Quantifying the Trendiness of Trends
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A statement often seen in the news concerning some public health outcome is that some trend has changed or been broken. Such statements are often based on longitudinal data from surveys, and the change in trend is claimed to have occurred at the time of the latest data collection. These types of statistical assessments are very important as they may potentially influence public health decisions on a national level. We propose two measures for quantifying the trendiness of trends. Under the assumption that reality evolves in continuous time we define what constitutes a trend and a change in a trend, and we introduce a probabilistic Trend Direction Index. This index has the interpretation of the probability that a latent characteristic has changed monotonicity at any given time conditional on observed data. We also define a global index of Expected Trend Instability quantifying the expected number of times that a trend has changed on an interval. Using a latent Gaussian process model we show how the Trend Direction Index and the Expected Trend Instability can be estimated from data in a Bayesian framework and give an application to development of the proportion of smokers in Denmark during the last 20 years.
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