Solved – What data structure is necessary for survival analysis

Assuming that by "parametric model" the OP means fully parametric, then this sounds like a question about the appropriate data structure for discrete time survival analysis (aka discrete time event history) models such as logit (1), probit (2), or complimentary log-log (3) hazard models, then the appropriate answer is that the data typically need to be structured in a person-period format.

1. $h_{t} = frac{e^{mathbf{BX}}}{1 + e^{mathbf{BX}}}$
2. $h_{t} = Phi(mathbf{BX})$
3. $h_{t} = 1 – e^{-e^{mathbf{BX}}}$

where $mathbf{BX}$ are the parameters and predictors in the model. Often discrete time survival analysis models will include dummy variables for each time period (see below) and also often include time period itself, or even functions of it, as a variable.

Here's what a person-period data set looks like:

ID period y x1 x2 x3 t1 t2 t3 . . . tT 1  1      0 1  3  12 1  0  0  . . . 0 1  2      0 1  0  12 0  1  0  . . . 0 1  3      1 1  9  12 0  0  1  . . . 0 2  1      0 0  4  6  1  0  0  . . . 0 3  1      0 1  0  17 1  0  0  . . . 0 3  2      0 1  3  17 0  1  0  . . . 0 3  3      0 1  3  17 0  0  1  . . . 0 etc. 

First of all notice both ID and period which define the hierarchical period of observation nested in person structure of these data. Also notice that x2 is time varying (i.e. within the same individual it can take different values in different periods), and that x1 and x3 are static; understand that the model is agnostic as to whether predictors are time-varying or static. Finally examine the relationship between period and the indicator variables for time/period (i.e. t1 through tT).

Often times you will receive data in a person-time format such as this:

ID TimeToEvent Censored x1 x2t1 x2t2 . . . x2tT x3, 

and will need to transform the data appropriately. Here TimeToEvent measures how many periods each subject was observed while in the study, and Censored indicates whether or not the subject left the study without experiencing the event (i.e. whether that subject was right censored). In your data TimeToEvent probably equals end – start, and Censored is certainly some function of state.

There are often tools available for transforming data such as these. For example, in Stata, see net describe dthaz, from(http://alexisdinno.com/stata)