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Confidence intervals and statistical testing for ratio measures of percent change


Carla Winston, Division of Tuberculosis Elimination, Centers for Disease Control and Prevention [CDC], Mailstop E-10, 1600 Clifton Road NE, Atlanta, GA, U.S.A.



In public health and medical research, ratio measures of percent change relative to baseline are often used to express a change in disease incidence. Estimating variance becomes more complex when the comparison is to an expectation based on previous data (E), rather than to an observed value (O). In 2009, the decline in reported tuberculosis (TB) cases was the largest single-year decrease since national TB surveillance began in 1953. To investigate the 2009 TB decline compared with expected counts, we analyzed TB cases reported to the Center for Disease Control and Prevention's National Tuberculosis Surveillance System. We log-transformed case counts for 2000–2008, and performed linear regression stratified by patient and clinical characteristics. We calculated relative declines from expectation as (O − E) ∕ E for patient subgroups, and constructed 95% confidence intervals for TB declines. We then formulated a Z-score test statistic comparing declines across patient subgroups under the null hypothesis that the difference of the two ratio measures was zero. We illustrate our methods by comparing 2009 declines from expectation for US-born versus foreign-born patients. Predicted values and confidence intervals assessed the magnitude of unexpected TB declines within patient groups, while statistical tests comparing ratio measures evaluated relative TB declines across groups. Published 2012. This article is a US Government work and is in the public domain in the USA.

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