Time-series analysis allows us to investigate trends over time at a population level and how two or more series co-vary, as well as the impact of population level policies and interventions. Several analyses are available which take into account seasonality and autocorrelation (where measurements taken closer in time are more similar). One popular analysis is ARIMA (and ARIMAX) modelling. A major assumption of these is that of stationarity which means that the mean, variance and autocorrelation structure do not change over time. For this to be achieved, underlying trends must be removed through what is known as differencing (and perhaps a transformation). Differencing involves using the difference between a value and the one for the time period immediately previous to it. Example data is shown in the graphs above before and after differencing. ARIMA then assesses how one series changes over time as a function of another without confounding from any underlying changes.
Traditional designs for epidemiological studies can be classified at a broad level into individual and population level studies. Individual level studies encompass designs such as case-control and cross-sectional and prospective cohort studies. These are characterised by measurements at the individual level. For example, participants may be asked if they smoke cigarettes and whether they have made a quit attempt. Population level studies on the other hand generally use average numbers/rate outcomes, which can be derived by aggregating individual level data. For example, the percentage of smokers at any one time in the population and the percentage of smokers who are attempting to quit at any one time in the population. Similar analyses can be used for both, but for the latter is often more complex. Failure to find associations using population level aggregated data does not = failure to find associations at an individual level. For example, in a recent population level study we found that the prevalence of e-cigarette use over time was not associated with average cigarette consumption among smokers (http://bmjopen.bmj.com/content/8/6/e016046?ct). It is still possible that at an individual level use of e-cigarettes does result in reductions in cigarette intake. Population level and individual level data are therefore assessing different things but can complement each other.