
110 Exposure-Response Modeling: Methods and Practical Implementation
Note that the second term in the bracket is a weighted average of X
i
. This
approach leads to a very efficient algorithm for estimating β and has been
implemented in common software such as SAS and R. The mo st important
large sample properties of the estimate
ˆ
β is
ˆ
β ∼ N(β, Σ), where Σ is the
asymptotic variance of β and is routinely provided by software for fitting the
Cox model. This asymptotic distribution is the bas is of statistical inference for
β. The derivation of the asymptotic properties and calculation of Σ involve
complex formulae, hence the reader is referred to a standard ...