TABLE 1.

Simulation results for the analysis of $P_{0,2}({\tau }_{0.4})$ and $P_{0,2}^{\prime }({\tau }_{0.4})$, where τ_0.4 is the 40th percentile of the follow‐up time, based on the standard approach which ignores the within‐cluster dependence (naïve) and the proposed method with (i) the influence function‐based variance estimator (IF) and (ii) the nonparametric cluster bootstrap (CB)

			$P_{0,2}({\tau }_{0.4})$				$P_{0,2}^{\prime }({\tau }_{0.4})$
n	$F_M$	Method	Biasa	MCSDa	ASEa	CP	Biasa	MCSDa	ASEa	CP
20	$\mathcal{U}[5,15]$	Naïve	0.006	3.229	2.625	0.890	−1.022	3.226	2.623	0.859
		IF	0.006	3.229	3.018	0.927	−0.063	3.517	3.311	0.926
		CB	0.006	3.229	3.040	0.928	−0.063	3.517	3.316	0.923
	$\mathcal{U}[10,30]$	Naïve	0.069	2.559	1.857	0.842	−0.928	2.558	1.855	0.816
		IF	0.069	2.559	2.483	0.939	0.077	2.787	2.702	0.940
		CB	0.069	2.559	2.494	0.935	0.077	2.787	2.698	0.939
40	$\mathcal{U}[5,15]$	Naïve	0.105	2.204	1.866	0.909	−0.939	2.199	1.863	0.866
		IF	0.105	2.204	2.196	0.944	0.080	2.403	2.411	0.948
		CB	0.105	2.204	2.198	0.943	0.080	2.403	2.407	0.947
	$\mathcal{U}[10,30]$	Naïve	0.006	1.811	1.312	0.846	−1.003	1.808	1.310	0.779
		IF	0.006	1.811	1.782	0.945	−0.012	1.940	1.941	0.946
		CB	0.006	1.811	1.786	0.944	−0.012	1.940	1.940	0.945
80	$\mathcal{U}[5,15]$	Naïve	−0.037	1.557	1.314	0.903	−1.083	1.551	1.312	0.820
		IF	−0.037	1.557	1.557	0.942	−0.055	1.699	1.715	0.940
		CB	−0.037	1.557	1.556	0.942	−0.055	1.699	1.711	0.940
	$\mathcal{U}[10,30]$	Naïve	0.044	1.287	0.929	0.844	−0.962	1.286	0.928	0.732
		IF	0.044	1.287	1.271	0.945	0.025	1.399	1.382	0.944
		CB	0.044	1.287	1.273	0.944	0.025	1.399	1.382	0.946

Abbreviations: ASE, average estimated standard error; CP, coverage probability; $F_M$, discrete uniform distribution of the cluster size; MCSD, Monte Carlo standard deviation of the estimates; n, number of clusters.

Note. Results under right censoring.

^aIndicates × 10².