Another approach to analyze survival data is to use regression analysis. This can be accomplished by applying Cox regression, which allows us to calculate a special form of rate ratios known as hazard ratios. Therefore, instead of just a P value provided by the log-rank test, we can obtain an effect estimate with its confidence intervals, and at the same time we can adjust for other categorical or continuous covariates and interactions.
Hazard vs rate
The true distinction is that a hazard is instantaneous, whereas a rate is calculated over a period of time (and usually it is implicitly assumed to be constant over this period).
An analogy could be made with speed; the rate is like average speed: you take the total distance you drove and divide it by the amount of time it took. The hazard is what your speedometer showed at any point in time.
In Table I , we used Cox regression to perform the same analysis as in the previous article with the log-rank test.
Hazard ratio | 95% CI | P value | |
---|---|---|---|
Type of wire | |||
Wire A | Reference | ||
Wire B | 1.28 | 0.70-2.36 | 0.42 |
The hazard ratio of 1.28 indicates that the hazard (instant probability) to experience the event (reach alignment) is 28% higher for wire B compared with wire A. The interpretation is similar to the previously encountered regression output. The P value is 0.423 (same as the log-rank test), and it indicates no statistically significant difference between the wires in terms of the instant probability of reaching the alignment.
In Table II , we compare the rates of alignment between wire B vs wire A after adjusting for the amount of crowding. This is logical, since it is likely that in small trials there could be imbalances between treatment groups in terms of crowding. If 1 group has greater mean crowding, then it is likely that the time to reach alignment (the event) will increase; hence, if we do not take it into account, we might incorrectly infer that 1 wire is inferior or superior to the other.
Hazard ratio | 95% CI | P value | |
---|---|---|---|
Type of wire | |||
Wire A | Reference | ||
Wire B | 1.43 | 0.78-2.65 | 0.25 |
Crowding | Per unit (mm) | ||
0.73 | 0.60-0.88 | 0.001 |