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
Code language: R (r)
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
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(pj) = a + bxj
where pj 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.