Correct understanding of risk ratio (HR) in clinical trials

One, what is it? In oncology randomized clinical trials (NCTs), risk ratios (HRs) are often used to estimate therapeutic effects, such as total lifetime (OS) and progress-free lifetime (PFS), up to the end of the event.
HR provided an estimate of the risk-rate ratio between the trial and control groups throughout the study period.
risk rate refers to the proportion of patients in each treatment group in the study who had an event of concern (including death, continued monitoring, or cessation of monitoring) over a short interval.
this concept can be illustrated by a hypothetical example: Table 1 shows an RCT study with two treatment groups and one primary endpoint OS.
week, the mortality rate (0.04) was higher in the control group than in the pilot group (0.03).
the second week of the study, the patient mortality rate was twice that of the first week: 0.08 in the control group and 0.06 in the trial group.
calculated weekly HR (trial and control group) by divided the patient mortality rate in the pilot group by the patient mortality rate in the control group.
the risk rate varies over time, the weekly HR is roughly constant (0.75) (Table 1).
, the HR reported by this RCT is 0.75.
HR is usually calculated based on the Cox scale risk model, one of the standard methods for analyzing survival endpoints in oncology RCT.
simplification, HR=1 implies the ethonthrecy of the trial and control treatment< (> Figure 1);
, why is it useful? The number rank and Wilcoxon tests are typically used to compare the entire survival data between treatment groups during the trial, but produce only p-values rather than estimates of the magnitude or direction of the therapeutic effect.
, the number of rankings and the Wilcoxon test only determine whether the treatment is different, but does not indicate that one treatment is superior to or inferior to the other.
three main methods for estimating the magnitude and direction of RCT survival outcomes include (i) HR, (ii) reporting the mid-life of each treatment group, and (iii) point-in-time analysis (e.g. 1 year OS rate), the latest two of which are usually generated by KM analysis.
, however, there are differences between HR and the other two indicators in the following areas.
, HR encompasses all the information in the entire KM survival curve, thus summarizing the therapeutic effect of RCT over the entire duration.
, the median lifetime focuses on only one point on the survival curve of the treatment group, representing the "average age of the group" at most, and is too simple as an indicator of the duration of disease control or OS in individual patients.
, HR provides an estimate of the relative efficacy between treatment groups (e.g., HR at the end of OS is 0.75, meaning that the risk of death in the trial group is about 25% lower than in the control group).
, because of these two characteristics, it is recommended to make a declaration of merit and non-effectiveness based on HR rather than the probability of survival at a neutral lifetime or a particular point in time.
, you can calculate the corrected and unrecaled HRs.
uncorred HR is calculated based on a single-variable Cox scale risk model, whereacorration of HR is typically performed using a multivariate Cox model, which also contains covariates that will be corrected, such as age, gender, disease stage, and physical state.
, the probability of survival based on the KMT survival curve, such as the one-year OS rate, is often not corrected.
, what are the limitations? The correct interpretation of HR is based on the assumption that the risk ratio ratio for each interval during the study period is approximately constant, which is also known as the Proportional Risk (PH) hypothesis.
the PH hypothesis can be determined by formal statistical tests and charts such as Martingale residuals, Schoenfeld residuals and time diagrams, and log-negative-log plots.
, however, assumptions are usually established by reviewing the shape of the KM survival curve, so the results of formal testing are rarely reported in the literature.
if the separation between curves is maintained over time, the PH hypothesis may hold (Figure 3A).
, a slight decrease or increase in separation may slightly violate the PH hypothesis (Figure 3B).
Given the low survival rate of most cancers, the KM curve usually gathers together if the trial lasts long enough, because advanced cancers are usually incurable and most patients have died or been deleted.
, the KM survival curve produced in most oncology clinical trials is quite consistent with the PH hypothesis.
it is worth noting that the fitting excellence of the Cox model should also be evaluated.
, how to explain? 1. Appropriate explanation Assuming that the HR of a trial evaluating OS is 0.75 and the PH hypothesis is true (Figure 3A), it can be interpreted as: at any point during the trial, the risk of death in the trial group was reduced by an average of about 25% or the survival time was improved by about 33% on average compared to the control group.
note that this is an average (assuming that survival data is exponentially distributed) and that such lifetime improvements or risk reductions should be explained in the context of the overall KM curve.
2, inappropriate interpretation, and common error 2.1 Cross-survival curve If the KM curve seriously violates the PH hypothesis (Figure 3C), it is not appropriate to interpret the overall HR, as HR changes significantly over time.
In this case, subgroup analysis should be used to explore whether qualitative interactions drive the KM curve to cross across the population (e.g., whether the male HR is in the opposite direction and whether there is a statistically significant difference with the female HR).
if significant qualitative interactions are found, the KM curves of a single sub-group should be analyzed to determine whether the PH hypothesis is true in these sub-groups.
, statements of efficacy should be avoided for all randomized patient populations.
As with any subgroup analysis, the excellence cannot be claimed in the patient subgroup unless the subgroup analysis is pre-defined, statistically significant interactions are observed, and there is sufficient empirical evidence to verify the subgroup effect.
2.2 Clinical significance HR is a relative indicator.
As a result, a statistically significant p-value associated with HR=0.75 (p -lt; 0.05) may be available, which may mean that (i) the experimental treatment is better or inferior to the control group, or (ii) there is a maximum 5% chance that the magnitude or more extreme effects will be observed if there is no difference between treatments.
seems to be a positive outcome for patients, but whether it is clinically significant remains to be seen.
, clinicians need to combine absolute indicators to find consistent clinically significant improvements, such as survival probability and mid-life at a particular point in time.
, if the 1-year and 2-year OS rates increased by 10% and 20% between the treatment groups in the late NSCLC trial, respectively, HR s 0.75 may be considered a clinically significant improvement.
the 50-day improvement can also be considered clinically significant if the difference in mid-life between groups is taken into account, while an improvement of about 10 days may not be clinically significant.
statistically significant HR can only be called clinical progress if descriptive absolute indicators show a consistent improvement in clinical significance.
2.3 HR extradescence beyond the duration of the study Using RCT-reported HR to predict the duration of the study (randomly assigned from the first patient to the last patient visit) should be very cautious and generally not recommended.
in the absence of follow-up information, it is not possible to determine whether the proportional risk assumption continues to hold.
, follow-up or palliative care will also seriously affect the patient's chances of survival.
using Cox proportional risk models to analyze RCT survival data to provide an HR that evaluates the relative efficacy of the trial and control groups.
like everything else in clinical medicine, testing statistical assumptions and estimating therapeutic outcomes should always take into account consistent clinical significance.
, all these statistical tests are designed to achieve the noble goal of uncovering the truth and improving the lives of patients, providing useful treatment and avoiding unnecessary exposure to ineffective or suspected effective treatment.
: Barraclough H, Simms L, Govindan R. Biostatistics Primer: What a clinician ought to know: hazard ratios. J Thorac Oncol. 2011 Jun; 6(6):978-82. doi: 10.1097/JTO.0b013e31821b10ab. Erratum in: J Thorac Oncol. 2011 Aug; 6(8):1454. PMID: 21623277.