# LRT.value.trend: Compute a test of trend in prevalences based on a... In RDS: Respondent-Driven Sampling

## 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

vs

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

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

 1 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.

Mark S. Handcock

## References

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

## Examples

 1 2 3 4 5 6 ## 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 documentation built on Dec. 2, 2017, 1:08 a.m.