@article{Struchen_Vial_Andersson_2017, title={Value of evidence from syndromic surveillance with delayed reporting}, volume={9}, url={https://ojphi.org/ojs/index.php/ojphi/article/view/7606}, DOI={10.5210/ojphi.v9i1.7606}, abstractNote={<div style="left: 90px; top: 335.758px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.08129);" data-canvas-width="63.778333333333336">Objective</div><div style="left: 105px; top: 350.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.971316);" data-canvas-width="380.0760833333334">We apply an empirical Bayesian framework to perform change</div><div style="left: 90px; top: 367.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.02939);" data-canvas-width="394.22291666666666">point analysis on multiple cattle mortality data streams, accounting</div><div style="left: 90px; top: 384.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00076);" data-canvas-width="203.405">for delayed reporting of syndromes.</div><div style="left: 90px; top: 415.758px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.11768);" data-canvas-width="82.63416666666666">Introduction</div><div style="left: 105px; top: 430.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.972746);" data-canvas-width="380.052">Taking into account reporting delays in surveillance systems is</div><div style="left: 90px; top: 447.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.019);" data-canvas-width="394.18183333333326">not methodologically trivial. Consequently, most use the date of the</div><div style="left: 90px; top: 464.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01754);" data-canvas-width="394.1265833333333">reception of data, rather than the (often unknown) date of the health</div><div style="left: 90px; top: 480.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.973947);" data-canvas-width="395.68208333333337">event itself. The main drawback of this approach is the resulting</div><div style="left: 90px; top: 497.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.04325);" data-canvas-width="239.60083333333333">reduction in sensitivity and specificity</div><div style="left: 329.733px; top: 497.751px; font-size: 8.5px; font-family: serif;">1</div><div style="left: 334.138px; top: 497.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03064);" data-canvas-width="152.82716666666664">. Combining syndromic</div><div style="left: 90px; top: 514.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.972686);" data-canvas-width="395.5588333333331">data from multiple data streams (most health events may leave a</div><div style="left: 90px; top: 530.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.986917);" data-canvas-width="393.07258333333334">“signature” in multiple data sources) may be performed in a Bayesian</div><div style="left: 90px; top: 547.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.942839);" data-canvas-width="394.64083333333326">framework where the result is presented in the form of a posterior</div><div style="left: 90px; top: 564.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00054);" data-canvas-width="136.52416666666667">probability for a disease</div><div style="left: 226.506px; top: 564.417px; font-size: 8.5px; font-family: serif;">2</div><div style="left: 230.756px; top: 564.043px; font-size: 14.1667px; font-family: serif;">.</div><div style="left: 90px; top: 595.758px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.07287);" data-canvas-width="58.23916666666666">Methods</div><div style="left: 105px; top: 610.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00269);" data-canvas-width="378.53049999999996">We used a historical national database on Swiss cattle mortality to</div><div style="left: 90px; top: 627.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.990541);" data-canvas-width="322.43758333333335">model daily baseline counts of two syndromic time series</div><div style="left: 412.424px; top: 627.751px; font-size: 8.5px; font-family: serif;">3</div><div style="left: 416.674px; top: 627.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.988541);" data-canvas-width="66.46291666666667">. Reporting</div><div style="left: 90px; top: 644.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.982965);" data-canvas-width="393.0385833333334">delay was defined as the number of days between reported occurrence</div><div style="left: 90px; top: 660.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.977127);" data-canvas-width="395.4596666666665">and reporting date. The cumulative probability distribution of the</div><div style="left: 90px; top: 677.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.963736);" data-canvas-width="394.92274999999995">estimated reporting delays was used to calculate for each day the</div><div style="left: 90px; top: 694.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.999895);" data-canvas-width="393.5584999999999">proportion of cases that were reported either on the same day or with</div><div style="left: 90px; top: 710.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.0003);" data-canvas-width="131.80666666666667">a delay of 1 to 14 days.</div><div style="left: 105px; top: 727.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.07661);" data-canvas-width="383.2210833333334">We evaluated outbreak detection performance under three</div><div style="left: 90px; top: 744.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.972349);" data-canvas-width="395.40583333333325">scenarios: (A) delayed data reporting occurs but is not accounted</div><div style="left: 90px; top: 760.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.02338);" data-canvas-width="394.2923333333333">for; (B) delayed data reporting occurs and is accounted for; and (C)</div><div style="left: 90px; top: 777.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.983643);" data-canvas-width="395.7033333333333">absence of delayed data reporting (i.e. an ideal system). Outputs</div><div style="left: 90px; top: 794.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.04194);" data-canvas-width="394.51191666666614">are presented as the value of evidence (V) in favour of an ongoing</div><div style="left: 90px; top: 810.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.970003);" data-canvas-width="162.49166666666665">outbreak accumulated over</div><div style="left: 252.533px; top: 810.709px; font-size: 14.1667px; font-family: serif;">n</div><div style="left: 259.704px; top: 810.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.923635);" data-canvas-width="224.96666666666664">points in time (30 days in this case).</div><div style="left: 90px; top: 827.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.05555);" data-canvas-width="80.09833333333333">At each time</div><div style="left: 170.038px; top: 827.376px; font-size: 14.1667px; font-family: serif;">t</div><div style="left: 174.055px; top: 827.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.05665);" data-canvas-width="310.7954166666667">, V is defined as the ratio between the posterior and</div><div style="left: 90px; top: 844.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00025);" data-canvas-width="91.6725">prior odds for H</div><div style="left: 181.675px; top: 853.767px; font-size: 8.5px; font-family: serif;">1</div><div style="left: 185.925px; top: 844.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00076);" data-canvas-width="53.507499999999986">versus H</div><div style="left: 239.438px; top: 853.767px; font-size: 8.5px; font-family: serif;">0</div><div style="left: 243.688px; top: 844.043px; font-size: 14.1667px; font-family: serif;">:</div><div style="left: 105px; top: 860.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.0007);" data-canvas-width="131.79250000000002">[insert equation 1 here]</div><div style="left: 105px; top: 877.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.0009);" data-canvas-width="380.97566666666654">Using sensitivity, time to detection and in-control run length,</div><div style="left: 90px; top: 894.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.0003);" data-canvas-width="393.3332500000001">performance of the (V-based) system on large and small non-specific</div><div style="left: 90px; top: 910.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00073);" data-canvas-width="142.02083333333334">outbreaks was measured.</div><div style="left: 90px; top: 942.425px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.08488);" data-canvas-width="51.17">Results</div><div style="left: 105px; top: 957.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.0155);" data-canvas-width="379.0022499999999">The evolution of V based on the information available on the 1st,</div><div style="left: 90px; top: 974.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.03191);" data-canvas-width="394.41274999999985">5th and 10th day after the onset of an outbreak can be visualised in</div><div style="left: 90px; top: 990.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.02645);" data-canvas-width="394.27675000000005">Fig. 1. After 5 days, V shows evidence in favour of an outbreak for</div><div style="left: 90px; top: 1007.38px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.970091);" data-canvas-width="392.8869999999998">both syndromes combined, as well as for on-farm deaths alone, only in</div><div style="left: 90px; top: 1024.04px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00797);" data-canvas-width="393.81350000000003">the “Delay aware” and “No delay” scenarios. The development of V</div><div style="left: 90px; top: 1040.71px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.979996);" data-canvas-width="393.02724999999987">for the perinatal deaths alone highlights the importance of considering</div><div style="left: 90px; top: 1057.38px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01555);" data-canvas-width="394.1350833333333">multiple syndromic data streams for outbreak detection, as it speaks</div><div style="left: 90px; top: 1074.04px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00529);" data-canvas-width="393.6902499999999">in favour of an outbreak at a later stage than on-farm deaths alone or</div><div style="left: 90px; top: 1090.71px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00101);" data-canvas-width="153.07083333333335">both syndromes combined.</div><div style="left: 90px; top: 1122.42px; font-size: 14.1667px; font-family: sans-serif; transform: scaleX(1.10336);" data-canvas-width="85.01416666666667">Conclusions</div><div style="left: 105px; top: 1137.38px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.02656);" data-canvas-width="381.86249999999995">Our empirical Bayes approach is an attractive alternative to</div><div style="left: 90px; top: 1154.04px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01947);" data-canvas-width="396.6765833333331">multivariate CUSUM algorithms offering a logical approach to</div><div style="left: 90px; top: 1170.71px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.998721);" data-canvas-width="393.42958333333337">weighting variables and incorporating additional information such as</div><div style="left: 90px; top: 1187.38px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.953962);" data-canvas-width="395.05166666666685">delayed reporting, and a performance on a comparable level to an</div><div style="left: 90px; top: 1204.04px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00104);" data-canvas-width="393.5599166666666">ideal (no delay) system. Outbreaks are detected earlier and with only</div><div style="left: 510px; top: 334.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.02047);" data-canvas-width="394.1747499999999">a marginal loss of specificity compared to a system where reporting</div><div style="left: 510px; top: 350.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00427);" data-canvas-width="208.5191666666667">delay is present but unaccounted for.</div><div style="left: 525px; top: 367.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.975214);" data-canvas-width="380.10583333333324">We also found that the accumulation of evidence from several</div><div style="left: 510px; top: 384.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.02592);" data-canvas-width="394.4991666666668">days resulted in a significantly better outbreak detection timeliness,</div><div style="left: 510px; top: 400.709px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.01291);" data-canvas-width="393.7865833333333">for a given specificity; or a similar timeliness, but higher specificity,</div><div style="left: 510px; top: 417.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.995778);" data-canvas-width="145.25083333333336">compared to an algorithm</div><div style="left: 655.243px; top: 417.751px; font-size: 8.5px; font-family: serif;">4</div><div style="left: 659.493px; top: 417.376px; font-size: 14.1667px; font-family: serif; transform: scaleX(0.991817);" data-canvas-width="243.78850000000003">that only looks for days with unusual high</div><div style="left: 510px; top: 434.043px; font-size: 14.1667px; font-family: serif; transform: scaleX(1.00076);" data-canvas-width="102.69416666666665">number of counts.</div><div style="left: 510px; top: 809.928px; font-size: 12.5px; font-family: serif; transform: scaleX(0.983792);" data-canvas-width="395.28749999999985">Fig. 1: Evolution of V over three time points (t) for the three scenarios.</div><div style="left: 510px; top: 823.261px; font-size: 12.5px; font-family: serif; transform: scaleX(1.02879);" data-canvas-width="393.8725000000004">Outbreak starts at t=651. Number of observed perinatal (circle) and on-farm</div><div style="left: 510px; top: 836.594px; font-size: 12.5px; font-family: serif; transform: scaleX(1.01602);" data-canvas-width="393.62125">deaths (cross), V for both (solid grey) and individual syndromes (dotted grey</div><div style="left: 510px; top: 849.928px; font-size: 12.5px; font-family: serif; transform: scaleX(0.961173);" data-canvas-width="394.48125">and black respectively), prior probability that an outbreak is ongoing (grey</div><div style="left: 510px; top: 863.261px; font-size: 12.5px; font-family: serif; transform: scaleX(1.01129);" data-canvas-width="395.835">dashed) and posterior probability that an outbreak is ongoing given the</div>evidence (black dashed). Horizontal grey solid line shows V=1.}, number={1}, journal={Online Journal of Public Health Informatics}, author={Struchen, Rahel and Vial, Flavie and Andersson, Gunnar}, year={2017}, month={May} }