Behaviour change apps can help people maintain healthy lifestyles, however a common challenge for many behaviour change apps is that they lack sufficient engagement strategies to achieve long-term behaviour change. Push notification policies are commonly used within behaviour change apps to maintain engagement over time. There is a growing recognition of the important factors which impact engagement that go beyond the static features of the app alone. Engagement fluctuates within and between users, and users’ varying contextual states, such as their environment, cognitive state or recent individual history, are likely to impact their engagement with the app over time, and in turn the app’s effectiveness. Tailoring the notification policy to support individuals, with considerations to such varying contextual states, may help improve effectiveness. The goal of developing a behaviour change app to be an adaptive, dynamic intervention presents unique statistical and methodological considerations. Such challenges include understanding the causal effect of time-varying interventions and creating an evidence base for developing decision rules to deliver adaptation. A novel trial design, called the Micro-Randomised Trial (MRT), allows for the estimation of the causal effect of a time-varying intervention, and to inform the development of such decision rules. The thesis includes (i) a scoping review of randomised trial designs for the development of behaviour change apps; (ii) through data visualisations, an exploration of patterns of engagement with Drink Less, a behaviour change app which aims to help reduce alcohol consumption, to inform the design of a Micro-Randomised Trial (MRT); (iii) a simulation study to explore the consistency and efficiency of two estimators to estimate the causal marginal near-term effect of the notification on engagement; and (iv) protocol and findings from an Micro-Randomised Trial (MRT), to both understand and inform the optimisation of the notification policy.