double truncation when fitting the Cox regression model. The first method uses a weighted estimating equation approach. This method assumes the survival and truncation times are independent. The second method relaxes this independence assumption to an assumption of conditional independence between the survival and truncation times. As opposed to methods that ignore truncation, we show that both proposed methods result in consistent and asymptotically normal regression coefficient estimators and have little bias in small samples. We use these proposed methods to assess the effect of cognitive reserve on survival in individuals with autopsy-confirmed Alzheimer's disease. We also conduct an extensive simulation study to compare survival distribution function estimators in the presence of double truncation and conduct a case study to compare the survival times of individuals with autopsy-confirmed Alzheimer's disease and frontotemporal lobar degeneration. Furthermore, we introduce an R-package for the above methods to adjust for double truncation when fitting the Cox model and estimating the survival distribution function.