Table 1 Sample size requirements at Levels 2 and 3, based on adding variability to each individual dose–response curve parameter.

From: A quantitative approach to the spread of variance in translational research using Monte Carlo simulation

 

Sample size (n)

Theoretical

Slope

EC50

MaxResp

MinResp

Level 2

Group mean difference = 0.01

 Variability

  0.0

1571

1643 (1.05x)

1636 (1.04x)

1657 (1.05x)

1658 (1.06x)

  0.1

1571

1666 (1.06x)

3467 (2.21x)

2016 (1.28x)

2103 (1.28x)

  0.5

1571

2298 (1.46x)

 > 10,000 (6.37x)

 > 10,000 (6.37x)

 > 10,000 (6.37x)

  1.0

1571

5743 (3.66x)

 > 10,000 (6.37x)

 > 10,000 (6.37x)

 > 10,000 (6.37x)

Group mean difference = 0.11

 Variability

  0.0

15

15 (1.00x)

15 (1.00x)

15 (1.00x)

15 (1.00x)

  0.1

15

16 (1.07x)

35 (2.33x)

20 (1.33x)

19 (1.27x)

  0.5

15

22 (1.47x)

679 (45x)

163 (11x)

118 (7.87x)

  1.0

15

66 (4.40x)

3313 (221x)

885 (59x)

692 (46x)

Level 3

Group mean difference = 0.01

 Variability

  0.0

1571

1708 (1.09x)

1708 (1.09x)

1714 (1.09x)

1714 (1.09x)

  0.1

1571

1741 (1.11x)

4117 (2.62x)

2181 (1.39x)

2331 (1.48x)

  0.5

1571

2652 (1.69x)

 > 10,000 (6.37x)

 > 10,000 (6.37x)

 > 10,000 (6.37x)

  1.0

1571

 > 10,000 (6.37x)

 > 10,000 (6.37x)

 > 10,000 (6.367x)

 > 10,000 (6.37x)

Group mean difference = 0.11

 Variability

  0.0

15

16 (1.07x)

16 (1.07x)

16 (1.07x)

16 (1.07x)

  0.1

15

17 (1.13x)

43 (2.87x)

23 (1.53x)

22 (1.47x)

  0.5

15

26 (1.73x)

1108 (74x)

267 (18x)

233 (16x)

  1.0

15

135 (9.00x)

3456 (230x)

2159 (144x)

2916 (194x)

  1. Standard sample size calculations (theoretical n) are compared to the sample size requirements based on simulations at Level 2 and Level 3, as a variability of 0.1 to 1 is added to each of the four dose–response curve parameters where mu0 = 0.5 and sigma = 0.1. The variability refers to the varSlope, varEC50, varMaxResp, or varMinResp parameters in Formula (2), which serves to add variability to better model real-world experimental data. The relative increase in sample size requirements from standard calculations (theoretical n) are presented in parentheses for all sample sizes calculated using the simulation.
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