A frequently encountered problem in practice is that of simultaneous interval estimation of p linear combinations of a parameter beta in the setting of (or equivalent to) a univariate linear model. This problem has been solved adequately only in a few settings when the covariance matrix of the estimator is diagonal; in other cases, conservative solutions can be obtained by the methods of Scheffé, Bonferroni, or Sidák (1967, Journal of the American Statistical Association 62, 626-633). Here we investigate the efficiency of using a simulated critical point for exact intervals, which has been suggested before but never put to serious test. We find the simulation-based method to be completely reliable and essentially exact. Sample size savings are substantial (in our settings): 3-19% over the Sidák method, 4-37% over the Bonferroni method, and 27-33% over the Scheffé method. We illustrate the efficiency and flexibility of the simulation-based method with case studies in physiology and marine ecology.
Screening and diagnostic procedures often require a physician's subjective interpretation of a patient's test result using an ordered categorical scale to define the patient's disease severity. Due to wide variability observed between physicians’ ratings, many large-scale studies have been conducted to quantify agreement between multiple experts’ ordinal classifications in common diagnostic procedures such as mammography. However, very few statistical approaches are available to assess agreement in these large-scale settings. Existing summary measures of agreement rely on extensions of Cohen's kappa [1 - 5]. These are prone to prevalence and marginal distribution issues, become increasingly complex for more than three experts or are not easily implemented. Here we propose a model-based approach to assess agreement in large-scale studies based upon a framework of ordinal generalized linear mixed models. A summary measure of agreement is proposed for multiple experts assessing the same sample of patients’ test results according to an ordered categorical scale. This measure avoids some of the key flaws associated with Cohen's kappa and its extensions. Simulation studies are conducted to demonstrate the validity of the approach with comparison to commonly used agreement measures. The proposed methods are easily implemented using the software package R and are applied to two large-scale cancer agreement studies.
Random sampling of paid Medicare claims has been a legally acceptable approach for investigating suspicious billing practices by health care providers (e.g. physicians, hospitals, medical equipment and supplies providers, etc.) since 1986. A population of payments made to a given provider during a given time frame is isolated and a probability sample selected for investigation. For each claim or claim detail line, the overpayment is defined to be the amount paid minus the amount that should have been paid, given all evidence collected by the investigator. Current procedures stipulate that, using the probability sample's observed overpayments, a 90% lower confidence bound for the total overpayment over the entire population is to be used as a recoupment demand to the provider. It is not unusual for these recoupment demands to exceed a million dollars. It is also not unusual for the statistical methods used in sampling and calculating the recoupment demand to be challenged in court.Though it is quite conservative in most settings, for certain types of overpayment populations the standard method for computing a lower confidence bound on the population total, based on the Central Limit Theorem, can fail badly even at relatively large sample sizes. Here, we develop "nonparametric sampling" inferential methods using simple random samples and the hypergeometric distribution, and study their performance on four real payment populations. These new methods are found to provide more than the nominal coverage probability for lower confidence bounds regardless of sample size, and to be surprisingly efficient relative to the Central Limit Theorem bounds in settings where overpayments are essentially all-or-nothing and where the payment population is relatively homogeneous and well separated from zero. The new methods are especially well-suited for sampling payment populations for providers of motorized wheelchairs, which at the time of this article's submission was a national crisis. Extensions to stratified random samples and to settings where there are frequent partial overpayments are discussed.
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