Tests for Trends in Repeated Cross Sectional Surveys

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

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

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(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.