Odds ration can not be negative. It is always positive. Whether or not there is a protective effect or negative effect will be judged by the odds ratio greater than 1 or less than one. The same applies to other ratios such as hazard ratio, risk ratio 2:34 PM The hazard ratio of death for the intervention group compared with the control group was 0.46 (0.22 to 0.95), which is smaller than unity (1.0). Therefore, the hazard of death in the isoniazid prophylaxis group was less than that in the control group. When events in the intervention group are significantly less frequent than in the control group, then relative risk, odds ratio and hazard ratio (and their confidence intervals) will be less than 1.0. If the converse holds true, these values will be greater than 1.0. That is, the hazard ratio comparing treat=1 to treat=0 is greater than one initially, but less than one later. We might interpret this to mean that the new treatment initially has a detrimental effect on survival (since it increases hazard), but later it has a beneficial effect (it reduces hazard). Hazard ratio=1 means no difference between the two. Getting one is as likely as getting the other. Flipping a coin will give you heads or tails equally lightly. Hazard ratio>1= there is a difference between the 2 groups, and that it is a causative effect. Hazard ratio<1= there is a difference between the 2 groups, but it's a protective effect. 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 ofby xx%" or "increase the chance of [event] by xx%". Assuming proportional hazards (as in a Cox model) and the hazard ratio for a 1 mg increase in nicotine smoked a day is 1.02, then this tells you that persons smoking 11 mgs were 1.02 as likely to die in the monitored time period than persons smoking 10 mgs. The same applies to 12 vs 11 mgs etc. As for the other measures of association, a hazard ratio of 1 means lack of association, a hazard ratio greater than 1 suggests an increased risk, and a hazard ratio below 1 suggests a smaller risk. We have presented here how to calculate the measures of association. What we obtain from these calculations is what we call the point estimates. If the hazard ratio is larger than 1 it means an increased risk of an event across all time points, on average, while if it is less than 1 there is a reduction in that same risk. If instead of risk you are measuring positive events like recovery from illness then the reverse is true: an HR greater than 1 means increased likelihood for a When there are ties, both methods are less accurate. The logrank methods tend to report hazard ratios that are even closer to 1.0 (so the reported hazard ratio is too small when the hazard ratio is greater than 1.0, and too large when the hazard ratio is less than 1.0).
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