Modelling Approaches

Statistical models

Statistical models use mathematical and probabilistic assumptions to describe relationships between the predictor and target variables. ^[1]

Many classical statistical models are relatively interpretable because their parameters can describe how the expected target changes with a predictor, conditional on the other variables in the model. Though it's important to note that these parameters should not be used to claim causal relationships and should be interpreted as associations only. For example, a positive rainfall coefficient may indicate that rainfall is useful for predicting dengue cases. It does not prove that changing rainfall would cause the predicted change in dengue cases. ^[2]

Parametric statistical models usually make assumptions about the outcome distribution, error structure, or relationship between variables. Thus, while utilising these models, it's important to understand and analyse the underlying distribution of the data. For example, when disease case counts are overdispersed (variance is greater than their mean) then, a Negative Binomial Regression may be more appropriate than a Poisson model.

Challenges like high dimensional data, deviations from the assumed distribution, non-linear relationship and multi-collinearity between variables can hinder the usage of these models. Some approaches, such as Generalized Additive Models, regularization, zero-inflated count models can help address specific issues.

Examples include: Poisson Regression, Negative Binomial Regression, Generalized Linear Models, Generalized Additive Models. ^[3]

Machine-learning models

Machine-learning models are data-driven methods that learn the relationship between the predictors and target variables by optimizing an objective function, without requiring the modeller to specify disease-transmission equations.

These models are useful when the relationships between predictors and the target are complex and non-linear or when multiple relevant features are available.

Machine-learning models often need more training data than simpler statistical models. A linear regression model, shallow decision tree, or regularized model may require relatively little data, but deep neural networks generally have higher data and computational requirements.

Interpretability varies across machine-learning models. Tree-based models can provide feature-importance measures ^[4], while neural networks are often more difficult to interpret.

Overfitting related issues can arise when a model learns noise or patterns that are specific to the training data. Hence, time aware validation ^[5], out-of-sample testing, regularization, and evaluation across multiple regions and forecast horizons become important.

Examples include: Random Forest ^[6], XGBoost, Long Short-Term Memory Networks, N-BEATS ^[7].

Foundation time-series models

Foundation time-series models are large pretrained models that use patterns learned from broad time-series datasets and adapt them to the forecasting task of interest. They can then be applied to a new forecasting task with zero-shot or limited task-specific training. ^{[8] [9]}

Foundational models can prove useful in data sparse settings since these can forecast without requiring a new model to be trained from scratch. Although, they do require data for validation and for historical context at inference time. Requirements such as sampling frequency, context length, multivariate inputs, and fine-tuning depend on the specific models.

Foundation models can also have some practical challenges like model size, computational requirements, licensing restrictions, and limited interpretability. Zero-shot performance on general time-series benchmarks should not be treated as evidence of performance for disease forecasting without a specific validation.

Examples include: TimesFM ^[8], Chronos ^[9].