Distributed Lag Neural Additive Models

Summary

The paper introduces Distributed Lag Neural Additive Models (DLNAMs), which replace the prespecified spline cross-basis of Distributed Lag Non-linear Models (DLNMs) with learned neural components inside an additive predictor, while preserving interpretable exposure–lag surfaces and cumulative summaries. Each component combines multivariate exp-centered unit (ExU) input layers, Mish smooth activations, a learned mixture of subnetworks, ensembling across initializations, and pointwise uncertainty from a conditional last-layer Laplace approximation plus between-member ensemble variation. In simulations spanning four data-generating processes (R=200, n=5000, Poisson outcomes, lags 0–14), DLNAM achieved the lowest cumulative RMSE on the three nonseparable DGPs and the smallest across-DGP error range, while the treed DLNM was best on the separable DGP 1; DLNAM was closest to nominal 95% coverage in 11 of 12 DGP-by-region cells, although no estimator attained nominal coverage anywhere. Ablations (R=50) show that ExU, mixture, and smooth activations each materially affect recovery. A joint simulation with four active exposures plus a correlated null exposure showed near-unity degradation ratios and low null leakage. Applications to Chicago temperature–mortality data and a 348,565-child DHS/MIS malaria analysis recovered established patterns. Limitations include below-nominal coverage throughout, uncertainty conditional on the learned representation, a likelihood-mismatched treed comparator, and a malaria comparison that changes adjustment representation between methods.