Left-censored recurrent event analysis in epidemiological studies: a proposal for when the number of previous episodes is unknown

Table 1 Characteristics of the simulated populations

Episode	Distribution	β₀	Ancillary	HR
1	Weibull	8.109	1	1
2	Weibull	7.927	1	1.20
≥ 3	Weibull	7.745	1	1.44
1	Weibull	8.109	1	1
2	Weibull	7.703	1	1.50
≥ 3	Weibull	7.298	1	2.25
1	Weibull	8.109	1	1
2	Weibull	7.193	1	2.50
≥ 3	Weibull	6.276	1	6.25
1	Log-normal	7.195	1.498	1
2	Log-logistic	6.583	0.924	1.77
≥ 3	Weibull	6.678	0.923	2.53
1	Log-logistic	7.974	0.836	1
2	Weibull	7.109	0.758	3.81
≥ 3	Log-normal	5.853	1.989	7.19
1	Log-normal	8.924	1.545	1
2	Log-normal	6.650	2.399	10.13
≥ 3	Log-normal	6.696	2.246	11.19

Weibull distribution: \(f(t)={\lambda pt}^{p-1}{e}^{-\lambda {t}^p},\lambda ={e}^{-p{\beta}_0}\)
Lognormal distribution: \(f(t)=\frac{1}{t\sigma \sqrt{2\pi }}{e}^{\left[\frac{-1}{2{\sigma}^2}{\left\{\log (t)-\mu \right\}}^2\right]},\mu ={\beta}_0\)
Loglogistic distribution: \(f(t)=\frac{\lambda^{1/\gamma }{t}^{1/\gamma -1}}{\gamma {\left\{1+{\left(\lambda t\right)}^{1/\gamma}\right\}}^2},\lambda ={e}^{-{\beta}_0}\)

ISSN: 1471-2288