Analysing Italian voluntary abortion data using a Bayesian approach to the time series decomposition

After the approval of the law on voluntary abortion in Italy, the Italian health care system started to practice voluntary abortion before the third month of pregnancy. Since 1980, the Italian Institute of Statistics (ISTAT) has collected data on the abortion frequency per month and per administrative local areas. Although a preliminary analysis of the data showed that, after an initial increase, the number of abortions progressively lowered over years, there is no insight on the existence of periodicity in the time series and on the local effects related to the regional habits and social environments. The aim of our study is therefore to extract local trends and periodicity from the data collected by ISTAT, by combining a 'structural model' of the time series and Bayesian statistics. This paper describes both the adopted stochastic model and its Bayesian estimation through a Markov chain Monte Carlo approach on the Italian abortion data. Abortion data are analysed both at national level and in each of the 95 Italian local areas. At the national level this analysis allows extraction of a trend component that clearly shows that the voluntary abortion trend has decreased constantly since June-July 1983 until the end of the study. The periodic component shows an astonishing regularity too, suggesting that the Italian people have a seasonal preference for voluntary abortion. In particular, abortions are concentrated in the central part of the year (April-August). Finally, at the local level this analysis allows us to find similarities/differences between different areas in trends and/or in seasonal preferences.