9 Survival – prognosis
Time to an event (e.g. recovery, death, etc.) is one of the main outcomes of interest in medicine. Data on the time to an event are called survival data, irrespective of whether the event is death or not, as it represents the time that the patient survives until they experience the event of interest e.g. time to pregnancy for women undergoing fertility treatment. Typically there will be some patients who do not experience the event of interest for example because they are lost to follow-up or they experience some other event. These are known as ‘censored’ observations and they require special handling in the data analysis. In particular methods such as the log rank test and Cox proportional hazards regression have been developed to analyse survival data as they can explicitly deal with censored observations. Survival data can be plotted using Kaplan-Meier curves. The Kaplan-Meier curve plots average patient survival over time for the outcome of interest. Survival curves for several groups can be plotted together to show the survival of the groups relative to each other. The plot below shows the survival curves until return to work for two groups of patients with lower back pain, one randomised to specialised treatment by an occupational therapist and the other randomised to receive usual care. It can be seen that patients in the occupational therapy group returned to work more quickly over the 1 year follow-up period than patients in the control group.
Log Rank test
The log rank test is used to compare the survival curves for two groups. It assumes that the survival times are ordinal or measurable and that the risk of an event in one group relative to the risk in the other group does not change over time (proportional hazards assumption). The null hypothesis assumes that the median survival is the same in the two groups and the test examines the difference between the observed and expected number of events in each group given the survival experience of the two groups. The p-value obtained from the comparison between the treatment groups in the occupational therapy trial was 0.003 indicating that the two groups differed significantly in their time to return to work.
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Figure 11: Kaplan-Meier curves for time until return to work for participants in a randomised controlled trial of treatments for lower back pain |
Cox proportional hazards regression
The log rank test can be extended to adjust for multiple risk factors. This is called Cox proportional hazards regression. For the OT example above, it may be that in comparing the return to work times of the two groups, it is necessary to adjust for age, severity of original back pain, and whether the pain was of an acute onset, or chronic as all may affect healing. The outcome measure from a Cox regression analysis is the hazard ratio which may be interpreted as a relative risk of survival between the two groups adjusted for survival times.
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