Richard M. Royall

Racial Differences in the Cause-Specific Prevalence of Blindness in East Baltimore

BACKGROUND Bilateral blindness unrelated to simple refractive error is twice as prevalent among blacks as among whites, although the difference narrows among the elderly. The reasons for this race- and age-related pattern are uncertain. METHODS AND RESULTS A randomly selected, stratified, multistage cluster sample of 2395 blacks and 2913 whites 40 years of age and older in East Baltimore underwent detailed ophthalmic examinations by a single team. We identified 64 subjects who were blind in both eyes. The leading causes of blindness were unoperated senile cataract (accounting for blindness in 27 of the total of 128 eyes), primary open-angle glaucoma (17 eyes), and age-related macular degeneration (16 eyes). Together, these three disorders accounted for 47 percent of all blindness in this sample. Unoperated cataract accounted for 27 percent of all blindness among blacks, among whom it was four times more common than among whites; whites were almost 50 percent more likely than blacks to have undergone cataract extraction before the age of 80 (P less than 0.002). Primary open-angle glaucoma accounted for 19 percent of all blindness among blacks; it was six times as frequent among blacks as among whites and began 10 years earlier, on average. By contrast, age-related macular degeneration resulting in blindness was limited to whites, among whom it was the leading cause of blindness (prevalence, 2.7 per 1000; 95 percent confidence interval, 1.2 to 5.4); it affected 3 percent of all white subjects 80 years of age or older. CONCLUSIONS The pattern of blindness in urban Baltimore appears to be different among blacks and whites. Whites are far more likely to have age-related macular degeneration, and blacks to have primary open-angle glaucoma. The high rate of unoperated cataracts among younger blacks and among elderly subjects of both races suggests that health services are underused. Half of all blindness in this urban population is probably preventable or reversible.

Robust Estimation in Finite Populations I

Abstract This is an application of a least-squares prediction approach to finite population sampling theory. One way in which this approach differs from the conventional one is its focus on characteristics of particular samples rather than on plans for choosing samples. Here we study samples in which many superpopulation models lead to the same optimal (BLU) estimator. Random sampling is considered in the light of these results.

Heparin-Associated Thrombocytopenia: A Comparison of Three Heparin Preparations

We performed a prospective, double-blind study of the incidence of thrombocytopenia in 149 patients randomly assigned to treatment with one of three heparin preparations--from bovine lung from intestinal-mucosa A, or from intestinal-mucosa O. Thrombocytopenia developed in 21 patients (platelets, < 100 x 10(9) per liter): 13 of the 50 receiving bovine lung heparin, four of 45 receiving intestinal-mucosa-A heparin, and four of 54 receiving intestinal-musoca-O heparin (P < 0.005). There was a significantly increased incidence of thrombocytopenia in the bovine-lung group (P < 0.002); estimated incidence rates after nine days of treatment were 24 per cent in this group and 7 per cent in the combined intestinal-mucosa A and O groups. Thrombocytopenia appeared in the bovine-lung group on days 3 to 16, in the intestinal-mucosa-A groups on Days 4 to 12, and in the intestinal-mucosa-O group on Days 3 to 7; it disappeared in all groups three to eight days after discontinuation of heparin. A total of 121 patients were subsequently given warfarin for four to six months, and thrombocytopenia was not observed.

The Linear Least-Squares Prediction Approach to Two-Stage Sampling

Abstract The linear least-squares prediction approach is applied to some problems in two-stage sampling from finite populations. A theorem giving the optimal (BLU) estimator and its error-variance under a general linear “superpopulation” model for a finite population is stated. This theorem is then applied to a model describing many populations whose elements are grouped naturally in clusters. Next, the probability model is used to analyze various conventional estimators and certain estimators suggested by the theory as alternatives to the conventional ones. Problems of design are considered, as are some consequences of regression-model failure.

An Empirical Study of the Ratio Estimator and Estimators of its Variance

Abstract This paper reports results from an empirical study of the ratio estimator for a finite population total. From each of six real populations, 1,000 simple random samples, 1,000 restricted random samples, and three nonrandom samples of size 32 are drawn. Performance of the ratio estimator and of five estimators of its variance is compared with theoretical results generated using (a) prediction (superpopulation) models and (b) probability sampling distributions. The results, presented graphically, show that theory based on prediction models can reveal relationships that are essential in making inferences, but that are concealed in probability sampling analyses.

The Effect of Sample Size on the Meaning of Significance Tests

Abstract Contradictory interpretations of how the meaning of a significance test depends on the sample size are examined.

Improving sterological estimates for the volume of structures identified in three-dimensional arrays of spatial data

Investigators frequently measure the volumes of anatomic structures. These volumes can answer important scientific questions such as whether a structure differs between two groups, which structures a disease affects, or how the size of a structure relates to its function. Magnetic resonance (MR) imaging, X-ray computed tomography and confocal microscopy are used more and more frequently in anatomic studies; each yields information that is spatially organized as a three-dimensional array. We describe how to improve an efficient stereological technique for estimating the volumes of structures that are identifiable in these arrays. As an example, we apply the technique to measuring brain volumes by MR imaging. We then show how the results of the technique may be used for solving a typical problem in experimental design. This technique is applicable to a wide range of experimental problems. We discuss its limitations and offer some suggestions and observations relating to its use.

On the Probability of Observing Misleading Statistical Evidence

Abstract The law of likelihood explains how to interpret statistical data as evidence. Specifically, it gives to the discipline of statistics a precise and objective measure of the strength of statistical evidence supporting one probability distribution vis-à-vis another. That measure is the likelihood ratio. But evidence, even when properly interpreted, can be misleading—observations can truly constitute strong evidence supporting one distribution when the other is true. What makes statistical evidence valuable to science is that this cannot occur very often. Here we examine two bounds on the probability of observing strong misleading evidence. One is a universal bound, applicable to every pair of probability distributions. The other bound, much smaller, applies to all pairs of distributions within fixed-dimensional parametric models in large samples. The second bound comes from examining how the probability of strong misleading evidence varies as a function of the alternative value of the parameter. We show that in large samples one curve describes how this probability first rises and then falls as the alternative moves away from the true parameter value for a very wide class of models. We also show that this large-sample curve, and the bound that its maximum value represents, applies to profile likelihood ratios for one-dimensional parameters in fixed-dimensional parametric models, but does not apply to the estimated likelihood ratios that result from replacing the nuisance parameters by their global maximum likelihood estimates.

Variance Estimation in Finite Population Sampling

Abstract Under a linear regression model, the best linear unbiased estimator (BLUE) for a finite population total can be obtained. The problem studied here is that of estimating the variance for setting large-sample confidence intervals about the BLUE when the model generating this estimate is inaccurate. A robust variance estimator is derived, and its asymptotic properties are shown to compare favorably with those of the weighted least-squares variance estimator. The robust variance estimator is shown to be asymptotically equivalent to the jackknife variance estimator under rather general conditions. These are extensions of results previously established for the ratio estimator by Royall and Eberhardt (1975).

Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions

The strength of statistical evidence is measured by the likelihood ratio. Two key performance properties of this measure are the probability of observing strong misleading evidence and the probability of observing weak evidence. For the likelihood function associated with a parametric statistical model, these probabilities have a simple large sample structure when the model is correct. Here we examine how that structure changes when the model fails. This leads to criteria for determining whether a given likelihood function is robust (continuing to perform satisfactorily when the model fails), and to a simple technique for adjusting both likelihoods and profile likelihoods to make them robust. We prove that the expected information in the robust adjusted likelihood cannot exceed the expected information in the likelihood function from a true model. We note that the robust adjusted likelihood is asymptotically fully efficient when the working model is correct, and we show that in some important examples this efficiency is retained even when the working model fails. In such cases the Bayes posterior probability distribution based on the adjusted likelihood is robust, remaining correct asymptotically even when the model for the observable random variable does not include the true distribution. Finally we note a link to standard frequentist methodology-in large samples the adjusted likelihood functions provide robust likelihood-based confidence intervals. Copyright 2003 Royal Statistical Society.