Instructor Resource Chapter 6 Copyright © Scott B. Patten, 2015. Permission granted for classroom use with Epidemiology for Canadian Students: Principles, Methods & Critical Appraisal (Edmonton: Brush Education Inc. www.brusheducation.ca).

Chapter 6. Measurement error that leads to misclassification

Objectives Define measurement error, and distinguish it from selection error. Distinguish among nominal, ordinal, and cardinal data, and continuous and discrete data. Define and explain statistical strategies for quantifying classification errors: sensitivity and specificity; positive and negative predictive value; Bayes’ theorem; likelihood ratios; and reliability.

What is measurement error? Errors of classification are a kind of measurement error—the most important kind of measurement error in epidemiology. Classification applies to data: the assignment of values to exposure and disease variables requires classification. Classification errors compromise epidemiological conclusions. This chapter is about methods for quantifying classification errors.

Types of data There are 3 types of data: nominal (named categories) ordinal (ordered categories) cardinal (meaningfully quantified variables)

Examples of nominal data marital status country of birth ethnicity

Examples of ordinal data psychological symptom scales perceived health

Examples of cardinal data height weight temperature Note that when cardinal data have a real zero (e.g., height and weight, but not temperature on the Celsius scale), ratios of measurements are meaningful. Intervals are always meaningful in cardinal data, even in the absence of a real zero.

Categorical and continuous variables Categorical data have meaningful categories. Continuous data can theoretically divide into infinitely smaller categories.

A note about the word data In its Latin origins, datum is singular and data is plural (the same as stratum and strata). Increasingly, data is being used in modern English as a singular noun.

Classification of continuous variables Artificial categorization is a theoretically problematic manoeuvre: it involves a loss of information. However, due to the utility of categories in medical therapeutics (e.g., diagnosis is a category), categorization often makes sense in epidemiology.

Quantifying classification errors This requires a gold standard against which the performance of an error-prone measure can be compared.   Has the disease Does not have the disease Test positive True positive (tp) False positive (fp) Test negative False negative (fn) True negative (tn)

Sensitivity sensitivity= tp tp+fn

Specificity specificity= tn tn+fp

Sensitivity & specificity as test characteristics Sensitivity and specificity are characteristics of a test or classification procedure. They do not depend very much on characteristics of the population in which the test is used.

Complements of sensitivity and specificity Complementary means probabilities add up to 1. The complement of sensitivity is the false-negative rate. The complement of specificity is the false-positive rate.

Sensitivity as a conditional probability Sensitivity is a conditional probability because it is conditional on disease status. Sensitivity is the probability of a positive test given that disease is present.

Specificity as a conditional probability Specificity is a conditional probability because it is conditional on disease status. Specificity is the probability of a negative test given that disease is absent.

Conditional probabilities False-positive and false-negative rates are also conditional on disease status. The problem is that they are conditional on an unknown: actual disease status. Predictive values have the advantage of being conditional on something that is known: disease status.

Positive predictive value Probability of disease given a positive test Positive Predictive Value= tp tp+fp

Negative predictive value Probability of no disease given a negative test Negative Predictive Value= tn tn+fn

Predictive values Predictive values of diagnostic tests and other classification procedures reflect the performance of the tests, and also the characteristics of the population in which the tests are administered. Unlike sensitivity and specificity, predictive values cannot be viewed as test characteristics. The key characteristic of a population that contributes to predictive value is the “base rate” or prior probability of disease in that population.

Bayes’ theorem PPV= Se x PP Se x PP + 1−Sp x[ 1−PP ] where: PPV is positive predictive value Se is sensitivity Sp is specificity PP is the prior probability

Likelihood ratios Likelihood Ratio= Sensitivity 1−Specificity

Using likelihood ratios Post Test Odds=Pretest Odds x LR Where LR = likelihood ratio

Converting between odds and proportions Odds= Proportion 1−Proportion Proportion= Odds 1+Odds

Reliability of a measure Reliability refers to the repeatability of a measure. In epidemiology, there are 2 key types of reliability: interrater reliability test-retest reliability

Parameters to quantify reliability Nominal data uses the kappa coefficient. Ordinal data uses Spearman’s correlation coefficient. Continuous data uses Pearson’s correlation coefficient or intraclass correlation coefficient.

End