The **Cochran-Armitage trend test **can be used to assess time trends in prevalence of outcomes across repeated cross-sectional surveys.

## Sample size Calculation in Stata

Statistics > Power and Sample Size > Outcome > Binary > Linear Trend in proportions in Jx2 table OR `power trend`

Examples follow

Sample size for probability of 0.80, 0.85, 0.9, 0.95 across four surveys

Code language: Stata (stata)`power trend 0.80 0.85 0.90 0.95, power(0.8)`

## What If there are just two Cross-sectional surveys ?

This situation is akin to comparing two proportions. Once cannot compare trend with just two comparison groups, minimum three are required. The sample size calculations of teh Cochran-Armitage test and two sample proportions comparison using chi-sqaured tests are going to yield same results

```
power trend 0.15 0.1
note: exposure levels are assumed to be equally spaced
Performing iteration ...
Estimated sample size for a trend test
Cochran-Armitage trend test
Ho: b = 0 versus Ha: b != 0; logit(p) = a + b*x
Study parameters:
alpha = 0.0500
power = 0.8000
N_g = 2
p1 = 0.1500
p2 = 0.1000
Estimated sample sizes:
N = 1,372
N per group = 686
power twoproportions 0.15 0.1, test(chi2)
Performing iteration ...
Estimated sample sizes for a two-sample proportions test
Pearson's chi-squared test
Ho: p2 = p1 versus Ha: p2 != p1
Study parameters:
alpha = 0.0500
power = 0.8000
delta = -0.0500 (difference)
p1 = 0.1500
p2 = 0.1000
Estimated sample sizes:
N = 1,372
N per group = 686
```

Code language: R (r)

## About the Cochran-Armitag test

From the STATA HELP manual: The Cochran–Armitage trend test (Cochran 1954 and Armitage 1955) is commonly used to test for trend in J X 2 tables. It is based on the linear logit model:

`logit(p`

_{j}) = a + bx_{j}

where p_{j} is the hypothesized probability of a success in group j, and a and b are unknown coefficients.

- Armitage, P. 1955. Tests for linear trends in proportions and frequencies. Biometrics 11: 375–386.
- Cochran, W. G. 1954. Some methods for strengthening the common chi-squared tests. Biometrics 10: 417–451.