hazard ratio vs relative risk

  • related: Biostats
  • tags: #literture #pulmonary

The patients in this large cohort receiving factor Xa inhibitors developed new ILD at a rate of 0.29 per 100 patient-years compared with 0.17 in the warfarin group. The increased chance of this adverse reaction can be converted into a number-needed-to-harm (NNH) outcome in the same manner that a beneficial treatment can be converted into a number needed to treat (NNT). To calculate the NNH, first calculate the absolute risk reduction (ARR), which is simply the arithmetic difference in the two rates: (0.29/100 − 0.17/100) = 0.12/100 = 0.0012. For trials with binary data, the NNH (or NNT) is simply the reciprocal of the ARR: 1 / 0.0012 = 833. This represents the incident risk and not just what may have happened in the first year of the study (choice A is correct).

Like ORs and relative risks, hazard ratios are statistical tools designed to help assess probabilities of events. However, unlike ORs and relative risks, which are probabilities at a specific point in time (eg, after 12 months of treatment), hazard ratios are time-to-event probabilities and account for developing an event at multiple points during the study period. This feature of hazard ratios allows better comparisons between groups and reduces the effect of biases that might develop when subjects drop out or cannot complete the study as planned. They also account for the effect of developing the event very early or very late in the study's time period.

For point-in-time measures of probability, both ORs and relative risks provide guidance, but in different ways. ORs are simply the odds of an event occurring in the intervention group divided by the odds of an event occurring in the control group. Figure 1 outlines a contingency table (2 × 2) that may help illustrate these definitions and their differences.

This study presents hazard ratios rather than relative risks or ORs, so the calculation of 1.7 is based on incorrect data (choice C is incorrect). From the data provided, it is not possible to determine how many patients developed ILD in the first year of this study (choice D is incorrect).

Sure! Here’s a simpler breakdown of the differences between relative risk and hazard ratio:

  1. Relative Risk (RR): This measures the probability of an event (like getting a disease) happening in one group compared to another group at a specific time (like after 12 months). It tells you how much more or less likely the event is in one group compared to the other at that point.
  2. Hazard Ratio (HR): This measures the rate at which events happen over time. Instead of looking at just one point in time, it considers the entire study period. So, it tells you how quickly events are happening in one group compared to another group, taking into account when those events happen (early or late in the study).
  3. Why HR is Helpful: Because it looks at the timing of events, the hazard ratio helps give a clearer picture of how groups compare over the whole study. It can handle situations where people drop out or don’t finish the study, which might skew the results if only looking at one point in time.

In summary, while relative risk focuses on a specific moment, hazard ratios look at the entire time frame and timing of events, making them more robust for certain analyses.