Statistical Methods for Analysis of Diagnostic Accuracy Studies
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Statistical Methods for Analysis of Diagnostic Accuracy Studies Jon Deeks University of Birmingham with acknowledgement to Hans Reitsma. Measures of diagnostic accuracy. Positive and negative predictive values Sensitivity and specificity Likelihood ratios Area under the ROC curve

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Statistical Methods for Analysis of Diagnostic Accuracy StudiesJon DeeksUniversity of Birminghamwith acknowledgement to Hans Reitsma


Measures of diagnostic accuracy
Measures of diagnostic accuracy Studies

  • Positive and negative predictive values

  • Sensitivity and specificity

  • Likelihood ratios

  • Area under the ROC curve

  • Diagnostic odds ratio


Diagnostic accuracy studies
Diagnostic accuracy studies Studies

  • Results from the index test are compared with the results obtained with the reference standard on the same subjects

  • Accuracy refers to the degree of agreement between the results of the index test and those from the reference standard


Basic design
Basic Design Studies

Series of patients

Index test

Reference standard

Cross-classification


Clinical problem
Clinical problem Studies

  • Diagnostic value of B type natriuretic (BNP) measurement

  • Does BNP measurement distinguish between those with and without left ventricular dysfunction in the elderly?

  • Smith et al. BMJ 2000; 320: 906.


Anatomy of diagnostic study
Anatomy of diagnostic study Studies

  • Target population: unscreened elderly

  • Index test: BNP

  • Target condition: LVSD

  • Final diagnosis (reference standard): echocardiography – global and regional assessment of ventricular function including measurement of LV ejection fraction


Our example
Our example Studies

Elderly patients

BNP measurement

Echocardiography for LVSD

Cross-classification



Measures of test performance
Measures of test performance Studies

  • sensitivity

    • 11 / 12 = 92% < Pr(T+|D+) >

  • specificity

    • 93 / 143 = 65% < Pr(T-|D-) >


Measures of test performance1
Measures of test performance Studies

  • positive predictive value

  • 11 / 61 = 18% < Pr(D+|T+) >

  • negative predictive value

  • 93 / 94 = 99% < Pr(D-|T-) >


Sensivity and specificity not directly affected by prevalence
Sensivity and Specificity not Studiesdirectly affected by prevalence

  • sensitivity

    • 131 / 143 = 92%

  • specificity

    • 93 / 143 = 65%


Predictive values directly affected by prevalence
Predictive values Studiesdirectly affected by prevalence

  • positive predictive value

  • 131 / 181 = 72%

  • negative predictive value

  • 93 / 105 = 89%


Do sensitivity and specificity vary with prevalence
Do sensitivity and specificity vary with prevalence? Studies

  • Test performance is sometimes observed to be different in different settings, patient groups, etc.

  • Occasionally attributed to differences in disease prevalence, but:

    • diseased and non-diseased spectrums differ as well.

  • e.g. using a test in primary care and secondary care referrals

    • the diseased group are different (cases more difficult)

    • the non-diseased group are different (conditions more similar)

    • sensitivity may decrease, specificity certainly decreases


Likelihood ratios
Likelihood ratios Studies

  • Why likelihood ratios?

  • Applicable in situations with more than 2 test outcomes

  • Direct link from pre-test probabilities to post-test probabilities


Likelihood ratios1
Likelihood ratios Studies

  • Information value of a test result expressed as likelihood ratio


Likelihood ratio of positive test
Likelihood Ratio of positive test Studies

  • How more often a positive test result occurs in persons with compared to those without the target condition


Likelihood ratios2
Likelihood ratios Studies

  • Likelihood ratio of a negative test result

  • How less likely a negative test result is in persons with the target condition compared to those without the target condition




Interpreting likelihood ratios
Interpreting likelihood ratios Studies

  • A LR=1 indicates no diagnostic value

  • LR+ >10 are usually regarded as a ‘strong’ positive test result

  • LR- <0.1 are usually regarded as a strong negative test result

  • But it depends on what change in probability is needed to make a diagnosis


92% Studies

LR+ = 10

55%

10%

50%


Advantages of likelihood ratios
Advantages of likelihood ratios Studies

  • Still useful when there are more than 2 test outcomes


Bnp is a continuous measurement
BNP is a continuous measurement Studies

  • Dichotomisation of BNP(high vs. low) means loss of information

  • Higher values of BNP are more indicative of LVSD



Likelihood ratios4
Likelihood ratios Studies

  • Stratum specific likelihood ratios in case of more than 2 test results



Bayes rule
Bayes’ rule Studies

Post-test odds for disease

=

Pre-test odds for disease x Likelihood ratio


Bayes rule1
Bayes’ rule Studies

  • Pre-test odds

    • chance of disease expressed in odds

    • example: if 2 out of 5 persons have the disease: probability = 2/5 in odds = 2/3


Bayes rule2
Bayes’ rule Studies

  • odds = probability / (1 – probability)

  • probability = odds / (1 + odds)


Bayes rule patient with bnp 26 7
Bayes’ rule Studiespatient with BNP >26.7

  • Pre-test probability = 0.5

  • Pre-test odds = 0.5 / (1-0.5) = 1

  • LR(BNP >26.7) = 3.83

  • Post-test odds = 1x3.83 = 3.83

  • Post-test probability = 3.83 / (1+3.83) = 0.79


Bayes rule patient with bnp lower than 18 7
Bayes’ rule Studiespatient with BNP lower than 18.7

  • Pre-test probability = 0.5

  • Pre-test odds = 0.5 / (1-0.5) = 1

  • LR(CK< 40) = 0.13

  • Post-test odds = 1 x 0.13 = 0.13

  • Post-test probability = 0.13 / (1+0.13)

    = 0.12



79% Studies

52%

12%

50%


5% Studies

17%

5%

1%



Confidence intervals
Confidence intervals Studies

  • Sample uncertainty should be described for all statistics, using confidence intervals

+ gives upper limit - gives lower limit

Standard error of estimate

estimate of effect

Normal deviate (1.96 for 95% CI)


Confidence intervals for proportions
Confidence Intervals for Proportions Studies

  • Sensitivity, specificity, positive and negative predictive values, and overall accuracy are all proportions


Exact or asymptotic ci
Exact or Asymptotic CI? Studies

  • Asymptotic CI are approximations

  • Inappropriate when

    • proportion is near 0% or near 100%

    • sample sizes are small

      (confidence intervals are not symmetric in these cases)

  • Preferable to use Binomial exact methods

    • can be computed in many statistics packages

    • or refer to tables



Confidence intervals for ratios of probabilities and odds
Confidence Intervals for Ratios of Probabilities and Odds Studies

  • Odds ratios are ratios of odds

  • Likelihood ratios are ratios of probabilities


Cis for study
CIs for study Studies

  • Sensitivity = 92% (62%, 100%)

  • Specificity = 65% (57%, 73%)

  • PPV = 82% (70%, 91%)

  • NPV = 99% (94%, 100%)

  • LR(>= 26.7) = 3.8 (2.4, 6.1)

  • LR(18.7 < 26.7) = 1.1 (0.3, 4.1)

  • LR(<18.7) = 0.13 (0.02, 0.84)


Roc curve
ROC-curve Studies

  • ROC stands for Receiver Operating Characteristic

  • ROC-curve shows the pairs of sensitivity and specificity that correspond to various cut-off points for the continuous test result








Threshold effects
Threshold effects Studies

Decreasing threshold increases sensitivity but decreases specificity

Increasing threshold increases specificity but decreases sensitivity


Change in cut off value and effect on sens spec
Change in cut-off value Studiesand effect on sens & spec


Roc curve bnp
ROC-curve BNP Studies

Cut-off:  18.7

Cut-off:  19.8

Cut-off:  26.7


Roc curve1
ROC curve Studies

  • Shows the effect of different cut-off values on sensitivity and specificity

  • Better tests have curves that lie closer to the upper left corner

  • Area under the ROC is a single measure of test performance (higher is better)

  • Shape

    • RAW continuous data gives steps

    • GROUPED data gives straight sloping lines

    • FITTED ROC curves are smoothed.


Variation in diagnostic threshold
Variation in diagnostic threshold Studies

At what level, is a test result categorised as +ve, and how should the threshold be selected?

Threshold affects the performance of the test, as described by ROC curves, and likelihood ratios

Depends on

disease prevalence (affects +ve and -ve predictive values)

relative costs of false positive and false negative misdiagnoses

relative benefits of true positive and true negative diagnoses


Workshop exercise erratum

LVSD Studies

+ve

-ve

MI or BNP

+ve

36

63

-ve

4

23

40

86

Workshop exercise – erratum

  • Q16 page 8

    Compute post-test probabilities for a high risk patient, pre-test prob=50%

    Q19 page 10


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