Power Calculations: Quantitative Traits - Revision history

Goncalo: /* A Simple Genetic Association Study */

2010-06-17T15:02:13Z

A Simple Genetic Association Study

← Older revision		Revision as of 11:02, 17 June 2010
Line 5:		Line 5:
	In this example, we will use [http://www.r-project.org/ R] to carry a simple power calculation for a genetic association study. We will assume that you are interested in a quantitative trait and that you have phenotyped and genptyped ''N'' randomly sampled individuals. Further, we will assume that you are using signficance level <math>alpha</math> for your analyses (typically, <math>alpha = 0.05 / M</math> where ''M'' the number of independent markers examined) and ''H2'' is the variance explained by additive effects at the marker of interest under an additive model.		In this example, we will use [http://www.r-project.org/ R] to carry a simple power calculation for a genetic association study. We will assume that you are interested in a quantitative trait and that you have phenotyped and genptyped ''N'' randomly sampled individuals. Further, we will assume that you are using signficance level <math>alpha</math> for your analyses (typically, <math>alpha = 0.05 / M</math> where ''M'' the number of independent markers examined) and ''H2'' is the variance explained by additive effects at the marker of interest under an additive model.

	Thus, we are assuming that you will ultimately analyze your data with a linear model such as <math>E(Y_i) = \mu + \beta_G * G_i</math>, with <math>E(Y_i)</math> denoting the expected phenotypic value for each individual, <math>\mu</math> denotine an overall mean, <math>\beta_G<\math> denoting the estimated per genotype effect, and <math>G_i<\math> denoting the observed genotype for each individual (coded as 0, 1 or 2 according to the number of copies of the rare alelele).		Thus, we are assuming that you will ultimately analyze your data with a linear model such as <math>E(Y_i) = \mu + \beta_G * G_i </math>, with <math>E(Y_i)</math> denoting the expected phenotypic value for each individual, <math> \mu </math> denotine an overall mean, <math> \beta_G </math> denoting the estimated per genotype effect, and <math>G_i </math> denoting the observed genotype for each individual (coded as 0, 1 or 2 according to the number of copies of the rare alelele).

	In this setting, a simple power calculation might look like:		In this setting, a simple power calculation might look like:
Line 15:		Line 15:
	threshold = qchisq(alpha, df = 1, lower.tail = FALSE)		threshold = qchisq(alpha, df = 1, lower.tail = FALSE)
	power = pchisq(threshold, df = 1, lower.tail = FALSE, ncp = N * H2)		power = pchisq(threshold, df = 1, lower.tail = FALSE, ncp = N * H2)

			== Considerations for Related Samples ==

			The above calculation assumes that you are studying a sample of unrelated individuals. If your sample includes related individuals, the effective sample size will typically be lower than the number of genotyped individuals and power will typically be lower. The loss in power depends on the heritability of the trait (there will be a greater loss in power for more heritable traits) and on the relatedness of individuals (there will be a greater loss in power for more closely related individuals).

			On the other hand, when analyzing samples that include related individuals in an association study, it may not be necessary to exhaustively genotype each sample -- resulting in substantial cost savings and increased power on a ''per genotype'' basis. For examples of the possibilities, see [http://www.sph.umich.edu/csg/abecasis/publications/17924335.html Chen and Abecasis (2007)].

Goncalo: /* A Simple Genetic Association Study */

2010-06-17T14:55:07Z

A Simple Genetic Association Study

← Older revision		Revision as of 10:55, 17 June 2010
Line 3:		Line 3:
	== A Simple Genetic Association Study ==		== A Simple Genetic Association Study ==

	In this example, we will use [http://www.r-project.org/ R] to carry a simple power calculation for a genetic association study. We will assume that you are interested in a quantitative trait and that you have phenotyped and genptyped ''N'' randomly sampled individuals. Further, we will assume that you are using signficance level <math>alpha</math> for your analyses (typically, <math>alpha = 0.05 / M</math> where ''M'' the number of independent markers examined) and ''H2'' is the variance explained by additive effects at the marker of interest.		In this example, we will use [http://www.r-project.org/ R] to carry a simple power calculation for a genetic association study. We will assume that you are interested in a quantitative trait and that you have phenotyped and genptyped ''N'' randomly sampled individuals. Further, we will assume that you are using signficance level <math>alpha</math> for your analyses (typically, <math>alpha = 0.05 / M</math> where ''M'' the number of independent markers examined) and ''H2'' is the variance explained by additive effects at the marker of interest under an additive model.

			Thus, we are assuming that you will ultimately analyze your data with a linear model such as <math>E(Y_i) = \mu + \beta_G * G_i</math>, with <math>E(Y_i)</math> denoting the expected phenotypic value for each individual, <math>\mu</math> denotine an overall mean, <math>\beta_G<\math> denoting the estimated per genotype effect, and <math>G_i<\math> denoting the observed genotype for each individual (coded as 0, 1 or 2 according to the number of copies of the rare alelele).

	In this setting, a simple power calculation might look like:		In this setting, a simple power calculation might look like:

Goncalo: /* A Simple Genetic Association Study */

2010-06-17T14:50:14Z

A Simple Genetic Association Study

← Older revision		Revision as of 10:50, 17 June 2010
Line 3:		Line 3:
	== A Simple Genetic Association Study ==		== A Simple Genetic Association Study ==

	In this example, we will use [http://www.r-project.org/ R] to carry a simple power calculation for a genetic association study. We will assume that you are interested in a quantitative trait and that you have phenotyped and genptyped N randomly sampled individuals. Further, we will assume that you are using signficance level <math>alpha</math> for your analyses (typically, <math>alpha = 0.05 / M</math> where M is the number of independent markers examined) and H2 is the variance explained by additive effects at the marker of interest.		In this example, we will use [http://www.r-project.org/ R] to carry a simple power calculation for a genetic association study. We will assume that you are interested in a quantitative trait and that you have phenotyped and genptyped ''N'' randomly sampled individuals. Further, we will assume that you are using signficance level <math>alpha</math> for your analyses (typically, <math>alpha = 0.05 / M</math> where ''M'' the number of independent markers examined) and ''H2'' is the variance explained by additive effects at the marker of interest.

	In this setting, a simple power calculation might look like:		In this setting, a simple power calculation might look like:

Goncalo: Created page with 'Calculating power for simple study designs is one of the most common tasks faced by a Biostatistician. However, for most of them, it barely makes the list of the top 1000 things …'

2010-06-17T14:49:23Z

Created page with 'Calculating power for simple study designs is one of the most common tasks faced by a Biostatistician. However, for most of them, it barely makes the list of the top 1000 things …'

New page

Calculating power for simple study designs is one of the most common tasks faced by a Biostatistician. However, for most of them, it barely makes the list of the top 1000 things they might enjoy doing. So, make your neighborhood biostatistician marginally happier by calculating your own power tables before you next meet with them (yes, even if you can calculate power, you will probably still need professional advice on study design!).

== A Simple Genetic Association Study ==

In this example, we will use [http://www.r-project.org/ R] to carry a simple power calculation for a genetic association study. We will assume that you are interested in a quantitative trait and that you have phenotyped and genptyped **N** randomly sampled individuals. Further, we will assume that you are using signficance level <math>alpha</math> for your analyses (typically, <math>alpha = 0.05 / M</math> where **M** is the number of independent markers examined) and **H2** is the variance explained by additive effects at the marker of interest.

In this setting, a simple power calculation might look like:

N = 1000
alpha = 0.05
H2 = 0.01

threshold = qchisq(alpha, df = 1, lower.tail = FALSE)
power = pchisq(threshold, df = 1, lower.tail = FALSE, ncp = N * H2)