Aplicaciones clínicas

In general, forecasting methods are classified into qualitative and quantitative

methods. In qualitative methods, the forecasts are often made based on the analyst’s

judgement, which relies heavily on the analyst’s intuition and experience. In contrast,

quantitative methods are based on mathematical or statistical models. In this study,

quantitative methods are used since they are commonly used in road safety research.

Commandeur et al. (2013) reviewed a number of time series analyses on national road

safety trends in Europe since the 1980s. Time series models have progressed from

descriptive towards explanatory models, as well as from deterministic towards stochastic

models under the form of structural models. In general, traditional regression models

(linear, generalized linear and non-linear models) are unable to capture the dependencies

inherent in time series data.

2.14.1 Univariate and multivariate methods

There are two types of quantitative forecasting methods: (1) multivariate methods

which includes explanatory factors and (2) univariate methods which exclude explanatory

factors and the forecasts are made based on the values of the response variables. In

multivariate methods, the forecasts of a variable depend, at least partly, on the values of

one or more additional time series variables (predictor or explanatory variables). If the

variables are dependent one way or another, the multivariate forecasts may require the

univariate forecasting methods are merely dependent on the present and past values of

the single series being forecasted, and may be augmented by a time function such as a

linear trend (Chatfield, 2000).

2.14.2 Deterministic and stochastic models

Quantitative models can also be classified as deterministic or stochastic (probabilistic)

models. The relationship between the dependent variable (Y) and the explanatory or

predictor variables (X) of a deterministic model and stochastic model is shown in

Equation (2.1) and Equation (2.2), respectively. Deterministic models are usually used in

the physical sciences since the function f and coefficients β1,… βm are known for certain.

The relationship of Y and X in the social sciences, however, is usually random (stochastic).

It shall be noted that measurement errors as well as the variability of other uncontrolled

variables will introduce stochastic components into the relationship. The error

components are a realization from a certain probability distribution and are generally

termed as ‘noise’. In most cases, the functional form f and the coefficients are unknown

and therefore, they need to be determined from past data. The data are typically presented

in the form of time-ordered sequences, which are known as time series. The statistical

models in which the available observations are used to determine the model

representation are also known as empirical models (Abraham & Ledolter, 2005).

𝑌 = 𝑓(𝑋₁, … , 𝑋_𝑝 ; 𝛽₁, … , 𝛽_𝑚) (2.1)

2.14.3 Microscopic and macroscopic levels

The scope of the forecasts is also critical in road safety research. Most of the studies

in this area fall under the microscopic level, and it can be observed from the literature that

the implementation of road safety policies, geometric characteristics and road elements

has been analysed extensively over the years. The forecasted number of road traffic

casualties at the macroscopic level is usually less accurate and therefore, forecasts made

at the microscopic level are preferable over those at the macroscopic level. There are

various factors which influence the road safety characteristics in a jurisdiction – however,

the lack of reliable data as well as inconsistencies in past research findings indicate that

there are still uncertainties in this area which need to be resolved.

2.14.4 Time series data patterns

There are four general types of time series data patterns: (1) horizontal, (2) trend, (3)

seasonal, and (4) cyclical. A horizontal pattern can be observed when the data

observations fluctuate around a constant level or mean. This pattern indicates that the data

series is stationary in its mean. A trend pattern is apparent when the data observations

increase or decrease over a time period. A cyclical pattern is evident when the

observations increase and decrease erratically within the time period. The cyclical

component is indicated by wavelike fluctuations around the trend. A seasonal pattern

exists when the observations are influenced by seasonal factors. The seasonal component

2.14.5 Models used for analysing and forecasting road traffic casualties

The time series models used to forecast road traffic casualties as presented in the COST

329 (2004) report are listed as follows:

(1) Dynamic univariate models such as deterministic component and ad hoc models,

ARIMA models, structural models, state-space models and autoregressive

Poisson models i.e., based on log-linear transition models.

(2) Explanatory models such as linear and non-linear models, transfer function-noise

models and intervention analysis.

(3) VAR and simultaneous equation models.

The report provides the following conclusions and recommendations regarding the use

of time series models in forecasting road traffic casualties:

(1) Models that are based on yearly or monthly number of accidents or casualties such

as polynomial spline models are not recommended for use as forecasting tools.

ARIMA models may be used for forecasting purposes up to two years.

(2) Models that are based on yearly or monthly vehicle kilometres as a measure of

exposure are suitable for forecasting up to 10 years. Deterministic risk models fall

in this category, and it is preferable that the analyst uses the exponential risk

model with or without interventions. Stochastic risk models, structural models

(Harvey), as well as extended exponential risk models are also suitable for

forecasting up to 10 years.

(3) Models which make use of additional variables such as simple regression models

(mostly of log-linear type) with up to four extra variables can be used for

forecasting up to five years. ARIMAX models with calendar effects and some

(4) Model which make use of medium to large numbers of explanatory variables for

forecasting such as DRAG-type econometric models (e.g. TAG or TRULS) are

suitable for long-term forecasting. Multivariate ARMAX or structural (Harvey)

models are also used for this purpose. However, it shall be noted that multivariate

ARMAX models are only suitable for short-term and medium-term forecasts up

to two years.