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Regular revisions of the classification of diseases and the consequent disruptions of mortality series are well-known issues in long-term cause-of-death analysis. Given basic assumptions and medical knowledge about possible exchanges across causes of death in the revision years, redistribution of counts of causes of death into a new classification can be viewed as a constrained optimization problem. Penalized likelihood within a quadratic programming framework allows estimation of exchanges that vary smoothly over age groups. The approach is illustrated using both German data on malignant neoplasms and French data on heart diseases.

Representing the conditional mean in Poisson regression directly as a sum of smooth components can provide a realistic model of the data generating process. Here, we present an approach that allows such an additive decomposition of the expected values of counts. The model can be formulated as a penalized composite link model and can, therefore, be estimated by a modified iteratively weighted least-squares algorithm. Further shape constraints on the smooth additive components can be enforced by additional penalties, and the model is extended to two dimensions. We present two applications that motivate the model and demonstrate the versatility of the approach.

In many applications data can be interpreted as indirect observations of a latent distribution. A typical example is the phenomenon known as digit preference, i.e. the tendency to round outcomes to pleasing digits. The composite link model (CLM) is a useful framework to uncover such latent distributions. Moreover, when applied to data showing digit preferences, this approach allows estimation of the proportions of counts that were transferred to neighbouring digits. As the estimating equations generally are singular or severely ill-conditioned, we impose smoothness assumptions on the latent distribution and penalize the likelihood function. To estimate the misreported proportions, we use a weighted least-squares regression with an added L1 penalty. The optimal smoothing parameters are found by minimizing the Akaike’s information Criterion (AIC). The approach is verified by a simulation study and several applications are presented.