Iranian journal of health sciences 013; 1(): 56-60 htt://jhs.mazums.ac.ir Original Article Comaring Two Formulas of Samle Size Determination for Prevalence Studies Hamed Tabesh 1 *Azadeh Saki Fatemeh Pourmotahari 3 1-Assistant Professor of Biostatistics, Deartment of Biostatistics and Eidemiology, School of Health, Ahvaz Jundishaur University of Medical Sciences, Ahvaz, Iran -Assistant Professor of Biostatistics, Deartment of Biostatistics and Eidemiology, School of Health, Ahvaz Jundishaur University of Medical Sciences, Ahvaz, Iran 3- MSc Student of Biostatistics, Deartment of Biostatistics and Eidemiology, School of Health, Ahvaz Jundishaur University of Medical Sciences,Ahvaz,Iran Abstract * azadehsaki@yahoo.com Background and urose: Samle size and its determination is one of the most imortant roblems in health researches. Calculating samle size for revalence studies is one of the common questions of samle size toics. Minimum samle size with least comlexity is desirable in order to achieve the basic goal of these studies. This study aims to comare two formulas of samle size calculation for revalence researches and finally, to use the simlest formula to get the most aroriate samle size. Materials and Methods: Samle size for roortions: 0.9, 0.95, 0.99, 0.999 candidates of close to 1 roortions; 10-5, 10-4, 10-3, 10 -, 0.05, 0.1 candidates of close to 0, and roortions 0.3, 0.4, 0.5, 0.6, 0.7 candidates of close to 0.5 were calculated. For comaring n 1, n ; φ = n 1 n, it was comuted by R ackage (.10.1). Results: Comuted samle size by (f ) is lightly greater than samle size comuted by (f 1 ) and maximum value of φ index for comaring the two formulas equals 1. Conclusion: Results show that the calculated samle size by (f 1 ) is similar to what was obtained by (f ), though, according to its interretation and easy comutation,it is suggested for all values of. [Tabesh H. * Saki A. Pourmotahari F. Comaring two Formulas of Samle Size Determination for revalence studies. IJHS 013; 1():56-60] htt://jhs.mazums.ac.ir ey words: Samle Size Calculation, Prevalence Study, Calculation Procedure. 56
1. Introduction If observational and exerimental studies are designed effectively, valuable results would be obtained. Good lanning has many asects such as exact definition of roblem and method and enough samle size due to the goals. Enough samle size for a research is determined based on the tye and object of a study, statistical methods for analyzing and interreting, available data, validity and reliability for the generalized results by two general techniques: confidence interval and Bayesian methods (1). In simle term, samle size estimation means to estimate the minimum number of the samle for a study by using statistical methods based on secific situation, basic information and recision requirement, and under the remise of guaranteeing the reliability of the conclusion.() Calculated samle size should be large enough so that an effort of such magnitude to be of scientific significance & also be statistically significant. It is just as imortant, however, that the study not to be too large, where an effect of little scientific imortance is nevertheless statistically detectable (3). Although, for such an imortant issue, there is not a large amount of ublished literature, there are several aroaches for samle size. For examle, one can secify the desired width of a confidence interval and determine the samle size that achieves that goal or Bayesian aroach can be used where we otimize some utility function. For conducting samle size, statistical inference is based on estimating a arameter or testing a hyothesis which demand one tye of the study. When estimating an infinite oulation arameter such as revalence, incidence and chance of illness recurrence is desirable. Several text books (4-7) recommended using (f 1 ) and (f ). n 1 = Zα (1 ) (f d 1 ) n = Z α sin 1 d ( ) (1 ) (f ) Where n 1, n are the estimated minimum samle size d and d are the desired level of recision and estimated roortion of an attribute resent in the oulation. It is clear that z is the abscissa of the normal curve that cuts off an area α at the fails. (1- α equals the desired confidence level). Simlicity is one of the greatest roerties of each statistical aroach. Denominator of (f 1 ) equals a half width of confidence interval which shows the estimation recision. So it is easy to understand and interret. Also calculating samle size by (f 1 ) is simle and does not have any comlexity. But unlike the denominator of (f ), to the best of our knowledge, there is not any interretation and comuting samle size by (f ) which is not as convenient as comuting by (f 1 ). some literatures recommended using (f 1 ) when is close to 0.5 and (f ) when is close to 0 or 1(6,8-9). In this study, comaring results of using (f 1 ) and (f ) in the same situation was desirable so if ossible, an alternative formula for (f ) could be suggested. IJHS 013; 1(): 57
. Materials and Methods As mentioned before, several literatures recommended using (f ) when crude estimation of revalence, incidence, and success roortion or illness recurrence robability is close to 0 or 1. In this study, to comare the oututs of (f 1 ) and (f ) samle size for roortions: 0.9, 0.95, 0.99, 0.999 as candidates of close to 1 and, 10-5, 10-4, 10-3, 10 -, 0.05, 0.1 as candidates of close to 0 and 0.3, 0.4, 0.5, 0.6, 0.7 as candidates of close to 0.5 considered. Since d < *min {, 1- } where < ¼. So k equal to 10%, 15%, 0%, and 5% have been considered. Whereas softwares for samle size determination such as PASS, UnifyPow and Power and Precision determine samle size based on (f 1 ) so for comaring (f ),ackage R (.10.1) was used and φ index (φ = n 1 n ) was comuted (10-1). As the most common confidence intervals in medical research cases are 95% and 99%, samle size was comuted for these confidence intervals. 3. Results Samle size for different estimated roortions in oulation,, and distinct values of k, was comuted by (f 1 ) and (f ). N 1, n are estimated minimum samle size by (f 1 ) and (f ) resectively. For comaring n 1, n, index φ = n 1 n was calculated. Comuted φfor close to 0, 1 and 0.5 with 0.95 confidence limit are shown in tables (1), () and (3) resectively. The findings of this study show that n 1 and n were very close to each other when estimated roortion of an attribute resent in the oulation was very small. Table1. Calculated φ index by (f 1 ) and (f ) for very small values of when confidence limit is 95% 10-5 10-4 10-3 10-0.05 0.10 10% 1.000000 1.000000 1.000003 1.000034 1.000175 1.000371 15% 1.000000 1.000001 1.000008 1.000076 1.000395 1.000834 0% 1.000000 1.000001 1.000013 1.000135 1.000703 1.001485 5% 1.000000 1.00000 1.00001 1.00011 1.001098 1.0033 Table. Calculated φ index by (f 1 ) and (f ) for very large values of when confidence limit is 95% 0.9 0.95 0.99 0.995 0.999 10% 1.000371 1.000175 1.000034 1.000017 1.000003 15% 1.000834 1.000395 1.000076 1.000076 1.000008 0% 1.001485 1.000703 1.000135 1.000067 1.000013 5% 1.0033 1.001098 1.00011 1.000105 1.00001 IJHS 013; 1(): 58
Table3. Calculated φ index by (f 1 ) and (f ) for mid- values of when confidence limit is 95% When was close to 1, φ index was aroximately equal to 1 which means that n 1 and n were similar. For mid-values of, similar conclusion could be drawn. The results revealed that both formulas, (f 1 ) and (f ), would erform similarly when the estimated roortion of an attribute resent in the oulation had very small, medium and very large values. The comutations were done for 99% confidence limit, and the results were closely similar. 4. Discussion In medical research, it is imortant to determine size sufficiently enough to ensure reliable conclusions. On the other hand, revalence studies are interesting research cases in medical sciences and consequently, adequate samle size for these research cases would be interesting, too. The most common formulas for revalence or incidence studies are (f1) and (f). (5-7). (f1) has simle structure made u of (f) so it has more ublic 0.3 0.4 0.5 0.6 0.7 10% 1.00143 1.0030 1.003351 1.0030 1.00143 15% 1.00331 1.005040 1.007591 1.005040 1.00331 0% 1.005767 1.009018 1.01365 1.009018 1.005767 5% 1.009058 1.01406 1.01557 1.01406 1.009058 interest than (f). But some literatures limited using (f1). They believe that (f1) could be useful when is not to be close to 1 or 0. This study showed that the estimated samle size by (f1) is aroximately similar to the estimated samle size by (f). On the other hand, comuting samle size by (f1) is easy. Therefore, using (f1) is recommended for estimating samle size of revalence or incidence studies for infinite oulation References 1. Lenth RV. Some ractical Guidelines Effective samle size Determination. The American Statistical, 001; 55(3): 187-193.. HU LP, Bao XL, Zhou SG, Guas X, Estimation of samle size and testing ower (art1). J chin Integr Med. 011;9(10): 1070-1074. 3. Sathian B, sreedharan y, Baboo NS, Sharan k, Abhilash ES, Rajesh E. Relevance of samle size Determination in Medical Researche., Neal Journal of Eidemiology, 010;1(1): 4-10. IJHS 013; 1(): 59
4. Daniel WW. Biostatistics: A Foundation for Analysis in the Health Sciences.7th edition. NewYork: John Wiley & Sons. 5. Lwanga sk and Lemeshow S. Samle size determination in Health Studies: A ractical Manual. Genevai World Health Organization.1999. 6. Cochran WG. Samling Techniques, 3 rd edition. NewYork: John Wiley & Sons.1997. 7. Naing L,Winn T and Rusli BN. Samle size calculator for revalence studies. Archives of Orofacial Sciences, 006;1:9-14 8. reamer, H.C, and Thiemann, S. How many subjects & statistical ower Analysis in Research, Newbury ark, CA: Sage Publications. 1987. 9. Desu MM, Raghavao D. samle size methodology. Boston, MA: Academic ress, Inc.1990 10. Hintze, J. PASS 000, aysville, UT: Number Cruncher Statistical System, Software for MS-DOS systems.001 11. O Brien R.G. Unifyow.sas: version 98.08.5, Deartment of Biostatistics and Eidemiology, Cleveland Clinic Foundation, Cleveland, OH.1998. 1. Borenstein, M., Rothstein, H., and Cohen, J. Power and Precision, Biostat, Teaneck, NY: software for MS-DOS systems.1997. IJHS 013; 1(): 60