secondary_ODS: Secondary analysis in ODS design
In Yinghao-Pan/ODS: Statistical Methods for Outcome-Dependent Sampling Designs

Description Usage Arguments Value Examples

secondary_ODS performs the secondary analysis which describes the association between a continuous scale secondary outcome and the expensive exposure for data obtained with ODS (outcome dependent sampling) design.

1	secondary_ODS(SRS, lowerODS, upperODS, NVsample, cutpoint, Z.dim)

`SRS`	A data matrix for subjects in the simple random sample. The first column is Y1: the primary outcome for which the ODS scheme is based on. The second column is Y2: a secondary outcome. The third column is X: the expensive exposure. Starting from the fourth column to the end is Z: other covariates.
`lowerODS`	A data matrix for supplemental samples taken from the lower tail of Y1 (eg. Y1 < a). The data structure is the same as SRS.
`upperODS`	A data matrix for supplemental samples taken from the upper tail of Y1 (eg. Y1 > b). The data structure is the same as SRS.
`NVsample`	A data matrix for subjects in the non-validation sample. Subjects in the non-validation sample don't have the expensive exposure X measured. The data structure is the same as SRS, but the third column (which represents X) has values NA.
`cutpoint`	A vector of length two that represents the cut off points for the ODS design. eg. cutpoint <- c(a,b). In the ODS design, a simple random sample is taken from the full cohort, then two supplemental samples are taken from {Y1 < a} and {Y1 > b}, respectively.
`Z.dim`	Dimension of the covariates Z.

A list which contains parameter estimates, estimated standard error for the primary outcome model:

Y1 = beta0 + beta1*X + beta2*Z,

and the secondary outcome model:

Y2 = gamma0 + gamma1*X + gamma2*Z.

The list contains the following components:

`beta_paramEst`	parameter estimates for beta in the primary outcome model
`beta_stdErr`	estimated standard error for beta in the primary outcome model
`gamma_paramEst`	parameter estimates for gamma in the secondary outcome model
`gamma_stdErr`	estimated standard error for gamma in the secondary outcome model

library(ODS)
# take the example data from the ODS package
# please see the documentation for details about the data set ods_data_secondary
data <- ods_data_secondary

# divide the original cohort data into SRS, lowerODS, upperODS and NVsample
SRS <- data[data[,1]==1,2:ncol(data)]
lowerODS <- data[data[,1]==2,2:ncol(data)]
upperODS <- data[data[,1]==3,2:ncol(data)]
NVsample <- data[data[,1]==0,2:ncol(data)]

# obtain the cut off points for ODS design. For this data, the ODS design
# uses mean plus and minus one standard deviation of Y1 as cut off points.
meanY1 <- mean(data[,2])
sdY1 <- sd(data[,2])
cutpoint <- c(meanY1-sdY1, meanY1+sdY1)

# the data matrix SRS has Y1, Y2, X and Z. Hence the dimension of Z is ncol(SRS)-3.
Z.dim <- ncol(SRS)-3

secondary_ODS(SRS, lowerODS, upperODS, NVsample, cutpoint, Z.dim)