phaseI {osDesign}

Expected phase I stratification

Description

phaseI() provides the expected phase I counts, based on a pre-specified population and outcome model. If phase II sample sizes are provided, the (expected) phase II sampling probabilities are also reported.

Usage

phaseI(betaTruth, X, N, strata=NULL, expandX="all", etaTerms=NULL,
      nII0=NULL, nII1=NULL,
      cohort=TRUE, NI=NULL, digits=NULL)

Arguments

betaTruth

Regression coefficients from the logistic regression model.

X

Design matrix for the logistic regression model. The first column should correspond to intercept. For each exposure, the baseline group should be coded as 0, the first level as 1, and so on.

N

A numeric vector providing the sample size for each row of the design matrix, X.

strata

A numeric vector indicating which columns of the design matrix, X, are used to form the phase I stratification variable. strata=1 specifies the intercept and is, therefore, equivalent to a case-control study.

expandX

Character vector indicating which columns of X to expand as a series of dummy variables. Useful when at least one exposure is continuous (and should not be expanded). Default is ‘all’; other options include ‘none’ or character vector of column names. See Details, below.

etaTerms

Character vector indicating which columns of X are to be included in the model. See Details, below.

nII0

A vector of sample sizes at phase II for controls. The length must correspond to the number of unique values for phase I stratification variable.

nII1

A vector of sample sizes at phase II for cases. The length must correspond to the number of unique values phase I stratification variable.

cohort

Logical flag. TRUE indicates phase I is drawn as a cohort; FALSE indicates phase I is drawn as a case-control sample.

NI

A pair of integers providing the outcome-specific phase I sample sizes when the phase I data are drawn as a case-control sample. The first element corresponds to the controls and the second to the cases.

digits

Integer indicating the precision to be used for the reporting of the (expected) sampling probabilities

Details

The correspondence between betaTruth and X, specifically the ordering of elements, is based on successive use of factor to each column of X which is expanded via the expandX argument. Each exposure that is expanded must conform to a 0, 1, 2, ... integer-based coding convention.

The etaTerms argument is useful when only certain columns in X are to be included in the model. In the context of the two-phase design, this might be the case if phase I stratifies on some surrogate exposure and a more detailed/accurate measure is to be included in the main model.

Value

phaseI() returns an object of class "phaseI" that, at a minimum includes:

phaseI

Expected phase I counts, based on a pre-specified population and outcome model

covm

Model based variance-covariance matrix. This is available for method = "PL" and "ML".

cove

Empirical variance-covariance matrix. This is available for all the three methods.

fail

Indicator of whether or not the phase I and/or the phase II constraints are satisfied; only relevant for the ML estimator.

If phase II sample sizes were provided as part of the initial call, the object additionally includes:

phaseII

The supplied phase II sample sizes.

phaseIIprobs

Expected phase II sampling probabilities.

Author(s)

Sebastien Haneuse, Takumi Saegusa

References

Haneuse, S. and Saegusa, T. and Lumley, T. (2011) "osDesign: An R Package for the Analysis, Evaluation, and Design of Two-Phase and Case-Control Studies." Journal of Statistical Software, 43(11), 1-29.

Examples

##
data(Ohio)

## Design matrix that forms the basis for model and phase I 
## stata specification 
##
XM <- cbind(Int=1, Ohio[,1:3])      ## main effects only
XI <- cbind(XM, SbyR=XM[,3]*XM[,4]) ## interaction between sex and race

## 'True' values for the underlying logistic model
##
fitM <- glm(cbind(Death, N-Death) ~ factor(Age) + Sex + Race, data=Ohio,
            family=binomial)
fitI <- glm(cbind(Death, N-Death) ~ factor(Age) + Sex * Race, data=Ohio,
            family=binomial)

## Stratified sampling by race
##
phaseI(betaTruth=fitM$coef, X=XM, N=Ohio$N, strata=4,
       nII0=c(125, 125),
       nII1=c(125, 125))

## Stratified sampling by age and sex
##
phaseI(betaTruth=fitM$coef, X=XM, N=Ohio$N, strata=c(2,3))
##
phaseI(betaTruth=fitM$coef, X=XM, N=Ohio$N, strata=c(2,3),
       nII0=(30+1:6),
       nII1=(40+1:6))