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3.1 Introduction and notation
The Cox proportional hazards model [36] has become by a wide margin
the most used procedure for modeling the relationship of covariates to a
survival or other censored outcome.
Let Xij (t) be the jth covariate of the ith person, where i = 1, ... , n and
j = 1, ... ,p. It is natural to think of the set of covariates as forming an n x p
matrix, and we use Xi to denote the covariate vector for subject i, that is,
the ith row of the matrix. When all covariates are fixed over time Xi is just
a vector of covariate values, familiar from multiple linear regression. For
other data sets one or more covariates may vary over time, for example a
repeated laboratory test. We use Xi for both time-fixed and time-varying
covariate processes, employing Xi(t) when we wish to emphasize the time
varying structure.
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