Nonparametric meta-analysis for diagnostic accuracy studies Antonia Zapf

Transcription

1 Nonparametric meta-analysis for diagnostic accuracy studies Antonia Zapf joint work with A. Hoyer, K. Kramer, and O. Kuss

2 Table of contents Motivation Nonparametric approach Simulation study Application Outlook Conclusion

3 Table of contents Motivation Nonparametric approach Simulation study Application Outlook Conclusion

4 Meta-analysis of transesophageal echocardiography for the assessment of artherosclerosis true positives / diseased true negatives / non-diseased Total Sensitivity Specificity [Van Zaane et al. (2008), Acta Anaesthesiol Scand, 52: ]

5 Meta-analysis of transesophageal echogardiography for assessment of artherosclerosis Convergence problems of the current approaches! nonparametric approach without convergence problems [Van Zaane et al. (2008), Acta Anaesthesiol Scand, 52: ]

6 Nonparametric methods for clustered data Clustered data many patients with few lesions Meta-analysis Few studies with many patients v [Lange (2011), Dissertation, University Göttingen] [Lange, Brunner (2012), Statistical Methodology, 9: ]

7 Table of contents Motivation Nonparametric approach Simulation study Application Outlook Conclusion

8 Statistical model Fixed effects model!

9 Meta-analysis point estimators Point estimators are unbiased and consistent!

10 Distribution and covariance matrix

11 Confidence interval

12 Table of contents Motivation Nonparametric approach Simulation study Application Outlook Conclusion

13 Comparison with Standard model Bivariate generalized linear mixed effects model Random effects bivariate normal distributed one single correlation structure [Chu, Cole (2006), J Clin Epidemiol, 59: ] Copula model Marginal beta-binomial distributions for true positives and true negatives Linked by copula distribution different correlations structures [Kuss et al. (2014), Stat in Med, 33: 17-30]

14 Varying factors True model (standard model, Plackett copula, Gauss copula) True sensitivity / specificity (70%/70%, 90%/70%, 90%/90%) True correlation (approx. 0, -0.2, -0.8) Number of studies (10, 50) Number of individuals per disease state (20, 100) 108 scenarios, each with 1000 simulation runs (results for sensitivity)

15 Bias compared to the current approaches NP worse NP better

16 Coverage probability of the nonparametric approach

17 Coverage probability compared to the current approaches NP better NP worse

18 Table of contents Motivation Nonparametric approach Simulation study Application Outlook Conclusion

19 Meta-analysis of transesophageal echocardiography for the assessment of artherosclerosis # diseased # non-diseased Total Sensitivity Specificity [Van Zaane et al. (2008), Acta Anaesthesiol Scand, 52: ]

20 Meta-analysis of eye examination for the diagnosis of primary melanoma Sensitivity Specificity [Vestergaard et al. (2008), BJD, 159: ]

21 Table of contents Motivation Nonparametric approach Simulation study Application Outlook Conclusion

22 Adjustment for covariates For example cut-off point [Bennett et al. (2007), Diabetic Medicine, 24(4): ]

23 Statistical model with covariates Regression approach for k covariates Least squares estimation of the regression coefficients Logit-transformation for range-keeping point estimators [Zapf (2009), PhD thesis, Göttingen]

24 Structure of the talk Motivation Nonparametric approach Simulation study Consideration of covariates Application Conclusion

25 Properties of the nonparametric model Fixed effects model Unbiased Anti-conservative (not as much as the current approaches) No restrictions on the correlation structure No convergence problems Consideration of covariates possible Article: Zapf et al. (2015), Statistics in Medicine, 34(29):

26 Table of contents Motivation Nonparametric approach Simulation study Application Outlook Conclusion Supplement

27 Bias of the nonparametric approach

28 Proof that the variance estimator is unbiased

29 Statistical model with covariates

30 Regression approach for adjusted sensitivity and specificity Regression coefficients by least-squares method

31 Logit-transformation