DOCSLIB.ORG

Propensity Score Analysis with Hierarchical Data

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Propensity Score Analysis with Hierarchical Data Section on Statistics in Epidemiology Propensity score analysis with hierarchical data Fan Li, Alan M. Zaslavsky, Mary Beth Landrum Department of Health Care Policy, Harvard Medical School 180 Longwood Avenue, Boston, MA 02115 October 29, 2007 Abstract nors et al., 1996; D’Agostino, 1998, and references therein). This approach, which involves comparing subjects weighted Propensity score (Rosenbaum and Rubin, 1983) methods are (or stratified, matched) according to their propensity to re- being increasingly used as a less parametric alternative to tra- ceive treatment (i.e., propensity score), attempts to balance ditional regression methods in medical care and health policy subjects in treatment groups in terms of observed character- research. Data collected in these disciplines are often clus- istics as would occur in a randomized experiment. Propensity tered or hierarchically structured, in the sense that subjects are score methods permit control of all observed confounding fac- grouped together in one or more ways that may be relevant tors that might influence both choice of treatment and outcome to the analysis. However, propensity score was developed using a single composite measure, without requiring specifi- and has been applied in settings with unstructured data. In cation of the relationships between the control variables and this report, we present and compare several propensity-score- outcome. weighted estimators of treatment effect in the context of hier- Propensity score methods were developed and have been archically structured data. For the simplest case without co- applied in settings with unstructured data. However, data col- variates, we show the “double-robustness” of those weighted lected in medical care and health policy studies are typically estimators, that is, when both of the true underlying treatment clustered or hierarchically structured, in the sense that sub- assignment mechanism and the outcome generating mecha- jects are grouped together in one or more ways that may be nism are hierarchically structured, the estimator is consistent relevant to the analysis. For example, subjects maybe grouped as long as the hierarchical structure is taken into account in at by geographical area, treatment center (e.g., hospital or physi- least one of the two steps in the propensity score procedure. cians), or in the example we consider in this paper, health This result holds for any balancing weight. We obtain the ex- plan. Generally, subjects are assigned to clusters by an un- act form of bias when clustering is ignored in both steps. We known mechanism that may be associated with measured sub- apply those methods to study racial disparity in the service of ject characteristics that we are interested in (e.g., race, age, breast cancer screening among elders who participate Medi- clinical characteristics), measured subject characteristics that care health plans. are not of intrinsic interest and are believed to be unrelated to outcomes except through their effects on assignment to clus- KEY WORDS: double robustness, health policy research, hi- ters (e.g., location), and unmeasured subject characteristics erarchical data, propensity score, racial disparity, weighting. (e.g., unmeasured severity of disease, aggressiveness in seek- ing treatment). 1. Introduction When subjects are hierarchically structured, a number of issues appear that are not present with an unstructured collec- Population-based observational studies often are the best tion of subjects. First of all, standard error calculations that methodology for obtaining generalizable results on access to, ignore the hierarchical structure will be inaccurate, leading to patterns of, and outcomes from medical care when large-scale incorrect inferences. A more interesting set of issues arises be- controlled experiments are infeasible. Comparisons between cause there may be both measured and unmeasured factors at groups can be biased, however, when the groups are unbal- the cluster level that create variation among clusters in quality anced with respect to measured and unmeasured confounders. of treatment and hence in outcomes. Hierarchical regression Standard analytic methods adjust for observed differences be- models have been developed to give a more comprehensive de- tween treatment groups by stratifying or matching patients on scription than non-hierarchical models provide for such data a few observed covariates or with regression analysis in the (e.g., Gatsonis et al., 1993). Despite the increasing popular- case of many observed confounders. But if treatment groups ity of propensity score analyses and the vast literature regard- differ greatly in observed characteristics, estimates of treat- ing regional and provider variation in medical care and health ment effects from regression models rely on model extrap- policy research (e.g., Nattinger et al., 1992; Farrow et al., olations and the resulting conclusions can be very sensitive 1996), however, to our knowledge, the implications of such to model mis-specification (Rubin, 1979). Propensity score data structures for propensity score analyses have been rarely methods (Rosenbaum and Rubin, 1983, 1984) have been pro- studied. Huang et al. (2005) applied propensity score methods posed as a less parametric alternative to regression adjustment to clustered health service data. But their goal was to rank the and are being increasingly used in health policy studies (Con- performance of multiple health service providers (clusters) in- 2474 Section on Statistics in Epidemiology stead of to estimate an overall treatment effect from data with ject k in cluster h (e.g., a clinical diagnosis); xhk the corre- clustered structure, which is the goal of this paper. Specif- sponding covariates (typically vector-valued, e.g., age, stage ically, we will present several propensity score models ana- of detection, comorbidity scores, etc.); vh the cluster-level co- logues to many of the commonly used regression models for variates (e.g., teaching status or measures of technical capac- clustered data in Section 2; investigate the behavior of those ity of a hospital); zhk the treatment assignment for the subject, estimators, especially the bias when clustering information is zhk 2 f0; 1g; and ehk the propensity score. ignored in the analysis in Section 3; and apply the methods to study racial disparities in the service of breast cancer screen- 2.1 Step 1. Estimating the propensity score ing among elders in Section 4. Summaries and remarks will be provided in Section 5. Our discussion concerns the case To estimate the propensity score, several logistic regression where a binary treatment is assigned at individual level. Also, models are available with various treatment of the hierarchical to illustrate the major point and yet without loss of generality, structure. we focus on data with two-level hierarchical structure. 2.1.1 Marginal model 2. Estimators As the name suggests, marginal regression models ignore clus- tering information. A typical marginal propensity score model The class of estimands considered in this paper is generally would be referred as a “treatment effect”, ehk e e ∆ = E [E(Y jX; Z = 1)] − E [E(Y jX; Z = 0)]; (1) log = β xhk + κ vh; (2) x x 1 − ehk i.e., the average difference in outcome between two treatment where ehk = P (zhk = 1 j xhk; vh). This model in fact as- groups that have same distribution of covariates. sumes the treatment assignment mechanism is the same across The propensity score e is defined as the conditional proba- all clusters. In other words, it assumes that two subjects are bility of being assigned to a particular treatment z given mea- exchangeable in terms of treatment propensity if they have the sured covariates x: e(x) = P (z = 1jx). In most observational same vector of covariates, whether or not they come from the studies, the propensity score is not known and thus needed to same cluster. be estimated. Therefore propensity score analysis usually in- This propensity score model can be thought of as a non- volves two steps. The first step is to estimate the propensity parametric alternative to a regression-based adjustment for in- score, typically by a logistic regression. The second step is to dividual and cluster covariates. The analogous marginal re- estimate the treatment effect by incorporating (e.g., by weight- gression model would be, ing or matching) the estimated propensity score. Hierarchi- y y cal structure leads to a range of different choices of modeling yhk = γzhk + β xhk + κ vh + hk; (3) in both steps. In this section, we will introduce several most 2 widely used models. where hk ∼ N(0; δ ), and γ is the treatment effect. As Before going into more details, here we make a note regard- model (2), estimates derived from this regression model rely ing the targeted estimand “treatment effect” defined above, on the assumption that the outcome generating mechanism is which is slightly different from those “causal treatment effect” the same across all clusters. defined using the conventional potential outcomes framework. Models (2) and (3) have a manifest similarity of form. A The propensity score originated from and has been widely deeper connection is that the sufficient statistics to estimate used in causal inference, but its use is certainly not restricted the treatment effect that are balanced under propensity score to studying causal effects. For instance, in many health pol- estimator are the same that must be balanced under model (3). icy studies, the major interest is to compare
Load more

Recommended publications
  • Auditor: an R Package for Model-Agnostic Visual Validation and Diagnostics
    auditor: an R Package for Model-Agnostic Visual Validation and Diagnostics APREPRINT Alicja Gosiewska Przemysław Biecek Faculty of Mathematics and Information Science Faculty of Mathematics and Information Science Warsaw University of Technology Warsaw University of Technology Poland Faculty of Mathematics, Informatics and Mechanics [email protected] University of Warsaw Poland [email protected] May 27, 2020 ABSTRACT Machine learning models have spread to almost every area of life. They are successfully applied in biology, medicine, finance, physics, and other fields. With modern software it is easy to train even a complex model that fits the training data and results in high accuracy on test set. The problem arises when models fail confronted with the real-world data. This paper describes methodology and tools for model-agnostic audit. Introduced tech- niques facilitate assessing and comparing the goodness of fit and performance of models. In addition, they may be used for analysis of the similarity of residuals and for identification of outliers and influential observations. The examination is carried out by diagnostic scores and visual verification. Presented methods were implemented in the auditor package for R. Due to flexible and con- sistent grammar, it is simple to validate models of any classes. K eywords machine learning, R, diagnostics, visualization, modeling 1 Introduction Predictive modeling is a process that uses mathematical and computational methods to forecast outcomes. arXiv:1809.07763v4 [stat.CO] 26 May 2020 Lots of algorithms in this area have been developed and are still being develop. Therefore, there are countless possible models to choose from and a lot of ways to train a new new complex model.
    [Show full text]
  • ROC Curve Analysis and Medical Decision Making
    ROC curve analysis and medical decision making: what’s the evidence that matters for evidence-based diagnosis ? Piergiorgio Duca Biometria e Statistica Medica – Dipartimento di Scienze Cliniche Luigi Sacco – Università degli Studi – Via GB Grassi 74 – 20157 MILANO (ITALY) [email protected] 1) The ROC (Receiver Operating Characteristic) curve and the Area Under the Curve (AUC) The ROC curve is the statistical tool used to analyse the accuracy of a diagnostic test with multiple cut-off points. The test could be based on a continuous diagnostic indicant, such as a serum enzyme level, or just on an ordinal one, such as a classification based on radiological imaging. The ROC curve is based on the probability density distributions, in actually diseased and non diseased patients, of the diagnostician’s confidence in a positive diagnosis, and upon a set of cut-off points to separate “positive” and “negative” test results (Egan, 1968; Bamber, 1975; Swets, Pickett, 1982; Metz, 1986; Zhou et al, 2002). The Sensitivity (SE) – the proportion of diseased turned out to be test positive – and the Specificity (SP) – the proportion of non diseased turned out to be test negative – will depend on the particular confidence threshold the observer applies to partition the continuously distributed perceptions of evidence into positive and negative test results. The ROC curve is the plot of all the pairs of True Positive Rates (TPR = SE), as ordinate, and False Positive Rates (FPR = (1 – SP)), as abscissa, related to all the possible cut-off points. An ROC curve represents all of the compromises between SE and SP can be achieved, changing the confidence threshold.
    [Show full text]
  • Estimating the Variance of a Propensity Score Matching Estimator for the Average Treatment Effect
    Observational Studies 4 (2018) 71-96 Submitted 5/15; Published 3/18 Estimating the variance of a propensity score matching estimator for the average treatment effect Ronnie Pingel [email protected] Department of Statistics Uppsala University Uppsala, Sweden Abstract This study considers variance estimation when estimating the asymptotic variance of a propensity score matching estimator for the average treatment effect. We investigate the role of smoothing parameters in a variance estimator based on matching. We also study the properties of estimators using local linear estimation. Simulations demonstrate that large gains can be made in terms of mean squared error, bias and coverage rate by prop- erly selecting smoothing parameters. Alternatively, a residual-based local linear estimator could be used as an estimator of the asymptotic variance. The variance estimators are implemented in analysis to evaluate the effect of right heart catheterisation. Keywords: Average Causal Effect, Causal Inference, Kernel estimator 1. Introduction Matching estimators belong to a class of estimators of average treatment effects (ATEs) in observational studies that seek to balance the distributions of covariates in a treatment and control group (Stuart, 2010). In this study we consider one frequently used matching method, the simple nearest-neighbour matching with replacement (Rubin, 1973; Abadie and Imbens, 2006). Rosenbaum and Rubin (1983) show that instead of matching on covariates directly to remove confounding, it is sufficient to match on the propensity score. In observational studies the propensity score must almost always be estimated. An important contribution is therefore Abadie and Imbens (2016), who derive the large sample distribution of a nearest- neighbour propensity score matching estimator when using the estimated propensity score.
    [Show full text]
  • An Introduction to Logistic Regression: from Basic Concepts to Interpretation with Particular Attention to Nursing Domain
    J Korean Acad Nurs Vol.43 No.2, 154 -164 J Korean Acad Nurs Vol.43 No.2 April 2013 http://dx.doi.org/10.4040/jkan.2013.43.2.154 An Introduction to Logistic Regression: From Basic Concepts to Interpretation with Particular Attention to Nursing Domain Park, Hyeoun-Ae College of Nursing and System Biomedical Informatics National Core Research Center, Seoul National University, Seoul, Korea Purpose: The purpose of this article is twofold: 1) introducing logistic regression (LR), a multivariable method for modeling the relationship between multiple independent variables and a categorical dependent variable, and 2) examining use and reporting of LR in the nursing literature. Methods: Text books on LR and research articles employing LR as main statistical analysis were reviewed. Twenty-three articles published between 2010 and 2011 in the Journal of Korean Academy of Nursing were analyzed for proper use and reporting of LR models. Results: Logistic regression from basic concepts such as odds, odds ratio, logit transformation and logistic curve, assumption, fitting, reporting and interpreting to cautions were presented. Substantial short- comings were found in both use of LR and reporting of results. For many studies, sample size was not sufficiently large to call into question the accuracy of the regression model. Additionally, only one study reported validation analysis. Conclusion: Nurs- ing researchers need to pay greater attention to guidelines concerning the use and reporting of LR models. Key words: Logit function, Maximum likelihood estimation, Odds, Odds ratio, Wald test INTRODUCTION The model serves two purposes: (1) it can predict the value of the depen- dent variable for new values of the independent variables, and (2) it can Multivariable methods of statistical analysis commonly appear in help describe the relative contribution of each independent variable to general health science literature (Bagley, White, & Golomb, 2001).
    [Show full text]
  • Njit-Etd2007-041
    Copyright Warning & Restrictions The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted material. Under certain conditions specified in the law, libraries and archives are authorized to furnish a photocopy or other reproduction. One of these specified conditions is that the photocopy or reproduction is not to be “used for any purpose other than private study, scholarship, or research.” If a, user makes a request for, or later uses, a photocopy or reproduction for purposes in excess of “fair use” that user may be liable for copyright infringement, This institution reserves the right to refuse to accept a copying order if, in its judgment, fulfillment of the order would involve violation of copyright law. Please Note: The author retains the copyright while the New Jersey Institute of Technology reserves the right to distribute this thesis or dissertation Printing note: If you do not wish to print this page, then select “Pages from: first page # to: last page #” on the print dialog screen The Van Houten library has removed some of the personal information and all signatures from the approval page and biographical sketches of theses and dissertations in order to protect the identity of NJIT graduates and faculty. ABSTRACT PROBLEMS RELATED TO EFFICACY MEASUREMENT AND ANALYSES by Sibabrata Banerjee In clinical research it is very common to compare two treatments on the basis of an efficacy vrbl Mr pfll f Χ nd Υ dnt th rpn f ptnt n th t trtnt A nd rptvl th
    [Show full text]
  • Logistic Regression, Part I: Problems with the Linear Probability Model
    Logistic Regression, Part I: Problems with the Linear Probability Model (LPM) Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised February 22, 2015 This handout steals heavily from Linear probability, logit, and probit models, by John Aldrich and Forrest Nelson, paper # 45 in the Sage series on Quantitative Applications in the Social Sciences. INTRODUCTION. We are often interested in qualitative dependent variables: • Voting (does or does not vote) • Marital status (married or not) • Fertility (have children or not) • Immigration attitudes (opposes immigration or supports it) In the next few handouts, we will examine different techniques for analyzing qualitative dependent variables; in particular, dichotomous dependent variables. We will first examine the problems with using OLS, and then present logistic regression as a more desirable alternative. OLS AND DICHOTOMOUS DEPENDENT VARIABLES. While estimates derived from regression analysis may be robust against violations of some assumptions, other assumptions are crucial, and violations of them can lead to unreasonable estimates. Such is often the case when the dependent variable is a qualitative measure rather than a continuous, interval measure. If OLS Regression is done with a qualitative dependent variable • it may seriously misestimate the magnitude of the effects of IVs • all of the standard statistical inferences (e.g. hypothesis tests, construction of confidence intervals) are unjustified • regression estimates will be highly sensitive to the range of particular values observed (thus making extrapolations or forecasts beyond the range of the data especially unjustified) OLS REGRESSION AND THE LINEAR PROBABILITY MODEL (LPM). The regression model places no restrictions on the values that the independent variables take on.
    [Show full text]
  • Homoskedasticity
    Homoskedasticity How big is the difference between the OLS estimator and the true parameter? To answer this question, we make an additional assumption called homoskedasticity: Var (ujX) = σ2: (23) This means that the variance of the error term u is the same, regardless of the predictor variable X. If assumption (23) is violated, e.g. if Var (ujX) = σ2h(X), then we say the error term is heteroskedastic. Sylvia Fruhwirth-Schnatter¨ Econometrics I WS 2012/13 1-55 Homoskedasticity • Assumption (23) certainly holds, if u and X are assumed to be independent. However, (23) is a weaker assumption. • Assumption (23) implies that σ2 is also the unconditional variance of u, referred to as error variance: Var (u) = E(u2) − (E(u))2 = σ2: Its square root σ is the standard deviation of the error. • It follows that Var (Y jX) = σ2. Sylvia Fruhwirth-Schnatter¨ Econometrics I WS 2012/13 1-56 Variance of the OLS estimator How large is the variation of the OLS estimator around the true parameter? ^ • Difference β1 − β1 is 0 on average • Measure the variation of the OLS estimator around the true parameter through the expected squared difference, i.e. the variance: ( ) ^ ^ 2 Var β1 = E((β1 − β1) ) (24) ( ) ^ ^ ^ 2 • Similarly for β0: Var β0 = E((β0 − β0) ). Sylvia Fruhwirth-Schnatter¨ Econometrics I WS 2012/13 1-57 Variance of the OLS estimator ^ Variance of the slope estimator β1 follows from (22): ( ) N 1 X Var β^ = (x − x)2Var (u ) 1 N 2(s2)2 i i x i=1 σ2 XN σ2 = (x − x)2 = : (25) N 2(s2)2 i Ns2 x i=1 x • The variance of the slope estimator is the larger, the smaller the number of observations N (or the smaller, the larger N).
    [Show full text]
  • HOMOSCEDASTICITY PLOT Graphics Commands
    HOMOSCEDASTICITY PLOT Graphics Commands HOMOSCEDASTICITY PLOT PURPOSE Generates a homoscedasticity plot. DESCRIPTION A homoscedasticity plot is a graphical data analysis technique for assessing the assumption of constant variance across subsets of the data. The first variable is a response variable and the second variable identifies subsets of the data. The mean and standard deviation are calculated for each of these subsets. The following plot is generated: Vertical axis = subset standard deviations; Horizontal axis = subset means. The interpertation of this plot is that the greater the spread on the vertical axis, the less valid is the assumption of constant variance. A common pattern is for the spread (i.e., the standard deviation) to increase as the location (i.e., the mean) increases. This indicates the need for some type of transformation such as a log or square root. SYNTAX HOMOSCEDASTICITY PLOT <y> <tag> <SUBSET/EXCEPT/FOR qualification> where <y> is a response variable; <tag> identifies the subsets; and where the <SUBSET/EXCEPT/FOR qualification> is optional. EXAMPLES HOMOSCEDASTICITY PLOT Y1 TAG HOMOSCEDASTICITY PLOT Y1 TAG SUBSET TAG > 2 NOTE 1 One limitation of the homoscedasticity plot is that it does not give a convenient way to label the groups on the plot. This can be done by using the SUBSET command as in this example (assume Y is the response variable, X the group-id variable): X1LABEL MEANS Y1LABEL STANDARD DEVIATIONS CHARACTER X; LINE BLANK XLIMITS 0 5; YLIMITS 0 4 CHARACTER NORM; TITLE HOMOSCEDASTICITY PLOT HOMOSCEDASTICITY PLOT Y X SUBSET X = 1 PRE-ERASE OFF CHARACTER T HOMOSCEDASTICITY PLOT Y X SUBSET X = 2 CHARACTER CHIS HOMOSCEDASTICITY PLOT Y X SUBSET X = 3 CHARACTER UNIF HOMOSCEDASTICITY PLOT Y X SUBSET X = 4 CHARACTER F HOMOSCEDASTICITY PLOT Y X SUBSET X = 5 NOTE 2 Bartlett’s test is an analytic test for the assumption of constant variance.
    [Show full text]
  • Chapter 10 Heteroskedasticity
    Chapter 10 Heteroskedasticity In the multiple regression model yX , it is assumed that VI() 2 , i.e., 22 Var()i , Cov(ij ) 0, i j 1, 2,..., n . In this case, the diagonal elements of the covariance matrix of are the same indicating that the variance of each i is same and off-diagonal elements of the covariance matrix of are zero indicating that all disturbances are pairwise uncorrelated. This property of constancy of variance is termed as homoskedasticity and disturbances are called as homoskedastic disturbances. In many situations, this assumption may not be plausible, and the variances may not remain the same. The disturbances whose variances are not constant across the observations are called heteroskedastic disturbance, and this property is termed as heteroskedasticity. In this case 2 Var()ii , i 1,2,..., n and disturbances are pairwise uncorrelated. The covariance matrix of disturbances is 2 00 1 00 2 Vdiag( ) (22 , ,..., 2 )2 . 12 n 2 00 n Regression Analysis | Chapter 10 | Heteroskedasticity | Shalabh, IIT Kanpur 1 Graphically, the following pictures depict homoskedasticity and heteroskedasticity. Homoskedasticity Heteroskedasticity (Var(y) increases with x) Heteroskedasticity (Var(y) decreases with x) Examples: Suppose in a simple linear regression model, x denote the income and y denotes the expenditure on food. It is observed that as the income increases, the expenditure on food increases because of the choice and varieties in food increase, in general, up to a certain extent. So the variance of observations on y will not remain constant as income changes. The assumption of homoscedasticity implies that the consumption pattern of food will remain the same irrespective of the income of the person.
    [Show full text]
  • Assumptions of Multiple Linear Regression
    Statistics Solutions Advancement Through Clarity http://www.statisticssolutions.com Assumptions of Multiple Linear Regression Multiple linear regression analysis makes several key assumptions: Linear relationship Multivariate normality No or little multicollinearity No auto-correlation Homoscedasticity Multiple linear regression needs at least 3 variables of metric (ratio or interval) scale. A rule of thumb for the sample size is that regression analysis requires at least 20 cases per independent variable in the analysis, in the simplest case of having just two independent variables that requires n > 40. G*Power can also be used to calculate a more exact, appropriate sample size. Firstly, multiple linear regression needs the relationship between the independent and dependent variables to be linear. It is also important to check for outliers since multiple linear regression is sensitive to outlier effects. The linearity assumption can best be tested with scatter plots, the following two examples depict two cases, where no and little linearity is present. 1 / 5 Statistics Solutions Advancement Through Clarity http://www.statisticssolutions.com Secondly, the multiple linear regression analysis requires all variables to be normal. This assumption can best be checked with a histogram and a fitted normal curve or a Q-Q-Plot. Normality can be checked with a goodness of fit test, e.g., the Kolmogorov-Smirnof test. When the data is not normally distributed a non-linear transformation, e.g., log-transformation might fix this issue. However it can introduce effects of multicollinearity. Thirdly, multiple linear regression assumes that there is little or no multicollinearity in the data. Multicollinearity occurs when the independent variables are not independent from each other.
    [Show full text]
  • Simple Linear Regression 80 60 Rating 40 20
    Simple Linear 12 Regression Material from Devore’s book (Ed 8), and Cengagebrain.com Simple Linear Regression 80 60 Rating 40 20 0 5 10 15 Sugar 2 Simple Linear Regression 80 60 Rating 40 20 0 5 10 15 Sugar 3 Simple Linear Regression 80 60 Rating 40 xx 20 0 5 10 15 Sugar 4 The Simple Linear Regression Model The simplest deterministic mathematical relationship between two variables x and y is a linear relationship: y = β0 + β1x. The objective of this section is to develop an equivalent linear probabilistic model. If the two (random) variables are probabilistically related, then for a fixed value of x, there is uncertainty in the value of the second variable. So we assume Y = β0 + β1x + ε, where ε is a random variable. 2 variables are related linearly “on average” if for fixed x the actual value of Y differs from its expected value by a random amount (i.e. there is random error). 5 A Linear Probabilistic Model Definition The Simple Linear Regression Model 2 There are parameters β0, β1, and σ , such that for any fixed value of the independent variable x, the dependent variable is a random variable related to x through the model equation Y = β0 + β1x + ε The quantity ε in the model equation is the “error” -- a random variable, assumed to be symmetrically distributed with 2 2 E(ε) = 0 and V(ε) = σ ε = σ (no assumption made about the distribution of ε, yet) 6 A Linear Probabilistic Model X: the independent, predictor, or explanatory variable (usually known).
    [Show full text]
  • Discriminatory Accuracy of Serological Tests for Detecting Trypanosoma
    107 Rev. Fac. Med. 2020 Vol. 68 No. 1: 107-16 ORIGINAL RESEARCH DOI: http://dx.doi.org/10.15446/revfacmed.v68n1.71092 Received: 18/03/2018 Accepted: 27/06/2018 Revista de la Facultad de Medicina Discriminatory accuracy of serological tests for detecting Trypanosoma cruzi using the ROC curve and the standard methodology Precisión discriminatoria de pruebas serológicas para Trypanosoma cruzi aplicando metodología estándar y de curva COR Marvin Querales1,2, Ana Rita De Lima2,3, Harú Martínez-de Cordero4, Domenica Carolina Cannova5, María Isabel Simons5, Luis Pérez-Ybarra6 1 Universidad de Carabobo - Faculty of Health Sciences - School of Biomedical and Technological Sciences - Department of Biochemistry - Valencia - Venezuela. 2 Universidad de Carabobo - Faculty of Health Sciences - Instituto de Biología Molecular de Parásitos (BioMolP) - Protozoology Laboratory - Valencia - Venezuela. 3 Universidad de Carabobo - Faculty of Health Sciences - Bioanalysis School - Department of Morphophysiology - Valencia - Venezuela. 4 Universidad Central de Venezuela - Faculty of Agronomy - Department of Agricultural Engineering - Maracay - Venezuela. 5 Universidad de Carabobo - Faculty of Health Sciences - School of Biomedical and Technological Sciences - Department of Parasitology - Leishmaniasis and Entomology Laboratory - Valencia - Venezuela. 6 Universidad de Carabobo - Faculty of Health Sciences - School of Bioanalysis - Department of Basic Sciences - Maracay - Venezuela. Corresponding author: Luis Pérez-Ybarra. Departamento de Ciencias Básicas, Escuela de Bioanálisis, Facultad de Ciencias de la Salud, Universidad de Carabobo. Campus La Morita, Núcleo Aragua, módulo A. Telephone number: +58 241 6004000, ext.: 404241. Maracay. Venezuela. Email: [email protected]. Abstract Introduction: Serological tests are used to confirmTrypanosoma cruzi infection and their discrim- Querales M, De Lima AR, Martínez-de inatory accuracy depends on the established decision threshold.
    [Show full text]