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Time Series Regression in Aquaculture

Henrik Stryhn1*, Beibei Jia1, Sophie St-Hilaire1 and Ben Armstrong2
  • 1 University of Prince Edward Island, Atlantic Veterinary College, Canada
  • 2 London School of Hygiene and Tropical Medicine, Dep of Social and Environmental Health, United Kingdom

Introduction Time series regression (TSR) is a collective term for a set of statistical techniques that combine ideas from ordinary regression and time series analysis. These methods have over the last decade been developed and become popular within environmental epidemiology, in studies “attempting to quantify short-term associations of environmental exposures [...] with health outcomes” (Bhaskaran et al., 2013). These methods are only slowly finding their way into studies of veterinary epidemiology (e.g. Levine and Moore, 2009; White, 2010; Lee et al., 2013). Monitoring or surveillance data in aquaculture commonly exist as time series of recordings on relevant units of observation, e.g. cages/pens or farms. The most obvious environmental exposures in aquaculture are related to fundamental water conditions such as temperature and salinity. The most obvious health outcome in aquaculture is fish mortality whereas disease-specific information is typically available at a higher level than the individual fish; for example, information may exist about when disease is thought to occur in a cage or farm. One particular feature of time series regression of particular potential interest in aquaculture is the ability to account for or even quantify the impact of interventions, which lead to so-called interrupted time series. The interruption occurs when the situation after the intervention is thought to be distinctly different than before the intervention. Typical examples of interrupted time series in environmental epidemiology are caused by new policies governing exposure to adverse health conditions, e.g. smoking bans (Feigl et al., 2015) or restricted access to dangerous medication (Hawton et al., 2013). Such interruptions may occur within a single series only or within multiple series in different locations and at different time points. In aquaculture and general animal farming, many management practices and decisions may be thought of as interventions that lead to interrupted time series. We mention vaccination, disease treatment and preemptive culling as some examples. In a sense the difficulty would be appear to lie less in thinking of interventions than to isolate certain management practices whose effect it would be meaningful or feasible to evaluate in isolation (ideally across a range of comparable settings) within the more general farm management occurring throughout the production. The objective of this study is to illustrate some of the main features of time series regression by an example of mortality monitoring in finfish aquaculture, and thereby to make a case for the usefulness of this general approach to assess the effect of management strategies in aquaculture. Materials and Methods Logbook recordings in a single grass carp (Ctenopharyngodon idella) farm (Guangdong province, China) included information about daily mortality, movements of fish and other management practices during a production cycle (Jan-Sep 2013). Using data for 13 ponds, we studied the two-week impact of movements of fish into ponds on mortality post an initial eight-day acclimation period. We included air temperature (averaged over the last week) as a proxy for water temperature, a potential confounder for the relationship. Further details about the data, including additional management variables that can be included in a more comprehensive TSR analysis, are described in (Jia, 2016). In the first stage of the TSR analysis, the time series in each pond is modelled separately to yield regression coefficients adjusted for the time-varying predictors. This stage involves decisions about distributional form, temporal patterns (in particular effect lags) and within-series autocorrelation. We modelled the daily mortality counts in each pond by a negative binomial regression model with an indicator of movements within the preceding two weeks and temperature as incidence predictors. The average air temperature over the preceding 7 days was used as a proxy for water temperature, which was not measured consistently. Temporal effects were incorporated by cubic spline functions with five knots, and two-step lagged deviance residuals were included to account for autocorrelation (Bhaskaran et al., 2013). In the second stage of the TSR analysis, the regression coefficients from individual ponds are combined by a random effects meta-analysis (Borenstein et al., 2009; McKenzie et al., 2013) with ponds as “studies”. The robustness of the overall estimates was explored by a sensitivity analysis for the first stage model settings. Results The time series for the 13 ponds comprised a total of 2567 observations, excluding the acclimation periods, and there were 57 movements of fish into these ponds, excluding initial stocking. Air temperature ranged from 13-35 degrees Celsius, and the 90% range for mortality counts was 0-61. The TSR analysis was summarized by a forest plot (Figure 1) across the 13 study ponds, showing a moderate between-pond heterogeneity/variability (I-squared=39%) and an overall estimated incidence risk ratio of 2.0 (95% CI: 1.58-2.56; p<0.001). Two ponds (ID 8,9) had remarkably different estimates than the rest, but due to their large standard errors they were given low weight in the overall estimate. The estimates across the remaining ponds were fairly consistent. The sensitivity analysis showed these results to be robust against other distribution types (zero-inflated negative binomial distribution), number of spline knots (increasing the number beyond 5 knots would lead to estimation failure in some ponds, and hence a potential selection bias), method of accounting for autocorrelation (number and types of lagged residuals included, or inclusion of previous lagged mortality counts), and inclusion/exclusion of additional predictors. The confounding effect of temperature for the effect of movements was only moderate in most ponds. Figure 1. Meta-analysis forest plot of log incidence risk ratios (log IRR) for time series regression analysis for movements into ponds (preceding two-week window) across 13 grass carp ponds at a single farm in China. Discussion TSR is a versatile analytical method that promises to be applicable to many datasets originating from aquaculture surveillance schemes. In a simplified example of mortality monitoring at a single grass carp farm, our analysis gave strong support for the hypothesis that partial restocking of ponds is associated with increased mortality during the subsequent two weeks. In order to draw general conclusions about this management practice one would need to expand the study to multiple farms, and the TSR analytical approach would carry over to such situations.

Figure 1
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Acknowledgements

The study was funded by Canadian Excellence Research Chair (CERC) Program in Aquatic Epidemiology at the University of Prince Edward Island, Canada.

References

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Jia B., 2016. Application of epidemiological methods in health management of farmed warm-water finfish in China. PhD thesis. Department of Health Management, Atlantic Veterinary College, University of Prince Edward Island, Canada.

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Keywords: time series, Grass carp, Aquaculture, intervention, Meta-analysis

Conference: AquaEpi I - 2016, Oslo, Norway, 20 Sep - 22 Sep, 2016.

Presentation Type: Oral

Topic: Aquatic Animal Epidemiology

Citation: Stryhn H, Jia B, St-Hilaire S and Armstrong B (2016). Time Series Regression in Aquaculture. Front. Vet. Sci. Conference Abstract: AquaEpi I - 2016. doi: 10.3389/conf.FVETS.2016.02.00036

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Received: 29 May 2016; Published Online: 14 Sep 2016.

* Correspondence: Prof. Henrik Stryhn, University of Prince Edward Island, Atlantic Veterinary College, Charlottetown, Prince Edward Island, C1A 4P3, Canada, hstryhn@upei.ca