GoKawiilModel
We recapitulated the formulation of the model and provide a full account of model assumptions and implementation details.
Mathematical formulation
The ALADYNOULLI model represents the probability of disease occurrence for patient i, disease d, at time t via a mixture of probabilities as follows:
$${\pi }_{idt}=\kappa \cdot \mathop{\sum }\limits_{k=1}^{K}{\theta }_{ikt}\cdot {\rm{sigmoid}}({\phi }_{kdt}),$$
where κ is a global calibration parameter, θ ikt represents patient i’s time-varying association with signature k, and ϕ kdt captures the relationship between signature k and disease d over time.
The patient–signature associations θ ikt are parameterized as a softmax function of latent variables λ ikt as:
$${\theta }_{ikt}=\frac{\exp ({\lambda }_{ikt})}{{\sum }_{{k}^{{\prime} }=1}^{K}\exp ({\lambda }_{i{k}^{{\prime} }t})}.$$
The ALADYNOULLI model is specified hierarchically, via distributional assumptions on many of these components, which we refer to as priors.
Indicating by λik the function of time describing the evolution of the latent variable over time for patient i and signature k, we specify this as a Gaussian process:
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