Statistics for Maintenance Modelling: Proportional Hazards and Accelerated Life Models

# Case Study 2 - Estimation of Survival Data Parameters¤

It is wise to centre some of the covariates to show the variation against the mean more clearly, and here just y1, y2 and y3 are centred since they are the dominant covariates. The log likelihood (from screen 7) is then:

Ln L () = Constant + r(ln ) -

where r is the number of complete life times.

Maximum likelihood estimates for = (1, 2, ... 7) and (the baseline constant hazard rate) are readily obtained by some numerical iteration algorithms, and are listed in this table.

| 1 | 2 | 3 | 4 | 5 | 6 | 7
4.722 | 0.054 | 0.0085 | 0.0034 | 0.3448 | -0.121 | -0.863 | -0.277

This suggests that y1 (performance status) is important in terms of confined impact of 1y1 to the hazard function, but that y2 and y3 are not. In addition, once performamce status has been accounted for, treatment and tumor type do not appear to have sizeable effects, though there is a suggestion that the Adeno tumor type is important.

Ln L () = Constant + +