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+ | ===== Power for Case Control Studies ===== | ||

+ | ==== Cumulative Minor Allele Frequency in Cases and Controls ==== | ||

+ | To compare the difference between cases/ctrls for cumulative MAF of all variants across a gene analytically, the case/ctrl group specific MAF have to be calculated given the MAF in population and effect size of variant sites. Consider a multi-site genotype having \(M\) sites, each with a MAF (population MAF) and an odds ratio associated with the site. It is then possible to calculate the corresponding MAF in //case// group under Bayesian arguments. Specifically \(Pr(genotype)\) is a function of MAF (\(p_{AA}=q^2, p_{aa} = (1-q)^2, p_{Aa} = 2q(1-q)\) under Hardy-Weinberg Equilibrium assumptions), \(Pr(status|genotype)\) is genotype penetrance, \(Pr(status)\) is prevalence; \(Pr(genotype|status)\) can thus be calculated and can be translated into MAF in cases \[Pr(g|s)=\frac{Pr(g)Pr(s|g)}{Pr(s)}\] and cumulative MAF \[p_s = 1 - \prod^M_i(1-p_{is})\] | ||

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+ | It is also possible to evaluate power and sample size for common variant analysis (e.g., in GWAS) using SEQPower. This is just a special scenario of \(M=1\) and the cumulative MAF is the locus MAF. | ||

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+ | ==== Analytic Power for Comparing Difference in Cumulative MAF ==== | ||

+ | Power and sample size can be evaluated using a test for binomial proportions as described by Fleiss et al((Joseph L. Fleiss, Alex Tytun and Hans K. Ury (1980). **A Simple Approximation for Calculating Sample Sizes for Comparing Independent Proportions**. //Biometrics//)) \[z_\beta=\frac{\sqrt{\Delta p^2rm^*-(r+1)\Delta p}-z_\alpha\sqrt{(r+1)\bar{p}\bar{q}}}{\sqrt{rp_{s1}q_{s1}+p_{s2}q_{s2}}}\] | ||

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+ | Sample size can be obtained via inverting the equation above. Please refer to Fless et al. 1980 for notations for the power function. | ||

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+ | Other statistical tests can also be applied, e.g, Casagrande et al((J. T. Casagrande, M. C. Pike and P. G. Smith (1978). **An Improved Approximate Formula for Calculating Sample Sizes for Comparing Two Binomial Distributions**. //Biometrics//)). [Power of different analytic tests yet to be discussed]. | ||

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+ | ==== Example ==== | ||

+ | Please find more details in [[http://bioinformatics.org/spower/analytic-tutorial|this tutorial]] on analytic power calculation for case control data. | ||