gm.si {gmvalid}R Documentation

Synergy Index

Description

Computes the synergy index of two discrete variables in relation to a binary group variable.

Usage

gm.si(X,Y,group,data=0,reference=c(1,1,2),conf.level = 0.95)

Arguments

X Index of the variable's position in data or a vector.
Y Index of the variable's position in data or a vector.
group Binary group or outcome variable addressed as variable index in data or as vector.
data Data frame or table.
reference Vector to define the reference categories of X, Y and group. By default, 2 is the reference category for group.
conf.level Confidence level of the interval (default is 0.95).

Details

Rothman's synergy index (S) is an interaction measure between two discrete variables on a dichotomous outcome. The index equals 1 under additivity, S > 1 in the case of synergy and S < 1 in the presence of antagonism.

The synergy index is originally constructed on (2 x 2)-tables, but (i x j)-tables can also be analyzed. Then (i-1) x (j-1) synergy indices are computed and combined to an overall synergy index.

The confidence intervalls are calculated using the asymptotic variance given in Rothman (1974).

Value

A list containing:

ratio A rate ratio table, more precise [P( group=reference,X,Y ) / P( group=NOT reference,X,Y )] / [min(P( group=reference,X,Y ) / P( group=NOT reference,X,Y ))]
covariance Covariances matrix of the single synergy indices. Not written if X or Y are binary.
measure Matrix containing the estimate(s), standard deviation(s), confidence interval(s) and p-value(s). Figures in brackets show the reference category respectively the category under consideration.
If both factors X and Y are binary, confidence intervals for case-control as well as cohort designs are computed. If at least one factor has more than 2 categories, the overall synergy index with its corresponding confidence interval is computed that follows a case-control design.

Note

It can occur that certain combinations of categories lead to a negative synergy indices. In that case no confidence intervals can be computed. If so, use the reference option to re-order the categories of the variable(s) in question (see example below).

Author(s)

Ronja Foraita, Fabian Sobotka
Bremen Institute for Prevention Research and Social Medicine
(BIPS) http://www.bips.uni-bremen.de

References

Rothman K (1974) The estimation of synergy or antagonism. American Journal of Epidemiology, 103(5):506-511

Rothman K (1986) Modern Epidemiology. Little, Brown and Company, Boston/Toronto.

See Also

gm.csi

Examples

  data(wynder)
  gm.si(1,2,3,wynder)

  # Smoking and alcohol in relation to oral cancer among male veterans under age 60.
  # (from "Modern Epidemiology")
  oral <- array(c(20,3,18,8,12,6,166,225),dim=c(2,2,2), 
            dimnames=list(Group=c("control","cases"),
            Smoker=c("no","yes"),Alcohol=c("no","yes")))
  oral.df <- expand.table(oral)
  # grouping variable is first in data frame
  gm.si(2,3,1,oral.df)
  
  # Effects must be ascending in respect to the reference category
  show.effect <- array(c(1,7,2,7,7,12,106,48),dim=c(2,2,2),
                        dimnames=list(A=1:2,B=1:2,C=1:2))
  # produces NaN
  gm.si(1,2,3,expand.table(show.effect))
  # > re-ordering variable B helps
  gm.si(1,2,3,expand.table(show.effect),reference=c(1,2,2))


[Package gmvalid version 1.0 Index]