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  • 1.
    Ekström, Joakim
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Institutionen för informationsvetenskap, Statistik.
    A generalized definition of the polychoric correlation coefficientManuskript (Övrigt vetenskapligt)
    Abstract [en]

    We generalize the polychoric correlation coefficient to a large class of parametric families of bivariate distributions. The generalized definition agrees with the conventional definition on the family of bivariate normal distributions, and with the generalized tetrachoric correlation coefficient for dichotomous variables. Furthermore, we provide some suggestions for goodness-of-fit tests. The theory is illustrated with examples, which show that the distributional assumption can have a substantial impact on the conclusions of the association analysis.

  • 2.
    Ekström, Joakim
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Institutionen för informationsvetenskap, Statistik.
    A generalized definition of the tetrachoric correlation coefficientManuskript (Övrigt vetenskapligt)
    Abstract [en]

    We generalize the tetrachoric correlation coefficient to a large class of parametric families of bivariate distributions. We also show that the generalized definition agrees with the conventional definition on the family of bivariate normal distributions. Furthermore, we provide a necessary and sufficient condition for the generalized tetrachoric correlation coefficient to be well defined for a given family of distributions, and some sufficient criteria which can be useful for practical purposes. Moreover, we illustrate with examples how the distributional assumption can have a profound impact on the conclusions of the association analysis. Using S&P 100 stock data, we exemplify the fact that a correct distributional assumption is vitally important for the analysis. Consequently, it is concluded that the tetrachoric correlation coefficient is not robust to changes of the distributional assumption.

  • 3.
    Ekström, Joakim
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Institutionen för informationsvetenskap, Statistik.
    An empirical polychoric correlation coefficientManuskript (Övrigt vetenskapligt)
    Abstract [en]

    We propose a new measure of association for ordinal variables. The new measure of association, named the empirical polychoric correlation coefficient, builds upon the polychoric correlation coefficient, but relaxes its fundamental assumption so that an underlying distribution is only assumed to exist, not to be of a particular parametric family. The empirical polychoric correlation coefficient has properties that are superior to those of the polychoric correlation coefficient; it rests on weaker assumptions, it is well defined for every contingency table, and it converges almost surely to the correct theoretical polychoric correlation. Consequentially, the empirical polychoric correlation coefficient is theoretically robust to changes of the distributional assumption, unlike the polychoric correlation coefficient. A simulation study confirms that the empirical coefficient is considerably more robust than the polychoric correlation coefficient, and it also indicates that it has lower standard deviation.

  • 4.
    Ekström, Joakim
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Institutionen för informationsvetenskap, Statistik.
    Contributions to the Theory of Measures of Association for Ordinal Variables2009Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    In this thesis, we consider measures of association for ordinal variables from a theoretical perspective. In particular, we study the phi-coefficient, the tetrachoric correlation coefficient and the polychoric correlation coefficient. We also introduce a new measure of association for ordinal variables, the empirical polychoric correlation coefficient, which has better theoretical properties than the polychoric correlation coefficient, including greatly enhanced robustness.

    In the first article, entitled ``On the relation between the phi-coefficient and the tetrachoric correlation coefficient'', we show that under given marginal probabilities there exists a continuous bijection between the two measures of association. Furthermore, we show that the bijection has a fixed point at zero for all marginal probabilities. Consequently, the choice of which of these measures of association to use is for all practical purposes a matter of preference only.

    In the second article, entitled ``A generalized definition of the tetrachoric correlation coefficient'', we generalize the tetrachoric correlation coefficient so that a large class of parametric families of bivariate distributions can be assumed as underlying distributions. We also provide a necessary and sufficient condition for the generalized tetrachoric correlation coefficient to be well defined for a given parametric family of bivariate distributions. With examples, we illustrate the effects on the polychoric correlation coefficient of different distributional assumptions.

    In the third article, entitled ``A generalized definition of the polychoric correlation coefficient'', we generalize the polychoric correlation coefficient to a large class of parametric families of bivariate distributions, and show that the generalized and the conventional polychoric correlation coefficients agree on the family of bivariate normal distributions. With examples, we illustrate the effects of different distributional assumptions on the polychoric correlation coefficient. In combination with goodness-of-fit p-values, the association analysis can be enriched with a consideration of possible tail dependence.

    In the fourth article, we propose a new measure of association for ordinal variables, named the empirical polychoric correlation coefficient. The empirical polychoric correlation coefficient relaxes the fundamental assumption of the polychoric correlation coefficient so that an underlying joint distribution is only assumed to exist, not to be of a particular parametric family. We also provide an asymptotical result, by which the empirical polychoric correlation coefficient converges almost surely to the true polychoric correlation under very general conditions. Thus, the proposed empirical polychoric correlation coefficient has better theoretical properties than the polychoric correlation coefficient.

    Delarbeten
    1. On the relation between the phi-coefficient and the tetrachoric correlation coefficient
    Öppna denna publikation i ny flik eller fönster >>On the relation between the phi-coefficient and the tetrachoric correlation coefficient
    (Engelska)Manuskript (Övrigt vetenskapligt)
    Abstract [en]

    We show existence of a continuous bijection between the tetrachoric correlation coefficient and the phi-coefficient under given marginal probabilities. Implications are that the tetrachoric correlation coefficient can be calculated using the assumptions of the phi-coefficient construction, and the phi-coefficient can be calculated using the assumptions of the tetrachoric correlation construction. As a consequence, whether to use the phi-coefficient or the tetrachoric correlation coefficient is a matter of preference only. The result can also be used to construct a numerical table of tetrachoric correlation coefficients, converted from the marginal probabilities and the phi-coefficient, which is easy to calculate by hand. Moreover, a mathematically rigorous definition of the tetrachoric correlation coefficient is provided, along with a proof that the coefficient is well defined.

    Nyckelord
    phi-coefficient, tetrachoric correlation coefficient, 2 x 2 contingency table, measure of association, dichotomous variables
    Nationell ämneskategori
    Sannolikhetsteori och statistik
    Forskningsämne
    Statistik
    Identifikatorer
    urn:nbn:se:uu:diva-100692 (URN)
    Tillgänglig från: 2009-04-06 Skapad: 2009-04-06 Senast uppdaterad: 2011-03-29Bibliografiskt granskad
    2. A generalized definition of the tetrachoric correlation coefficient
    Öppna denna publikation i ny flik eller fönster >>A generalized definition of the tetrachoric correlation coefficient
    (Engelska)Manuskript (Övrigt vetenskapligt)
    Abstract [en]

    We generalize the tetrachoric correlation coefficient to a large class of parametric families of bivariate distributions. We also show that the generalized definition agrees with the conventional definition on the family of bivariate normal distributions. Furthermore, we provide a necessary and sufficient condition for the generalized tetrachoric correlation coefficient to be well defined for a given family of distributions, and some sufficient criteria which can be useful for practical purposes. Moreover, we illustrate with examples how the distributional assumption can have a profound impact on the conclusions of the association analysis. Using S&P 100 stock data, we exemplify the fact that a correct distributional assumption is vitally important for the analysis. Consequently, it is concluded that the tetrachoric correlation coefficient is not robust to changes of the distributional assumption.

    Nyckelord
    tetrachoric correlation, generalization, 2 x 2 contingency table, dichotomous variables, measure of association, robustness
    Nationell ämneskategori
    Sannolikhetsteori och statistik
    Forskningsämne
    Statistik
    Identifikatorer
    urn:nbn:se:uu:diva-100694 (URN)
    Tillgänglig från: 2009-04-06 Skapad: 2009-04-06 Senast uppdaterad: 2011-03-29Bibliografiskt granskad
    3. A generalized definition of the polychoric correlation coefficient
    Öppna denna publikation i ny flik eller fönster >>A generalized definition of the polychoric correlation coefficient
    (Engelska)Manuskript (Övrigt vetenskapligt)
    Abstract [en]

    We generalize the polychoric correlation coefficient to a large class of parametric families of bivariate distributions. The generalized definition agrees with the conventional definition on the family of bivariate normal distributions, and with the generalized tetrachoric correlation coefficient for dichotomous variables. Furthermore, we provide some suggestions for goodness-of-fit tests. The theory is illustrated with examples, which show that the distributional assumption can have a substantial impact on the conclusions of the association analysis.

    Nyckelord
    polychoric correlation, generalization, contingency table, ordinal variables, measure of association, robustness, goodness-of-fit
    Nationell ämneskategori
    Sannolikhetsteori och statistik
    Forskningsämne
    Statistik
    Identifikatorer
    urn:nbn:se:uu:diva-100695 (URN)
    Tillgänglig från: 2009-04-06 Skapad: 2009-04-06 Senast uppdaterad: 2011-03-29Bibliografiskt granskad
    4. An empirical polychoric correlation coefficient
    Öppna denna publikation i ny flik eller fönster >>An empirical polychoric correlation coefficient
    (Engelska)Manuskript (Övrigt vetenskapligt)
    Abstract [en]

    We propose a new measure of association for ordinal variables. The new measure of association, named the empirical polychoric correlation coefficient, builds upon the polychoric correlation coefficient, but relaxes its fundamental assumption so that an underlying distribution is only assumed to exist, not to be of a particular parametric family. The empirical polychoric correlation coefficient has properties that are superior to those of the polychoric correlation coefficient; it rests on weaker assumptions, it is well defined for every contingency table, and it converges almost surely to the correct theoretical polychoric correlation. Consequentially, the empirical polychoric correlation coefficient is theoretically robust to changes of the distributional assumption, unlike the polychoric correlation coefficient. A simulation study confirms that the empirical coefficient is considerably more robust than the polychoric correlation coefficient, and it also indicates that it has lower standard deviation.

    Nyckelord
    empirical polychoric correlation coefficient, polychoric correlation, contingency table, ordinal variables, measure of association, robust statistics
    Nationell ämneskategori
    Sannolikhetsteori och statistik
    Forskningsämne
    Statistik
    Identifikatorer
    urn:nbn:se:uu:diva-100696 (URN)
    Tillgänglig från: 2009-04-06 Skapad: 2009-04-06 Senast uppdaterad: 2011-03-29Bibliografiskt granskad
  • 5.
    Ekström, Joakim
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Institutionen för informationsvetenskap, Statistik.
    On the relation between the phi-coefficient and the tetrachoric correlation coefficientManuskript (Övrigt vetenskapligt)
    Abstract [en]

    We show existence of a continuous bijection between the tetrachoric correlation coefficient and the phi-coefficient under given marginal probabilities. Implications are that the tetrachoric correlation coefficient can be calculated using the assumptions of the phi-coefficient construction, and the phi-coefficient can be calculated using the assumptions of the tetrachoric correlation construction. As a consequence, whether to use the phi-coefficient or the tetrachoric correlation coefficient is a matter of preference only. The result can also be used to construct a numerical table of tetrachoric correlation coefficients, converted from the marginal probabilities and the phi-coefficient, which is easy to calculate by hand. Moreover, a mathematically rigorous definition of the tetrachoric correlation coefficient is provided, along with a proof that the coefficient is well defined.

  • 6.
    Hammarström, Klara
    et al.
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Medicinska fakulteten, Institutionen för immunologi, genetik och patologi, Experimentell och klinisk onkologi.
    Imam, Israa
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Medicinska fakulteten, Institutionen för immunologi, genetik och patologi, Experimentell och klinisk onkologi.
    Korsavidou Hult, Nafsika
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Medicinska fakulteten, Institutionen för kirurgiska vetenskaper, Radiologi.
    Ekström, Joakim
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Medicinska fakulteten, Institutionen för immunologi, genetik och patologi, Experimentell och klinisk onkologi.
    Sjöblom, Tobias
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Medicinska fakulteten, Institutionen för immunologi, genetik och patologi, Experimentell och klinisk onkologi.
    Glimelius, Bengt
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Medicinska fakulteten, Institutionen för immunologi, genetik och patologi, Experimentell och klinisk onkologi.
    Determining the use of preoperative (chemo)radiotherapy in primary rectal cancer according to national and international guidelines2019Ingår i: Radiotherapy and Oncology, ISSN 0167-8140, E-ISSN 1879-0887, Vol. 136, s. 106-112Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Background: Pre-operative radiotherapy (RT) or chemoradiotherapy (CRT) is frequently used prior to rectal cancer surgery to improve local control and survival. The treatment is administered according to guidelines, but these recommendations vary significantly between countries. Based on the stage distribution and risk factors of rectal cancers as determined by magnetic resonance imaging (MRI) in an unselected Swedish population, the use of RT/CRT according to 15 selected guidelines is described. Materials and methods: Selected guidelines from different countries and regions were applied to a wellcharacterized unselected population-based material of 686 primary non-metastatic rectal cancers staged by MRI. The fraction of patients assigned to surgery alone or surgery following pre-treatment with (C) RT was determined according to the respective guideline. RT/CRT administered to rectal cancer patients for other reasons, for example, for organ preservation or palliation, was not considered. Results: The fraction of patients with a clear recommendation for pre-treatment with (C) RT varied between 38% and 77% according to the different guidelines. In most guidelines, CRT was recommended to all patients who were not operated directly, and, in others, short-course RT was also recommended to patients with intermediate risk tumours. If only non-resectable or difficult to resect tumours were recommended pre-treatment, as stated in many Japanese publications, 9% would receive CRT followed by a delay to surgery. Conclusions: According to most guidelines, well over 50% of primary non-metastatic rectal cancer patients from a general population, in which screening for colorectal cancer is not practised, are recommended treatment with pre-operative/neo-adjuvant therapy. (C) 2019 Elsevier B. V. All rights reserved. Radiotherapy and Oncology

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