There is a mathematical relation between a survival function and a hazard function (e.g. Fisher & van Belle,1993: Chp. 16). The survival functions in slide 17 give hazard functions that look roughly like those shown in this slide. On the left panel, the two hazard functions have roughly the same patterns. A lower hazard function (blue line) indicates a survival function that is decreasing less sharply. The ratio of hazard given by the blue line divided by that of the red line is approximately 0.6 at any time; hence proportional hazard is true. On the right panel, initially the red line is above the blue line, but they cross over at about time 12. The hazard ratio moves from below one (blue group better) to above one (blue group worse), violating the proportional hazard assumption.