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RegisterPower of equality [Software]
Dear Helmut,
Meeting You, yes it was, really
!
For that I feel sorry for you. Eventually we should had smoked to a lesser degree?
Regarding the WLN power I must correct myself to a certain degree.
Chow, Shao and Wang1) call a test with the hypotheses pair
a test of equality to distinguish it from a superiority test with the hypothesis pair
with delta the superiority margin. Ok, I think this is semantics.
These authors give for the cross-over design the following formula for the power of the 'equality test' (have translated it in R notation):
where eps is the true difference for which the power shall calculated and tcrit is the quantile of the central t-distribution to the confidence level 1-alpha/2 with df = n-2 degrees of freedom.
Setting
we get
With the approximation of the non-central t-distri via 'shifted' central t-distri according to
we obtain yicaotings formulas!
Lets calculate via non-central t-distribution using your given data:
Full dataset, untransformed
Seems to agree within the approximation used in WNL. At least the right order of magnitude.
Full dataset, logtransformed
Seem not to function! No agreement to the WNL results. Due to insufficient degree of approximation for large non-centrality or due to false formula?
Seems also not to function! This is surprising!
yicaoting: Which SEdiff did you use?
Reduced dataset is the homework for all.
Sorry for all that numbers with insufficient decimals.
1) Chow, Shao and Wang
"Sample size calculations in clinical research"
Marcel Dekker, New York, NY 2003
❝ was really nice meeting you yesterday!
Meeting You, yes it was, really
!❝ BTW, fog at both Berlin’s and Vienna’s airports; arrived at home at midnight… 
For that I feel sorry for you. Eventually we should had smoked to a lesser degree?
Regarding the WLN power I must correct myself to a certain degree.
Chow, Shao and Wang1) call a test with the hypotheses pair
H0 µT = µR
HA µT ≠ µR a test of equality to distinguish it from a superiority test with the hypothesis pair
H0 µT-µR ≤ delta
HA µT-µR > deltawith delta the superiority margin. Ok, I think this is semantics.
These authors give for the cross-over design the following formula for the power of the 'equality test' (have translated it in R notation):
power = 1 - pt(tcrit,df,ncp=eps*sqrt(2*n)/sigma)
+ pt(-tcrit,df,ncp=eps*sqrt(2*n)/sigma)where eps is the true difference for which the power shall calculated and tcrit is the quantile of the central t-distribution to the confidence level 1-alpha/2 with df = n-2 degrees of freedom.
Setting
eps=0.2*LSMref and sigma/sqrt(2*n)=SEdiff and let b=0.2*LSMref/SEdiffwe get
power = 1 - pt(tcrit,df,ncp=b) + pt(-tcrit,df,ncp=b)With the approximation of the non-central t-distri via 'shifted' central t-distri according to
pt(x,df,ncp) ~ pt(x-ncp,df) we obtain yicaotings formulas!
Lets calculate via non-central t-distribution using your given data:
Full dataset, untransformed
b = 4.42291
df = 22
tcrit = qt(0.95,22) = 1.717144...
power = 1 - 0.004184843 + 1.415275e-09 = 0.9958152Seems to agree within the approximation used in WNL. At least the right order of magnitude.
Full dataset, logtransformed
b = 30.57179
df = 22
tcrit = qt(0.95,22) = 1.717144...
power = 1-2.395435e-180+0 = 1Seem not to function! No agreement to the WNL results. Due to insufficient degree of approximation for large non-centrality or due to false formula?
b = ln(0.8)/SEdiff = -7.788037 (yicaotings formula)
df = 22
tcrit = qt(0.95,22) = 1.717144...
power = 1-1+1 = 1Seems also not to function! This is surprising!
yicaoting: Which SEdiff did you use?
Reduced dataset is the homework for all
.Sorry for all that numbers with insufficient decimals.
1) Chow, Shao and Wang
"Sample size calculations in clinical research"
Marcel Dekker, New York, NY 2003
—
Regards,
Detlew
Regards,
Detlew
Complete thread:
- The secret of WinNonlin's BE's post-hoc Power analysis yicaoting 2011-11-08 14:40 [Software]
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- The secret of WinNonlin's BE's post-hoc Power analysis yicaoting 2011-11-08 14:55
- The secret of WinNonlin's BE's post-hoc Power analysis Helmut 2011-11-08 15:06
- Power of superiority d_labes 2011-11-10 09:49
- Power of superiority Helmut 2011-11-10 14:39
- Power of equalityd_labes 2011-11-10 16:42
- Power of equality Helmut 2011-11-10 17:00
- Power of equality test - 2nd try for the logs d_labes 2011-11-11 09:55
- Crtl-C/Ctrl-V Helmut 2011-11-11 14:39
- Power of equality test - 2nd try for the logs d_labes 2011-11-11 09:55
- Power of equality yicaoting 2011-11-12 07:05
- Power of equality Helmut 2011-11-10 17:00
- Power of equalityd_labes 2011-11-10 16:42
- Power of superiority Helmut 2011-11-10 14:39
Ing. Helmut Schütz