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Chapter 6-2. Comparing Test Characteristics *** This chapter is under construction *** Comparison of sensitivity and specificity between two diagostic tests, each measured on the same patient, when the same reference standard is used For this situation, we want to test whether the two diagnostic tests perform equally against a common reference standard. For Test A and Test B, the hypothesis test for a comparison of sensitivity can be stated, H0: SeA = SeB versus H1: SeA ≠ SeB For Test A, the data layout is Reference Standard Present (1) Absent (0) Total Test Positive (1) Negative (0) Total n11A n10A r1A n01A n00A r0A c1A c0A where n = cell count, r = row total , c = column total subscripts represent score (1=present or positive, 0 = absent or negative) and test label (A) Sensitivity (SeA) = { true positives } / {all patients with disease} = n11A / r1A For Test B, the data layout is Reference Standard Present (1) Absent (0) Total Test Positive (1) Negative (0) Total n11B n10B r1B n01B n00B r0B c1B c0B Sensitivity (SeB) = { true positives } / {all patients with disease} = n11B / r1B _________________ Source: Stoddard GJ. Biostatistics and Epidemiology Using Stata: A Course Manual [unpublished manuscript] University of Utah School of Medicine, 2010. Chapter 2 (revision 16 May 2010) p. 1 We see that all information for sensitivity for each test is contained in the first row, where the first row of each table is the true presence of disease as identified by the common reference standard. For a paired comparison of sensitivity, then, all we need are the cell counts in these rows, combined into a paired crosstabulation table. The paired data layout for a sensitivity comparison is Test A Test B Positive (1) Negative (0) Positive (1) m11 m10 Negative (0) m01 m00 Total n11A n10A Total n11B n10B Where the cell counts, the m’s, simply fill in by the crosstabulation procedure. Since the data are not independent, being repeated measures on the same patient (both tests done on same patient), we must apply a paired proportions comparision. To compare sensitivity, we simply apply the McNemar test, which is the standard way to compare two paired binary variables expressed in this paired data layout (Lachenbruch and Lynch, 1998; Zhou et al, 2002, pp.166-169). paired data layout for a sensitivity comparison Test A Test B Positive (1) Negative (0) Total Positive (1) m11 m10 n11B Negative (0) m01 m00 n10B Total n11A n10A The McNemar test is commonly referred to as the “McNemar change test”, as it only uses information from the discordant pairs (the cells where the two diagnostic tests are different). It is simply a chi-square test (Siegel and Castellan, 1988, p.76) expressed as, 2 df 1 (m10 m01 ) 2 m10 m01 Small Expected Frequencies The chi-square test requires a sufficiently large sample size to provide an accurate p value. The rule-of-thumb for the McNemar test version of the chi-square test is that when (m10 + m01) < 10, the exact form of the test should be used (Siegel and Castellan, 1988, p.79). Since the data are paired, the Fisher’s exact test is not appropriate, and so the binomial test is used. In Stata, this binomial test is labeled “Exact McNemar”. Chapter 2 (revision 16 May 2010) p. 2 Specificity The comparison of specificity is done is an anologous fashion. The hypothesis becomes H0: SpA = SpB versus H1: SpeA ≠ SpB For Test A, the data layout is Test Gold Standard Positive (1) Negative (0) Present (1) n11A n10A Absent (0) n01A n00A Total c1A c0A Total r1A r0A where n = cell count, r = row total , c = column total subscripts represent score (1=present or positive, 0 = absent or negative) and test label (A) Specificity (SpA) = { true negative } / {all patients without disease} = n00A / r0A For Test B, the data layout is Gold Standard Positive (1) Present (1) n11B Absent (0) n01B Total c1B Test Negative (0) n10B n00B c0B Total r1B r0B Specificity (SpB) = { true negative } / {all patients without disease} = n00B / r0B We see that all information for specificity for each test is contained in the second row, where the second row of each table is the true absence of disease as identified by the common reference standard. For a paired comparison of specificity, then, all we need are the cell counts in these rows, combined into a paired crosstabulation table. The paired data layout for a specificity comparison is Test A Test B Positive (1) Negative (0) Total Positive (1) m11 m10 n01B Negative (0) m01 m00 n00B Total n01A n00A Where the cell counts, the m’s, simply fill in by the crosstabulation procedure. Then, McNemar’s test is applied in an identical way to the sensitivity comparison. Chapter 2 (revision 16 May 2010) p. 3 Protocol Suggestion For comparison of sensitivity and specificity between two diagnostic tests, you could describe the statistical method as: Within the same patients, both Test A and Test B will be compared to a common Test C gold standard and test characteristics will be calculated. The sensitivity between Test A and Test B will be compared using a McNemar test, or exact McNemar test, as appropriate [Lachenbruch and Lynch, 1998]. The specificity will similarly be compared. Example We will use the CASS dataset (see Appendix 1 for references). These data come from the coronary artery surgery study (CASS). In a cohort study of N=1465 men undergoing coronary arteriography (the gold standard) for suspected or probable coronary heart disease, both an exercise stress test (EST) and chest pain history (CPH) were recorded. The data are coded as cad est cph coronary artery disease (gold standard), 1 = yes, 0 = no exercise stress test (diagnostic test for CAD), 1 = positive, 0 = negative chest pain history (diagnostic test for CAD), 1 = positive, 0 = negative Reading in the data into Stata, File Open Find the directory where you copied the course CD: Find the subdirectory datasets & do-files Single click on cass.dta Open use "C:\Documents and Settings\u0032770.SRVR\Desktop\ Biostats & Epi With Stata\datasets & do-files\cass.dta", clear * which must be all on one line, or use: cd "C:\Documents and Settings\u0032770.SRVR\Desktop\" cd "Biostats & Epi With Stata\datasets & do-files" use cass.dta, clear To obtain the sensitivity and specificity for est, we use the diagt command, which is not available from the Stata menu bar. Chapter 2 (revision 16 May 2010) p. 4 If you have not already updated your Stata to include it, then while connected to the internet, use findit diagt Search of official help files, FAQs, Examples, SJs, and STBs SJ-4-4 sbe36_2 . . . . . . . . . . . . . . . . . . Software update for diagt (help diagt if installed) . . . . . . . . . . P. T. Seed and A. Tobias Q4/04 SJ 4(4):490 new options added to diagt Click on the sbe36_2 link, or a later version if one appears, to install the diagt command. To obtain the test characteristics to est, use diagt cad est Coronary | artery | Exercise Stress test disease | Pos. Neg. | Total -----------+----------------------+---------Abnormal | 815 208 | 1,023 Normal | 115 327 | 442 -----------+----------------------+---------Total | 930 535 | 1,465 [95% Confidence Interval] --------------------------------------------------------------------------Prevalence Pr(A) 70% 67% 72.2% --------------------------------------------------------------------------Sensitivity Pr(+|A) 79.7% 77.1% 82.1% Specificity Pr(-|N) 74% 69.6% 78% --------------------------------------------------------------------------- To obtain the sensitivity for cph, diagt cad cph Coronary | artery | Chest pain history disease | Pos. Neg. | Total -----------+----------------------+---------Abnormal | 969 54 | 1,023 Normal | 245 197 | 442 -----------+----------------------+---------Total | 1,214 251 | 1,465 [95% Confidence Interval] --------------------------------------------------------------------------Prevalence Pr(A) 70% 67% 72.2% --------------------------------------------------------------------------Sensitivity Pr(+|A) 94.7% 93.2% 96% Specificity Pr(-|N) 44.6% 39.9% 49.3% --------------------------------------------------------------------------- Chapter 2 (revision 16 May 2010) p. 5 To compute the McNemar test for the sensitivity comparison between the two diagnostic tests, we restrict the data to the disease present rows, using an if qualifier mcc cph est if cad==1 | Controls | Cases | Exposed Unexposed | Total -----------------+------------------------+-----------Exposed | 786 183 | 969 Unexposed | 29 25 | 54 -----------------+------------------------+-----------Total | 815 208 | 1023 McNemar's chi2(1) = 111.87 Prob > chi2 = 0.0000 Exact McNemar significance probability = 0.0000 We see that the sum of the discordent pairs, 183+29 > 10, so that the sample size is large enough to provide an accurate chi-square test p value. Therefore, we report the chi-square version of McNemar’s test (p < 0.001). If, however, the discordant pairs had summed to a number < 10, we would report the Exact McNemar test (p < .001). Unfortunately, the variables are labeled cases and controls, which is rather confusing. It is labelled this way because the McNemar test is part of the epitab suite of commands (the epidemiology statistical procedures). To verify which variable represents cases, and which represents controls, we can use, tab cph est if cad==1 Chest pain | Exercise Stress test history | 0. neg 1. pos | Total -----------+----------------------+---------0. neg | 25 29 | 54 1. pos | 183 786 | 969 -----------+----------------------+---------Total | 208 815 | 1,023 This output has the row and column variables consistent with the mcc command, but displays it in ascending sort order. Chapter 2 (revision 16 May 2010) p. 6 To compute the McNemar test for the specificity comparison between the two diagnostic tests, we restrict the data to the disease absent rows, using an if qualifier mcc cph est if cad==0 tab cph est if cad==0 | Controls | Cases | Exposed Unexposed | Total -----------------+------------------------+-----------Exposed | 69 176 | 245 Unexposed | 46 151 | 197 -----------------+------------------------+-----------Total | 115 327 | 442 McNemar's chi2(1) = 76.13 Prob > chi2 = 0.0000 Exact McNemar significance probability = 0.0000 Chest pain | Exercise Stress test history | 0. neg 1. pos | Total -----------+----------------------+---------0. neg | 151 46 | 197 1. pos | 176 69 | 245 -----------+----------------------+---------Total | 327 115 | 442 Comparing ROCs Protocol Suggestion For Comparison of ROCs Using roccomp Is Used In Stata, the method for comparing two ROCs, as programmed in the roccomp command, is described by DeLong et al (1988). You could describe this in your protocol as, The area under the receiver operating characteristic (ROC) curves were computed. For comparisons of the ROC from different prediction rules, or prognostic models, using a common reference standard, the method of DeLong et al (1988) was used. ---DeLong ER, Delong DM, Clark-Pearson DL. Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach. Biometrics 1988;44(3):837-845. Chapter 2 (revision 16 May 2010) p. 7 References DeLong ER, Delong DM, Clark-Pearson DL. (1988). Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach. Biometrics 44(3):837-845. Lachenbruch PA, Lynch C. (1998). Assessing screening tests: extensions of McNemar’s test. Statist Med 17:2207-2217. Siegel S, Castellan NH Jr. (1988). Nonparametric Statistics for the Behavioral Sciences. 2nd ed. New York, McGraw Hill. Zhou X-H, Obuchowski NA, McClish DK. (2002). Statistical Methods in Diagnostic Medicine. New York, John Wiley & Sons. Chapter 2 (revision 16 May 2010) p. 8