{smcl}
{hline}
help for {hi:geipower} {right:(SJ3-1: st0032)}
{hline}

{title:Syntax}

{p 8 14 2}{cmd:geipower} {cmd:using} {it:filename}


{title:Input file}

{p 4 4 2}The input file must contain the following variables; there is no
limit on the number of observations. Each observation should contain one set
of parameters for which power, and sample sizes are required.

{col 5}Variable name{col 22}Details

{col 5}{cmd:pg}{col 22}The population frequency of the susceptibility genotype
	  	     (permitted range 0 < {cmd:pg} < 1)

{col 5}{cmd:pe}{col 22}The population frequency of the environmental risk factor
		     (permitted range 0 < {cmd:pe} < 1)

{col 5}{cmd:rrg0e1}{col 22}The relative risk of disease in people exposed to the
	     	     environmental risk factor but not the genetic risk factor,
		     compared with those people exposed to neither factor.
		     (permitted range 0 < {cmd:rrg0e1})

{col 5}{cmd:rrg1e0}{col 22}The relative risk of disease in people exposed to the
		     genetic risk factor but not the	environmental risk factor,
		     compared with those people exposed to neither factor
		     (permitted range 0 < {cmd:rrg1e0})

{col 5}{cmd:rrint}{col 22}The interaction relative risk (such that the risk of
		     disease in people exposed to both risk factors
		     = {cmd:rrg0e1} * {cmd:rrg1e0} * {cmd:rrint}; permitted range 0 < {cmd:rrint})

{col 5}{cmd:pd}{col 22}The population disease frequency (permitted range 0 < {cmd:pd} < 1)

{col 5}{cmd:sibore}{col 22}The odds ratio for the association of the environmental
		     risk factor among siblings (permitted range 0 < {cmd:sibore})

{col 5}{cmd:rrsibm}{col 22}The multiplication in risk of disease to sibs of cases due
		     to unmeasured risk factors (permitted range 0 < {cmd:rrsibm})

{col 5}{cmd:alpha_1}{col 22}The required significance level for the interaction test
		     (permitted range 0 < {cmd:alpha_1} < 1) 

{col 5}{cmd:ssize}{col 22}The sample size (number of cases) for which power
		     calculations are required (number of cases equals number of
		     controls) (permitted range {cmd:ssize} < 0)

{col 5}{cmd:power}{col 22}The power for which sample size calculations are required
		     (%) (permitted range {cmd:alpha_1} (x 100%) <= {cmd:power} < 100)


{title:Description}

{p 4 4 2}{cmd:geipower} calculates power, sample size, and expected odds
ratios for departure from multiplicative joint effects (gene-environment
interaction) for the following study designs for a given set(s) of population
parameters.

{col 5}{ul:Case}{col 28}{ul:Control}{col 51}{ul:Inheritance}{col 65}{ul:Analysis}
{col 5}Population based{col 28}Population based{col 65}Unmatched
{col 5}Population based{col 28}Has affected sibling{col 51}Recessive{col 65}Matched
{col 5}Population based{col 28}Has affected sibling{col 51}Dominant{col 65}Matched
{col 5}Population based{col 28}Has affected sibling{col 51}Recessive{col 65}Unmatched
{col 5}Population based{col 28}Has affected sibling{col 51}Dominant{col 65}Unmatched
{col 5}Has affected sibling{col 28}Population based{col 51}Recessive{col 65}Unmatched
{col 5}Has affected sibling{col 28}Population based{col 51}Dominant{col 65}Unmatched
{col 5}Has affected sibling{col 28}Has affected sibling{col 51}Recessive{col 65}Unmatched
{col 5}Has affected sibling{col 28}Has affected sibling{col 51}Dominant{col 65}Unmatched


{title:Method}

{p 4 4 2}Power calculations for case-control studies is carried out using a
large sample likelihood-ratio approximation method.  The method assumes that
the distribution of the likelihood ratio is approximately a central chi2
distribution under the null hypothesis and a non-central chi2 distribution
under the alternative hypothesis. An approximation to the non-centrality
parameter can be calculated as the likelihood-ratio statistic from the
analysis of an exemplary dataset.  In addition sample size can also be
calculated as it is directly proportional to the non-centrality parameter.
These methods are detailed in Brown et al. (1999) and the exemplary data
method, with examples, is outlined by Longmate (2001).


{title:Example}

{p 4 8 2}{cmd:. geipower using gei_parameters}


{title:Results}

{p 4 4 2}Results are saved in the dataset that conatins the original sets of
parameters.  When only one set of parameters is considered (initial dataset
only has one observation), results are also written in the results window.

{p 4 4 2}Note:  There is often little difference in power between recessive
and dominant modes of inheritance for the same design.  This is because
susceptibility genotype frequency, rather than allele frequency is specified.


{title:References}

{p 4 8 2}Brown, B. W., J. Lovato, and K. Russell. 1999. Asymptotic power
calculations: description, examples, computer code. {it:Statistics in}
{it:Medicine} 18: 3137--3151.

{p 4 8 2}Longmate, J. A. 2001. Complexity and power in case-control
association studies. {it:American Journal of Human Genetics} 68: 1229--1237.

{p 4 8 2}Self, S. G., R. H. Mauritsen, and J. Ohara. 1992. Power calculations
for likelihood ratio tests in generalized linear models. {it:Biometrics} 48:
31--39.


{title:Author}

        Catherine Saunders
        Genetic Epidemiology Divison
        Cancer Research UK Clinical Centre in Leeds
        Cancer Genetics Building
        St James's University Hospital
        Beckett Street
        Leeds, LS9 7TF
        UK
        Email: catherine.saunders@cancer.org.uk
