Table 6.

GLM estimated through MLE with Firth correction for T=200, J=10, b=20, K=3 in a case of scenario 2 in which q _j=[0.5:0.05:0.95]

(II) GLM fitting with correction for CR
$\widehat{{\beta }_0}$	$E\left(\widehat{{\beta }_i}\right)$	$E\left(\text{MSE}\right)$	$E\left(p_{value}<0.05\right)$
$\widehat{{\beta }_0}$	−0.8816	0.1324	0.7078
$\widehat{{\beta }_z}$	1.3006	0.1239	0.9726
$\widehat{{\beta }_1}$	0.9355	0.1549	0.6954
$\widehat{{\beta }_2}$	−0.0032	0.1356	0.0516
(IV) GLM fitting with correction for FLGI
$\widehat{{\beta }_0}$	−1.1635	0.5391	0.3994
$\widehat{{\beta }_z}$	1.3492	0.1300	0.9762
$\widehat{{\beta }_1}$	1.1300	0.5845	0.3672
$\widehat{{\beta }_2}$	0.0041	0.7740	0.0246
(VI) GLM fitting with correction for CFLGI
$\widehat{{\beta }_0}$	−0.8861	0.1378	0.6966
$\widehat{{\beta }_z}$	1.3127	0.1243	0.9718
$\widehat{{\beta }_1}$	0.8862	0.2077	0.7718
$\widehat{{\beta }_2}$	−0.2487	0.5027	0.0288

Abbreviations: CR, complete randomisation; CFLGI, controlled forward‐looking Gittins index rule; 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 _z≈1.2528 and β ₁=0.8473, β _t=β ₂=0.