twophase: Two-phase designs

Description

In a two-phase design a sample is taken from a population and a subsample taken from the sample, typically stratified by variables not known for the whole population. The second phase can use any design supported for single-phase sampling. The first phase must currently be one-stage element or cluster sampling

Usage

twophase(id, strata = NULL, probs = NULL, weights = NULL, fpc = NULL,
subset, data, method=c("full","approx","simple"), pps=NULL)
twophasevar(x,design)
twophase2var(x,design)

Value

twophase returns an object of class twophase2 (for

method="full") or twophase. The structure of

twophase2 objects may change as unnecessary components are removed.

twophase2var and twophasevar return a variance matrix with an attribute containing the separate phase 1 and phase 2 contributions to the variance.

Arguments

id: list of two formulas for sampling unit identifiers
strata: list of two formulas (or NULLs) for stratum identifies
probs: list of two formulas (or NULLs) for sampling probabilities
weights: Only for method="approx", list of two formulas (or NULLs) for sampling weights
fpc: list of two formulas (or NULLs) for finite population corrections
subset: formula specifying which observations are selected in phase 2
data: Data frame will all data for phase 1 and 2
method: "full" requires (much) more memory, but gives unbiased variance estimates for general multistage designs at both phases. "simple" or "approx" uses the standard error calculation from version 3.14 and earlier, which uses much less memory and is correct for designs with simple random sampling at phase one and stratified random sampling at phase two.
pps: With method="full", an optional list of two PPS specifications for svydesign. At the moment, the phase-one element must be NULL
x: probability-weighted estimating functions
design: two-phase design

Details

The population for the second phase is the first-phase sample. If the second phase sample uses stratified (multistage cluster) sampling without replacement and all the stratum and sampling unit identifier variables are available for the whole first-phase sample it is possible to estimate the sampling probabilities/weights and the finite population correction. These would then be specified as NULL.

Two-phase case-control and case-cohort studies in biostatistics will typically have simple random sampling with replacement as the first stage. Variances given here may differ slightly from those in the biostatistics literature where a model-based estimator of the first-stage variance would typically be used.

Variance computations are based on the conditioning argument in Section 9.3 of Sarndal et al. Method "full" corresponds exactly to the formulas in that reference. Method "simple" or "approx" (the two are the same) uses less time and memory but is exact only for some special cases. The most important special case is the two-phase epidemiologic designs where phase 1 is simple random sampling from an infinite population and phase 2 is stratified random sampling. See the tests directory for a worked example. The only disadvantage of method="simple" in these cases is that standardization of margins (marginpred) is not available.

For method="full", sampling probabilities must be available for each stage of sampling, within each phase. For multistage sampling this requires specifying either fpc or probs as a formula with a term for each stage of sampling. If no fpc or probs are specified at phase 1 it is treated as simple random sampling from an infinite population, and population totals will not be correctly estimated, but means, quantiles, and regression models will be correct.

The pps argument allows for PPS sampling at phase two (or eventually at phase one), and also for Poisson sampling at phase two as a model for non-response.

References

Sarndal CE, Swensson B, Wretman J (1992) "Model Assisted Survey Sampling" Springer.

Breslow NE and Chatterjee N, Design and analysis of two-phase studies with binary outcome applied to Wilms tumour prognosis. "Applied Statistics" 48:457-68, 1999

Breslow N, Lumley T, Ballantyne CM, Chambless LE, Kulick M. (2009) Improved Horvitz-Thompson estimation of model parameters from two-phase stratified samples: applications in epidemiology. Statistics in Biosciences. doi 10.1007/s12561-009-9001-6

Lin, DY and Ying, Z (1993). Cox regression with incomplete covariate measurements. "Journal of the American Statistical Association" 88: 1341-1349.

Examples

Run this code

 ## two-phase simple random sampling.
 data(pbc, package="survival")
 pbc$randomized<-with(pbc, !is.na(trt) & trt>0)
 pbc$id<-1:nrow(pbc)
 d2pbc<-twophase(id=list(~id,~id), data=pbc, subset=~randomized)
 svymean(~bili, d2pbc)

 ## two-stage sampling as two-phase
 data(mu284)
 ii<-with(mu284, c(1:15, rep(1:5,n2[1:5]-3)))
 mu284.1<-mu284[ii,]
 mu284.1$id<-1:nrow(mu284.1)
 mu284.1$sub<-rep(c(TRUE,FALSE),c(15,34-15))
 dmu284<-svydesign(id=~id1+id2,fpc=~n1+n2, data=mu284)
 ## first phase cluster sample, second phase stratified within cluster
 d2mu284<-twophase(id=list(~id1,~id),strata=list(NULL,~id1),
                     fpc=list(~n1,NULL),data=mu284.1,subset=~sub)
 svytotal(~y1, dmu284)
 svytotal(~y1, d2mu284)
 svymean(~y1, dmu284)
 svymean(~y1, d2mu284)

 ## case-cohort design: this example requires R 2.2.0 or later
 library("survival")
 data(nwtco)

 ## stratified on case status
 dcchs<-twophase(id=list(~seqno,~seqno), strata=list(NULL,~rel),
         subset=~I(in.subcohort | rel), data=nwtco)
 svycoxph(Surv(edrel,rel)~factor(stage)+factor(histol)+I(age/12), design=dcchs)

 ## Using survival::cch 
 subcoh <- nwtco$in.subcohort
 selccoh <- with(nwtco, rel==1|subcoh==1)
 ccoh.data <- nwtco[selccoh,]
 ccoh.data$subcohort <- subcoh[selccoh]
 cch(Surv(edrel, rel) ~ factor(stage) + factor(histol) + I(age/12), data =ccoh.data,
        subcoh = ~subcohort, id=~seqno, cohort.size=4028, method="LinYing")


 ## two-phase case-control
 ## Similar to Breslow & Chatterjee, Applied Statistics (1999) but with
 ## a slightly different version of the data set
 
 nwtco$incc2<-as.logical(with(nwtco, ifelse(rel | instit==2,1,rbinom(nrow(nwtco),1,.1))))
 dccs2<-twophase(id=list(~seqno,~seqno),strata=list(NULL,~interaction(rel,instit)),
    data=nwtco, subset=~incc2)
 dccs8<-twophase(id=list(~seqno,~seqno),strata=list(NULL,~interaction(rel,stage,instit)),
    data=nwtco, subset=~incc2)
 summary(glm(rel~factor(stage)*factor(histol),data=nwtco,family=binomial()))
 summary(svyglm(rel~factor(stage)*factor(histol),design=dccs2,family=quasibinomial()))
 summary(svyglm(rel~factor(stage)*factor(histol),design=dccs8,family=quasibinomial()))

 ## Stratification on stage is really post-stratification, so we should use calibrate()
 gccs8<-calibrate(dccs2, phase=2, formula=~interaction(rel,stage,instit))
 summary(svyglm(rel~factor(stage)*factor(histol),design=gccs8,family=quasibinomial()))

 ## For this saturated model calibration is equivalent to estimating weights.
 pccs8<-calibrate(dccs2, phase=2,formula=~interaction(rel,stage,instit), calfun="rrz")
 summary(svyglm(rel~factor(stage)*factor(histol),design=pccs8,family=quasibinomial()))

 ## Since sampling is SRS at phase 1 and stratified RS at phase 2, we
 ## can use method="simple" to save memory.
 dccs8_simple<-twophase(id=list(~seqno,~seqno),strata=list(NULL,~interaction(rel,stage,instit)),
    data=nwtco, subset=~incc2,method="simple")
 summary(svyglm(rel~factor(stage)*factor(histol),design=dccs8_simple,family=quasibinomial()))

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