Interpreting Hazard Ratio: Can we say "percent reduction in risk"?

For time to event variable, the most commonly used statistics is hazard ratio. Hazard ratio is the ratio of hazards and equals to the hazard rate in the treatment group ÷ the hazard rate in the control group. Hazard rate represents the instantaneous event rate, which means the probability that an individual would experience an event at a particular given point in time after the intervention. While the hazard rate is associated with the event rate or median survival time, the hazard rate itself does not have a lot of meaning in interpreting the clinical trial results (see a previous post "Some Explanations about Survival Analysis or Time to Event Analysis"). However, we use hazard ratio (HR) to measure the treatment effect (i.e., the effect of an intervention on an outcome of interest over time comparing to the control group). 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). Hazard ratio can be obtained and calculated from the Cox regression - or Cox proportional hazard regression model.

The event outcome could be an adverse/negative outcome, for example, progression-free survival (PFS) and overall survival (OS) in oncology studies or a positive outcome, for example, time to cure/discharge/conceive/heal/virus not detectable. The very publicized trial by NIAID "A Multicenter, Adaptive, Randomized Blinded Controlled Trial of the Safety and Efficacy of Investigational Therapeutics for the Treatment of COVID-19 in Hospitalized Adults" demonstrated the benefit of Remdesivir in treatment of Covid-19 through the primary efficacy endpoint of 'time to recovery' where the event of recovery is a positive outcome defined as "the first day on which the subject satisfies one of the following three categories from the ordinal scale: 1) Hospitalized, not requiring supplemental oxygen - no longer requires ongoing medical care; 2) Not hospitalized, limitation on activities and/or requiring home oxygen; 3) Not hospitalized, no limitations on activities."

How to interpret the hazard ratio in lay language? 

According to ScienceDirect.com, The hazard ratio is the ratio of (chance of an event occurring in the treatment arm)/(chance of an event occurring in the control arm). The HR has also been defined as, the ratio of (risk of outcome in one group)/(risk of outcome in another group), occurring at a given interval of time.

While these interpretations of the hazard ratio may be clear to the statisticians, they are not straight forward to the public and non-statisticians. 

As described in an article by Sashegyi and Ferry "On the Interpretation of the Hazard Ratio and Communication of Survival Benefit", people would like to use an interpretation of hazard ratio in lay language. 

For a study with time to event variable where the event is a negative outcome, a hazard ratio < 1 is desirable for a successful trial. The hazard ratio will be interpreted as "percent reduction in risk". The hazard ratio is converted into "percent reduction in risk" using: 

     (1 − HR) ×100%

We could find many examples where that hazard ratio (and its 95% confidence interval) was used in the scientific papers, but "percent of reduction in risk" was used in the press releases or public announcements. 

In an article by de Bono et al (2020) "Olaparib for Metastatic Castration-Resistant Prostate Cancer", the result for PFS was presented as:

In cohort A, imaging-based progression-free survival was significantly longer in the olaparib group than in the control group (median, 7.4 months vs. 3.6 months; hazard ratio for progression or death, 0.34; 95% confidence interval, 0.25 to 0.47; P less than 0.001); a significant benefit was also observed with respect to the confirmed objective response rate and the time to pain progression.

In Sponsor's press release, "Submission based on PROfound, the first positive Phase III trial testinga targeted treatment in biomarker-selected prostate cancer patients"

Results of the PROfound trial showed Lynparza significantly reduced the risk of disease progression or death by 66% based on a hazard ratio of 0.34 (p less than 0.0001) vs. abiraterone or enzalutamide in patients with BRCA1/2 or ATM-mutated mCRPC, the primary endpoint of the trial.

In an article by Kato et al (2019) "Nivolumab versus chemotherapy in patients with advanced oesophageal squamous cell carcinoma refractory or intolerant to previous chemotherapy (ATTRACTION-3): a multicentre, randomised, open-label, phase 3 trial"

overall survival was significantly improved in the nivolumab group compared with the chemotherapy group (median 10·9 months, 95% CI 9·2–13·3 vs 8·4 months, 7·2–9·9; hazard ratio for death 0·77, 95% CI 0·62–0·96; p=0·019).

However, in the sponsor's press release, "% reduction in risk of death" was also added in addition to HR:

Opdivo demonstrated a 23% reduction in the risk of death and 2.5-month improvement in median overall survival compared to chemotherapy.

Opdivo demonstrated a statistically significant improvement over chemotherapy, with a 23% reduction in risk of death [Hazard Ratio (HR) 0.77; 95% Confidence Interval (CI): 0.62 to 0.96; p=0.019] and a 2.5-month improvement in median OS [10.9 months (95% CI: 9.2 to 13.3)] compared to patients treated with chemotherapy [8.4 months (95% CI: 7.2 to 9.9)]. The safety profile of Opdivo in this trial was consistent with previously reported studies in ESCC and other solid tumors.

The press release by BMS: "Phase III CheckMate -067 Trial Demonstrates Superior Progression-Free Survival of Opdivo+Yervoy Regimen or Opdivo Monotherapy vs. Yervoy Monotherapy in Previously Untreated Patients with Advanced Melanoma":

The Opdivo+Yervoy regimen demonstrated a 58% reduction in the risk of disease progression vs. Yervoy (hazard ratio: 0.42; 99.5% CI, 0.31 to 0.57; P less than 0.0001), while Opdivo monotherapy demonstrated a 43% risk reduction versus Yervoy monotherapy (hazard ratio: 0.57; 99.5% CI, 0.43 to 0.76; P less than 0.00001).

"Medivation and Astellas Announce The Phase 3 PREVAIL Trial of Enzalutamide Meets Both Co-Primary Endpoints of Overall Survival and Radiographic Progression-Free Survival in Chemotherapy-Naïve Patients With Advanced Prostate Cancer":

30% Reduction in the Risk of Death, Hazard Ratio=0.70 (p less than0.0001)

81% Reduction in the Risk of Radiographic Progression or Death, Hazard Ratio=0.19 (p less than 0.0001)

We can see from these examples that when an event is a negative outcome, it is pretty common to interpret the hazard ratio to "percent reduction in risk".

Similarly, when an event is a positive outcome, a hazard ratio greater than 1 is desirable for a successful trial. We may interpret the hazard ratio as "increase the probability of ...by xx%" or "increase the chance of [event] by xx%".

 xx% =  ( HR - 1) ×100%

In an article by Statnews "Data for Gilead’s potential coronavirus therapy are coming soon. Here’s what you need to know", it says the following about the hazard ratio:

If people who take the placebo show clinical improvement after 16 days, remdesivir would have to track at 13 days to demonstrate superiority with statistical significance, Raffat said. This would be described in what researchers call a “hazard ratio.” The magic number would be 1.2, meaning that patients do 20% better on remdesivir than placebo.

If the median time to event can be calculated, it is also straight forward to list the median time to event. It is easy for people to compare the median time to event between treatment groups to determine which group performs better. For example, if the overall survival (OS) is the endpoint and if at least 50% patients die in both treatment groups, the median survival times can be calculated using the Kaplan-Meier approach and the group with longer median survival time performs better.

The issue with this approach is that a lot of clinical trials with time to event variable as efficacy endpoint, the median time to event may not be calculable because of the low frequency of the events. 

Similarly, "percent reduction in risk" may also come from the odds ratio or risk ratio. In a recent press release by Gilead "Comparative Analysis of Phase 3 SIMPLE-Severe Study and Real-World Retrospective Cohort of Patients Diagnosed with Severe COVID-19 Receiving Standard of Care", remdesivir treatment was associated with significantly improved clinical recovery and a 62 percent reduction in the risk of mortality compared to standard of care. The '62 percent reduction...' was based on the odd ratio.

The mortality rate for patients treated with remdesivir in the analysis was 7.6 percent at Day 14 compared with 12.5 percent among patients not taking remdesivir (adjusted odds ratio 0.38, 95% confidence interval 0.22-0.68, p=0.001).