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Table 2 Type-I error, power, position bias and SD of the treatment effect estimates

From: Evaluating the impact of calibration of patient-reported outcomes measures on results from randomized clinical trials: a simulation study based on Rasch measurement theory

J

M

Ntrial

μ

γ = 0

γ = 0.2

Type-I error

Power

Position bias

SD of the estimates

Non calibrated

Calibrated

Non calibrated

Calibrated

Non calibrated

Calibrated

Non calibrated

Calibrated

\(\hat{\gamma}\)

t test on \(\hat{\theta_i}\)

\(\hat{\gamma}\)

t test on \(\hat{\theta_i}\)

\(\hat{\gamma}\)

t test on \(\hat{\theta_i}\)

\(\hat{\gamma}\)

t test on \(\hat{\theta_i}\)

\(\hat{\gamma}\)

t test on \(\hat{\theta_i}\)

\(\hat{\gamma}\)

t test on \(\hat{\theta_i}\)

\(\hat{\gamma}\)

t test on \(\hat{\theta_i}\)

\(\hat{\gamma}\)

t test on \(\hat{\theta_i}\)

4

3

200

0

5.6

5.6

5.6

5.6

32.8

32.8

32.8

32.6

0.01

0.08

0.01

0.08

0.13

0.08

0.13

0.08

0.5

4.4

4.4

4.6

4.4

32.8

32.8

33.2

33.0

0.00

0.08

0.00

0.08

0.13

0.08

0.13

0.08

2

5.8

5.6

5.6

5.4

29.6

29.6

29.8

29.6

0.00

0.10

0.01

0.10

0.15

0.07

0.15

0.07

500

0

6.8

6.6

6.8

6.8

68.0

68.0

68.0

68.0

0.00

0.08

0.00

0.08

0.08

0.05

0.08

0.05

0.5

2.6

2.6

2.6

2.6

68.4

68.4

68.6

68.4

0.00

0.08

0.00

0.08

0.08

0.05

0.08

0.05

2

4.6

4.6

4.6

4.6

58.6

58.6

58.4

58.4

0.00

0.11

0.00

0.10

0.09

0.04

0.09

0.05

5

200

0

4.6

4.6

4.8

4.6

41.2

41.2

41.2

40.6

0.00

0.05

0.00

0.05

0.12

0.09

0.12

0.09

0.5

4.6

4.6

4.6

4.4

40.8

40.8

40.6

40.4

0.00

0.05

0.00

0.05

0.12

0.09

0.12

0.09

2

5.4

5.4

5.6

5.4

32.2

32.4

32.6

32.4

0.00

0.08

0.00

0.07

0.13

0.08

0.13

0.08

500

0

5.2

5.2

5.2

5.2

76.6

76.6

76.8

76.6

0.00

0.05

0.00

0.05

0.07

0.06

0.07

0.06

0.5

4.6

4.6

4.6

4.6

75.6

75.6

75.8

75.8

0.00

0.05

0.00

0.05

0.08

0.06

0.08

0.06

2

4.2

4.2

4.2

4.2

69.8

69.8

69.4

69.4

0.00

0.08

0.00

0.07

0.08

0.05

0.08

0.05

7

3

200

0

7.6

7.2

7.4

7.2

40.8

40.8

40.8

40.8

0.00

0.05

0.00

0.05

0.12

0.09

0.12

0.09

0.5

5.4

5.2

5.6

5.2

40.0

40.0

40.2

40.0

0.00

0.06

0.00

0.06

0.12

0.08

0.12

0.08

2

5.2

5.2

5.2

5.2

36.6

36.6

36.6

36.4

0.01

0.08

0.01

0.08

0.13

0.08

0.13

0.08

500

0

5.2

5.2

5.2

5.2

76.8

76.6

77.0

76.8

0.00

0.05

0.00

0.05

0.07

0.05

0.07

0.05

0.5

5.2

5.2

5.2

5.2

75.0

75.0

75.0

75.0

0.00

0.05

0.00

0.05

0.08

0.06

0.08

0.06

2

3.6

3.6

3.6

3.6

67.8

67.8

67.8

67.8

0.00

0.08

0.00

0.08

0.08

0.05

0.09

0.05

5

200

0

5.2

5.2

5.2

5.2

42.6

42.6

42.8

42.6

0.00

0.03

0.00

0.03

0.11

0.09

0.11

0.09

0.5

5.2

5.0

5.2

5.0

46.0

45.6

46.0

46.0

0.00

0.03

0.00

0.03

0.11

0.10

0.11

0.10

2

6.4

6.4

6.4

6.4

41.2

40.6

41.2

40.6

0.00

0.05

0.01

0.05

0.12

0.09

0.12

0.09

500

0

6.8

6.8

6.8

6.8

80.8

80.8

80.8

80.6

0.00

0.03

0.00

0.03

0.07

0.06

0.07

0.06

0.5

3.2

3.0

3.2

3.2

80.8

80.8

80.6

80.6

0.00

0.03

0.00

0.03

0.07

0.06

0.07

0.06

2

5.2

5.2

5.4

5.2

73.6

73.6

73.4

73.2

0.01

0.06

0.01

0.06

0.07

0.05

0.08

0.06

10

3

200

0

4.2

4.2

4.2

4.2

42.6

42.4

42.6

42.2

0.00

0.04

0.00

0.04

0.11

0.09

0.12

0.09

0.5

5.2

5.2

5.2

5.2

42.0

41.6

42.2

41.6

0.00

0.04

0.00

0.04

0.11

0.09

0.11

0.09

2

4.0

3.6

4.0

3.6

39.2

39.0

39.2

39.0

0.00

0.07

0.00

0.07

0.13

0.08

0.13

0.09

500

0

4.8

4.4

4.6

4.4

79.4

79.2

79.4

79.2

0.00

0.04

0.00

0.04

0.07

0.06

0.07

0.06

0.5

6.2

6.2

6.2

6.2

78.8

78.8

78.8

78.8

0.00

0.04

0.00

0.04

0.07

0.06

0.07

0.06

2

8.2

8.2

8.2

8.2

76.0

75.8

75.8

75.6

0.00

0.07

0.00

0.06

0.08

0.05

0.08

0.05

5

200

0

5.0

5.0

5.2

5.0

46.0

45.8

45.4

45.4

0.00

0.02

0.00

0.02

0.10

0.09

0.10

0.09

0.5

5.6

5.6

6.0

5.6

47.2

46.8

47.2

46.4

0.00

0.02

0.00

0.02

0.11

0.09

0.11

0.10

2

4.4

4.2

4.4

4.0

42.0

41.6

42.0

41.6

0.00

0.04

0.00

0.04

0.11

0.09

0.11

0.09

500

0

5.6

5.4

5.6

5.6

84.4

84.2

84.4

84.2

0.00

0.02

0.00

0.02

0.07

0.06

0.07

0.06

0.5

6.2

6.2

6.2

6.2

83.8

83.8

84.2

83.8

0.00

0.02

0.00

0.02

0.07

0.06

0.07

0.06

2

6.6

6.4

6.6

6.4

81.8

81.6

81.8

81.6

0.00

0.04

0.00

0.04

0.07

0.06

0.07

0.06

  1. Legend: results are presented for selected scenarios, with Ncalibration = 250, distribution of the item parameters = second archetype with SD of 1.5 and range of 2, and variance of the calibration sample = 1