Fusion of data sets in multivariate linear regression with errors-in-variables

We consider the application of normal theory methods to the estimation and testing of a general type of multivariate regressionmodels with errors--in--variables, in the case where various data setsare merged into a single analysis and the observable variables deviatepossibly from normality. The various samples to be merged can differ on the set of observable variables available. We show that there is a convenient way to parameterize the model so that, despite the possiblenon--normality of the data, normal--theory methods yield correct inferencesfor the parameters of interest and for the goodness--of--fit test. Thetheory described encompasses both the functional and structural modelcases, and can be implemented using standard software for structuralequations models, such as LISREL, EQS, LISCOMP, among others. An illustration with Monte Carlo data is presented.

Scaled and adjusted restricted tests in multi-sample analysis of moment structures

We extend to score, Wald and difference test statistics the scaled and adjusted corrections to goodness-of-fit test statistics developed in Satorra and Bentler (1988a,b). The theory is framed in the general context of multisample analysis of moment structures, under general conditions on the distribution of observable variables. Computational issues, as well as the relation of the scaled and corrected statistics to the asymptotic robust ones, is discussed. A Monte Carlo study illustrates thecomparative performance in finite samples of corrected score test statistics.

Three-dimensional patient-specific dosimetry in radioimmunotherapy with 90Y-ibritumomab-tiuxetan.

Aim of the present article was to perform three-dimensional (3D) single photon emission tomography-based dosimetry in radioimmunotherapy (RIT) with (90)Y-ibritumomab-tiuxetan. A custom MATLAB-based code was used to elaborate 3D images and to compare average 3D doses to lesions and to organs at risk (OARs) with those obtained with planar (2D) dosimetry. Our 3D dosimetry procedure was validated through preliminary phantom studies using a body phantom consisting of a lung insert and six spheres with various sizes. In phantom study, the accuracy of dose determination of our imaging protocol decreased when the object volume decreased below 5 mL, approximately. The poorest results were obtained for the 2.58 mL and 1.30 mL spheres where the dose error evaluated on corrected images with regard to the theoretical dose value was -12.97% and -18.69%, respectively. Our 3D dosimetry protocol was subsequently applied on four patients before RIT with (90)Y-ibritumomab-tiuxetan for a total of 5 lesions and 4 OARs (2 livers, 2 spleens). In patient study, without the implementation of volume recovery technique, tumor absorbed doses calculated with the voxel-based approach were systematically lower than those calculated with the planar protocol, with average underestimation of -39% (range from -13.1% to -62.7%). After volume recovery, dose differences reduce significantly, with average deviation of -14.2% (range from -38.7.4% to +3.4%, 1 overestimation, 4 underestimations). Organ dosimetry in one case overestimated, in the other underestimated the dose delivered to liver and spleen. However, both for 2D and 3D approach, absorbed doses to organs per unit administered activity are comparable with most recent literature findings.

Measuring the stability of histogram appearance when the anchor position is changed

Although the histogram is the most widely used density estimator, itis well--known that the appearance of a constructed histogram for a given binwidth can change markedly for different choices of anchor position. In thispaper we construct a stability index $G$ that assesses the potential changesin the appearance of histograms for a given data set and bin width as theanchor position changes. If a particular bin width choice leads to an unstableappearance, the arbitrary choice of any one anchor position is dangerous, anda different bin width should be considered. The index is based on the statisticalroughness of the histogram estimate. We show via Monte Carlo simulation thatdensities with more structure are more likely to lead to histograms withunstable appearance. In addition, ignoring the precision to which the datavalues are provided when choosing the bin width leads to instability. We provideseveral real data examples to illustrate the properties of $G$. Applicationsto other binned density estimators are also discussed.

Using composite estimators to improve both domain and total area estimation

In this article we propose using small area estimators to improve the estimatesof both the small and large area parameters. When the objective is to estimateparameters at both levels accurately, optimality is achieved by a mixed sampledesign of fixed and proportional allocations. In the mixed sample design, oncea sample size has been determined, one fraction of it is distributedproportionally among the different small areas while the rest is evenlydistributed among them. We use Monte Carlo simulations to assess theperformance of the direct estimator and two composite covariant-freesmall area estimators, for different sample sizes and different sampledistributions. Performance is measured in terms of Mean Squared Errors(MSE) of both small and large area parameters. It is found that the adoptionof small area composite estimators open the possibility of 1) reducingsample size when precision is given, or 2) improving precision for a givensample size.

On the performance of small-area estimators: Fixed vs. random area parameters

Most methods for small-area estimation are based on composite estimators derived from design- or model-based methods. A composite estimator is a linear combination of a direct and an indirect estimator with weights that usually depend on unknown parameters which need to be estimated. Although model-based small-area estimators are usually based on random-effects models, the assumption of fixed effects is at face value more appropriate.Model-based estimators are justified by the assumption of random (interchangeable) area effects; in practice, however, areas are not interchangeable. In the present paper we empirically assess the quality of several small-area estimators in the setting in which the area effects are treated as fixed. We consider two settings: one that draws samples from a theoretical population, and another that draws samples from an empirical population of a labor force register maintained by the National Institute of Social Security (NISS) of Catalonia. We distinguish two types of composite estimators: a) those that use weights that involve area specific estimates of bias and variance; and, b) those that use weights that involve a common variance and a common squared bias estimate for all the areas. We assess their precision and discuss alternatives to optimizing composite estimation in applications.

Cost-effectiveness of low-molecular-weight heparin for treatment of pulmonary embolism.

BACKGROUND: Low-molecular-weight heparin (LMWH) appears to be safe and effective for treating pulmonary embolism (PE), but its cost-effectiveness has not been assessed. METHODS: We built a Markov state-transition model to evaluate the medical and economic outcomes of a 6-day course with fixed-dose LMWH or adjusted-dose unfractionated heparin (UFH) in a hypothetical cohort of 60-year-old patients with acute submassive PE. Probabilities for clinical outcomes were obtained from a meta-analysis of clinical trials. Cost estimates were derived from Medicare reimbursement data and other sources. The base-case analysis used an inpatient setting, whereas secondary analyses examined early discharge and outpatient treatment with LMWH. Using a societal perspective, strategies were compared based on lifetime costs, quality-adjusted life-years (QALYs), and the incremental cost-effectiveness ratio. RESULTS: Inpatient treatment costs were higher for LMWH treatment than for UFH (dollar 13,001 vs dollar 12,780), but LMWH yielded a greater number of QALYs than did UFH (7.677 QALYs vs 7.493 QALYs). The incremental costs of dollar 221 and the corresponding incremental effectiveness of 0.184 QALYs resulted in an incremental cost-effectiveness ratio of dollar 1,209/QALY. Our results were highly robust in sensitivity analyses. LMWH became cost-saving if the daily pharmacy costs for LMWH were < dollar 51, if > or = 8% of patients were eligible for early discharge, or if > or = 5% of patients could be treated entirely as outpatients. CONCLUSION: For inpatient treatment of PE, the use of LMWH is cost-effective compared to UFH. Early discharge or outpatient treatment in suitable patients with PE would lead to substantial cost savings.

Estimating uncertainty of alcohol-attributable fractions for infectious and chronic diseases.

Background: Alcohol is a major risk factor for burden of disease and injuries globally. This paper presents a systematic method to compute the 95% confidence intervals of alcohol-attributable fractions (AAFs) with exposure and risk relations stemming from different sources.Methods: The computation was based on previous work done on modelling drinking prevalence using the gamma distribution and the inherent properties of this distribution. The Monte Carlo approach was applied to derive the variance for each AAF by generating random sets of all the parameters. A large number of random samples were thus created for each AAF to estimate variances. The derivation of the distributions of the different parameters is presented as well as sensitivity analyses which give an estimation of the number of samples required to determine the variance with predetermined precision, and to determine which parameter had the most impact on the variance of the AAFs.Results: The analysis of the five Asian regions showed that 150 000 samples gave a sufficiently accurate estimation of the 95% confidence intervals for each disease. The relative risk functions accounted for most of the variance in the majority of cases.Conclusions: Within reasonable computation time, the method yielded very accurate values for variances of AAFs.

A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in realistic, i.e., nonasymptotic and nonnormal, applications. In a recent paper, Satorra (1999) shows that the difference between two Satorra-Bentler scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are notavailable in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of models ${\cal M}_0$ and ${\cal M}_1$. A Monte Carlo study is provided to illustrate the performance of the competing statistics.

Estimating parliamentary composition through electoral polls

Any electoral system has an electoral formula that converts voteproportions into parliamentary seats. Pre-electoral polls usually focuson estimating vote proportions and then applying the electoral formulato give a forecast of the parliament's composition. We here describe theproblems arising from this approach: there is always a bias in theforecast. We study the origin of the bias and some methods to evaluateand to reduce it. We propose some rules to compute the sample sizerequired for a given forecast accuracy. We show by Monte Carlo simulationthe performance of the proposed methods using data from Spanish electionsin last years. We also propose graphical methods to visualize how electoralformulae and parliamentary forecasts work (or fail).

Improving small area estimation by combining surveys: new perspectives in regional statistics

A national survey designed for estimating a specific population quantity is sometimes used for estimation of this quantity also for a small area, such as a province. Budget constraints do not allow a greater sample size for the small area, and so other means of improving estimation have to be devised. We investigate such methods and assess them by a Monte Carlo study. We explore how a complementary survey can be exploited in small area estimation. We use the context of the Spanish Labour Force Survey (EPA) and the Barometer in Spain for our study.

Estimating learning models from experimental data

We study the statistical properties of three estimation methods for a model of learning that is often fitted to experimental data: quadratic deviation measures without unobserved heterogeneity, and maximum likelihood withand without unobserved heterogeneity. After discussing identification issues, we show that the estimators are consistent and provide their asymptotic distribution. Using Monte Carlo simulations, we show that ignoring unobserved heterogeneity can lead to seriously biased estimations in samples which have the typical length of actual experiments. Better small sample properties areobtained if unobserved heterogeneity is introduced. That is, rather than estimating the parameters for each individual, the individual parameters are considered random variables, and the distribution of those random variables is estimated.

An empirical evaluation of small area estimators

This paper investigates the comparative performance of five small areaestimators. We use Monte Carlo simulation in the context of boththeoretical and empirical populations. In addition to the direct andindirect estimators, we consider the optimal composite estimator withpopulation weights, and two composite estimators with estimatedweights: one that assumes homogeneity of within area variance andsquare bias, and another one that uses area specific estimates ofvariance and square bias. It is found that among the feasibleestimators, the best choice is the one that uses area specificestimates of variance and square bias.

Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical {\sc vc} dimension, empirical {\sc vc} entropy, andmargin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

Activity measurements of 18F and 90Y with commercial radionuclide calibrators for nuclear medicine in Switzerland.

The activity of radiopharmaceuticals in nuclear medicine is measured before patient injection with radionuclide calibrators. In Switzerland, the general requirements for quality controls are defined in a federal ordinance and a directive of the Federal Office of Metrology (METAS) which require each instrument to be verified. A set of three gamma sources (Co-57, Cs-137 and Co-60) is used to verify the response of radionuclide calibrators in the gamma energy range of their use. A beta source, a mixture of (90)Sr and (90)Y in secular equilibrium, is used as well. Manufacturers are responsible for the calibration factors. The main goal of the study was to monitor the validity of the calibration factors by using two sources: a (90)Sr/(90)Y source and a (18)F source. The three types of commercial radionuclide calibrators tested do not have a calibration factor for the mixture but only for (90)Y. Activity measurements of a (90)Sr/(90)Y source with the (90)Y calibration factor are performed in order to correct for the extra-contribution of (90)Sr. The value of the correction factor was found to be 1.113 whereas Monte Carlo simulations of the radionuclide calibrators estimate the correction factor to be 1.117. Measurements with (18)F sources in a specific geometry are also performed. Since this radionuclide is widely used in Swiss hospitals equipped with PET and PET-CT, the metrology of the (18)F is very important. The (18)F response normalized to the (137)Cs response shows that the difference with a reference value does not exceed 3% for the three types of radionuclide calibrators.