  Analyses of population-based surveys are instrumental to research on
prevention and treatment of mental and substance use disorders.
Population-based data provides descriptive characteristics of multiple
determinants of public health and are typically available to researchers as an
annual data release. To provide trends in national estimates or to update the
existing ones, a meta-analytical approach to year-by-year data is typically
employed with ORs as effect sizes. However, if the estimated ORs exhibit
different patterns over time, some normalization of ORs may be warranted. We
propose a new normalized measure of effect size and derive an asymptotic
distribution for the respective test statistic. The normalization constant is
based on the maximum range of the standardized log(OR), for which we establish
a connection to the Laplace Limit Constant. Furthermore, we propose to employ
standardized log(OR) in a novel way to obtain accurate posterior inference.
Through simulation studies, we show that our new statistic is more powerful
than the traditional one for testing the hypothesis OR=1. We then applied it to
the United States population estimates of co-occurrence of side effect
problem-experiences (SEPE) among newly incident cannabis users, based on the
the National Survey on Drug Use and Health (NSDUH), 2004-2014.
