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Dictionary of Evidence-based Medicine.pdf

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128 <strong>Dictionary</strong> <strong>of</strong> <strong>Evidence</strong>-<strong>based</strong> <strong>Medicine</strong><br />

Probability <strong>of</strong> superiority estimate<br />

In a comparative study, the probability <strong>of</strong> superiority estimate (PS) is the<br />

probability that a randomly sampled patient from a population given a test<br />

treatment will have a superior outcome to that <strong>of</strong> a randomly sampled<br />

patient from a population given the control treatment.<br />

An unbiased estimate <strong>of</strong> PS is given by U/nji 2 where IT is the Mann-<br />

Whitney statistic and n^ and n 2 are the sample sizes for the two groups. The<br />

PS is an attractive method for expressing comparative efficacy <strong>of</strong> two<br />

interventions. Note, however, that it requires dichotomizing continuous<br />

response data and defining when a treatment is superior to another, which<br />

may not always be easy (Grissom RJ (1994) The probability <strong>of</strong> superiority<br />

<strong>of</strong> one treatment over another. Journal <strong>of</strong> Applied Psychology. 79: 314-16.<br />

Colditz GA, Miller JN, Mosteller F (1988) The effect <strong>of</strong> study design on gain<br />

in the evaluation <strong>of</strong> new treatments in medicine and surgery. Drug Information<br />

Journal 22: 343-52).<br />

Standardizing the continuous data to the standard normal deviate Z has<br />

been proposed (see Effect size and Appendix in Colditz et al. referred to<br />

above). PS has also been called the common language effect size in this<br />

context (McGraw KO, Wong SP (1992) A common language effect size<br />

statistic. Psychological Bulletin. Ill: 361-5).<br />

The PS is then the area to the left <strong>of</strong> the Z value under the standard normal<br />

curve. Thus, if the Z value is 1.645, the PS = 0.95. If Z = -1.645 then the<br />

PS = 0.05.<br />

If a series <strong>of</strong> PS values are available from k trials then a pooled PS can be<br />

obtained by first obtaining a pooled Z value:<br />

A sample weighted pooled Z score (Z ps = ~—-') can be obtained and the<br />

corresponding PS read from the appropriate standard normal table.

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