Event history studies based on disease clinic data often face several complications. Specifically, patients may visit the clinic irregularly, and the intermittent observation times could depend on disease-related variables; this can cause a failure time outcome to be dependently interval-censored. We propose a weighted estimating function approach so that dependently interval-censored failure times can be analysed consistently. A so-called inverse-intensity-of-visit weight is employed to adjust for the informative inspection times. Left truncation of failure times can also be easily handled. Additionally, in observational studies, treatment assignments are typically non-randomized and may depend on disease-related variables. An inverse-probability-of-treatment weight is applied to estimating functions to further adjust for measured confounders. Simulation studies are conducted to examine the finite sample performances of the proposed estimators. Finally, the Toronto Psoriatic Arthritis Cohort Study is used for illustration. Copyright (C) 2017 John Wiley & Sons, Ltd.