pis.fit: Estimating the incubation period distribution of a...

In postinfectious: Estimating the Incubation Period Distribution of Post-Infectious Syndrome

Description

This function estimates the incubation period distribution of a post-infectious syndrome with maximum likelihood estimation. The incubation period distribution of the antecedent infection and the post-infectious syndrome are allowed to be lognormal ("LN"), Weibull ("WB") or gamma ("GM") distributed. The data set is allowed to have cases with the actecedent diseases whose incuation periods come from different distributions (see Examples).

Usage

pis.fit(data,postinfect=c("LN","WB","GM"),theta)

Arguments

data	A data.frame containing at least 4 columns. The first two columns represent (1) the time between the symptom onset of the antecedent infection and post-infectious syndrome and (2) the incubation period distribution of the antecedent infection (only "LN", "WB" and "GM"). The last two columns refer to the parameters of the incubation period distribution of the antecedent infection; for "LN", they are meanlog and sdlog as in dlnorm; for "WB", they are shape and scale as in dweibull; for "GM", they are shape and rate as in dgamma.
postinfect	The incubation period distribution of the post-infectious disease. It can only be "LN", "WB" and "GM".
theta	A vector of two numbers as the initial value for optimisation.

Details

For each observed case, let S_{0} and S be the incubation period of the antecedent infection and post-infectious syndrome, respectively. As the antecedent infection is the antigenic factor of the post-infectious syndrome, they both share the same time of infection exposure. The difference between S_{0} and S, denoted by X, is the time between the two symptom onsets. Also let θ_{0} and θ be the set of the parameters of the distribution of S_{0} and S then the likelihood of such observed case is given by,

\int_{-∞}^{∞}f_0(S_0,θ_0)f(S_0+X,θ)dS_0

where f_0 and f are the probability density function of S_{0} and S, respectively. θ is then estimated by maximising the sum of likelihood of all observed cases.

Value

Parameter	Estimates of the parameters of the incubation period distribution of the post-infectious syndrome.
SE	Standard errors of Parameter
AIC	Akaike Information Criterion.
Convergence	The convergence message of optim
Median	The median incubation period distribution of the post-infectious syndrome.
Theta.initial	Initial values used in optim
Distribution	The Distribution assumed in the estimation, i.e. "LN", "WB" or "GM".

Author(s)

Char Leung

Examples

#generate artificial data
S<-c(56,37,32,7,8,3,5)
S0<-c(2,1,3,1,1,1,3)
X<-S-S0
f0<-c(rep("LN",4),rep("WB",3))
phi<-matrix(c(rep(c(0,1),4),rep(c(1,2),3)),byrow=TRUE,ncol=2)
data<-data.frame(X,f0,phi)
pis.fit(data,"LN",theta=c(2.5,1))

Example output

$Parameter
[1] 2.536181 1.076804

$SE
[1] 0.4176702 0.3025093

$AIC
[1] 60.48329

$Convergence
[1] 0

$Median
[1] 12.63134

$Theta.initial
[1] 2.5 1.0

$Distribution
[1] "LN"

postinfectious documentation built on May 1, 2019, 11:32 p.m.