The time spent in dependence and the type of care an elderly receives are the two main cost drivers of long-term care (LTC). We aim to provide a better understanding of the duration of care by using a comprehensive social insurance dataset covering the LTC needs in Switzerland over a 20-years-period and including 230 000 observations on dependent elderly. First, using the framework of survival analysis, we calculate Kaplan-Meier estimates for the care duration and derive the main explaining factors through econometric models when care is received at home and in an institution. Retaining only significant covariates, the final accelerated failure time models allow us to predict the duration for different profiles of elderly along their age, gender, region of residence, type of household composition, acuity level and pre-retirement income. Second, we study the interaction of care durations when care is provided at home and in an institution. While our data supports that for short at-home care durations the time spent in institutional care is reduced, we find that both types of care are non-substitutes when the time spent at home has been longer. Under the latter regime, the time spent in institutional care remains at a constant level. Finally, given the longevity improvements over the period of observation, we analyze the impact of living longer on the time spent in dependence. Our results show that while the mean age at entry in dependence grows, the overall care duration does not significantly change. Given the expected increasing number of elderly in most developed countries, our study is relevant for government planning, budgeting social insurance schemes, estimating personal savings needs and calculating private insurance premiums.