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

{title:Syntax}

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


{title:Description}

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


{title:Designs considered}

{p 4 4 2}Flexible matching the frequency of the exposure in controls using
exposure or surrogate exposure/genotype information from cases.  equal numbers
of cases and controls are assumed.

{p 4 4 2}Countermatching the control exposure or control exposure/genotype
combination on surrogate information, assuming that a nested case-control
study is being sampled from a cohort with exposure information available.
Three controls are selected for each case in a matched sampling scheme.

{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 e;nvironmental 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:orge}{col 22}The odds ratio for the population association of the two
		    risk factors under study.  {cmd:orge}=1 when risk factors are
		    independent (permitted range 0 < {cmd:orge})

{col 5}{cmd:spece}{col 22}Specificity of exposure surrogate measure. 
		    (permitted range 0 < {cmd:spece} < 1)

{col 5}{cmd:spece}{col 22}Sensitivity of exposure surrogate measure.
		    (permitted range 0 < {cmd:spece} < 1)

{col 5}{cmd:specg}{col 22}Sensitivity of genotype surrogate measure.
		    (permitted range 0 < {cmd:spece} < 1)

{col 5}{cmd:sensg}{col 22}Sensitivity of genotype surrogate measure.
		    (permitted range 0 < {cmd:spece} < 1)

{col 5}{cmd:dm}{col 22}degree of matching defined by:
		    dm=(P(E)matched controls-P(E)population)/(P(E)cases-P(E)population)
		    (usual range 0 < {cmd:dm} < 2)

{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)

{p 4 4 2}NB Sensitivity is the probability that the surrogate is present given
the exposure/genotype is present.  Specificity is the probability that the
surrogate is absent given the exposure/genotype is absent.


{title:Method}

{p 4 4 2}Power calculations for the matching designs are 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:. gei_matching using match_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.


{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
