pis.fit {postinfectious}

Estimating the incubation period distribution of a 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 \theta_{0} and \theta 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_{-\infty}^{\infty}f_0(S_0,\theta_0)f(S_0+X,\theta)dS_0

where f_0 and f are the probability density function of S_{0} and S, respectively. \theta 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))