Real-time predictions of the final size and the turning point at the end of the epidemic, the incidence and the cumulative number of cases in future observations.

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Description

This function provides real-time predictions of the final size and the turning point at the end of the epidemic for each built-in model and model averaged, as well as the incidence and the cumulative number of cases in future observations. Also this function, when all the built-in models are used, gives the AIC of each model, the model averaged weights and predicted incidence and cumulative cases.

Usage

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## Object of the S3 class dengue
allmodelpredict(inc,time,pred,start=NULL,model)

Arguments

inc,time

Vector of equal length specifying incidence (number of reported cases per time unit) and time interval (from the start of outbreak).

pred

Number of observation in which the incidence and the cumulative number of cases will be predicted.

start

A list with the starting values of the model to be used for fitting the data. If model="all" the imput must be a list of a list with the starting values of Richards, 3P logistic, Sigmoid Emax, Gompertz, Weibull and 5P logistic model parameters. By default, the initial values are provided by self-starting functions (see argument start in allmodels function).

model

The nonlinear model to be used for fitting the data. Built-in models are "Richards"", "Logistic3P", "SigmEmax", "Gompertz", "Weibull" and "Logistic5P" (see argument model in allmodels function). If model = "all" the parameter estimate will be done taking into account all built-in models via model averaging.

Value

An object with the parameter estimate for each built-in model and model averaged estimate for final size and turning point of outbreak. It is a list:

Incidence

All the available incidences

Time

All the available time points

PredTime

Period of time for which the prediction is required

AIC

The AIC for each built-in model and model averaged

tTable

A table with parameter estimates and t test. It is not available when all the model are used.

Weights

Model averaged weights. It is not availabe when is used only one built-in model

FinalSize

95% confidence interval and point estimate of the final size of outbreak for each built-in model and model averaged estimate

TurningPoint

95% confidence interval and point estimate of the turning point of outbreak for each built-in model and model averaged estimate

Predict

Predicted cumulative cases for each built-in model

PredictMA

Predicted cumulative cases for model averaged

PredInc

Predicted incidence for each built-in model

PredMAInc

Predicted incidence for model averaged

function.type

Name of the function

model.type

models used to estimate

Generic functions such as plot and summary have methods to show the results of the fit

Author(s)

Carlos Sebrango, Lizet Sanchez, Ziv Shkedy

References

K. Burnham, D. R. Anderson, Model Selection and Multimodel Inference: A Practical Information - theoretic Approach, 2nd Edition, Springer-Verlag, New York, 2002.
G. Claeskens, N. L. Hjort, Model selection and model averaging, Cambridge University Press, 2008.

Examples

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## Not run: 
## (data example 1)
data("dengueoutbreak1")

## Using only the information until time point 20
## Prediction of the final size and turning point at the end of epidemic,  
## the incidence and the cumulative number of cases in the observation  
## number 36 using only the Richards model
allmodelpredict(dengueoutbreak1$Incidence[1:20],dengueoutbreak1$Time[1:20],36, 
model = "Richards")

## Using only the information until time point 22
## Now using all built-in model, Prediction of the final size and turning point  
## at the end of epidemic, the incidence and the cumulative number of cases 
## in the observation number 30 
allmodelpredict(dengueoutbreak1$Incidence[1:22],dengueoutbreak1$Time[1:22],30, 
model = "all")
## End(Not run)

## (data example 2)
data("dengueoutbreak2")
## Using only the information until time point 18, Prediction of the final size and  
## turning point at the end of epidemic, the incidence and the cumulative number  
## of cases in the observation number 31 using only the 3P logistic model

allmodelpredict(dengueoutbreak2$Incidence[1:18],dengueoutbreak2$Time[1:18],31,
model = "logistic3P")

## Not run: 
## Using only the information until time point 20
## Now using all built-in model, Prediction of the final size and turning point 
## at the end of  epidemic, the incidence and the cumulative number of cases  
## in the observation number 30
allmodelpredict(dengueoutbreak2$Incidence[1:20],dengueoutbreak2$Time[1:20],34, 
model = "all")
## End(Not run)