Preditive Models and Health Sciences : a Brief Analysis

Results: Predictive techniques largely evolved in second half of XX century. The development of AR, MA, ARMA, ARIMA and SARIMA models, through Box-Jenkins methodology, constitute a robust conjunct of mechanisms able to help in solution of epidemiological modeling problems, mainly in Health Sciences, once it allows to evaluate individual characteristics of living beings and its correlation with pathologies in the same space-time. Nevertheless, AR, MA and ARMA does not have tendency in seasonality, which weakens the analysis.


Introduction
There are reports since Ancient Egypt about infectious diseases course and their catastrophic effects due the precarious medicine that was practiced and the low sanitary conditions [1,2].In modern society, epidemics like Spanish Flu, smallpox and malaria were responsible for the death of millions of infected [3,4], causing several economic and social disorders.
Aiming to analyze the course of diseases in order to execute a conscious management of them and a diminishment of morbimortality indexes, several methodologies are being developed all over the world, mainly observational epidemiologic studies, once, differently from experimental studies, they are not limited by ethical and economic issues [5].
The epidemiological approach by time series is a rising methodology applied in studies about health [6].A sequence of observations registered in an ordinated way, following regular and successive interval of instants, characterizes a time series [7], which has as main objective to comprehend the course of analyzed variable in order to allow the elaboration of predictive models that can support the development of public health actions [8].
In a general way, the predictive models largely evolved in second half of XX century, and they are utilized in several fields, like economy [9], environment [10] and in technology areas [11].In health sciences, they support the understanding about epidemiologic course of diseases and they are capable to provide alert concerning future episodes of infirmities like tuberculosis [12], hepatitis [13], dengue [14], typhoid fever [8], for instance.

Results
Autoregressive models are those models in which the present value of the variable addressed depends only on the past values, added the white noise (characterized as unpredictable, independent, and impartial terms) [15,16].Formula 01 describes AR models.The Moving Average models (MA) (Formula 02) surge after the analysis of the correlation among white noises of analyzed series [17].The union of AR and MA models originate the Autoregressive Moving Average models (ARMA) (Formula 03), largely studied in last 40 years by specialists in time series, mainly in areas like Econometry.Nevertheless, like AR and MA models, ARMA model is only utilized to modulate stationary time series, defined as those in which the values randomly occur through a constant average.In other words, they do not have tendency nor seasonality [18].
3 AR and ARMA models were utilized to monitor the dynamics of SARS in China.In this case, the time series were built through the number of new suspected cases, notified by Chinese government [19].However, the most of the real time series that describes the epidemiological course of diseases is not stationary and, thus, it cannot be modulated by processes presented here.To do so, simple techniques capable to transform nonstationary series in stationary ones were developed, and the differentiation form is one of the most utilized [17].
The union of stationary series through differencing steps and ARMA models originate ARIMA models 1 , robust methodology capable to modulate great part of time series due to its adaptive capacity.ARIMA models evolve to seasonal ARIMA (SARIMA) when exists the need to add seasonal course [20].The incorporation of seasonality is extremely relevant once the incidence of certain diseases suffers seasonal temporal variation: e.g., Hand-Foot-Mouth Disease [21], respiratory syncytial [22] and Dengue [14].
One of the reasons to the popularization of this family of models was the development of a methodologic procedure well stablished, known as Box-Jenkins (1976) [23], iterative process made of three phases [24]: 1. Identification: characteristics and statistics of time series are analyzed in a way to relate them with a specific model; 2. Estimation: autoregressive and moving average parameters of each model are estimated through the available data; 3. Diagnostic: the proposal models and their residues are examined to verify their adequacy to the analyzed phenomenon.Further aforementioned models, the use of Artificial Neural Networks (ANN) (RNA) [25,26], and of Copulas Formalism [27] also conquered space among predictive techniques.The last model is conceived as one of the most advanced model used in researches involving predictive modelling.
ANN are computational models based on cerebral biology that can simulate neuronal physiology [28].They are capable to perform complexes calculus and, so, provide prevision diagnosis.Regarding Epidemiology, ANN are extremely relevant, once they have the capacity to adequate their analysis to different contexts inside health-disease process.In a study performed in China, the authors could, through ANN, select a female group with high risk of development of breast mama cancer in order to be submitted to mammography, once the performance of mammography in all China female population could bring elevated costs to the government [29].
Comparative studies demonstrated a tender superiority in ANN models compared to other models, as the Logistic Regression (LR), more common on [30], and the Proportional Hazards Cox models [31].
Nevertheless, analyzing the number of studies published in PubMed, the total of works utilizing neuronal network ("artificial neural network model", 9.288) is still much lower than the total of studies performed with Logistic Regression models ("logistic regression model", 48.313).
The Copulas Formalism arises from the idea that statistically, in relation to its accuracy and efficiency, the union of predictive models is superior to the use of simple models.
Regarding Box-Jenkins methodology, the number of published works ("Box-Jenkins model", 110) is much lower, especially when comparative studies are searched among the other model families.Referred to Formalism of Copulas study, there are no PubMed published work, which characterizes a scientific gap in medical sciences.This creates a barrier to bolder studies, which results can be more trustworthy.

Conclusions
These models have extreme relevance to epidemiology and, subsequently, to Public Health [32], once they allow to evaluate the individual characteristics of living beings and its correlation with pathologies in a same space-time, similarly as in the case of the study about epidemiological course of Dengue in Campinas city, Brazilian southeast [33].Therefore, predictive models gain more meaning in the ability to reliably correlate two health events, rather than by their mere calculation, showing their applicability and necessity.
Thus, to predict the natural history of endemic/ epidemic and its health-disease processes in a determined population, measuring its aggravations and mapping its determinants is a sine que non condition to its adequate management in Public Health context and in adoption of affirmative measures that aims health promotion.