spsurvey (version 1.6.2)

relrisk: Relative Risk

Description

This function calculates the relative risk estimate for a 2x2 table of cell counts defined by a categorical response variable and a categorical explanatory (stressor) variable for an unequal probability design. Relative risk is the ratio of two probabilities: the numerator is the probability that the first level of the response variable is observed given occurrence of the first level of the stressor variable, and the denominator is the probability that the first level of the response variable is observed given occurrence of the second level of the stressor variable. The standard error of the base e log of the relative risk estimate and confidence limits for the estimate also are calculated.

Usage

relrisk(dframe, response="response", stressor="stressor",
   response.levels=c("Poor", "Good"), stressor.levels=c("Poor", "Good"),
   wgt="wgt", xcoord="xcoord", ycoord="ycoord", stratum=NULL, cluster=NULL,
   N.cluster=NULL, wgt1=NULL, xcoord1=NULL, ycoord1=NULL, popsize=NULL,
   stage1size=NULL, support=NULL, swgt=NULL, swgt1=NULL, unitsize=NULL,
   vartype="Local", conf=95, check.ind=TRUE)

Arguments

dframe

a data frame containing the variables required for the analysis. If variable names are not provided in the corresponding arguments, then variables should be named as follows: response = the categorical response variable values stressor = the cat

response

name of the column in dframe containing the categorical response variable. The default is "response".

stressor

name of the column in dframe containing the categorical stressor variable. The default is "stressor".

response.levels

category values (levels) for the categorical response variable, where the first level is used for calculating the relative risk estimate. If response.levels is not supplied, then values "Poor" and "Good" are used for the first level and s

stressor.levels

category values (levels) for the categorical stressor variable, where the first level is used for calculating the numerator of the relative risk estimate and the second level is used for calculating the denominator of the estimate. If st

wgt

the final adjusted weight (inverse of the sample inclusion probability) for each site, which is either the weight for a single-stage sample or the stage two weight for a two-stage sample.

xcoord

x-coordinate for location for each site, which is either the x-coordinate for a single-stage sample or the stage two x-coordinate for a two-stage sample. The default is NULL.

ycoord

y-coordinate for location for each site, which is either the y-coordinate for a single-stage sample or the stage two y-coordinate for a two-stage sample. The default is NULL.

stratum

the stratum for each site. The default is NULL.

cluster

the stage one sampling unit (primary sampling unit or cluster) code for each site. The default is NULL.

N.cluster

the number of stage one sampling units in the resource, which is required for calculation of finite and continuous population correction factors for a two-stage sample. For a stratified sample this variable must be a vector containing a

wgt1

the final adjusted stage one weight for each site. The default is NULL.

xcoord1

the stage one x-coordinate for location for each site. The default is NULL.

ycoord1

the stage one y-coordinate for location for each site. The default is NULL.

popsize

the known size of the resource - the total number of sampling units of a finite resource or the measure of an extensive resource, which is required for calculation of finite and continuous population correction factors for a single-stage

stage1size

the known size of the stage one sampling units of a two- stage sample, which is required for calculation of finite and continuous population correction factors for a two-stage sample and must have the names attribute set to identify the

support

the support value for each site - the value one (1) for a site from a finite resource or the measure of the sampling unit associated with a site from an extensive resource, which is required for calculation of finite and continuous pop

swgt

the size-weight for each site, which is the stage two size-weight for a two-stage sample. The default is NULL.

swgt1

the stage one size-weight for each site. The default is NULL.

unitsize

the known sum of the size-weights of the resource, which for a stratified sample must be a vector containing a value for each stratum and must have the names attribute set to identify the stratum codes. The default is NULL.

vartype

the choice of variance estimator, where "Local" = local mean estimator and "SRS" = SRS estimator. The default is "Local".

conf

the confidence level. The default is 95%.

check.ind

a logical value that indicates whether compatability checking of the input values is conducted, where TRUE = conduct compatibility checking and FALSE = do not conduct compatibility checking. The default is TRUE.

Value

Value is a list containing the following components:

• RelRisk- the relative risk estimate
• RRnum- numerator ("elevated" risk) of the relative risk estimate
• RRdenom- denominator ("baseline" risk) of the relative risk estimate
• RRlog.se- standard error for the log of the relative risk estimate
• ConfLimits- confidence limits for the relative risk estimate
• WeightTotal- sum of the final adjusted weights
• CellCounts- cell and margin counts for the 2x2 table
• CellProportions- estimated cell proportions for the 2x2 table

Details

The relative risk estimate is computed using the ratio of a numerator probability to a denominator probability, which are estimated using cell and marginal totals from a 2x2 table of cell counts defined by a categorical response variable and a categorical stressor variable. An estimate of the numerator probability is provided by the ratio of the cell total defined by the first level of response variable and the first level of the stressor variable to the marginal total for the first level of the stressor variable. An estimate of the denominator probability is provided by the ratio of the cell total defined by the first level of response variable and the second level of the stressor variable to the marginal total for the second level of the stressor variable. Cell and marginal totals are estimated using the Horvitz-Thompson estimator. The standard error of the base e log of the relative risk estimate is calculated using a first-order Taylor series linearization (Sarndal et al., 1992).

References

S�rndal, C.-E., B. Swensson, and J. Wretman. (1992). Model Assisted Survey Sampling. Springer-Verlag, New York.

Examples

dframe <- data.frame(response=sample(c("Poor", "Good"), 100, replace=TRUE),
   stressor=sample(c("Poor", "Good"), 100, replace=TRUE),
   wgt=runif(100, 10, 100))
relrisk(dframe, vartype="SRS")

dframe$xcoord <- runif(100)
dframe$ycoord <- runif(100)
relrisk(dframe)