RDS: LRT.value.trend – R documentation

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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, …, p_K. We test the null hypothesis:

H_0 : p_1 = … = p_K

H_1 : p_1 ≥ p_2 … ≥ 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 ≥ p_2 … ≥ p_K

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)

Arguments

`x`	A vector of prevalence estimates in the order (e.g., time).
`sigma`	A vector of standard error estimates corresponding to `x`.

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.

Author(s)

Mark S. Handcock

References

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

Examples

## Not run: 
x <- c(0.16,0.15,0.3)
sigma <- c(0.04,0.04,0.1)
LRT.value.trend(x,sigma)

## End(Not run)

RDS

Respondent-Driven Sampling

v0.9-3

LGPL-2.1

Authors

Mark S. Handcock [aut, cre], Krista J. Gile [aut], Ian E. Fellows [aut], W. Whipple Neely [aut]

Initial release

2021-03-11