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Table 3 Exemplary data sets. The first ten of the replicate data sets for the first parameter set. Statistical and design parameters sampled according to Table 1, data generated according to Eq. (5), and maximum likelihood estimators (MLE) calculated according to Eq. (6)

From: Comparison of Bayesian and frequentist methods for prevalence estimation under misclassification

 

Statistical

Design

Data

MLE

Data set

\(\widetilde {{Se}\phantom {.}}\)

\(\widetilde {{Sp}}\)

\(\widetilde {\pi }\)

nSe

nSp

n

xSe

xSp

x

\(\widehat {{Se}\phantom {.}}\)

\(\widehat {{Sp}}\)

\(\widehat {{AP}}\)

1

0.7479478

0.9332674

0.4459405

100

200

323

74

193

129

0.74

0.965

0.3993808

2

0.7479478

0.9332674

0.4459405

100

200

323

70

189

125

0.70

0.945

0.3869969

3

0.7479478

0.9332674

0.4459405

100

200

323

78

189

124

0.78

0.945

0.3839009

4

0.7479478

0.9332674

0.4459405

100

200

323

73

191

109

0.73

0.955

0.3374613

5

0.7479478

0.9332674

0.4459405

100

200

323

76

184

117

0.76

0.920

0.3622291

6

0.7479478

0.9332674

0.4459405

100

200

323

66

188

132

0.66

0.940

0.4086687

7

0.7479478

0.9332674

0.4459405

100

200

323

76

179

121

0.76

0.895

0.3746130

8

0.7479478

0.9332674

0.4459405

100

200

323

75

188

118

0.75

0.940

0.3653251

9

0.7479478

0.9332674

0.4459405

100

200

323

74

187

127

0.74

0.935

0.3931889

10

0.7479478

0.9332674

0.4459405

100

200

323

75

191

127

0.75

0.955

0.3931889