Tutorial about Hazard Ratios

Posted on April 5, 2016

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You have been asked to run a journal club in your department about heart failure. You followed the key steps of Evidence-Based Practice that you have learned: formulated a clear searchable clinical question, searched the main databases and came across this recent hypothetical article.

In this hypothetical article, the authors conducted a randomised controlled trial to investigate the effectiveness of a new treatment for improving the survival of patients with heart failure. A total of 105 patients were randomised to the treatment group and a total of 106 were randomised to the control group. The primary outcome was the overall survival rate.

The main result of this trial can be summarised in this paragraph: “After a median follow-up of 1500 days, the hazard ratio for death in the treatment group, 0.38; 95% confidence interval [CI], 0.28 to 0.53; P<0.0001).”

In addition, the authors presented the figure below summarizing their main results:

Figure 1 - Loai (JPEG)

Figure produced by the author using R software
(Blue line represents treatment group and green line represents control group).

You want to critically appraise the article. However, you have some difficulty understanding its main results and have a few questions:

In this blog, you may find the answers to these questions.

What is a Hazard Ratio & what are Confidence Intervals?

Hazard ratio (HR) is a measure of an effect of an intervention on an outcome of interest over time. Hazard ratio is reported most commonly in time-to-event analysis or survival analysis (i.e. when we are interested in knowing how long it takes for a particular event/outcome to occur).

The outcome could be an adverse/negative outcome (e.g. time from treatment/surgery until death/relapse) or a positive outcome (e.g. time to cure/discharge/conceive/heal or disease-free survival).

Hazard Ratio (i.e. the ratio of hazards) = Hazard in the intervention group ÷ Hazard in the control group

Hazard represents the instantaneous event rate, which means the probability that an individual would experience an event (e.g. death/relapse) at a particular given point in time after the intervention, assuming that this individual has survived to that particular point of time without experiencing any event.

Confidence Interval (CI): is the range of values that is likely to include the true population value and is used to measure the precision of the study’s estimate (in this case, the precision of the Hazard Ratio). The narrower the confidence interval, the more precise the estimate. (Precision will be affected by the study’s sample size). If the confidence interval includes 1, then the hazard ratio is not significant.

Interpretation of Hazard Ratio

Because Hazard Ratio is a ratio, then when:
HR = 0.5: at any particular time, half as many patients in the treatment group are experiencing an event compared to the control group.
HR = 1: at any particular time, event rates are the same in both groups,
HR = 2: at any particular time, twice as many patients in the treatment group are experiencing an event compared to the control group.

Applying this to our hypothetical study results:

In the results, the authors reported that the hazard ratio for death with the new treatment = 0.38 (95% CI, 0.28-0.53; P<0.0001). What does that mean?

Patients in the new treatment group at any time point during the study period were 62% less likely to die than patients in the control group, and we are 95% confident that the true value is lying between 47%-72%. (i.e. we are 95% sure that patients in the new treatment group were between 47% and 72% less likely to die than patients in the control group). 

Kaplan-Meier curve (or Survival curve)

Figure 2 - Loai (JPEG)

Figure produced by the author using R software
(Blue line represents treatment group and green line represents control group).

Kaplan-Meier curve: is a graphical method of displaying survival data or time-to-event analysis (i.e. the proportion of patents surviving against time) and is usually drawn as a step function.

Interpretation of this figure

The results of this graph can be communicated in various ways:

Hazard Ratios vs. Risk Ratios (or Relative Risk)

Hazard ratio is frequently interpreted as risk ratio (or relative risk), but they are not technically the same. However, if that helps you to understand hazard ratio then it is OK.  But keep in mind HR is not RR.

One of the main differences between risk ratio and hazard ratio is that risk ratio does not care about the timing of the event but only about the occurrence of the event by the end of the study (i.e. whether they occurred or not: the total number of events by the end of the study period). In contrast, hazard ratio takes account not only of the total number of events, but also of the timing of each event.

References & Further Reading

  1. Altman D.G., Bland J.M. Time to event (survival) data. BMJ 1998; 317:468
  2. Bland J.M., Altman D.G. Survival probabilities (the Kaplan-Meier method). BMJ 1998;317:1572
  3. Spruance S.L., Reid J.E., Grace M., Samore M. Hazard ratio in clinical trials. Antimicrob Agents Chemother 2004; 48: 2787–2792.
  4. Sedgwick P. How to read a Kaplan-Meier survival plotBMJ 2014; 349: g5608
  5. Sedgwick P. Hazards and hazard ratiosBMJ 2012; 345: e5980

 

Loai Albarqouni

Hi, I am Loai Albarqouni, a Ph.D. candidate at the Center for Research in Evidence-Based Practice, Bond University, Australia. Before, I completed my medical degree (MD) at AlQuds University and a masters degree in Epidemiology at Ludwig Maximilian University of Munich.

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Tutorial about Hazard Ratios by Loai Albarqouni is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. Unless otherwise stated, all images used within the blog are not available for reuse or republication as they are purchased for Students 4 Best Evidence from shutterstock.com.

22 thoughts on “Tutorial about Hazard Ratios

  1. Alvaro Whittembury

    I would recommend to add that the intervention reduced the risk of death by 62% (1-(0.38)*100) when compared to the comparison group.

    Reply
    1. Loai Albarqouni Post author

      Sure, and i did something similar in the definition of hazard ratio : “Patients in the new treatment group at any time point during the study period were 62% less likely to die than patients in the control group”

      Reply
  2. April

    Hi Loai. Could you please clarify this statement:

    we are 95% confident that the true value is lying between 47%-72%. (i.e. we are 95% sure that patients in the new treatment group were between 28% and 53% less likely to die than patients in the control group.

    Wouldn’t it be (i.e. we are 95% sure that patients in the new treatment group were between 47% and 72%. less likely to die than patients in the control group?

    Thanks in advance.

    Reply
  3. MedTrial

    Hi, Loai!
    I have a question related to this topic, please.
    I have 4 groups (let’s call them A, B, C and D) and I am given hazard ratios with confidence intervals for groups B, C and D with A being the comparator. What I really want to do is combine A, B and C ‘s data and have that whole group compared to group D. Possible? How?
    Thanks in advance!

    Reply
  4. Janine Khuc

    HI there, thank you for the explanation it was super helpful. If I had the average age for the treatment and control group, would it be possible to “translate” Hazard Ratios in years of life expectancy following treatment relative to control?

    Many Thanks,
    Janine

    Reply
  5. Scott Lonning

    Loai
    Very nice explanation on HR. The best I’ve ever seen and much appreciated. I’m sharing with my staff!
    Thank you

    Reply
  6. Simon

    I am still confused about the difference between HR and RR. You say HR takes into account timing. Does this mean HR is actually a function of time, HR(t)? If so, then is the reported HR basically an average at the end of the study? Doesn’t that make a single HR number quite equivalent to Risk Ratio? Or what? Thanks

    Reply

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