Quantifying temporal trends of age-standardized rates with odds

Abstract

Background

To quantify temporal trends in age-standardized rates of disease, the convention is to fit a linear regression model to log-transformed rates because the slope term provides the estimated annual percentage change. However, such log-transformation is not always appropriate.

Methods

We propose an alternative method using the rank-ordered logit (ROL) model that is indifferent to log-transformation. This method quantifies the temporal trend using odds, a quantity commonly used in epidemiology, and the log-odds corresponds to the scaled slope parameter estimate from linear regression. The ROL method can be implemented by using the commands for proportional hazards regression in any standard statistical package. We apply the ROL method to estimate temporal trends in age-standardized cancer rates worldwide using the cancer incidence data from the Cancer Incidence in Five Continents plus (CI5plus) database for the period 1953 to 2007 and compare the estimates to their scaled counterparts obtained from linear regression with and without log-transformation.

Results

We found a strong concordance in the direction and significance of the temporal trends in cancer incidence estimated by all three approaches, and illustrated how the estimate from the ROL model provides a measure that is comparable to a scaled slope parameter estimated from linear regression.

Conclusions

Our method offers an alternative approach for quantifying temporal trends in incidence or mortality rates in a population that is invariant to transformation, and whose estimate of trend agrees with the scaled slope from a linear regression model.