On Fri, 16 Jun 2000, in reply to Bernd Genser's query
> > Does anybody know how to calculate the sample size needed to prove
> > EQUIVALENCE, not difference of two treatments concerning survival
> > data (log-rank test, cox regression).
Robert Dawson wrote:
> Infinite?
>
> The only situation in which I would consider a test as proving the
> equivalence of two parameters would be in a situation where plausible
> values were discrete and one could assign a low probability to the
> observations under _any_ situation in which the values differed.
> Usually there are cases of H_a which approach arbitrarily closely to
> H_0 so that that does not hold.
Assuming that both of you are using "prove" in the corrupted modern
connotation of "demonstrate" (it properly means "to test", but I'll save
that harangue for another time), I would agree with Robert if "equality"
be substituted for "equivalence". But I took the querent to be asking
about power, hence about the probability of a Type II error against some
specified point alternative (which he hasn't specified yet): that is,
to determine n so that beta = Pr{accepting H0|Ha} is satisfactorily
small (say, not larger than 0.10?) when Ha specifies a satisfactorily
small (say, delta) departure from H0 when conducting the test at a
specified significance level alpha.
This is a solvable problem, provided one can specify alpha, beta (or
power = 1 - beta), delta, and the sampling distribution of the test
statistic. I do not know enough about Cox regression and/or the
log-rank test to comment further.
-- DFB.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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