In longitudinal epidemiological studies consisting of a baseline stage and a follow-up stage, observations at the baseline stage may contain a countable proportion of negative responses. The time-to-event outcomes of those observations corresponding to negative responses at baseline can be denoted as zeros, which are excluded from standard survival analysis. Consequently, some important information on these subjects is therefore lost in the analysis. Furthermore, subjects are often clustered within hospitals, communities or health service centers, resulting in correlated observations. The framework of the two-part model has been developed and utilized widely to analyze semi-continuous data or count data with excess zeros, but its application to clustered time-to-event data with clumping at zero remains sparse.A two-part mixed-effects modeling approach was proposed. A logistic mixed-effects regression model was used in the first part to determine factors associated with the prevalence of the baseline event of interest. Parametric frailty models (including Weibull, exponential, log-logistic and log-normal) were used in the second part to assess associations between exposures and time-to-event outcomes. Correlated random effects were incorporated within the two regression models to accommodate the inherent correlation within each clustering unit and the correlation between the two parts. As an illustrative example, the method was applied to exclusive breastfeeding data from a community-based prospective cohort study in Nepal.A significantly positive correlation between the baseline prevalence of exclusive breastfeeding and exclusive breastfeeding duration was confirmed (ρ = 0.67, P < 0.001). The correlated two-part model outperformed the independent two-part model (likelihood ratio test statistic = 8.6, df = 1, P = 0.003).The proposed approach makes full use of all available information at baseline and during the follow-up, compared to the conventional survival analysis. In addition to breastfeeding studies, the method can be applied to other research areas where clustered time-to-event data with clumping at zero arise.