Letter to Editor 5.
6.
7.
8.
9.
Ayida G, Chamberlain P, Barlow D, Koninckx P, Golding S, Kennedy S. Is routine diagnostic laparoscopy for infertility still justified? A pilot study assessing the use of hysterosalpingo‑contrast sonography and magnetic resonance imaging. Hum Reprod 1997;12:1436‑9. Winter L, Glücker T, Steimann S, Fröhlich JM, Steinbrich W, De Geyter C, et al. Feasibility of dynamic MR‑hysterosalpingography for the diagnostic work‑up of infertile women. Acta Radiol 2010;51:693‑701. De Felice C, Rech F, Marini A, Stagnitti A, Valente F, Cipolla V, et al. Magnetic resonance hysterosalpingography in the evaluation of tubal patency in infertile women: An observational study. Clin Exp Obstet Gynecol 2012;39:83‑8. Freeman‑Walsh CB, Fahrig R, Ganguly A, Rieke V, Daniel BL. A hybrid radiography/MRI system for combining hysterosalpingography and MRI in infertility patients: Initial experience. AJR Am J Roentgenol 2008;190:W157‑60. Carrascosa PM, Capuñay C, Vallejos J, Martín López EB, Baronio M, Carrascosa JM. Virtual hysterosalpingography: A new multidetector CT technique for evaluating the female reproductive system. Radiographics 2010;30:643‑61. Access this article online Quick Response Code:
Website: www.jhrsonline.org DOI: 10.4103/0974-1208.138877
Error in sample size formula Sir, Re: Suresh K, Chandrashekara S. Sample size estimation and power analysis for clinical research studies. J Hum Reprod Sci 2012;5:7‑13. Although informative and useful Suresh and Chandrashekara’s article on sample size estimation and power analysis contains a serious error (Suresh and Chandrashekara, 2012). In the section titled “sample size estimation with two means” they state the minimum required sample size for detecting a mean difference between two groups is:
( r + 1) ( Zα /2 + Z1−β )
2
N=
r is the ratio of size (n1 and n2) of the two groups, that is, r = n1/n2 Z is the standard normal distribution deviate, note this is the absolute of the z-score, as in (Suresh and Chandrashekara, 2012) Tables 2 and 3. The formula as stated cannot be correct as relabeling of the two groups results in different values of N. Example: If n1 = 100 and n2 = 200 then r = 1/2 and
rd2
Where α is the false positive rate β is the false negative rate N is the sample size required to detect an inter‑group mean difference of d with specified α and power of 1−β σ2 is the variance in each group (both groups having the same variance)
r
Swapping the two groups around: Then n1 = 200 and n2 = 100 then r = 2 and
( r + 1) = 1.5 r
The N calculated for the first case is twice that of the second; they should be identical. In fact, the formula given is the formula for n2, which I prove thus. In the ‘Sample Size estimation with two means’ case, the z-score of the test statistic d is related to the required false positive rate and power by[1] d =Z +Z stdErr ( d ) α /2 1-β Where the standard error of d is stdErr ( d ) =
σ2 σ2 σ2 σ2 + = + = n1 n2 rn2 n2
( 1 + r )σ 2 rn2
Substituting the expression for stdErr (d) into the first equation and rearranging gives:
( r + 1) ( Zα /2 + Z1-β )
2
n2 =
σ2
rd2
The formula for N is then N = n1 + n2 = rn2 + n2 = ( r + 1) n2 2 ( r + 1) ( Zα /2 + Z1− β ) N=
2
r
σ2
(r + 1) = 3
σ2
d2
With the new formula group labels can be swapped without changing the value calculate for N. The original erroneous formula could result in studies seriously underestimating their required sample size. For instance, the required sample size (as calculated by the current formula) is half that truly required, given equal numbers in the two groups. I therefore draw this error to your attention. The illustrative
Journal of Human Reproductive Sciences / Volume 7 / Issue 2 / Apr - Jun 2014
155
examples that follow the formula presentation are also in error.
REFERENCE 1.
Desmond Dedalus Campbell1,2 2
1 Department of Psychiatry, Centre for Genomic Sciences, University of Hong Kong, Hong Kong, China
Wittes J. Sample size calculations for randomized controlled trials. Epidemiol Rev 2002;24:39‑53. Access this article online Quick Response Code:
Address for correspondence: Dr. Desmond Dedalus Campbell, L10‑64 Lab Block, Faculty of Medicine, 21 Sassoon Road, Central and Western, Hong Kong, China. E‑mail: [email protected]
156
Journal of Human Reproductive Sciences / Volume 7 / Issue 2 / Apr - Jun 2014
Website: www.jhrsonline.org DOI: 10.4103/0974-1208.138878
Copyright of Journal of Human Reproductive Sciences is the property of Medknow Publications & Media Pvt. Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use.
6.
7.
8.
9.
Ayida G, Chamberlain P, Barlow D, Koninckx P, Golding S, Kennedy S. Is routine diagnostic laparoscopy for infertility still justified? A pilot study assessing the use of hysterosalpingo‑contrast sonography and magnetic resonance imaging. Hum Reprod 1997;12:1436‑9. Winter L, Glücker T, Steimann S, Fröhlich JM, Steinbrich W, De Geyter C, et al. Feasibility of dynamic MR‑hysterosalpingography for the diagnostic work‑up of infertile women. Acta Radiol 2010;51:693‑701. De Felice C, Rech F, Marini A, Stagnitti A, Valente F, Cipolla V, et al. Magnetic resonance hysterosalpingography in the evaluation of tubal patency in infertile women: An observational study. Clin Exp Obstet Gynecol 2012;39:83‑8. Freeman‑Walsh CB, Fahrig R, Ganguly A, Rieke V, Daniel BL. A hybrid radiography/MRI system for combining hysterosalpingography and MRI in infertility patients: Initial experience. AJR Am J Roentgenol 2008;190:W157‑60. Carrascosa PM, Capuñay C, Vallejos J, Martín López EB, Baronio M, Carrascosa JM. Virtual hysterosalpingography: A new multidetector CT technique for evaluating the female reproductive system. Radiographics 2010;30:643‑61. Access this article online Quick Response Code:
Website: www.jhrsonline.org DOI: 10.4103/0974-1208.138877
Error in sample size formula Sir, Re: Suresh K, Chandrashekara S. Sample size estimation and power analysis for clinical research studies. J Hum Reprod Sci 2012;5:7‑13. Although informative and useful Suresh and Chandrashekara’s article on sample size estimation and power analysis contains a serious error (Suresh and Chandrashekara, 2012). In the section titled “sample size estimation with two means” they state the minimum required sample size for detecting a mean difference between two groups is:
( r + 1) ( Zα /2 + Z1−β )
2
N=
r is the ratio of size (n1 and n2) of the two groups, that is, r = n1/n2 Z is the standard normal distribution deviate, note this is the absolute of the z-score, as in (Suresh and Chandrashekara, 2012) Tables 2 and 3. The formula as stated cannot be correct as relabeling of the two groups results in different values of N. Example: If n1 = 100 and n2 = 200 then r = 1/2 and
rd2
Where α is the false positive rate β is the false negative rate N is the sample size required to detect an inter‑group mean difference of d with specified α and power of 1−β σ2 is the variance in each group (both groups having the same variance)
r
Swapping the two groups around: Then n1 = 200 and n2 = 100 then r = 2 and
( r + 1) = 1.5 r
The N calculated for the first case is twice that of the second; they should be identical. In fact, the formula given is the formula for n2, which I prove thus. In the ‘Sample Size estimation with two means’ case, the z-score of the test statistic d is related to the required false positive rate and power by[1] d =Z +Z stdErr ( d ) α /2 1-β Where the standard error of d is stdErr ( d ) =
σ2 σ2 σ2 σ2 + = + = n1 n2 rn2 n2
( 1 + r )σ 2 rn2
Substituting the expression for stdErr (d) into the first equation and rearranging gives:
( r + 1) ( Zα /2 + Z1-β )
2
n2 =
σ2
rd2
The formula for N is then N = n1 + n2 = rn2 + n2 = ( r + 1) n2 2 ( r + 1) ( Zα /2 + Z1− β ) N=
2
r
σ2
(r + 1) = 3
σ2
d2
With the new formula group labels can be swapped without changing the value calculate for N. The original erroneous formula could result in studies seriously underestimating their required sample size. For instance, the required sample size (as calculated by the current formula) is half that truly required, given equal numbers in the two groups. I therefore draw this error to your attention. The illustrative
Journal of Human Reproductive Sciences / Volume 7 / Issue 2 / Apr - Jun 2014
155
examples that follow the formula presentation are also in error.
REFERENCE 1.
Desmond Dedalus Campbell1,2 2
1 Department of Psychiatry, Centre for Genomic Sciences, University of Hong Kong, Hong Kong, China
Wittes J. Sample size calculations for randomized controlled trials. Epidemiol Rev 2002;24:39‑53. Access this article online Quick Response Code:
Address for correspondence: Dr. Desmond Dedalus Campbell, L10‑64 Lab Block, Faculty of Medicine, 21 Sassoon Road, Central and Western, Hong Kong, China. E‑mail: [email protected]
156
Journal of Human Reproductive Sciences / Volume 7 / Issue 2 / Apr - Jun 2014
Website: www.jhrsonline.org DOI: 10.4103/0974-1208.138878
Copyright of Journal of Human Reproductive Sciences is the property of Medknow Publications & Media Pvt. Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use.
