Adverse events in single-arm clinical trials with non-fatal time-to-event efficacy endpoint: from clinical questions to methods for statistical analysis

Table 1 Simulated example data of \(N=300\) subjects and estimators

j	\(t_j\)	\(n_j\)	\(d_{jAE}\)	\(d_{jRL}\)	\(\hat{S}(t_j)\)	\(\hat{h}_{AE}(t_j)\)	\(\hat{h}_{AE}(t_j)\hat{S}(t_j-)\)	\(\hat{CI}_{AE}(t_j)\)	\(\hat{AN}_{AE}(t_j)\)	\(\hat{KM}_{AE}(t_j)\)
1	0.0	300	29	75	0.653	0.097	0.097	0.097	0.097	0.097
2	0.1	196	21	60	0.383	0.107	0.070	0.167	0.204	0.194
3	0.2	115	11	39	0.217	0.096	0.037	0.204	0.300	0.271
4	0.3	65	4	12	0.163	0.062	0.013	0.217	0.362	0.316
5	0.4	49	6	7	0.120	0.122	0.020	0.237	0.484	0.400
6	0.5	36	1	10	0.083	0.028	0.003	0.240	0.512	0.416
7	0.6	25	3	4	0.060	0.120	0.010	0.250	0.632	0.486
8	0.7	18	0	3	0.050	0.000	0.000	0.250	0.632	0.486
9	0.8	15	2	2	0.037	0.133	0.007	0.257	0.765	0.555
10	1.0	11	1	3	0.023	0.091	0.003	0.260	0.856	0.595
11	1.1	7	0	2	0.017	0.000	0.000	0.260	0.856	0.595
12	1.2	5	0	2	0.010	0.000	0.000	0.260	0.856	0.595
13	1.3	3	1	1	0.003	0.333	0.003	0.263	1.189	0.730
14	2.1	1	1	0	0.000	1.000	0.003	0.266	2.189	1.000

\(t_j\) are the distinct failure times measured in years; \(n_j\) is the number of patients at risk at time \(t_j\); \(d_{jAE}\) and \(d_{jRL}\) are the number of patients developing AE or relapse at time \(t_j\), respectively; \(\hat{S}(t_j)\) is the survival function at time \(t_j\), estimated according to KM estimator on failures due to AE or relapse; \(\hat{h}_{AE}(t_j)\) corresponds to the instantaneous rate of AE and it is the non-parametric ML estimator of the \(CSH_{AE}(t)\); \(\hat{h}_{AE}(t_j)\hat{S}(t_j-)\) is the product of instantaneous rate of AE with the KM estimator of the proportion of patients free from treatment failure up to time \(t_j-\); \(\hat{CI}_{AE}(t_j)\) is the AJ estimator of \(CI_{AE}(t)\) of AE; \(\hat{AN}_{AE}(t_j)\) and \(\hat{KM}_{AE}(t_j)\) are the AN and KM estimates of the \(CSH_{AE}(t)\)

ISSN: 1471-2288