A simulation study of the reliability and accuracy of Cox-TEL method for estimating hazard ratio and difference in proportions for long-term survival data containing cured patients

doi:10.12122/j.issn.1673-4254.2024.06.20

Abstract

Abstract:

Objective To explore the applicable conditions of the Cox-TEL (Cox PH-Taylor expansion adjustment for long-term survival data) method for analysis of survival data that contain cured patients. Methods The simulated survival data method based on Weibull distribution was used to simulate and generate the survival data with different cure rates, censored rates, and cure rate differences. The Cox-TEL method was used for analysis of the generated simulation data, and its performance was evaluated by calculating its type I error and power. Results Almost all the type I error of the hazard ratios (HRs) obtained by the Cox-TEL method under different conditions were slightly greater than 0.05, and this method showed a good test power for estimating the HRs for data with a large sample size and a large difference in proportions (DPs). For the data of cured patients, the type I error of the DPs obtained by the Cox-TEL method was well around 0.05, and its test power was robust in most of the scenarios. Conclusion The Cox-TEL method is effective for analyzing data of uncured patients and obtaining reliable HRs for most of the survival data with a sample size, a low censored rates, and a large difference in cure rates. The method is capable of accurately estimating the DPs regardless of the sample size, censored rates, or the cure rates.

Key words: Cox-TEL, cure model, survival analysis, power

Biqing ZOU, Lishan XU, Keke LI, Shengli AN. A simulation study of the reliability and accuracy of Cox-TEL method for estimating hazard ratio and difference in proportions for long-term survival data containing cured patients[J]. Journal of Southern Medical University, 2024, 44(6): 1182-1187.

Figures/Tables 6

References 32

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Project	Parameter settings
The type I error of the HRs of the Cox-TEL method	Cure rates (Censored rates): 0.10 (0.25, 0.30, 0.35, 0.40)、0.30 (0.45, 0.50, 0.55, 0.60)、0.50 (0.65, 0.70, 0.75, 0.80) Sample size:200、400、600、800、1000 Number of simulations:1000
The type I error of the DPs of the Cox-TEL method	Cure rates (Censored rates): 0.10 (0.25, 0.30, 0.35, 0.40)、0.30 (0.45, 0.50, 0.55, 0.60)、0.50 (0.65, 0.70, 0.75, 0.80) Sample size:200、250、300、350、400 Number of simulations:200
The power of the HRs of the Cox-TEL method	Censored rates (Difference in cure rates): 0.30 (0.10, 0.15, 0.20, 0.25, 0.30)、0.50 (0.10, 0.15, 0.20, 0.25, 0.30)、0.70 (0.10, 0.15, 0.20, 0.25, 0.30) Sample size:200、400、600、800、1000 Number of simulations:1000
The power of the DPs of the Cox-TEL method	Censored rates (Difference in cure rates): 0.50 (0.010, 0.012, 0.014, 0.016, 0.018, 0.020)、0.70 (0.010, 0.012, 0.014, 0.016, 0.018, 0.020) Sample size:200、250、300、350、400 Number of simulations:200

Project	Parameter settings
The type I error of the HRs of the Cox-TEL method	Cure rates (Censored rates): 0.10 (0.25, 0.30, 0.35, 0.40)、0.30 (0.45, 0.50, 0.55, 0.60)、0.50 (0.65, 0.70, 0.75, 0.80) Sample size:200、400、600、800、1000 Number of simulations:1000
The type I error of the DPs of the Cox-TEL method	Cure rates (Censored rates): 0.10 (0.25, 0.30, 0.35, 0.40)、0.30 (0.45, 0.50, 0.55, 0.60)、0.50 (0.65, 0.70, 0.75, 0.80) Sample size:200、250、300、350、400 Number of simulations:200
The power of the HRs of the Cox-TEL method	Censored rates (Difference in cure rates): 0.30 (0.10, 0.15, 0.20, 0.25, 0.30)、0.50 (0.10, 0.15, 0.20, 0.25, 0.30)、0.70 (0.10, 0.15, 0.20, 0.25, 0.30) Sample size:200、400、600、800、1000 Number of simulations:1000
The power of the DPs of the Cox-TEL method	Censored rates (Difference in cure rates): 0.50 (0.010, 0.012, 0.014, 0.016, 0.018, 0.020)、0.70 (0.010, 0.012, 0.014, 0.016, 0.018, 0.020) Sample size:200、250、300、350、400 Number of simulations:200

Cure rates	Censored rates	Sample size
Cure rates	Censored rates	200	400	600	800	1000
0.10	0.25	0.050	0.068	0.067	0.063	0.063
	0.30	0.065	0.069	0.065	0.072	0.061
	0.35	0.054	0.076	0.067	0.058	0.067
	0.40	0.059	0.065	0.076	0.058	0.061
0.30	0.45	0.062	0.077	0.074	0.066	0.073
	0.50	0.072	0.073	0.077	0.091	0.077
	0.55	0.070	0.058	0.078	0.074	0.069
	0.60	0.063	0.074	0.079	0.077	0.065
0.50	0.65	0.047	0.061	0.078	0.070	0.064
	0.70	0.061	0.073	0.070	0.062	0.084
	0.75	0.054	0.073	0.069	0.071	0.055
	0.80	0.073	0.070	0.081	0.051	0.065

Cure rates	Censored rates	Sample size
Cure rates	Censored rates	200	400	600	800	1000
0.10	0.25	0.050	0.068	0.067	0.063	0.063
	0.30	0.065	0.069	0.065	0.072	0.061
	0.35	0.054	0.076	0.067	0.058	0.067
	0.40	0.059	0.065	0.076	0.058	0.061
0.30	0.45	0.062	0.077	0.074	0.066	0.073
	0.50	0.072	0.073	0.077	0.091	0.077
	0.55	0.070	0.058	0.078	0.074	0.069
	0.60	0.063	0.074	0.079	0.077	0.065
0.50	0.65	0.047	0.061	0.078	0.070	0.064
	0.70	0.061	0.073	0.070	0.062	0.084
	0.75	0.054	0.073	0.069	0.071	0.055
	0.80	0.073	0.070	0.081	0.051	0.065

Censored rates	Difference in cure rates*	Sample size
Censored rates	Difference in cure rates*	200	400	600	800	1000
0.30	0.10	0.157	0.294	0.417	0.495	0.592
	0.15	0.267	0.550	0.710	0.819	0.885
	0.20	0.367	0.713	0.878	0.949	0.978
	0.25	0.588	0.899	0.982	0.996	0.998
	0.30	0.909	0.996	1.000	1.000	1.000
0.50	0.10	0.147	0.275	0.342	0.442	0.511
	0.15	0.259	0.490	0.638	0.763	0.839
	0.20	0.311	0.671	0.850	0.942	0.981
	0.25	0.530	0.831	0.945	0.985	0.996
	0.30	0.728	0.948	0.985	0.991	0.997
0.70	0.10	0.163	0.248	0.345	0.428	0.487
	0.15	0.254	0.486	0.644	0.752	0.833
	0.20	0.312	0.677	0.867	0.942	0.973
	0.25	0.308	0.712	0.913	0.981	0.989
	0.30	0.629	0.921	0.985	0.994	0.999