result, in step 5 of the estimation procedure, apart from computing the mediator and treatment weights, one needs to additionally derive the censoring weight. More precisely, the weight for the $i^{th}$ individual at visit $k$ is now $w_i^{ttm}(a,a^*)\cdot w_i^{med}(k,a)\cdot w_i^{cen}(k,a)$, where the subscript *cen* denotes censoring, i.e., $$w_i^{cen}(k,a)=\frac{1}{\prod_{s: 0\le s \le t_k} \left[1- \hat{\lambda}_C(s|T_{i}>s, \overline{m}_{s ,c,i}, \overline{l}_{s,c,i},l_{0,i},a)\right]}$$ while $w_i^{ttm}(a,a^*)$ and $w_i^{med}(k,a,a^*)$ are computed as above. If a proportional hazard censoring model as (6) is fitted, the baseline censoring hazard $\lambda_{0C}(t)$ and $\lambda'_{0C}(t)$ at time $t$ can be estimated by the standard Breslow estimator. Once the individual weights are computed, the natural effect cause-specific proprotional hazard model (1) and (2) can be fitted using these weights and the confidence intervals for the estimates can be derived via the nonparametric bootstrap, as described above.

Illustrating example
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We illustrate the proposed approach on the ELSA data. In this ongoing study, the first contact with the participants was in 2002/03 (wave 1). These participants were then followed up biennially, with measures collected via computer-assisted face-to-face interview and self-completion questionnaires. For this illustration, the data are available until one year after the last wave in 2016/17. As stated above, the question of interest here 