asypow (version 2015.6.25)

info.expsurv.design: Expected Information Matrix for a Clinical Trial with Exponential Survival Design

Description

Calculates expected information matrix for a clinical trial with exponential survival.

The clinical trial will accrue subjects over a time period $L$. Each subject will enter the study at a random time between 0 and $L$, so the subject's follow up time, $U$, will be uniformly distributed between 0 and $L$. A subject with follow up time $U$, can die at a time $t$ between 0 and $U$, or the subject can be withdrawn alive at time $U$. The density of time to death is exponential distribution with hazard, $w$.

The parameter $w$ depends on a covariate, $x$, via the exponentiation of a linear or quadratic function of $x$, $w = exp(a + b*x)$ or $w = exp(a + b*x + c*x^2)$.

This model is both the proportional hazards model and the accelerated failure model for exponential survival.

Usage

info.expsurv.design(model="linear", theta, L, xpoints, natx=1, group.size=1)

Arguments

theta

Matrix of parameters for the linear combination of the covariate x. Each row represents a group so theta[i,] = c(a,b) if model = "linear" or theta[i,] = c(a,b,c) if model = "quadratic".

L

The length of the clinical trial. If all groups have the same trial length, L should be a single number; otherwise, L should be a vector the same length as the number of rows in w where L[i] is the length of the clinical trial for the i'th group.

xpoints

Matrix of covariate values for each group. If there is only 1 group or all groups have the same covariate value, xpoints should be a vector; otherwise, the number of rows in xpoints must each the number of rows in theta.

model

One of {"linear", "quadratic"}. Specifies the function of the covariate x that will be used. Linear indicates, $u = a + b*x$, and quadratic indicates, $u = a + b*x + c*x^2$. Only enough to ensure a unique match need be supplied.

natx

Needed only if there are unequal sample sizes used at any of the values in xpoints. At covariate value xpoint[i,j] there are natx[i,j] observations. If specified, the dimensions of natx should be the same as the dimensions of xpoints.

group.size

Needed only if there are to be several groups with unequal sample sizes. The value of the i'th component is the relative sample size of the i'th group. The calculation made is for a single observation spread over the several groups in proportion to the specified relative sizes. If this value is specified, it should be a vector whose length is the same as the number of columns in theta.

Value

The information matrix for one observation for this design.If model = "linear" and there are k groups, the information matrix is a square $(2*k)x(2*k)$ matrix which is indexed by the parameters (a,b) for group 1, then (a,b) for group 2, etc.If model = "quadratic", the information matrix is a square $(3*k)x(3*k)$ matrix which is indexed by the parameter (a,b,c) for group 1, then (a,b,c) for group 2, etc.

References

Cox, D.R. and Hinkley, D.V. (1974). Theoretical Statistics Chapman and Hall, London.

See Also

info.binomial.design, info.poisson.design, info.ordinal.design

Examples

# Find the information matrix for a clinical trial
# with hazard w(x) = -0.848 + 0.7*x which lasts
# three years and has 10 x values equally spaced
# between -3 and 3 with equal sample sizes.
ab <- c(-.848, .7)
covar <- seq(-3, 3, length=10)
LL <- 3
info.expsurv <- info.expsurv.design(theta = ab, L = LL, xpoints = covar)
print(info.expsurv)