With increasing data availability, treatment causal effects can be evaluated across different datasets, both randomized trials and observational studies. Randomized trials isolate the effect of the treatment from that of unwanted (confounding) co-occurring effects. But they may be applied to limited populations, and thus lack external validity. On the other hand, large observational samples are often more representative of the target population but can conflate confounding effects with the treatment of interest. In this work, we review the growing literature on methods for causal inference on combined randomized trial and observational studies, striving for the best of both worlds. We first discuss identification and estimation methods that improve generalizability of randomized controlled trials (RCTs) using the representativeness of observational data. Classical estimators include weighting, difference between conditional outcome models, and double robust estimators. We then discuss methods that combine RCTs and observational data to improve the (conditional) average treatment effect estimation, handling possible unmeasured confounding in the observational data. We also connect and contrast works developed in both the potential outcomes framework and the structural causal models framework. This work is motivated by a large prospective database counting about over 20,000 severely traumatized patients in France and a multi-centered international randomized clinical trial studying the effect of tranexamic acid administration on mortality among patients with traumatic brain injury. The former is complex in the sense that it presents a multi-level and heterogeneous structure and contains large fractions of missing values, the latter contains a more homogeneous and restrictive patient population. Based on these two databases we are interested in assessing the external and internal validity of both studies. This is a joint work with Bénédicte Colnet, Gaël Varoquaux, Jean-Philippe Vert, Julie Josse, Shu Yang and others.

Broken-heart syndrome is the most common form of short-term dependence, inducing a temporary increase in an individual’s force of mortality upon the occurrence of extreme events, such as the loss of a spouse. Socioeconomic influences on bereavement processes allow for the suggestion of variability in the significance of short-term dependence between couples in countries of differing levels of economic development. Motivated by analysis of a Ghanaian data set, we propose a stochastic mortality model of the joint mortality of paired lives and the causal relation between their death times, in a less economically developed country than those considered in existing studies. The paired mortality intensities are assumed to be non-mean-reverting Cox–Ingersoll–Ross processes, reflecting the reduced concentration of the initial loss impact apparent in the data set. The effect of the death on the mortality intensity of the surviving spouse is given by a mean-reverting Ornstein–Uhlenbeck process which captures the subsiding nature of the mortality increase characteristic of broken-heart syndrome. Inclusion of a population wide volatility parameter in the Ornstein–Uhlenbeck bereavement process gives rise to a significant non-diversifiable risk, heightening the importance of the dependence assumption in this case. Applying the model proposed to an insurance pricing problem, we obtain the appropriate premium under consideration of dependence between coupled lives through application of the indifference pricing principle. This is a joint work with Corina Constantinescu and Olivier Menoukeu Pamen.