Table 2 Parameter estimates following heterogeneous cluster merges: scenario 3 ^a

Empirical estimates

0

1

2

5

10

20

Assigned to control

Intercept, β₀

0.001 (−0.003, 0.004)

0.004 (0.000, 0.007)

0.006 (0.002, 0.009)

0.015 (0.012, 0.019)

0.032 (0.029, 0.035)

0.057 (0.054, 0.060)

Treatment effect, β₁

0.199 (0.195, 0.204)

0.197 (0.192, 0.202)

0.194 (0.189, 0.198)

0.186 (0.181, 0.190)

0.170 (0.165, 0.175)

0.001 (−0.003, 0.004)

${\mathit{\sigma }}_{\mathit{b}}^2$

0.051 (0.049, 0.052)

0.050 (0.049, 0.051)

0.049 (0.047, 0.0498)

0.048 (0.046, 0.049)

0.046 (0.045, 0.047)

0.039 (0.038, 0.040)

${\mathit{\sigma }}_{\mathit{w}}^2$

0.951 (0.948, 0.954)

0.951 (0.949, 0.954)

0.953 (0.951, 0.956)

0.953 (0.951, 0.956)

0.958 (0.955, 0.961)

0.969 (0.966, 0.971)

Intracluster correlation coefficient

0.050 (0.048, 0.051)

0.050 (0.049, 0.051)

0.049 (0.047, 0.0494)

0.048 (0.046, 0.049)

0.046 (0.044, 0.047)

0.039 (0.037, 0.040)

Empirical power

82.5%

79.0%

78.8%

74.3%

64.3%

46.9%

Assigned to intervention

Intercept, β₀

0.002 (−0.002, 0.005)

−0.002 (−0.006, 0.001)

0.000 (−0.004, 0.003)

0.001 (−0.003, 0.005)

0.000 (−0.004, 0.004)

−0.003 (−0.008, 0.001)

Treatment effect, β₁

0.201 (0.197, 0.206)

0.198 (0.194, 0.203)

0.192 (0.187, 0.196)

0.185 (0.180, 0.190)

0.166 (0.161, 0.171)

0.146 (0.141, 0.152)

${\mathit{\sigma }}_{\mathit{b}}^2$

0.050 (0.048, 0.051)

0.050 (0.048, 0.051)

0.049 (0.047, 0.0499)

0.047 (0.046, 0.049)

0.045 (0.043, 0.046)

0.039 (0.038, 0.040)

${\mathit{\sigma }}_{\mathit{w}}^2$

0.948 (0.946, 0.950)

0.950 (0.947, 0.952)

0.950 (0.948, 0.953)

0.956 (0.953, 0.958)

0.958 (0.956, 0.961)

0.968 (0.965, 0.970)

Intracluster correlation coefficient

0.049 (0.048, 0.051)

0.050 (0.048, 0.051)

0.049 (0.047, 0.0498)

0.047 (0.046, 0.048)

0.045 (0.043, 0.046)

0.039 (0.037, 0.040)

Empirical power

82.7%

80.7%

79.5%

72.9%

64.2%

45.1%

Dropped from analysis

Intercept, β₀

0.001 (−0.003,0.004)

−0.002 (−0.006, 0.001)

−0.001 (−0.004, 0.003)

−0.004 (−0.007, −0.001)

−0.001 (−0.005, 0.003)

0.000 (−0.004, 0.005)

Treatment effect, β₁

0.202 (0.197, 0.207)

0.201 (0.196, 0.206)

0.199 (0.194, 0.204)

0.202 (0.197, 0.207)

0.202 (0.196, 0.207)

0.198 (0.192, 0.205)

${\mathit{\sigma }}_{\mathit{b}}^2$

0.051 (0.049, 0.052)

0.050 (0.048, 0.051)

0.050 (0.048, 0.051)

0.049 (0.048, 0.051)

0.049 (0.047, 0.051)

0.050 (0.048, 0.051)

${\mathit{\sigma }}_{\mathit{w}}^2$

0.949 (0.947, 0.952)

0.951 (0.948, 0.953)

0.952 (0.950, 0.955)

0.950 (0.947, 0.953)

0.953 (0.950, 0.956)

0.950 (0.946, 0.953)

Intracluster correlation coefficient

0.051 (0.049, 0.052)

0.050 (0.048, 0.051)

0.050 (0.048, 0.051)

0.049 (0.048, 0.051)

0.049 (0.047, 0.0499)

0.049 (0.048, 0.051)

Empirical power

81.7%

81.0%

78.3%

77.6%

70.2%

53.1%