wse {svyROC}R Documentation

Estimation of the sensitivity with complex survey data

Description

Estimate the sensitivity parameter for a given cut-off point considering sampling weights with complex survey data.

Usage

wse(
  response.var,
  phat.var,
  weights.var = NULL,
  tag.event = NULL,
  cutoff.value,
  data = NULL,
  design = NULL
)

Arguments

response.var

A character string with the name of the column indicating the response variable in the data set or a vector (either numeric or character string) with information of the response variable for all the units.

phat.var

A character string with the name of the column indicating the estimated probabilities in the data set or a numeric vector containing estimated probabilities for all the units.

weights.var

A character string indicating the name of the column with sampling weights or a numeric vector containing information of the sampling weights. It could be NULL if the sampling design is indicated in the design argument. For unweighted estimates, set all the sampling weight values to 1.

tag.event

A character string indicating the label used to indicate the event of interest in response.var. The default option is tag.event = NULL, which selects the class with the lowest number of units as event.

cutoff.value

A numeric value indicating the cut-off point to be used. No default value is set for this argument, and a numeric value must be indicated necessarily.

data

A data frame which, at least, must incorporate information on the columns response.var, phat.var and weights.var. If data=NULL, then specific numerical vectors must be included in response.var, phat.var and weights.var, or the sampling design should be indicated in the argument design.

design

An object of class survey.design generated by survey::svydesign indicating the complex sampling design of the data. If design = NULL, information on the data set (argument data) and/or sampling weights (argument weights.var) must be included.

Details

Let S indicate a sample of n observations of the vector of random variables (Y,\pmb X), and \forall i=1,\ldots,n, y_i indicate the i^{th} observation of the response variable Y, and \pmb x_i the observations of the vector covariates \pmb X. Let w_i indicate the sampling weight corresponding to the unit i and \hat p_i the estimated probability of event. Let S_0 and S_1 be subsamples of S, formed by the units without the event of interest (y_i=0) and with the event of interest (y_i=1), respectively. Then, the sensitivity parameter for a given cut-off point c is estimated as follows:

\widehat{Se}_w(c)=\dfrac{\sum_{i\in S_1}w_i\cdot I (\hat p_i\geq c)}{\sum_{i\in S_1}w_i}.

See Iparragirre et al. (2022) and Iparragirre et al. (2023) for more details.

Value

The output of this function is a list of 4 elements containing the following information:

References

Iparragirre, A., Barrio, I., Aramendi, J. and Arostegui, I. (2022). Estimation of cut-off points under complex-sampling design data. SORT-Statistics and Operations Research Transactions 46(1), 137–158. (https://doi.org/10.2436/20.8080.02.121)

Iparragirre, A., Barrio, I. and Arostegui, I. (2023). Estimation of the ROC curve and the area under it with complex survey data. Stat 12(1), e635. (https://doi.org/10.1002/sta4.635)

Examples

data(example_data_wroc)

se.obj <- wse(response.var = "y", phat.var = "phat", weights.var = "weights",
              tag.event = 1, cutoff.value = 0.5, data = example_data_wroc)

# Or equivalently
se.obj <- wse(response.var = example_data_wroc$y,
              phat.var = example_data_wroc$phat,
              weights.var = example_data_wroc$weights,
              tag.event = 1, cutoff.value = 0.5)

[Package svyROC version 1.0.0 Index]