Brands use cookies and device identifiers to link different web visits to the same consumer. However, with increasing demands for privacy, these identifiers are about to be phased out, making identity fragmentation a permanent feature of the online world. Assessing treatment effects via randomized experiments (A/B testing) in such a scenario is challenging because identity fragmentation causes a) users to receive hybrid/mixed treatments, and b) hides the causal link between the historical treatments and the outcome. In this work, we address the problem of estimating treatment effects when a lack of identification leads to incomplete knowledge of historical treatments. This is a challenging problem which has not been addressed in literature yet. We develop a new method called DIET, which can adjust for users being exposed to mixed treatments without the entire history of treatments being available. Our method takes inspiration from the Cox model, and uses a proportional outcome approach under which we prove that one can obtain consistent estimates of treatment effects even under identity fragmentation. Our experiments, on one simulated and two real datasets, show that our method leads to up to 20% reduction in error and 25% reduction in bias over the naive estimate.