Hi Jacob, thenare you agree with this paragraph when hazard ratio=2 or 3? For any randomly selected pair of patients, one from the treatment group and one from the control group, the hazard ratio is the odds that the time to healing is less in the patient from the treatment group than in the patient from the control group. With the following equation, the probability of healing first can easily be derived from the odds of healing first, which is the probability of healing first divided by the probability of not healing first: hazard ratio (HR) = odds = P/(1 − P); P = HR/(1 + HR). A hazard ratio of 2 therefore corresponds to a 67% chance of the treated patient's healing first, and a hazard ratio of 3 corresponds to a 75% chance of healing first. ... View more

Hi Jacob, thanks for answer, I appreciate your interest in this discussion... For me the different between RR and HR is clear Hazard ratios differ from relative risk (or risk ratio not relative risk rations) in that risk ratios are cumulative over an entire study (you must use a defined endpoint which is pre-selected during design phase), while hazard ratios represent instantaneous risk at some particular time period during study, or a subset thereof. Hazard ratios suffer somewhat less from selection bias with respect to the endpoints chosen, and can indicate risks that happen before the endpoint. But...still I can see in the literature papers talking about the HR in terms of probabilities, and still I want to understand it, because there not only one paper saying that, i have seen many, maybe we are missing something here: Please can you have a look in these two ones and let me know if they are still wrong considering HR as a probability? This one: What does a 13% increased risk of death mean? | Understanding Uncertainty where the author saying.. An extremely elegant mathematical result, proved here , says that if we assume a hazard ratio h is kept up throughout their lives, the odds that Mike dies before Sam is precisely h. Now odds is defined as p/(1−p), wherep is the chance that Mike dies before Sam. Hence p=h/(1+h)=0.53. and looks like the mathematical prove is shown in this other one: Can we say whether a drug would have enabled someone to live longer? Sadly not. | Understanding Uncertainty Please, can you have a look on these two articles, and let me know what do you think? Thanks, . ... View more

Thanks for the explanation.more clear now...but My question is, in terms of HR=2.563, can we say something about the percentage 156.3% increase in hazard for using IV drugs controlling for age? Or how you interprete it? Thanks. ... View more

In other words: I have the next result applying PHREG: phreg data=test; model time*censor(0)=age drug / risklimits; 'Cox model for TEST data-- ties'; ; run; age HR=1.096 Treatment(drug use) HR=2.563 I should understand it as: 9.6% increase in hazard for every 1-year increase in age, controlling for the effect of IV drug use; and 156.3% increase in hazard for using IV drugs, controlling for age....but I think this 156.3% doesnt have many sense. Thanks. ... View more

Thnaks, but can you explain me this from wikipedia: The hazard ratio and survival[edit] Hazard ratios are often treated as a ratio of death probabilities. [2] For example, a hazard ratio of 2 is thought to mean that a group has twice the chance of dying than a comparison group. In the Cox-model, this can be shown to translate to the following relationship between group survival functions: (where r is the hazard ratio). [2] Therefore, with a hazard ratio of 2, if (20% survived at time t), (4% survived at t). The corresponding death probabilities are .8 and .96. [9] It should be clear that the hazard ratio is a relative measure of effect and tells us nothing about absolute risk. [11] While hazard ratios allow for hypothesis testing, they should be considered alongside other measures for interpretation of the treatment effect, e.g. the ratio of median times (median ratio) at which treatment and control group participants are at some endpoint. If the analogy of a race is applied, the hazard ratio is equivalent to the odds that an individual in the group with the higher hazard reaches the end of the race first. The probability of being first can be derived from the odds, which is the probability of being first divided by the probability of not being first: HR = P/(1 − P); P = HR/(1 + HR). In the previous example, a hazard ratio of 2 corresponds to a 67% chance of an early death. The hazard ratio does not convey information about how soon the death will occur. [1] ... View more