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two-phase sampling, the second-phase sample is often a stratified sample based on the information observed in the first-phase sample. For the total of a population characteristic, either the double-expansion estimator or the reweighted expansion estimator can be used. Given a consistent first-phase replication variance estimator, we propose a consistent variance estimator that is applicable to both the double-expansion estimator and the reweighted expansion estimator. The proposed method can be extended to multiphase sampling. [ABSTRACT FROM AUTHOR]

Because randomized trials have shown a reduction in breast cancer mortality, analog mammography for the early detection of breast cancer has gained widespread use. Recently, several manufacturers have developed digital mammography, which promises great advantages in the storage and transmission of images. We were asked to design a study to compare the two types of mammography in terms of their performance for the early detection of breast cancer. A standard measure of mammography performance is the receiver operating characteristic (ROC) curve, which is a plot of false- and true-positive rates for each ordered classification of the mammography images. Methods for study design and data analysis based on ROC curves have been well developed for diagnostic tests, particularly in radiology. But for comparing the performance of mammography for the early detection of breast cancer among asymptomatic women, special considerations motivate new designs and methodology. First, digital mammography may cost substantially more than analog mammography. If this is the case, then the standard paired design, in which each subject undergoes both types of mammography, may be more expensive than necessary. To reduce costs, we propose a partial testing design, in which all subjects undergo analog mammography and those recommended for biopsy and a random sample not recommended for biopsy also undergo digital mammography. Second, the false-positive rate for analog mammography, defined as the rate of unnecessary biopsy, is near 1%. A standard ROC analysis that compares areas under the entire ROC curve would summarize performance over false-positive rates that are not relevant for evaluating the performance of cancer screening. As a more appropriate alternative, we propose basing inference on the areas under the small part of the ROC curves near the false-positive rates corresponding to a biopsy recommendation. Third, the vast majority of screened subjects are not biopsied and so have an unknown cancer state at the time of screening. To make inference about the performance of a cancer screening test, the standard approach is to follow subjects not biopsied for some period, usually 1 year, and assume that those who developed cancer were missed on screening and those who did not develop cancer were cancer-free at screening. Unfortunately, this follow-up period can greatly lengthen the duration of the study. To compare the performance of digital and analog mammography without the need for a follow-up period, we propose estimating the ratio of areas under the ROC curves near the small false-positive rates associated with a biopsy recommendation. To compute sample sizes, our null hypothesis is that the ratio of partial ROC areas is 1, and our two possible alternative hypotheses are ratios of 1.6 and 2, both indicating superior performance for digital mammography. We assume a breast cancer prevalence of .003 and specify various parameters for the shapes of the ROC curves and their dependence. For a two-sided type I error of .05 and a power of .9, a standard paired design would require that 22,000 subjects undergo both analog and digital mammography. For the same type I error and power, the proposed partial testing design would require that 35,000 subjects undergo analog mammography and 10,000 subjects undergo both analog and digital mammography. Compared to the paired design, the reduction in the cost per subject is 23% if digital mammography costs four times as much as analog mammography and 41% if digital mammography costs 10 times as much as analog mammography. [ABSTRACT FROM AUTHOR]

This article reports on the proposal for a Bayesian sequential two-phase sampling design to accommodate applications where conventional two-phase sampling cannot be used. Researchers first derive the optimal, the optimal myopic, and several approximate optimal myopic sequential decision procedures for subsampling a first-phase sample. Then they compared the procedure to that of the optimal (nonsequential) conventional two-phase sample design. In our application, the objective is inference about the age distribution of a population of fish using data on covariates like lengths and weight obtained from all members of the first-phase sample and data on age obtained from the fish in the second-phase subsample. The routine monitoring of commercial fish stocks often requires estimates of the age distribution for modeling and forecasting. Typically, an initial random sample of fish is selected from either a commercial catch or research vessel catch, and these fish are assigned to strata, defined by length or weight measurements.

States that administer federal family welfare programs review samples of the beneficiaries to guide corrective actions. Federal agencies review subsamples of the state samples to compute overpayment error rates using a regression estimator. These federal estimates make state-to-state comparisons of quality possible and are also used for fiscal sanctions. Such applications of the regression estimator have been widely challenged. We show that the regression estimates and estimates of their variances are closely unbiased, and we examine their statistical characteristics. We also comment on the recent reports of the National Research Council Panel on Quality Control of Family Assistance Programs. [ABSTRACT FROM AUTHOR]

Double-sampling experiments can be expressed as incomplete multiway contingency tables and analyzed by using techniques appropriate for fitting log-linear models. The framework described can be applied to experiments with any number of factors and measurement devices. Maximum likelihood estimation via the EM algorithm leads to straightforward expressions for covariances of estimates of the parameters and functions of the parameters. [ABSTRACT FROM AUTHOR]

Errors in the collection of categorical data lead to misclassification of observed counts. Several authors have proposed a double sampling scheme. This article develops a method for analysis of double sampling data. First, a log-linear model is selected for the misclassification matrix that relates the fallible to the correct data; then another log-linear model is built on the distribution of the correct classifications. Thus, the error structure can be utilized in inference of the relationships among the correct classifications. The statistical principles used are maximum likelihood estimation and goodness-off-it tests. An example from epidemiology illustrates the methodology. [ABSTRACT FROM AUTHOR]