Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 38 / 5 / iv / Solution

For the mild-to-moderate transition intensity, an increment $\Delta$ in a single covariate, with the others held fixed, gives the multiplicative ratio $\exp (b_{12,k}\Delta )$. Of the four printed effects on this transition, sex and HAQ have $95\%$ confidence intervals excluding zero on the log-intensity scale.

With male coded $1$ and female coded $0$, the estimated hazard ratio for males relative to females isThus, conditional on currently being mildly fatigued and on the other covariates, males have an estimated mild-to-moderate transition intensity about $54\%$ lower than females. The conclusion concerns this particular instantaneous transition, rather than a general $54\%$ reduction in fatigue probability.

For a one-point increase in HAQ, indicating greater physical disability, the estimated intensity multiplier isGreater disability is therefore associated with a substantially faster mild-to-moderate transition, after adjustment for sex, arthritis duration and haemoglobin. Both conclusions use the specified log-linear transition intensity model and the nominal individual $95\%$ intervals. Arthritis duration and haemoglobin have intervals including zero for this transition, so their effects here are not statistically significant at $5\%$; this says neither that their effects are zero nor that they are insignificant for all other transitions.