Evaluating Impact Using Time-Series Data
Authors: Hannah S. Wauchope, Tatsuya Amano, Jonas Geldmann, Alison Johnston, Benno I. Simmons, William J. Sutherland, Julia P.G. Jones
Journal: Trends in Ecology & Evolution (2020)

Ecologists have called for more robust studies on the impact of conservation interventions, or environmental shocks, on outcomes of interest, such as populations, habitat loss, or pressures.Time-series data are increasingly available and can, if appropriately analysed, allow such causal inferences.However, there are important pitfalls that make large-scale analyses involving multiple time series problematic.There has been progress in a range of fields, but the literature is fragmented and not all is easily accessible to ecologists.A framework is presented, with clear and consistent terminology, to support ecologists to conduct effective impact evaluation with time-series data. This will allow them to contribute to better-informed environmental management decisions. Humanity's impact on the environment is increasing, as are strategies to conserve biodiversity, but a lack of understanding about how interventions affect ecological and conservation outcomes hampers decision-making. Time series are often used to assess impacts, but ecologists tend to compare average values from before to after an impact; overlooking the potential for the intervention to elicit a change in trend. Without methods that allow for a range of responses, erroneous conclusions can be drawn, especially for large, multi-time-series datasets, which are increasingly available. Drawing on literature in other disciplines and pioneering work in ecology, we present a standardised framework to robustly assesses how interventions, like natural disasters or conservation policies, affect ecological time series. Humanity's impact on the environment is increasing, as are strategies to conserve biodiversity, but a lack of understanding about how interventions affect ecological and conservation outcomes hampers decision-making. Time series are often used to assess impacts, but ecologists tend to compare average values from before to after an impact; overlooking the potential for the intervention to elicit a change in trend. Without methods that allow for a range of responses, erroneous conclusions can be drawn, especially for large, multi-time-series datasets, which are increasingly available. Drawing on literature in other disciplines and pioneering work in ecology, we present a standardised framework to robustly assesses how interventions, like natural disasters or conservation policies, affect ecological time series. 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These methods assume that a change in an average response variable, can capture how the time series responds to the intervention, by assuming that the data fluctuate around pre- and post- intervention averages. In reality, many time series show trends through time independently of the intervention. They could therefore respond to an intervention not only with an immediate change, but with a change in trend, which is not always captured by comparing average differences. Other fields, such as medicine [23.Karapinar-Çarkıt F. et al.The effect of a pharmaceutical transitional care program on rehospitalisations in internal medicine patients: an interrupted-time-series study.BMC Health Serv. 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Thus, change in trend is needed to accurately assess the impact of an intervention on a time series with trends. Including trend does not negate that there can also be an abrupt shift following the intervention; this immediate change can also be analysed (Figure 1E). In this example, if conservationists had used average change, they would have erroneously concluded that the hunting ban had a negative impact on elephant populations, and the beneficial intervention may have been stopped. Since most ecological time-series impact evaluation studies have focused on only one or a handful of time series [32.Fisher R. et al.epower: an r package for power analysis of before-after-control-impact (BACI) designs.Methods Ecol. 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A clearer framework for analysis is needed to avoid inadvertent mistakes in large datasets, and to improve clarity of analysis in smaller ones (see S2 in the supplemental information online, which details all potential mistakes that the presented framework averts). Drawing from other disciplines and pioneering work in ecology [9.Chevalier M. et al.Changes in forest bird abundance, community structure and composition following a hurricane in Sweden.Ecography. 2019; 42: 1862-1873Crossref Scopus (2) Google Scholar], we present a framework for conducting impact evaluation with ecological time-series data. Our framework is directed towards those working with time series that show trends through time; if there is no expectation of trend change, the models given here for 'average change' can be used, though more sophisticated fixed effects panel regression methods also exist [44.Brüderl J. Ludwig V. Fixed-effects panel regression.in: Best H. Wolf C. 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Finally, a frequentist statistical framework is generally used through this paper for simplicity, but the concepts are readily transferrable to Bayesian or information theoretic approaches. BA, CI, and BACI methods are all techniques to infer the counterfactual. BA analysis assumes that, were it not for the intervention, the trajectory of the time series would not have changed, while CI assumes that the difference observed between the control and intervention time series is a result of the intervention, and that no other unobserved differences exist between the control and intervention sites. BACI addresses these assumptions, by combining BA and CI components. Further discussions of the relative merits of the three approaches are given in other papers [20.Larsen A.E. et al.Causal analysis in control–impact ecological studies with observational data.Methods Ecol. 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For simplicity, 'control' is referred to as a control in either space or time, and 'temporal-control' or 'spatial-control' are used to distinguish between the 'before period' or 'control' time series, respectively. For BACI comparisons, statistical matching can be used to identify a control time series that is as equivalent as possible to the intervention time series, based on a set of matching variables [49.Stuart E.A. Matching methods for causal inference: a review and a look forward.Stat. Sci. 2010; 25: 1-21Crossref PubMed Scopus (2099) Google Scholar,50.Schleicher J. et al.Statistical matching for conservation science.Conserv. Biol. 2020; 34: 538-549Crossref PubMed Scopus (21) Google Scholar]. Crucially, the matched control and intervention time series should show similar trends in the 'before' time period [51.Linden A. A matching framework to improve causal inference in interrupted time-series analysis.J. Eval. Clin. Pract. 2018; 24: 408-415Crossref PubMed Scopus (12) Google Scholar]; this is often referred to as the parallel trends assumption. For example, if trends in populations of elephants were being compared before and after a hunting ban was introduced in one population, the parallel trends assumption is met if the elephants at both sites were declining at approximately the same rate over the 'before' years (Figure 1D). Many matching methods are available to facilitate the matching process [49.Stuart E.A. Matching methods for causal inference: a review and a look forward.Stat. Sci. 2010; 25: 1-21Crossref PubMed Scopus (2099) Google Scholar,50.Schleicher J. et al.Statistical matching for conservation science.Conserv. Biol. 2020; 34: 538-549Crossref PubMed Scopus (21) Google Scholar,52.Ho D. et al.MatchIt: nonparametric preprocessing for parametric causal inference.J. Stat. Softw. 2011; 42: 1-28Crossref Scopus (1355) Google Scholar,53.King G. Nielsen R. Why propensity scores should not be used for matching.Polit. Anal. 2019; 27: 435-454Crossref Scopus (198) Google Scholar], though it always requires careful consideration of the assumptions involved [50.Schleicher J. et al.Statistical matching for conservation science.Conserv. Biol. 2020; 34: 538-549Crossref PubMed Scopus (21) Google Scholar]. [31.Chevalier M. et al.New measures for evaluation of environmental perturbations using before-after-control-impact analyses.Ecol. Appl. 2019; 29e01838Crossref PubMed Scopus (10) Google Scholar] provides 'CI- measures' to estimate the similarity of control and intervention groups before and after an intervention, which can be useful for further interrogating the nature of impact, especially when matches are imperfect. Time series can respond to an intervention either by an abrupt change when the intervention is introduced, a gradual change over time, or both. The change can be measured in three ways: average, trend, or immediate (Figure 1; note these terms were introduced to ecology by [9.Chevalier M. et al.Changes in forest bird abundance, community structure and composition following a hurricane in Sweden.Ecography. 2019; 42: 1862-1873Crossref Scopus (2) Google Scholar]). Box 1 gives simplified models to calculate these metrics, and Box 2 gives a real-world example. Full models can be found in S3 in the supplemental information online. An example of interpreting coefficients can be found in S4 in the supplemental information online.Box 1Simplified Formulae for Calculating Average, Trend, and Immediate ChangeAverage ChangeTo compare the change in average with BA data, each value of the time series (where value could be population count, percentage forest cover, etc.) is predicted by a binary Before-After variable (BA), which is 0 pre-intervention and 1 after.Value~BA[I] (BA average) If the coefficient of BA is significantly positive, the average value of the time series is higher post-intervention.In a BACI analysis, this average change is then compared between intervention and spatial-control time series (Figure 1b), this is often termed the BACI contrast [31.Chevalier M. et al.New measures for evaluation of environmental perturbations using before-after-control-impact analyses.Ecol. Appl. 2019; 29e01838Crossref PubMed Scopus (10) Google Scholar,60.McDonald T.L. et al.Analysis of count data from before-after control-impact studies.J. Agric. Biol. Environ. Stat. 2000; 5: 262Crossref Scopus (84) Google Scholar]. A Control-Intervention variable (CI) is included, which is 0 for the spatial-control time series and 1 for the intervention time series.Value~BA+CI+BA×CI[II] (BACI average) The interaction between BA and CI describes how the intervention affects the change from before to after. A positive coefficient indicates that the average difference from before to after is more positive in the intervention time series.Trend and Immediate ChangeTo estimate trend and immediate change, we must include time in the model. In order to compare immediate change between the last time step before intervention, to the first time step after intervention, the simplest way to construct the model is for time to be centred around 0, with 0 being the first time step after intervention {similar to [9.Chevalier M. et al.Changes in forest bird abundance, community structure and composition following a hurricane in Sweden.Ecography. 2019; 42: 1862-1873Crossref Scopus (2) Google Scholar], though see [52.Ho D. et al.MatchIt: nonparametric preprocessing for parametric causal inference.J. Stat. Softw. 2011; 42: 1-28Crossref Scopus (1355) Google Scholar,61.Linden A. Conducting interrupted time-series analysis for single- and multiple-group comparisons.Stata J. 2015; 15: 480-500Crossref Google Scholar] and https://nawmp.org/sites/default/files/2018-01/1986%20OriginalNAWMP.pdf for an alternative method}.For a BA study, the value of the time series is predicted by Time and the BA coefficient.Value~Time+BA+Time×BA[III] (BA trend/immediate) The BA coefficient gives the change in values from before to after at Year 0 – this is the immediate change. The interaction between BA and Time gives the trend change from before to after. A positive coefficient indicates the trend after the intervention is more positive than before the intervention (note that it could still be negative, just less negative than before).As before, for a BACI study an intervention (CI) coefficient is introduced.Value~Time+BA+CI+BA×CI+BA×Time+CI×Time+BA×CI×Time[IV] (BACI trend/immediate) The interaction between BA and CI describes the BACI immediate change and BA, CI, and Time the BACI trend change, (i.e., the difference in before-after immediate, or trend change, respectively, between control and intervention time series). A positive coefficient for these interactions indicates that the intervention time series has had a more positive change in immediate/trend than the control time series.Box 2Case Study: Interpreting the Impact of a Protected Area on Populations of the Common MerganserWe use trends in a population of common merganser, or goosander (Mergus merganser), from a protected and unprotected site as a worked example to demonstrate how to interpret model coefficients from BACI time series analysis, and the importance of using the right metric of change.The common merganser is a sea duck that is distributed across Europe and North America. It is currently classified as 'Least Concern' but has previously been a target species for conservation in the United States [61.Linden A. Conducting interrupted time-series analysis for single- and multiple-group comparisons.Stata J. 2015; 15: 480-500Crossref Google Scholar]. We analysed Christmas Bird Count data to determine how a wintering population of common merganser was impacted by a protected area's designation in 1997, when compared to a similar but unprotected population, identified through statistical matching (Figure I, see [38.Wauchope H. et al.Quantifying the impact of protected areas on near-global waterbird population trends, a pre-analysis plan.PeerJ Prepr. 2019; 7e27741vGoogle Scholar] for detailed methodology).We ran Model 4 (see Equation IV in Box 1), using a generalised linear model with a negative binomial distribution [38.Wauchope H. et al.Quantifying the impact of protected areas on near-global waterbird population trends, a pre-analysis plan.PeerJ Prepr. 2019; 7e27741vGoogle Scholar], and conducted a robustness check by comparing models constructed with and without the BA term (see 'Is there any change at all?'). The model with BA had a better fit to the data, so analysis proceeded (Figure I). To evaluate the impact of the protected area, we were most interested in three coefficients: (i) the BA:CI term, which indicates immediate change; (ii) the BA:CI:Year term; which indicates trend change; and (iii) the CI:Year term, which tells us if the parallel trends assumption is satisfied (see S4 in the supplemental information online for details of how to interpret all coefficients).The CI:Year term was not significant (P = 0.09), meaning the parallel trends assumption was satisfied. The immediate change term (BA:CI) was also insignificant (P = 0.97), however, the trend change term (BA:CI:Year) was significantly positive (Estimate = 0.31 ± 0.12, P = 0.01), indicating that the trend change from before to after was more positive in the protected site.If we had applied an average change model to this data (i.e., Model 2, see Equation II in Box 1), we would have detected no significant impact of the protected area (P = 0.38), indicating the importance of adopting the trend and immediate change model when wo