Worked example using Method 2: Hazard ratio calculated using event counts.

HR = Hazard Ratio, CI = Confidence Interval, eq. = equation, est. = estimated, Vr is the inverse variance of the log hazard ratio for the robotic group, OTotal is the total number of events in the robotic plus the comparison group, “Ln” denotes the natural logarithm (loge), Φ-1 is the inverse of the standard normal distribution, and the p-value is assumed to be 2-sided and from the log-rank test if not otherwise stated. Because p-values were assumed to be two-sided, manual assignment of direction was adjusted by multiplying the term by -1 or 1 so that the result was negative when survival in the robotic group was higher/better and positive when survival in the robotic group was lower/worse.