1. No category

Sample Size logistic regression
.
! "# $#%
Email: [email protected]
Web: http://home.kku.ac.th/nikom
Sample Size simple logistic regression
#9: dichotomous Hosmer & Lemeshow (2000)

1
1
1
1
Z
+
+
Z
+
1− β
*
 1− α 1− π π
1 − π π exp β1
n = ( 1 + 2 P0 )x 
P0 β1*2
e β0
P0 =
1 + e β0




2
(Hosmer & Lemeshow 2000)
β1* = ln (odds ratio); π = ;%
;" Sample Size Multiple logistic regression
n
#9: dichotomous
2
∑ ( yi − πˆi )
n
nm =
(1 − r 2 )
r2 =
i =1
n
∑ ( yi − y )
i =1
2
<9=> ?
;? myocardial
infraction ?;" (adjusted) " ;@# LDL
;@# HDL :"A <=>$A % B%
odds ratio = 1.5 r = 0.1123 ; β 0 = −1.041 ;π = 0.5
P0 =
e −1.041
1+ e
−1.041
= 0.261

1
1.645 1 + 1 + 0.842 1 +

1 − .5 .5
1 − .5 .5e [ ln ( 1.5 )]

n = ( 1 + 2( 0.261 ))x
0.261[ ln ( 1.5 )] 2
nm =
827
2
(1 − 0.1123 )
= 836.86




2
= 827
STATA : sampsi_logit (Thanomsieng,N, 2006)
sampsi_logit
p0(#) p(#)
cov(str)]
or(#)
[r(#)] alpha(#)
power(#) [tailed(str)
.sampsi_logit,p0(0.261) r(.1123) p(.5) or(1.5) alpha(.05) power(.80) tailed(one)
Sample Size for Logistic Regression (covariate is dichotomous)
Logistic all n
n/2
alpha
power
Odds ratio
R square
=
=
=
=
=
=
837
419
(per group)
.05
Zalpha =
.8
Zbeta =
1.5
.01261129
1.645
0.842
Sample Size logistic regression
#9: continuous
(
− 0.25 β1*2
(1 − 2 p0δ ) z1−α + z1− β e
n=
x
2
*2
1− ρ
p0 β1
e β0
p0 = P( y = 1 | x = 0) =
β0
1+ e
δ =
(
1+ 1+ β
1+ e
)e
*2 1.25 β1*2
1
− 0.25 β1*2
(Hosmer & Lemeshow 2000)
)
2
<9=> " ;?C< coronary
?;9 adjusted dm, ldl, smoking (sk) ?;#9:<
$ pilot study ;D <C9#;%$%C; EA9$;
"
F one tailed (alpha = 0.05 ,beta = .20)
. logit coro sk ldl dm age
Logistic regression
Log likelihood =
-42.00821
Number of obs
LR chi2(4)
Prob > chi2
Pseudo R2
=
=
=
=
100
54.61
0.0000
0.3939
-----------------------------------------------------------------------------coro |
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------sk |
1.225443
.7900385
1.55
0.121
-.3230043
2.77389
ldl |
.1235868
.9591088
0.13
0.897
-1.756232
2.003406
dm |
1.824256
.8701591
2.10
0.036
.1187758
3.529737
age |
.1791178
.0642733
2.79
0.005
.0531444
.3050911
_cons | -1.08303
.088567 -12.23
0.000
-16.13651
-4.02955
------------------------------------------------------------------------------
STATA : sampsi_logit (Thanomsieng,N, 2006)
sampsi_logit
p0(#) p(#)
cov(str)]
or(#)
[r(#)] alpha(#)
power(#) [tailed(str)
. di (exp(-1.08303))/(1+exp(-1.08303) )
.25293305
. di sqrt(.3939)
.62761453
. di exp(.1791178)
1.1961616
.sampsi_logit,p0(0.25293305) r(.62761453) or(1.1961616) alpha(.05) power(.80)
tailed(one) cov(c)
Sample Size for Logistic Regression (covariate is continuous)
Logistic all n
n/2
alpha
power
Odds ratio
R square
=
=
=
=
=
=
1909
955
(per group)
.05
Zalpha =
.8
Zbeta =
1.196162
.39389996
1.645
0.842
Sample Size simple logistic regression
#9: continuous (Hsieh, F.Y. (1989)
n=
[ Zα + exp(−θ *2 / 4) Z β ]2 (1 + 2 P0δ )
( Pθ *2 )
θ * = log odds ratio = ln(or ) = coefficient
δ = [1 + (1 + θ *2 ) exp(5θ *2 / 4)][1 + exp(−θ *2 / 4)]−1
P0 = exp(β 0) /[1 + exp(β 0 )]
Sample Size Multiple logistic regression
#9: continuous
n
nm =
(1 − r 2 )
Reference: Sample Size logistic regression
-Hosmer DW., Lemeshow S.(2000). Applied Logistic Regression: Second Edition.
John Wiley & Sons,Inc.,New York.
-Hsieh, F.Y. (1989). Sample Size tables for logistic regression. Statistics in Medicine,
16, 965-802
-Whitemore, A.S. (1981). Sample Size tables for logistic regression with small response
probability. Journal of the American Statistical Association,76, 27-32.