page_title: Hazard ratio
section_title: Interpretation
hierarchical_section_title: Hazard ratio / Interpretation
caption_attribution_description: English: The Kaplan-Meier curves representing the survival outcomes of 275 patients treated for newly diagnosed brain metastases at Cancer Care Northwest and Gamma Knife of Spokane between 1998 and 2008.
context_page_description: In survival analysis, the hazard ratio is the ratio of the hazard rates corresponding to the conditions described by two levels of an explanatory variable. For example, in a drug study, the treated population may die at twice the rate per unit time as the control population. The hazard ratio would be 2, indicating higher hazard of death from the treatment. Or in another study, men receiving the same treatment may suffer a certain complication ten times more frequently per unit time than women, giving a hazard ratio of 10.
  Hazard ratios differ from relative risks and odds ratios in that RRs and ORs are cumulative over an entire study, using a defined endpoint, while HRs represent instantaneous risk over the study time period, or some 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.
context_section_description: In its simplest form, the hazard ratio 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 hazard). The hazard ratio is simply the relationship between the instantaneous hazards in the two groups and represents, in a single number, the magnitude of distance between the Kaplan–Meier plots.
  Hazard ratios do not reflect a time unit of the study. The difference between hazard-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 hazard ratio per time period, it is assumed that difference between groups was proportional. Hazard ratios become meaningless when this assumption of proportionality is not met.
  If the proportional hazard assumption holds, a hazard ratio of one means equivalence in the hazard rate of the two groups, whereas a hazard ratio other than one indicates difference in hazard 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 hazard ratio, e.g. derived from the standard deviation of the Cox-model regression coefficient, i.e. .  Statistically significant hazard ratios cannot include unity (one) in their confidence intervals.
caption: Kaplan-Meier curve illustrating overall survival based on volume of brain metastases. Elaimy et al. (2011)[4]
exif: {}