Biostatistical methods : the assessment of relative risks by John M Lachin; Wiley InterScience (Online service)

By John M Lachin; Wiley InterScience (Online service)

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24 RELATIVE RISK ESTIMATES AND TESTS FOR INDEPENDENT GROUPS The asymptotic distribution under the alternative leads to the usual expression for the large sample (1 — a)-level confidence interval for the population risk difference based on the estimate of the variance under the alternative: (θΙι,θυ)=θ±Ζ1-α/2σι. 30) Although common in practice, these confidence limits are not necessarily bounded by —1 and +1, and in rare circumstances limits are obtained that lie outside these bounds. Unlike the case of a single proportion, there is no convenient function that may be used to yield asymmetric confidence limits on the risk difference that are then bounded by (—1,1).

The Fisher-Irwin exact test has been criticized as being too conservative because other unconditional tests such as that originally proposed by Barnard (1945) have been shown to yield a smaller p-value and thus are more powerful. 78) where Pu [a;i, a¡2 | π] = Lu{it\, π<ι \ Έ\ = π?. 53). This test deals with the nuisance parameter π by computing the p-value using that value π for which the p-value is maximized. The principal reason that this test is more powerful than the Fisher-Irwin exact test is because the exact p-value includes the probability of the observed table.

Given that diabetes is the leading cause of end-stage renal disease, it can be anticipated that implementation of intensive therapy in the wide population with type 1 diabetes will ultimately reduce the progression of nephropathy to end-stage renal disease, with pursuant reductions in the incidence of morbidity and mortality caused by diabetic kidney disease and the costs to the public. The methods used to reach these conclusions, and their statistical basis, are described in the chapters to follow.

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