Kaplan-Meier curve illustrating overall survival based on volume of brain metastases. Elaimy et al. (2011) In its simplest form, the<unk>  can be interpreted as the chance of an event occurring in the treatment arm divided by the chance of the event occurring in the control arm, or vice versa, of a study. The resolution of these endpoints are usually depicted using Kaplan–Meier survival curves. These curves relate the proportion of each group where the endpoint has not been reached. The endpoint could be any dependent variable associated with the covariate (independent variable), e.g. death, remission of disease or contraction of disease. The curve represents the odds of an endpoint having occurred at each point in time (the<unk> . The<unk>  is simply the relationship between the instantaneous<unk> s in the two groups and represents, in a single number, the magnitude of distance between the Kaplan–Meier plots.<unk> s do not reflect a time unit of the study. The difference between<unk> -based and time-based measures is akin to the difference between the odds of winning a race and the margin of victory. When a study reports one<unk>  per time period, it is assumed that difference between groups was proportional.<unk> s become meaningless when this assumption of proportionality is not met. If the proportional<unk>  assumption holds, a<unk>  of one means equivalence in the<unk>  rate of the two groups, whereas a<unk>  other than one indicates difference in<unk>  rates between groups. The researcher indicates the probability of this sample difference being due to chance by reporting the probability associated with some test statistic. For instance, the from the Cox-model or the log-rank test might then be used to assess the significance of any differences observed in these survival curves. Conventionally, probabilities lower than 0.05 are considered significant and researchers provide a 95% confidence interval for the<unk> , e.g. derived from the standard deviation of the Cox-model regression coefficient, i.e. . Statistically significant<unk> s cannot include unity (one) in their confidence intervals. The proportional<unk> s assumption The proportional<unk> s assumption for<unk>  estimation is strong and often unreasonable. Complications, adverse effects and late effects are all possible causes of change in the<unk>  rate over time. For instance, a surgical procedure may have high early risk, but excellent long term outcomes. If the<unk>  between groups remain constant, this is not a problem for interpretation. However, interpretation of<unk> s become impossible when selection bias exists between groups. For instance, a particularly risky surgery might result in the survival of a systematically more robust group who would have fared better under any of the competing treatment conditions, making it look as if the risky procedure was better. Follow-up time is also important. A cancer treatment associated with better remission rates might on follow-up be associated with higher relapse rates. The researchers' decision about when to follow up is arbitrary and may lead to very different reported<unk> s. The<unk>  and survival<unk> s are often treated as a<unk>  of death probabilities. For example, a<unk>  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<unk> . Therefore, with a<unk>  of 2, if (20% survived at time t), (4% survived at t). The corresponding death probabilities are 0.8 and 0.96. It should be clear that the<unk>  is a relative measure of effect and tells us nothing about absolute risk. While<unk> s allow for hypothesis testing, they should be considered alongside other measures for interpretation of the treatment effect, e.g. the<unk>  of median times (median<unk>  at which treatment and control group participants are at some endpoint. If the analogy of a race is applied, the<unk>  is equivalent to the odds that an individual in the group with the higher<unk>  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: *<unk>  = P/(1 − P); P =<unk> /(1 +<unk> . In the previous example, a<unk>  of 2 corresponds to a 67% chance of an early death. The<unk>  does not convey information about how soon the death will occur. The<unk> , treatment effect and time-based endpoints Treatment effect depends on the underlying disease related to survival function, not just the<unk> . Since the<unk>  does not give us direct time-to-event information, researchers have to report median endpoint times and calculate the median endpoint time<unk>  by dividing the control group median value by the treatment group median value. While the median endpoint<unk>  is a relative speed measure, the<unk>  is not. The relationship between treatment effect and the<unk>  is given as . A statistically important, but practically insignificant effect can produce a large<unk> , e.g. a treatment increasing the number of one-year survivors in a population from one in 10,000 to one in 1,000 has a<unk>  of 10. It is unlikely that such a treatment would have had much impact on the median endpoint time<unk> , which likely would have been close to unity, i.e. mortality was largely the same regardless of group membership and clinically insignificant. By contrast, a treatment group in which 50% of infections are resolved after one week (versus 25% in the control) yields a<unk>  of two. If it takes ten weeks for all cases in the treatment group and half of cases in the control group to resolve, the ten-week<unk>  remains at two, but the median endpoint time<unk>  is ten, a clinically significant difference.
Hazard ratio
Odds ratio
Risk difference
Minimal important difference
Absolute threshold
Threshold limit value
Standardized mortality ratio
Indicative limit value