RDS (version 0.9-9)

LRT.value.trend: Compute a test of trend in prevalences based on a likelihood-ratio statistic

Description

This function takes a series of point estimates and their associated standard errors and computes the p-value for the test of a monotone decrease in the population prevalences (in sequence order). The p-value for a monotone increase is also reported. More formally, let the \(K\) population prevalences in sequence order be \(p_1, \ldots, p_K\). We test the null hypothesis:
$$H_0 : p_1 = \ldots = p_K$$ vs $$H_1 : p_1 \ge p_2 \ldots \ge p_K$$ with at least one equality strict. A likelihood ratio statistic for this test has been derived (Bartholomew 1959). The null distribution of the likelihood ratio statistic is very complex but can be determined by a simple Monte Carlo process.
We also test the null hypothesis:
$$H_0 : p_1 \ge p_2 \ldots \ge p_K$$ vs $$H_1 : \overline{H_0}$$ The null distribution of the likelihood ratio statistic is very complex but can be determined by a simple Monte Carlo process. The function requires the isotone library.

Usage

LRT.value.trend(x, sigma)

Value

A list with components

• pvalue.increasing: The p-value for the test of a monotone increase in population prevalence.

• pvalue.decreasing: The p-value for the test of a monotone decrease in population prevalence.

• L: The value of the likelihood-ratio statistic.

• x: The passed vector of prevalence estimates in the order (e.g., time).

• sigma The passed vector of standard error estimates corresponding to x.

Arguments

x

A vector of prevalence estimates in the order (e.g., time).

sigma

A vector of standard error estimates corresponding to x.

Author

Mark S. Handcock

References

Bartholomew, D. J. (1959). A test of homogeneity for ordered alternatives. Biometrika 46 36-48.

Examples

if (FALSE) {
x <- c(0.16,0.15,0.3)
sigma <- c(0.04,0.04,0.1)
LRT.value.trend(x,sigma)
}