# Approaches for Dealing with Seasonality in Clinical Prediction Models for Infections
## 2 Related Work  
It is widely accepted that seasonal variations are a common trait of many infectious diseases [1]. As stated in [8], several methods are employed in epidemiological studies to examine the effect of seasonality, including the statistical comparison of two different time periods, geometrical models assuming sinusoidal cyclic patterns, and generalized linear models in which seasonality is included as an extra term. These approaches make it possible to assess the effect of seasonality on the number of cases and identify factors that might be associated with these variations [2; 7].  
When the outcome of the model is to predict a condition regarding a particular patient, a common strategy is to include the season among the possible features to be explored. For example, the season can be included as an additional feature with four possible values (spring, summer, autumn, and winter) in northern and southern countries [9] or two values (dry and wet) in models for countries with subtropical or tropical climates [10]. Another strategy is to build separate models for each season [11], or at least different models for summer and winter [12; 13].  
From a different perspective, we can consider seasonality in clinical data as a particular case of concept drift in a datastream. Datastream mining is a recent research field that is focused on the development of models over huge amounts of online data obtained from sources such as sensors, bank transactions, or social networks [16; 17]. When dealing with datastreams, certain particularities must be considered. For example, it is assumed that the whole stream can neither be stored in memory nor accessed repeatedly, signifying that the algorithms working with it can manage only a limited number of data items at the same time or even that the model must be trained by observing each item only once [18]. Another common assumption is that the datastream is non-stationary, which means that the distribution of the features and/or the target outcomes varies over time [16]. This aspect of data is commonly known as _concept drift_[19; 20; 21], and is an open and fast-growing research topic [22]. This effect often occurs in clinical research, in which the study of clinical models capable of evolving over time, known as dynamic models, is a recent and active topic [23]. A more comprehensive study of the state of the art in these research lines can be found in [16; 22; 23].  
However, problems arise when attempting to apply these approaches to open clinical data in order to validate and share results. First, de-identification policies force the removal of most of the elements from real timestamps when sharing clinical datasets in order to ensure patient privacy [24]. In the case of the MIMIC-III Database [14], which is the public data source used in this work, the date of each patient's admission is randomized, although both the day of the week and the season shown in the original source are maintained. Consequently, approaches that rely on strict temporal ordering of the data cannot be readily applied in such cases. Another challenge is that many of these algorithms are not designed to work with a relatively small number of samples, which is common when working with certain diseases. Furthermore, the need for interpretable models and the effects of high dimensionality and class imbalance are not usually considered in the design and validation of these frameworks.  
In this paper, we propose and evaluate two approaches based on sound strategies from datastream mining that we have adapted to the particular problem of seasonality in open clinical data, as described in the following sections.