FAMES: Federated additive model using piecewise exponential survival data

Introduction In analyses of time-to-event data, clinical characteristics can have non-linear impacts on survival outcomes, and understanding this dynamic behavior is crucial for producing real-world evidence (RWE). Nonetheless, estimating these dynamic effects is inherently challenging when utilizing real-world data (RWD), especially since sharing individual-level patient data (IPD) is heavily restricted due to regulatory limitations. Additionally, computational difficulties are exacerbated by the high dimensionality, inter-dependency, rarity, sparsity, and scarcity of features. While data augmentation through collaboration across multiple sites might address these challenges, such collaboration is often infeasible and hindered by regulatory measures that protect patient privacy, thereby preventing the sharing of IPD between sites. Objectives To address this challenge, we propose a privacy-preserving regularized algorithm that eliminates the necessity of aggregating any protected health information across sites. This algorithm employs a penalized federated additive model utilizing piecewise exponential survival (FAMES) data and estimates non-linear effects of features while accounting for non-varying confounding effects. The model is flexible and can accommodate both multiple and multivariate smooth effects simultaneously. Methods The proposed model transforms survival data into a piecewise exponential data (PED) structure and casts the semi-parametric optimization problem into a generalized additive modeling framework assuming Poisson distribution. The model uses orthonormal splines to approximate non-linear effects and incorporates L2-norm based penalty terms to control the smoothness and goodness-of-fit of these effects. The algorithm is optimized using site-specific aggregated summary statistics and is solved iteratively through the Newton-Raphson method. Results The model is employed to assess the smooth effects of clinical features, such as age and numeric laboratory values, on overall survival using RWD from approximately 874 newly diagnosed Acute Myeloid Leukemia (AML) patients treated at seven distinct sites in the United States. The model exhibited non-linear smooth effects for lactate dehydrogenase, platelets, and others underscoring their strong association with disease prognosis. The model demonstrates a lossless property, providing estimates of smooth and fixed effects that are comparable to those derived from the pooled PED. Additionally, the inference of parameters for testing the nullity of effects remains consistent. This model is communication-efficient, necessitating roughly twelve rounds of communication across sites. Conclusion We anticipate that this model can facilitate multisite collaboration and enable smaller sites to participate in generating and validating RWE, especially for rare diseases. While the model was applied within the context of AML, it is disease-agnostic and can be implemented in any other clinical context and across various sites globally without losing any generality.