hbrr {hbim}

Calculate expected relative risk or percent protected from Hill model with Bliss Independence

Description

Assuming that the log10 transformed doses are normally distributed, we calculate the expected relative risk (using hbrr) or percent protected (using hbpp) from the Hill model using Bliss Independence. Numeric integration is the default for up to three components for hbrr, while simulation is the default for two or three components for hbpp.

Usage

hbrr(mu, v, a = rep(1, length(mu)), simulate = FALSE, nsim = 10^4, ...)
hbpp(mu, v, a = rep(1, length(mu)), rp = 0.1, simulate = FALSE, nsim = 10^5, ...)

Arguments

mu

mean vector of the log10 dose

v

variance matrix of the log10 dose

a

vector of slope parameters in the Hill model, one for each component

simulate

estimation by simulation (TRUE) or numeric integration (FALSE)

nsim

number of simulations, ignored if simulate=FALSE

rp

protection bound, an individual is protected if relative risk is greater than rp

...

additional parameters to pass to the integrate function

Details

Although the package adapt can do multidimensional integration, we have written specific functions to do this for up to 3 dimensions. This allows faster and more accurate integration. The integration is done by repeated calls to the integrate function. The functions which do the actual integration or simulation are internal functions which are not intended to be called by the user. These internal functions are: for hbrr, when simulate=FALSE, the function calls one of either hbrr.integrate1, hbrr.integrate2, hbrr.integrate2.rhoeq1, hbrr.integrate3, or hbrr.integrate3.rhoeq1 (for 1,2, or 3 component, with or without rho=1, taken from the size of the mu vector and dimension of the v matrix) and when simulation=TRUE it calls hbrr.simulate. Similar functions exist for hbpp; however, the hbpp.integrate2 and hbpp.integrate3 may have problems because of the discontinuity in the integration function. That is why for two or three component models hbpp.simulate is used by default.

Value

a numeric value of the expected relative risk or percent protected.

Author(s)

M.P. Fay

References

Saul A, Fay MP (2007). Human Immunity and the Design of Multi-Component, Single Target Vaccines. PLoS ONE 2(9): e850. doi:10.1371/jounal.pone.0000850

Examples

 
## example of two dimensional integral
hbrr(c(.123,.432),matrix(c(1,.5,.5,1),2,2))
## faster but less accurate estimation by simulatin
hbrr(c(.123,.432),matrix(c(1,.5,.5,1),2,2),simulate=TRUE,nsim=10^4)