pandemics (version 0.1.0)

forecasting: Forecasting infections, hospitalizations and deaths in hospital.

Description

Forecasting infections, hospitalizations and deaths in hospital. From estimated two-dimensional rates of infections and hospilizations and estimated hazards of deaths and recoveries, new infections, hospitalizations and deaths are predicted in a forecasting period.

Usage

forecasting(Cval=1, period, RoInf, RoHosp, RoDeath, RoRec,
            Pz, newHz, Hz, Dz, Rz)

Value

Pz.fitted

a vector with the fitted values for the number of infections in the past.

Pz.pred

a vector with the predicted values for the number of infections in the forecasting period.

newHz.fitted

a vector with the fitted values for the number of hospitalizations in the past.

newHz.pred

a vector with the predicted values for the number of hospitalizations in the forecasting period.

Dz.fitted

a vector with the fitted values for the number of deaths in the past.

Dz.pred

a vector with the predicted values for the number of deaths in the forecasting period.

Rz.fitted

a vector with the fitted values for the number of recoveries in the past.

Rz.pred

a vector with the predicted values for the number of recoveries in the forecasting period.

Arguments

Cval

a numeric value with the infection indicator. Default value is Cval=1.

period

an integer value with the number of days to forecast.

RoInf

a matrix with the estimated rate of infection (M-1 times M-1) estimated from M days, evaluating the function rate2Dmiss.

RoHosp

(optional) a matrix with the estimated rate of hospitalization (M times M), obtained evaluating the function rate2Dmiss.

RoDeath

(optional) a matrix with the estimated hazard of deaths (M times M), obtained evaluating the function hazard2Dmiss.

RoRec

(optional) a matrix with the estimated hazard of recoveries (M times M), obtained evaluating the function hazard2Dmiss.

Pz

a vector with the observed (past) number of people tested positive each day (length M).

newHz

a vector with the observed number of new hospitalizations each day (length M).

Hz

a vector with the observed total number people in hospitals each day (length M).

Dz

a vector with the observed number of deaths each day (length M).

Rz

a vector with the observed number of recoveries each day (length M).

Author

M.L. Gámiz, E. Mammen, M.D. Martínez-Miranda and J.P. Nielsen.

Details

To create estimated rates and hazards for the arguments evaluate the functions hazard2Dmiss and rate2Dmiss. If the argument RoHosp is missing then only infections are predicted. If any of the argument RoDeath or RoRec is missing then deaths (recoveries) are not predicted.

The infection indicator Cval is typically provided by experts. At the more recent observation (t), it indicates whether the future (t+h, h > 0) will be different or equal to the immediate past. If Cval=1 then we can forecast the immediate future based on the immediate past. There might be periods where little is happening (and the indicator might have a tendency to increase slowly) and there might be few but very important change-points where measures (e.g. lock down) are introduced to minimize future infections (and the indicator might drop dramatically in a matter of days). See Gámiz et al. (2024a) for more details and the relationship to the well-known reproduction number.

References

Gámiz, M.L., Mammen, E., Martínez-Miranda, M.D. and Nielsen, J.P. (2024a). Low quality exposure and point processes with a view to the first phase of a pandemic. arXiv:2308.09918.

Gámiz, M.L., Mammen, E., Martínez-Miranda, M.D. and Nielsen, J.P. (2024b). Monitoring a developing pandemic with available data. arXiv:2308.09919.

See Also

hazard2Dmiss, rate2Dmiss

Examples

## Forecasting October 2020 from past data
data('covid')
## We remove the first 56 rows(no data on testing until 13th May)
covid2<-covid[-c(1:56),]
M2<-nrow(covid2)
Hi<-covid2$Hospi
Hi<-Hi[-1]
Ri<-covid2$Recov
Ri<-diff(Ri)
Di<-covid2$Death
Di<-diff(Di)
Pi<-covid2$Posit
M2<-length(Di)
# New hospitalizations are Hi-Ri-Di
newHi<-Hi[-1]-(Hi[-M2]-Ri[-M2]-Di[-M2])
newHi<-as.integer(c(Hi[1],newHi))
newHi[newHi<0]<-0
ddates<-covid2$Date

## 1. First we estimate the death and recovery hazards,
## and the infection and hospitalization rates.
## Estimation using data up to 30-Sep-2020
Ms<-141   # up to 30-Sep

## 1.1. Infection rate
Ei.new<-Pi[1:Ms]
delay<-1;Msd<-Ms-delay
Oi.z<-Ei.new[-(1:delay)]
Ei.z1<-Ei.new[1:Msd];
t.grid<-z.grid<-1:Msd
bs<-t(c(5,10))
RInf<-rate2Dmiss(t.grid,z.grid,Oi.z,Ei.z1,
     bs.grid=bs,cv=FALSE)
RoInf<-RInf$hi.zt

## 1.2. Hospitalization rate
Oi.z<-newHi[1:Ms]
# The exposure are the positives data
Ei.z1<-Pi[1:Ms]
t.grid<-z.grid<-1:Ms
bs<-t(c(150,150))
RHosp<-rate2Dmiss(t.grid,z.grid,Oi.z,Ei.z1,
     bs.grid=bs,cv=FALSE)
RoHosp<-matrix(as.numeric(RHosp$hi.zt),Ms,Ms)

## 1.3. Hazards of deaths and recoveries
Oi1.z<-Di[1:Ms]  # deaths
Oi2.z<-Ri[1:Ms]   # recoveries
Ei.z<-Hi[1:Ms]    # exposure is left as cumulative
t.grid<-z.grid<-1:Ms
bs<-t(c(150,40))
res.h<-hazard2Dmiss(t.grid,z.grid,Oi1.z,Oi2.z,Ei.z,
     bs.grid=bs,cv=FALSE)
RoDeath<-as.matrix(res.h$hi1.zt,Ms,Ms) ## 2D-hazard of deaths
RoRec<-as.matrix(res.h$hi2.zt,Ms,Ms) ## 2D-hazard of recoveries

## 2. Forecasting with a given infection indicator
Cval<-1.5
period<-32  # forecasts up to 1st November, 32 days
fore<-forecasting(Cval,period,RoInf,RoHosp,RoDeath,RoRec,
    Pi[1:Ms],newHi[1:Ms],Hi[1:Ms],Di[1:Ms],Ri[1:Ms])
Hz.pred<-fore$newHz.pred
Pz.pred<-fore$Pz.pred
Dz.pred<-fore$Dz.pred

## 3. Plot forecasts and compare with observed values
## (future values are shown for predictions validation)
Pz.obs<-Pi
Hz.obs<-newHi
Dz.obs<-Di

## Graph with the new infections up to 30-Sep and forecasts
yy<-range(Pz.pred,Pz.obs,na.rm=TRUE)
plot(1:(Ms-1),Pz.obs[3:(Ms+1)],ylab='',xlab='Date of notification',
     main='Forecasts of new positives in October 2020',pch=19,
     ylim=yy,xaxt='n',xlim=c(1,Ms+1+period))
oat<-c(1,17,32,47,62,78,93,109,124,139,154,170)
olab<-ddates[oat]
axis(1,at=oat,labels=olab)
## forecasts start on 30-sep but we only plot from 1-October
points(Ms:(Ms+period-2),Pz.obs[(Ms+2):(Ms+period)],col=1,pch=1)
lines(Ms:(Ms+period-2),Pz.pred[-1],col=2,lty=2,lwd=3)
legend('topleft',c('Data: daily number of new positives until 30-Sep',
    paste('Forecasts with Cval=',round(Cval,2)),
    'True numbers of new positives in October'),
    pch=c(19,NA,1),col=c(1,2,1),lty=c(NA,2,NA),lwd=c(NA,3,NA),bty='n')

## Graph with the new hospitalizations up to 30-Sep and forecasts
ylim1<-range(Hz.pred,Hz.obs[-(1:2)],na.rm=TRUE)
plot(1:(Ms-1),Hz.obs[3:(Ms+1)],ylab='',xlab='Date of admission',
     main='Forecasts of new hospitalizations in October 2020',
     pch=19,
     ylim=ylim1,xaxt='n',xlim=c(1,Ms+1+period))
oat<-c(1,17,32,47,62,78,93,109,124,139,154,170)
olab<-ddates[oat]
axis(1,at=oat,labels=olab)
points(Ms:(Ms+period-2),Hz.obs[(Ms+2):(Ms+period)])
lines(Ms:(Ms+period-2),Hz.pred[-1],col=2,lty=2,lwd=2)
legend('topleft',c('Data: daily number of new hospitalizations until 30-Sep',
    paste('Forecasts with Cval=',round(Cval,2)),
    'True numbers of new hospitalizations in October'),
    pch=c(19,NA,1),col=c(1,2,1),lty=c(NA,2,NA),lwd=c(NA,3,NA),bty='n')


## Graph with deaths up to 30-Sep and forecasts
ylim1<-range(Dz.pred,Dz.obs[-(1:2)],na.rm=TRUE)
plot(1:(Ms-1),Dz.obs[3:(Ms+1)],ylab='',xlab='Date of admission',
     main='Forecasts of deaths in October 2020',
     pch=19,ylim=ylim1,xaxt='n',xlim=c(1,Ms+1+period))
oat<-c(1,17,32,47,62,78,93,109,124,139,154,170)
olab<-ddates[oat]
axis(1,at=oat,labels=olab)
points(Ms:(Ms+period-2),Dz.obs[(Ms+2):(Ms+period)])
lines(Ms:(Ms+period-2),Dz.pred[-1],col=2,lty=2,lwd=2)
legend('topleft',c('Data: daily number of deaths until 30-Sep',
    paste('Forecasts with Cval=',round(Cval,2)),
    'True numbers of deaths in October'),
    pch=c(19,NA,1),col=c(1,2,1),lty=c(NA,2,NA),
    lwd=c(NA,3,NA),bty='n')