Research updates
Phase III clinical trials   page 6
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5. The endpoint   Link to the Medical Research Council web site
The endpoint
Endpoints are the outcome measures or events that are used to judge how effective or safe a treatment is. Ideally a trial would have an objective or 'hard' endpoint such as death, the complete disappearance of a tumour or no trace of infection in a sample. There is unlikely to be any bias in the way these events are reported since they can be detected with consistency in different patients and by different observers.

In designing a trial it is necessary to predict how many events will be needed to detect reliably if there are differences between two treatments which are likely to be clinically important. The time the trial will take is affected by the choice of endpoint. If the prognosis is good, a trial with survival as the main endpoint will take longer and, as a consequence, treatments will evolve more slowly. In such cases measures of the progression of the disease may be used as surrogate endpoints.

Surrogate endpoints

In many cases objective endpoints cannot be identified. For example, people with HIV infection may live for 20 years or longer after diagnosis. Therefore they are likely to receive a number of different treatments during their lifetime; it would be unethical to withhold a new treatment from an HIV positive participant if the trial treatment is not working. It is difficult to compare the effects of Treatment A on a long-term, objective endpoint like survival against Treatment B when participants subsequently use Treatments C, D, or E. In this instance the trial would be likely to have a different type of endpoint.

Markers of disease progression are widely used as surrogate endpoints. In an HIV trial, for example, the marker might be a specified increase in viral load or fall in the number of CD4 cells, both laboratory measures which predict how rapidly HIV disease will progress. Although the measurements are objective, the definitions of surrogate endpoints are open to debate. What markers should be used? At what time should levels be tested? And what values signal disease progression or treatment failure? Does the surrogate event always predict the event you are interested in?

The statistics of survival

The curves shown in Figure 6 are known as Kaplan Meier (KM) plots or survival curves (although they can be plotted for time to any event, not just death). The proportion of patients surviving is plotted on the y-axis against the time after randomisation on the x-axis. Two curves are drawn, one for the treatment A group and the other for the treatment B group. Under the x-axis are the number of patients who are at risk (have not reached the end-point) at the times shown and, in brackets, the number of events between these times. The data are not taken from a real trial because of issues such as confidentiality.

The short vertical lines on each curve denote censored patients. When a patient is censored, their follow-up only goes up to this point, and they have not yet reported the event. Although we know they are still alive they no longer count as a ‘patient at risk’ after this time on the graph. Therefore, they contribute no information further to the right of the curve. In the calculations the effect of censoring is to reduce the ‘number at risk’ without affecting the shape of the survival curve.

Censored patients are the reason why the data in brackets under the x-axis are not straightforward sums e.g. on Arm A the number of patients at risk at 24 months (174 patients) is not the number of patients at risk at 12 months (272 patients) minus the events on between 12 and 24 months (52 patients) i.e. 46 patients have been censored between these points.

Statisticians use datasets like the one presented here to calculate the Hazard ratio HR. The hazard ratio is the ratio of the hazards or risks for patients on the two treatments. The hazard relates to the endpoint of interest e.g. the chance or risk of death or progression of the disease or fall in CD4 cells. A calculation using all the data in Figure 5 gives a Hazard Ratio of 0.66. This represents a 34% reduction in the risk of death on arm A. (Note that HR = 1.0 would represent no difference between the treatment arms.)

Graph of survival
Graph of survival Graph of survival
Graph of survival
Figure 6. Survival (S) against time in months from randomisation. The hazard ratio is 0.66 with a 95% Confidence Interval of 0.54 to 0.80. This shows a statistically significant improvement in favour of Treatment A.
Making a rough estimate of HR
Although the statistical methods needed for the full analysis are beyond our scope here, you can make a rough estimate of the Hazard Ratio quite easily using the two approximate methods below. They both require you to read information from the curves.
  • If the proportion surviving on arm A is S(A) and the proportion surviving on arm B is S(B), then the ratio of the logarithms of these two quantities at any given survival time gives a rough estimate of the Hazard Ratio
    Equation 1

    The value of this ratio is constant because the survival curves are approximately exponential.

  • Another approximation uses the fact that the Hazard Ratio is roughly equal to the ratio of the median survival times for each treatment.
    Equation 2

    The median survival time is reached when the proportion of patients surviving is 0.5 (i.e. 50% of the patients are still alive or have not reached the end-point). In Equation 2, Median(A) is the median survival time for treatment A and Median (B) is the median survival time for treatment B.
These two methods are not reliable enough for the real analysis but they give a good enough approximation for our purposes. Try them out for yourself in Question 5.

Question 5
Use the Kaplan Meier survival curves in Figure 5 to estimate the Hazard Ratio HR by

a) reading off values for the proportion of patients surviving at 24 months for treatments A and B and substituting them into Equation 1

b) taking values for the median survival times for treatments A and B and substituting them into Equation 2.

c) How do your answers compare with the value obtained from the full analysis?

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