On equivalence problem in linear regression models. II. Unbiased estimation of the covariance matrix scalar factor

summary:There exist many different ways of determining the best linear unbiased estimation of regression coefficients in general regression model. In Part I of this article it is shown that all these ways are numerically equivalent almost everyvhere. In Part II conditions are considered under which all the unbiased estimations of the unknown covariance matrix scalar factor are numerically equivalent almost everywhere

Linear-quadratic estimators in a special structure of the linear model

summary:The paper deals with the linear model with uncorrelated observations. The dispersions of the values observed are linear-quadratic functions of the unknown parameters of the mean (measurements by devices of a given class of precision). Investigated are the locally best linear-quadratic unbiased estimators as improvements of locally best linear unbiased estimators in the case that the design matrix has none, one or two linearly dependent rows

Advanced mathematical and statistical methods in evaluating instrumented indentation measurements

This publicly available research report provides a detailed overview of the results achieved within the TACR project TJ02000203 "Advanced mathematical and statistical methods in evaluating instrumented indentation measurements". The introductory section contains necessary background on instrumented indentation data evaluation procedures using the method due to Oliver and Pharr, as described in ISO 14577 standard. The next section provides detailed derivation of a novel algorithm "OEFPIL" for nonlinear data regression with errors in both variables, as well as guidelines for efficient implementation of the algorithm. The algorithm calculates both the optimum estimate of function parameters and an estimate of the parameter covariance matrix. The algorithm performance is demonstrated on reference data for nonlinear regression, and validated by comparison to another method. In the next section some existing advanced methods for uncertainty propagation (higher-order uncertainty propagation, Latin hypercube sampling for Monte Carlo) are also discussed. The last section presents application of the aforementioned methods for data regression and uncertainty propagation in processing data from instrumented indentation measurements. These methods have been newly added to the the free software tool Niget to improve data fitting of the unloading curve and to provide capability for indenter contact area function calibration. Combination of the regression and uncertainty propagation methods enables a better insight into evaluation of indentation data and provides basis for e.g. identifying main sources of measurement uncertainty or designing measurement strategy. Although the methods were designed and assessed with Oliver and Pharr's evaluation method in mind, they can be easily adapted to other evaluation models, too. All software developed and used in this project is freely available.Tato veřejně dostupná výzkumná zpráva obsahuje detailní přehled o výsledcích dosažených v rámci TAČR projektu TJ02000203 "Pokročilé matematické a statistické metody ve vyhodnocování měření instrumentovanou indentací". Úvodní sekce obsahuje nezbytný úvod k procedurám vyhodnocení dat instrumentované indentace, které využívají metodu Olivera a Pharra, jež je popsána v normě ISO 14577. Další kapitola poskytuje detailní odvození nového algoritmu OEFPIL pro nelineární regresi s chybami v obou proměnných a také návod pro efektivní implementaci algoritmu. Algoritmus počítá jak optimální odhad funkčních parametrů, tak odhad kovarianční matice parametrů. Použití algoritmu je demonstrováno na referenčních datech pro nelineární regresi a je ověřeno porovnáním s jinou metodou. Další kapitola se zabývá některými existujícími pokročilými metodami šíření nejistot (šíření nejistot vyšších řádů a metodou tzv. "Latin hypercube sampling" pro Monte Carlo). V poslední části najdeme aplikace výše zmíněných metod pro datovou regresi a propagaci nejistot ve zpracování dat získaných z měření instrumentovanou indentací. Tyto metody byly nově přidány do zdarma dostupného softwaru Niget k vylepšení prokládání dat odtěžovací křivky a k poskytnutí možnosti kalibrace funkce kontaktní plochy indentoru. Kombinace metod regrese a šíření nejistot dovoluje lepší náhled na vyhodnocování indentačních dat a poskytuje základ pro např. identifikování hlavních zdrojů nejistot měření nebo pro dizajn strategie získávání měření. Ačkoli byly metody navrženy a ověřeny pomocí Oliverovy a Pharrovy metody, mohou být lehce upraveny na jiné vyhodnocovací modely. Všechen software, který byl vyvinut a použit v tomto projektu, je volně dostupný

Non-Adherence to Statin Treatment in Older Patients with Peripheral Arterial Disease Depending on Persistence Status

The effectiveness of statins in secondary prevention of peripheral arterial disease (PAD) largely depends on patients' adherence to treatment. The aims of our study were: (a) to analyze non-adherence during the whole follow-up in persistent patients, and only during persistence for non-persistent patients; (b) to identify factors associated with non-adherence separately among persistent and non-persistent patients. A cohort of 8330 statin users aged >= 65 years, in whom PAD was newly diagnosed between January 2012-December 2012, included 5353 patients persistent with statin treatment, and 2977 subjects who became non-persistent during the 5-year follow-up. Non-adherence was defined using the proportion of days covered <80%. Patient- and statin-related characteristics associated with non-adherence were identified with binary logistic regression. A significantly higher proportion of non-adherent patients was found among non-persistent patients compared to persistent subjects (43.6% vs. 29.6%; p < 0.001). Associated with non-adherence in both persistent and non-persistent patients was high intensity statin treatment, while in non-persistent patients, it was employment and increasing number of medications. In patients with a poor adherence during their persistent period, an increased risk for discontinuation may be expected. However, there is also non-adherence among persistent patients. There are differences in factors associated with non-adherence depending on patients' persistence