The limitations of the two-way fixed effects for the impact evaluation of interventions that occur at different times for each group have meant that ‘staggered interventions’ have been highlighted in recent years in the econometric literature and, more recently, in epidemiology. Although many alternative strategies (such as staggered difference-in-differences) have been proposed, the focus has predominantly been on scenarios in which one or more control groups are available. However, control groups are often unavailable, due to limitations in the available data or because all units eventually receive the intervention. In this context, interrupted time series (ITS) designs can constitute an appropriate alternative. The extent to which common model specifications for ITS analyses are limited in the case of staggered interventions remains an underexplored area in the methodological literature. In this work, we aim to demonstrate that standard ITS model specifications typically yield biased results for staggered interventions and we propose alternative model specifications that were inspired by recent developments in the difference-in-differences literature to propose adapted analytical strategies.