Forecasting epidemic: Time series modelling

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Forecasting epidemic Time series modelling

• Dr Cho-Min-Naing
• Medical Officer (Malaria/DHF)
• The National Vector Borne Diseases Control
  Project, Yangon, Insein PO, Myanmar
  
• Email

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Learning objectives At the end of this
session,

• 1. the participant should understand
  forecasting methods.
• 2. the participant should know concepts behind
  forecasting models.

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Performance objectives 1. the participant
should be able to develop times series model for
forecasting epidemic.
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I. Background

• Unaided, subjective judgements to warn of
  forthcoming events and changes are not as
  accurate and effective as systematic, explicit
  approaches to forecasting.
• This does not mean there is error free
  forecasts. This does mean explicit systematic
  forecasting approaching can provide substantial
  benefits when used properly as all types and
  forms of forecasting techniques are made
  available within the existing data.

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II. Forecasting methods There are three major
categories as stated below.

• 1. Judgmental method
• 2. Quantitative method
• 3. Technological method

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1. Judgmental method Forecasts are made as
individual judgements or by committee agreement
or decisions.
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2. Quantitative method To know what will
happen, but not why something happens.There are
three subcategories of this method2.1 Times
series methods Seek to identify historical
patterns (using time as a reference) and then
forecast using a time-based extrapolation of
those patterns.2.2 Explanatory methods Seek to
identify the relationships that lead to observed
outcomes in the past and then forecast by
applying those relationships to the
future.2.3 Monitoring methods Seek to identify
changes in patterns and relationships.
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• 3. Technological method
• Address long-term issues of a technological,
  societal, political or economic nature.
• 3.1 Extrapolative methods using historical
  patterns and relationships as a basic for
  forecasts
• 3.2 Analogy-based methods using historical and
  other analogies to make forecasts
• 3.3 Expert-based methods
• 3.4 Normative-based methods using objectives,
  goals, and desired outcomes as a basic for
  forecasting, thereby influencing future events.

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• III. Selection points for the appropriate
  forecasting techniques.
• When we have to concern with application of
  forecasting in our decision making, we need to
  iterate the importance of selecting the
  appropriate forecasting techniques. In this
  context, there are six points that play an
  important role in determining the requirements
  for an appropriate technique.
• 1.Time horizon Generally, time horizon can be
  divided into short term (1 to 3 months) immediate
  term (less than 1 month), medium term (3 months
  to 2 years), and long term (2 years or more). The
  exact length of time used to classify these four
  categories is subject to vary by organization and
  situation.

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III. Selection points for the appropriate
forecasting techniques. (cont.)

• 2. Level of aggregate detail In general, the
  greater the level of detail (and frequency) that
  is required, the greater the need for an
  automated forecasting procedure, and vice versa.
• 3. Number of items The larger the number of
  items involved (all other things being equal),
  the more accurate the forecasts.
• 4. Control versus planning In control,
  management by except is the general procedure.
  Thus, a forecasting method in such situation
  should be able to recognize changes in basic
  patterns or relationships at an early stage. On
  the planning side, it is generally assumed that
  the existing patterns will continue in the
  future, the major emphasis is on identifying
  those patterns and extrapolating them into
  future.

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III. Selection points for the appropriate
forecasting techniques. (cont.)

• 5. Constancy Forecasting a situation that is
  constant over time is very different from
  forecasting one that is in a state of flux. In
  the stable situation a quantitative forecasting
  method can be adopted and checked periodically to
  reconfirm its appropriateness. In changing
  circumstances, what is needed is a method that
  can adopt continually to reflect the most recent
  results and the latest information.
• 6. Existing planning procedure The greater the
  competition (all other things being equal), the
  more difficult to forecast. Based on the outcomes
  of forecasting models, there is built in
  resistance to change in any organization. The
  change can be made in a stepwise manner, rather
  than all at once.

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IV. Concepts behind the times series
analysisIn man, the conflict is what is
desired and what should be desired. In the
animal, the conflict is what is and what is
desired.Rabindranath Tagore, Personality What
is art?
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• Time series forecasting treats the system as
  black box and makes no attempt to discover the
  factors affecting its behavior. It explains only
  what will happen, but not why something happens.
  The general formula for the time series model is
• Actual pattern randomness
• The common goal in the application of forecasting
  techniques is to minimize these deviations or
  errors in the forecast. The errors are defined as
  the differences between the actual value and what
  was predicted.

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• V. The decomposition method
• We will selectively present the decomposition
  method, assuming that the data can be broken down
  into the various components and a forecast
  obtained for each component.
• Advantage 1. The simplicity of the procedures
• 2. Ease for computational
  procedures
• 3. The minimal start-up time
• 4. Accuracy especially for short-term
  forecasting
• Disadvantage Not having sound statistical theory
  behind the method
• Times series model can basically be classified
  into two types additive model and multiplicative
  model.

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• The forecast for Y in the year t is generally
  written as
• Yt f (Trt, Snt, Clt, ?t )
• Y forecast y
• f function
• Tr trend
• Sn seasonal variation
• Cl cycle
• ? error
• t the time period
  being examined (t 1, 2, i ).

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• Additive model
• 1. We assume that the data is the sum of the time
  series components.
• Yt Trt Snt Clt
• 2. If the data do not contain one of the
  components (e.g., cycle) the value for that
  missing component is zero. Suppose there is no
  cycle, then
• Yt Trt Snt t
• 3. The seasonal component is independent of
  trend, and thus magnitude of the seasonal swing
  is constant over time.

• Multiplicative model
• 1. We assume that the data is
• the product of the various components.
• Yt Trt Snt Clt ?t
• 2. If trend, seasonal variation, or cycle is
  missing, then the value
• is assumed to be 1.
• Suppose there is no cycle, then
• Yt Trt Snt t
• 3. The seasonal factor of multiplicative model is
  a proportion (ratio) to the trends, and thus the
  magnitude of the seasonal swing increases or
  decreases according to the behaviour of trend.

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VI. Case study Quarterly malaria
cases of a Township in Myanmar between 1984-1992
is shown in Table 1. Using the multiplicative
decomposition method, a) calculate the centered
moving average for the time series data.b) find
the equation to model the linear trend.c)
estimate the seasonal factors.d) calculate the
final forecast values over the estimation
period.e) discuss the model.
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Objectives of modelling 1) to monitor the
malaria situation in the study area and forecast
with modelling 2) to detect seasonal
transmission patterns in the distribution of
malaria in the study area
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Methods1. This is a
documentary study using time series data covering
1984 to 1992. 2. The dependent variable was the
incidence of malaria occurring during a given
time including both out-patient and in-patient
malaria cases.3. For a starting point, we
demonstrated a simple, two-variable regression
model using the independent variable, time
factor.4. For the centred moving average, we
computed a four-period moving centred average.5.
The data were processed using MINITAB release
11.12.
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ResultsThe output for MINITAB program
illustrating seasonal indices and centred moving
average. Times series (multiplicative
decomposition method)Seasonal Indices Period
Index 1 1.18483 2 0.309150 3
0.738706 4 1.76732Accuracy of
ModelMAPE 494 MAD 234
MSD 101789
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Linear regression model (simple, two-variable
model) in MINITABThe regression equation isY
21 10.9 XPredictor Coef StDev
T P Constant 21.1
110.5 0.19 0.850 X
10.932 5.209 2.10 0.043S
324.7 R-Sq 11.5 R-Sq(adj) 8.9
Dependent variable quarterly malaria cases
Independent variable time
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Evaluating the modelBefore completing
the analysis, diagnostic tests taking account of
statistical pathology are to be investigated.
Graphing the actual values with the predicted
values closeness of the differences?
see Figure 1Graphing the residual Checked for
a normal distribution. T-test for slope, F test,
and Durbin-Watsin Are they greater than their
tabled values (alpha 0.05)?. Further details
are available in standard texts (see references).
An example, see Cho-Min-Naing et al (2000)
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Discussion 1.Epidemic of
malaria What? 1.1 Periodical rapid and
great increase in malaria morbidity and perhaps
mortality, reaching levels above local average
endemicity.1.2 A rapid increase in malaria
morbidity and mortality in a given population
(independent of seasonal variations) which
clearly surpasses.1.3 The usual levels, or
the appearance of the infection in an area where
it was not known before.A sharp increase of the
incidence of malaria among a population in which
disease was unknown.
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Points to ponder1. Among diverse
factors, the selection of independent variables
should be judiciously based on theoretical
considerations. 2. It is worth emphasizing that
the simple, two-variable regression model is
limited in information. 3. The preferred
approach is to perform regression model for more
than one independent Variable. That is,
multiple regression analysis It allows the
investigator to assess the separate effects of
several unconfounded independent variables on a
single dependent variable.
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A cautionary noteFor real progress, the
mathematical modeller as well as the
epidemiologist must have mud on his boots.
Bradley,1982.
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References1. Armitage P, Berry
G. Automatic selection procedures and
colinearity. InStatistical Methods in Medical
Research. 3rd ed. Blackwell Scientific
Publications, Oxford. 1994 321-323.2. Centred
for Health Economics, Chulalongkorn University,
Bangkok, Thailand. Lecture Notes on Econometrics.
(1995/96) (unpublished) 3. Doti JL, Adibi E.
Identifying and correcting econometric problems.
In Econometric Analysis An Application
Approach. Prentice-Hall, Inc, New Jersey. 1987
203-265.
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References (cont)4. Foster
DP, Stine RA, Waterman RP. Summary regression
case. InBusiness Analysis Using Regression A
Case Book. Springer-Verlag New York, Inc. 1998
227.5. Gujarati DN. Test of specification
errors. In Basic Econometric. 3rd ed.
Mcgraw-Hill, Inc. Singapore. 1995461.6.
Kleinbaum DG, Kupper LL, Muller KE. Regression
diagnostics. In Applied Regression Analysis and
Other Multivariable Methods. 2nd ed. PWS-KENT
publishing Company. Boston. 1988 181-225.7.
Roll Back Malaria. Malaria Early Warning
Systems. WHO/CDS/RBM/2001.32. 2001