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Table 2 Performance of the estimators when second stage sample size is modified by Δ n 2: bias and root mean squared error in selected situations

From: What inference for two-stage phase II trials?

  

Δ n 2 =−2

Δ n 2 =−1

Δ n 2 = +1

Δ n 2 = +2

Δ n 2 = +5

Settings

Estimator

Bias

RMSE

Bias

RMSE

Bias

RMSE

Bias

RMSE

Bias

RMSE

Optimal design with Π 0 = 0.05, Π 1 = 0.2: n 1=21, n 2=20, r 1=1, r t =4

        

Π = Π 0

Π ̂ m

-0.008

0.038

-0.009

0.037

-0.009

0.037

-0.009

0.037

-0.010

0.036

 

Π ̂ g

-0.002

0.041

-0.003

0.041

-0.003

0.040

-0.003

0.040

-0.003

0.040

 

Π ̂ u

0.000

0.046

0.000

0.046

0.000

0.046

0.000

0.045

0.000

0.045

 

Π ̂ c

-0.018

0.036

-0.018

0.036

-0.018

0.036

-0.018

0.036

-0.018

0.035

 

Π ̂ p

-0.018

0.037

-0.018

0.037

-0.018

0.036

-0.018

0.036

-0.018

0.035

 

Π ̂ k

-0.006

0.039

-0.006

0.039

-0.006

0.038

-0.006

0.038

-0.006

0.038

Π = Π 1

Π ̂ m

-0.004

0.071

-0.004

0.071

-0.005

0.069

-0.005

0.069

-0.005

0.067

 

Π ̂ g

0.001

0.068

0.001

0.068

0.001

0.066

0.001

0.066

0.001

0.064

 

Π ̂ u

0.000

0.068

0.000

0.067

0.000

0.066

0.000

0.065

0.000

0.064

 

Π ̂ c

-0.012

0.077

-0.012

0.076

-0.011

0.074

-0.011

0.073

-0.011

0.071

 

Π ̂ p

-0.009

0.076

-0.009

0.075

-0.009

0.074

-0.009

0.073

-0.009

0.071

 

Π ̂ k

-0.012

0.071

-0.013

0.070

-0.013

0.069

-0.013

0.068

-0.013

0.067

Minimax design with Π 0=0.4, Π 1=0.6: n 1=29, n 2=25, r 1=12, r t =27

        

Π = Π 0

Π ̂ m

-0.015

0.078

-0.016

0.078

-0.016

0.077

-0.017

0.077

-0.018

0.076

 

Π ̂ g

-0.004

0.080

-0.004

0.080

-0.004

0.080

-0.004

0.079

-0.004

0.079

 

Π ̂ u

0.000

0.087

0.000

0.087

0.000

0.087

0.000

0.087

0.000

0.087

 

Π ̂ c

-0.037

0.082

-0.037

0.082

-0.036

0.081

-0.036

0.080

-0.036

0.079

 

Π ̂ p

-0.035

0.083

-0.035

0.082

-0.035

0.081

-0.035

0.081

-0.035

0.080

 

Π ̂ k

-0.010

0.079

-0.010

0.078

-0.010

0.078

-0.010

0.078

-0.010

0.078

Π = Π 1

Π ̂ m

-0.003

0.074

-0.003

0.074

-0.003

0.073

-0.003

0.073

-0.003

0.071

 

Π ̂ g

0.001

0.070

0.001

0.070

0.002

0.069

0.002

0.068

0.002

0.067

 

Π ̂ u

0.000

0.071

0.000

0.070

0.000

0.069

0.000

0.069

0.000

0.068

 

Π ̂ c

-0.011

0.082

-0.011

0.081

-0.010

0.080

-0.010

0.079

-0.010

0.077

 

Π ̂ p

-0.007

0.080

-0.007

0.079

-0.007

0.078

-0.007

0.077

-0.007

0.076

 

Π ̂ k

-0.012

0.073

-0.012

0.072

-0.011

0.071

-0.011

0.071

-0.011

0.070