Package '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))

---

Bootstrap estimates of the output in pis.fit

Description

This function creates bootstrap estimates of the output of pis.fit by creating bootstrap samples

Usage

pis.fit.boots(data,postinfect=c("LN","WB","GM"),theta,n.boots=1000,collective=100)

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	Text input only and it is an R expression to be evaluated (i.e. eval) so as to create initial values used in optim. The reason behind this is to allow random numbers as the initial values in optimisation. See Examples.
n.boots	The number of bootstrap samples.
collective	The number of bootstrap samples to be estimated at once as the estimation process uses the apply function.

Value

Same as those in pis.fit.

Author(s)

Char Leung

See Also

pis.fit

Examples

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.boots(data,"LN",theta="c(runif(1,2,3),runif(1,0,1))",n.boots=20,collective=15)

---