Table 3.

GLM estimated through MLE with and without Firth correction for T=100, J=5, b=20 in a case of scenario 1 with D=0.24

(I) GLM fitting without correction for CR
$\widehat{{\beta }_0}$	$E\left(\widehat{{\beta }_i}\right)$	$E\left(\text{MSE}\right)$	$E\left(p_{value}<0.05\right)$
$\widehat{{\beta }_0}$	−0.8684	0.1992	0.5174
$\widehat{{\beta }_t}$	0.2610	0.0243	0.4018
$\widehat{{\beta }_1}$	0.0070	0.1900	0.0544
(II) GLM fitting with correction for CR
$\widehat{{\beta }_0}$	−0.8370	0.1838	0.5224
$\widehat{{\beta }_t}$	0.2509	0.0227	0.4012
$\widehat{{\beta }_1}$	0.0067	0.1775	0.0534
(III) GLM fitting without correction for FLGI
$\widehat{{\beta }_0}$	−1.4465	8.9957	0.4110
$\widehat{{\beta }_t}$	0.1898	0.0307	0.1844
$\widehat{{\beta }_1}$	0.0038	18.2440	0.0142
(IV) GLM fitting with correction for FLGI
$\widehat{{\beta }_0}$	−0.9307	0.3947	0.4670
$\widehat{{\beta }_t}$	0.1825	0.0301	0.1858
$\widehat{{\beta }_1}$	0.0048	0.7993	0.0456

Abbreviations: CR, complete randomisation; FLGI, forward‐looking Gittins index rule; GLM, generalised linear model; MLE, maximum likelihood estimation; MSE, mean squared error. Results for 5000 trials. True values were assumed to be β ₀≈−0.8473, β _t≈0.2719 and β _z=β ₁=0.