relrisk(psurvey.analysis)S-PLUS Documentation
Relative Risk

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)

REQUIRED 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 categorical explanatory (stressor) variable values
wgt = the final adjusted weights
xcoord = the x-coordinates for location
ycoord = the y-coordinates for location
stratum = the stratum codes

OPTIONAL ARGUMENTS:

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 second level of the response variable, respectively. The default is c("Poor", "Good").
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 stressor.levels is not supplied, then values "Poor" and "Good" are used for the first level and second level of the stressor variable, respectively. The default is c("Poor", "Good").
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 value for each stratum and must have the names attribute set to identify the stratum codes. The default is NULL.
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 discrete resource or the measure of a continuous resource, which is required for calculation of finite and continuous population correction factors for a single-stage sample. This variable is also used to adjust estimators for the known size of a resource. For a stratified sample this variable 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.
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 stage one sampling unit codes. For a stratified sample, the names attribute must be set to identify both stratum codes and stage one sampling unit codes using a convention where the two codes are separated by the # symbol, e.g., "Stratum 1#Cluster 1". The default is NULL.
support
the support value for each site - the value one (1) for a site from a discrete resource or the measure of the sampling unit associated with a site from a continuous resource, which is required for calculation of finite and continuous population correction factors. The default is NULL.
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:

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 tabl
CellProportions
estimated cell proportions for the 2x2 table

SIDE EFFECTS:

None

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).

Authors

Tom Kincaid Kincaid.Tom@epa.gov Tony Olsen Olsen.Tony@epa.gov John Vansickle Vansickle.John@epa.gov

REFERENCES:

Särndal, 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)

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