Compute the Relative Risk Estimate

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

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relrisk.est(response, stressor, response.levels=c("Poor", "Good"),
   stressor.levels=c("Poor", "Good"), wgt, xcoord=NULL, ycoord=NULL,
   stratum=NULL, cluster=NULL, wgt1=NULL, xcoord1=NULL, ycoord1=NULL,
   popcorrect=FALSE, pcfsize=NULL, N.cluster=NULL, stage1size=NULL,
   support=NULL, sizeweight=FALSE, swgt=NULL, swgt1=NULL, vartype="Local",
   conf=95, check.ind=TRUE, warn.ind=NULL, warn.df=NULL, warn.vec=NULL)

Arguments

response

the categorical response variable values.

stressor

the categorical explanatory (stressor) variable values.

response.levels

category values (levels) for the categorical response variable, where the first level is used for calculating the numerator and the denominator of 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.

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.

popcorrect

a logical value that indicates whether finite or continuous population correction factors should be employed during variance estimation, where TRUE = use the correction factors and FALSE = do not use the correction factors. The default is FALSE. To employ the correction factor for a single-stage sample, values must be supplied for arguments pcfsize and support. To employ the correction factor for a two-stage sample, values must be supplied for arguments N.cluster, stage1size, and support.

pcfsize

size of the resource, which is required for calculation of finite and continuous population correction factors for a single-stage sample. For a stratified sample this argument 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 NULLL.

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.

stage1size

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 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 population correction factors. The default is NULL.

sizeweight

a logical value that indicates whether size-weights should be used in the analysis, where TRUE = use the size-weights and FALSE = do not use the size-weights. The default is FALSE.

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.

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.

warn.ind

a logical value that indicates whether warning messages were generated, where TRUE = warning messages were generated and FALSE = warning messages were not generated. The default is NULL.

warn.df

a data frame for storing warning messages. The default is NULL.

warn.vec

a vector that contains names of the population type, the subpopulation, and an indicator. The default is NULL.

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 (Van Sickle and Paulsen, 2008). An estimate of the numerator probability is provided by the ratio of the cell total defined by the first level of the 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).

Value

If the function was called by the relrisk.analysis function, then value is a list containing the following components:

  • Results - a list containing estimates, confidence bounds, and associated values

  • warn.ind - a logical value indicating whether warning messages were generated

  • warn.df - a data frame containing warning messages

If the function was called directly, then value is the Results list, which contains 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

Author(s)

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

References

Van Sickle, J. and S. G. Paulsen. (2008). Assessing the attributable risks, relative risks, and regional extent of aquatic stressors. Journal of the North American Benthological Society 27, 920-931.
Sarndal, C.E., B. Swensson, and J. Wretman. (1992). Model Assisted Survey Sampling. Springer-Verlag, New York.

Examples

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

xcoord <- runif(100)
ycoord <- runif(100)
relrisk.est(response, stressor, wgt=wgt, xcoord=xcoord, ycoord=ycoord)

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