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Alert Threshold Algorithms andMalaria Epidemic DetectionHailay Desta Teklehaimanot,* Joel Schwartz,* Awash Teklehaimanot,t and Marc Lipsitch*

We describe a method for comparing the ability of dif-ferent alert threshold algorithms to detect malaria epi-demics and use it with a dataset consisting of weeklymalaria cases collected from health facilities in 10 districtsof Ethiopia from 1990 to 2000. Four types of alert thresholdalgorithms are compared: weekly percentile, weekly meanwith standard deviation (simple, moving average, and log-transformed case numbers), slide positivity proportion, andslope of weekly cases on log scale. To compare dissimilaralert types on a single scale, a curve was plotted for eachtype of alert, which showed potentially prevented casesversus number of alerts triggered over 10 years. Simpleweekly percentile cutoffs appear to be as good as morecomplex algorithms for detecting malaria epidemics inEthiopia. The comparative method developed here may beuseful for testing other proposed alert thresholds and forapplication in other populations.

A ccurate, well-validated systems to predict unusualincreases in malaria cases are needed to enable time-ly action by public health officials to control such epi-demics and mitigate their impact on human health. Suchsystems are particularly needed in epidemic-prone regions,such as the East African highlands. In such places, trans-mission is typically highly seasonal, with considerablevariation from year to year, and immunity in the popula-tion is often incomplete. Consequently, epidemics, whenthey occur, often cause high illness and death rates, even inadults (1,2). The value of timely interventions-such aslarviciding, residual house spraying, and-mass drug admin-istration-to control malaria epidemics has been docu-mented (3), bu t much less evidence exists about ho w toidentify appropriate times to take such action whenresources are limited (4). Ideally, public health and vectorcontrol workers would have access to a system that pro-vides alerts when substantial numbers of excess cases areexpected, and such alerts should be sensitive (so that alertsare reliably generated when excess cases are imminent),specific (so that there are few false alarms or alerts that do

no t precede significant excess cases), and timely (so thadespite some inevitable delays between sounding the aleand completing interventions, adequate lead time existstake actions that will reduce cases before they decline "naurally").A number of such systems have been proposedimplemented, but the comparative utility of these systemfor applied public health purposes has no t been rigorousl

established. For example, the World Health Organizatiohas advocated the use of alerts when weekly cases exceethe 75th percentile of cases from the same week in prevous years (5), and other methods, based on smoothingparametric assumptions, have also been considered (6-8Such methods, known as early detection systems becauthey detect epidemics once they have begun, can correctidentify periods that are defined by expert observers as epdemic, albeit with varying specificity. However, the abity of early detection systems to generate timely alerts thprospectively identify periods of ongoing excess transmision has not, to our knowledge, been evaluated. A detetion algorithm is useful for identifying interventions onif it identifies epidemics at an early phase (9), and it (opposed to prediction) will work only to the extent thepidemics persist (and indeed grow) over time. Thudetecting unusual cases at one time point will be a reliabindicator that an epidemic is under way (and will be so flong enough that action taken after the waming can sthave an effect).

Another approach, known as early waming, attemptspredict epidemics before unusual transmission activibegins, usually by the use of local weather or global cmatic variables that are predictors of vector abundance aefficiency, and therefore of transmission potential (10-14Such systems have the advantage of providing moadvance waming than systems that rely on case counts, bclimate- and w eather-based systems require data not widly available to local malaria control officials in Africareal time. Such systems also depend on relatively complprediction algorithms that may be difficult to implementthe field. Studies of the forecasting ability of such systemare beginning to emerge (15); initial studies have focus*Harvard School of Public Health, Boston, Massachusetts, USA;an d tColumbia University, New York, New York, USA


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Malaria Epidemic Detection

on the sensitivity rather than on the specificity or timeli-ness of the alerts.

We describe a method for evaluating the public healthvalue of a system to detect malaria epidemics. We use thismethod to evaluate several simple early detection systemsfor their ability to provide timely, sensitive, and specificalerts in a data series of weekly case counts from 10 loca-tions in Ethiopia for approximately 10 years. The fanda-mental question we address is whether detecting excesscases fo r 2 weeks in a row, under a variety of working def-initions of "excess," can be the basis for a system thatanticipates ongoing excess malaria cases in time for actionto be taken.Materials and MethodsStudy Area and Data

We collected datasets consisting ofweekly parasitolog-ically confirmed malaria cases over an average of 10 yearsfrom health facilities in 10 districts of Ethiopia (onlineAppendix Figure 1; available from http://www.cdc.gov/ncidod/EID/voll Ono7/03-0722_app.G 1 htm). Thedata arise from passive surveillance systems in selecteddistricts for the years 1990-2000. Original data collectedon the basis of Ethiopian weeks (which range from 5 to 9days) were normalized to obtain mean daily cases for eachEthiopian week, and normalized data were used for allanalysis. Data are summarized in Table 1.Epidemic Detection Algorithms To Be TestedWe investigated four classes of algorithms for trigger-ing alert thresholds. In each case, an alert was triggered ifthe defined threshold was exceeded for 2 consecutiveweeks. (This choice is intended to improve the specificityof the alert system for any given threshold.) If another alertwas triggered within 6 months, it was ignored, on theassumption that intervening after the first alert would pre-vent another epidemic within the next 6 months. For thepurposes of historically based thresholds (I and 2 below),the thresholds for each year were calculated on the basis of

all other years in the dataset for a given health facility,excluding the year under consideration.

Weekly PercentileThe threshold was defined as a given percentile of thecase numbers obtained in the same week of all years otherthan the one under consideration. Th e use of percentile asalert threshold is straightforward, and the method is rela-tively insensitive to extreme observations.

Weekly Mean with Standard Deviation (SD)We defined the threshold as the weekly mean plus a

defined number of SDs. Mean and SD were calculatedfrom case counts, smoothed case counts, or log-trans-formed case counts.

Slide Positivity PercentageSome studies have indicated that the proportions ofpositive slides were significantly.higher than the usual rate

during epidemics (16,17), bu t whether the rise in propor-tion of positive slides occurs early enough to serve as auseful early detection system is not known. Slide positivi-ty proportion was calculated from the number of bloodslides tested and positive slides for malaria parasites.

Slope of Weekly Cases on Log ScaleWe hypothesized that rapid multiplication of the num-

be r of normalized cases from week to week might signalonset of an epidemic. To test this hypothesis and the use-fulness of detecting such changes as a predictor of epi-demics, we defined a set of alert thresholds on the basis ofthe slope of the natural logarithm of the number ofnormal-ized cases. An advantage of the slide positivity and logslope methods over the others is that they can, in principle,be used to construct alert thresholds in the absence of ret-rospective data.Comparison of Alert Thresholds

To circumvent the difficulties inherent in defining a"true" epidemic and to compare the properties of these

Table 1.Characteristics of the study areasDaily microscopically confirmed cases

District Follow-up (y) Mean SD Minimum MaximumAlaba 11.3 39.0 27.3 0 163.0Awasa 7.7 11.3 11.0 0 77.4Bahirdar 7.3 22.1 15.2 0 83.3Debrezeit 11.2 25.3 25.8 0.9 146.7Diredawa 9.8 25.3 29.5 0.4 329.9Hosana 11.3 19.4 17.4 0.1 95.7Jimma 10.3 13.2 14.0 0.3 85.3Nazareth 9.3 17.7 16.0 0 109.3Wolayita 9.3 13.9 12.1 0 113.1Zeway 8.3 22.0 17.5 1.1 102.0


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thresholds on a scale that reflects the potential, operationaluses of alert thresholds, we evaluated each alert thresholdalgorithm for the number of alerts triggered and the num-ber of cases that could be anticipated and prevented("potentially prevented cases") if that alert threshold werein place. Potentially prevented cases .(PPC) for each alertwere defined as a function of the number of cases in adefined window starting 2 weeks after each alert (to allowfor time to implement control measures). The window ofeffectiveness was assumed to last either 8 or 24 weeks (toaccount for control measures whose effects are of differentdurations). Since no control measure would be expected toabrogate malaria cases completely, we considered two pos-sibilities for the number of cases in each week of the win-dow that could be prevented: 1) cases in excess of theseasonal mean and 2) cases in excess of the seasonal meanminus 1 SD. When the observed number of cases in a weekis less than the seasonal mean or the seasonal mean minusthe SD, PP C is se t to a minimum value of zero for thatweek. Figure 1 depicts graphically how the PPC was cal-culated. For each value of each type of threshold at eachhealth facility, the number of PP C was transformed into aproportion (percentage), by adding the number of PPC forthe alerts obtained and dividing this sum by the sum of thenumber of potentially prevented cases, over all weeks inthe dataset.

To compare the performance of dissimilar alert types ona single scale, a curve was plotted for each type of algo-rithm that showed mean percent of PP C (%PPC) over alldistricts versus average number of alerts triggered per year,with each point representing a particular threshold value."Better" threshold types and values are those that poten-tially preven t higher numbers of malaria cases with small-er numbers of alerts.Random, Annual, and Optimally Timed Alerts

To evaluate the improvement in timing of alerts provid-ed by each of these algorithms, we calculated PPC foralerts chosen on random weeks during the sampling peri-od. We also made comparisons to two alert-generatingpolicies that could no t have been implemented bu t are insome sense optimal in hindsight. First, we evaluated a pol-icy of triggering one alert each year on the "optimal" week,i.e., the week with the maximum value of PPC. Th e valueof PP C corresponding to the optimal week simulated an"optimally timed" policy of annual interventions; thus, itrepresents one alert every year. Second, we retrospectivelywent through data for each site to identify the optimal tim-ing of alerts if one had perfect predictive ability; namely,we compared PP C for a single alert generated on everyweek of the dataset and chose the optimal week for onealert; then we went through the remaining weeks and chosethe optimal week for a second alert, and so on. This system

g200

100-Seasonal Mean

O~~ '__ _ -_ __-1 3 0 7 9 11 13 10 17 19 20 23 25 27

Tlm (- dll

Figure 1. Method for calculating potentially preventable case(PPC) by using weekly mean. PPC is obtained from casesexcess of the weekly mean with an 8-week window.

allowed us to plot an upper bound curve for the best choicof alert times, given a defined alert frequency.ResultsThe dataset consists of a total of 687,903 microscopcally collected malaria cases from a health facility in eacof 10 districts over an average of 10 years. On averageeach of the 10 health facilities treated 11-39 malaria casedaily and >300 cases per day during the peak transmissioseason (Table 1). In most districts, including AwasZeway, Nazareth, Jimma, Diredawa, Debrezeit, anWolayita, the number of cases showed clear seasonal fluctuation over time. Alaba, Bahirdar, and Hosana showelonger term variation, with an increasing trend in Alaband more complex pattems in Hosana and Bahirdar. Thnumber of cases in all districts shows a clear year-to-yeavariation.The number of alerts triggered and %PPC obtained foeach level of a threshold by type of algorithm varied in th10 districts (online Appendix Figure 2). Number of alertriggered and %PPC for a single alert threshold level arrepresented by a point. These points are summarizedFigure 2, which compares the performance of all algorithms on a single scale and explores the sensitivity oresults to the choice of function for determining PP[reducing cases to weekly mean. (a) and (b), or weeklmean minus I SD, (c) and (d)] and the choice of windowof effectiveness [8 weeks, (a) and (c); 24 weeks, (b) an(d)]. All alert threshold algorithms potentially preventedlarger number of cases than random alerts, whose performance is shown as a straight line with cases increasingproportion to the number of alerts.The alert threshold algorithm based on percentile peformed as well as or better than the other algorithms ovthe range of number of alerts triggered that we examinedFor a given number of alerts triggered, it preventedgreater %PPC compared to other methods. Relative t


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100.A-80C:3 60a

II40C0.-- 20-

0 0.25 0.50 0.75

C

0.25 0.50 0.75No. of alerts pe r y---- Mean SD-Log slope

1.00 1.25 0.{100,

80

3 60gi40a-2La* 20,

1.00 1.25

--*-- Optimal- Random

B

'0 0.25 0.50 0.75 1.00 1.25

Figure 2. Percent of potentially pre-ventable cases (PPC) by number ofalerts per year for different algorithms.(A) and (B)were obtained from casesin excess of the weekly mean withwindow of effectiveness of 8 and 24weeks, respectively. (C) and (D)wereobtained from cases in excess of theweekly mean minus one SD for win-dow of 8 and 24 weeks, respectively.The scale of y-axis is higher for (B)and (D)because they are based on 24weeks of PPC (based on the randomalert, the %PPC for the 24-week win-dow is three times that of the 8-weekwindow of effectiveness).D

0.00 0.25 0.50 0.75 1.0No. of alerts pe r y

- Percentile 3 Annual-v Slide positive

l0 1.25

optimally timed alerts, the percentile algorithm perfornedwell, within 10% to 20% of the best achievable perform-ance. The slope on log scale algorithm performed slightlybetter than the random but much worse than the other algo-rithms.

Threshold algorithms defined as the weekly mean plusSD s based on different forms of the data (normalized casecounts, smoothed case counts, or log-transformed casecounts) performed similarly, except that the algorithmsbased on the smoothed cases and log-transformed casestriggered fewer alerts at a given threshold value comparedto the algorithm based on normalized cases.

For highly specific threshold values (triggering rela-tively few alerts), the slide positivity proportion showed alower %PPC than any other algorithm except the log slope.This pattern was reversed at more sensitive threshold val-ues; slide positivity thresholds of


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Table 2. Potentially preventable cases (PPC) by level of the seasonal percentile threshold in relation to number of alerts per year (8-week window)Six alert threshold levels based on seasonal percentile

95th percentile 90th percentile 85th percentile 80th percentile 75th percentile 70th percentileNo. No. No. No. No. No.District alerts %PPC alerts %PPC alerts %PPC alerts %PPC alerts %PPC alerts %PPC

Alaba 0.44 18.6 0.53 20.1 0.62 24.5 0.62 23.4 0.8 28.8 0.97 30.1Awasa 0.55 28.1 0.65 28.1 0.65 35.6 0.91 32.9 0.91 32.9 1.0 20.2Bahirdar 0.55 27.9 0.55 27.9 0.55 27.9 0.82 37.6 0.82 38.4 0.82 38.4Debrezeit 0.27 19.8 0.54 28.5 0.54 37 0.54 36.2 0.54 36.2 0.8 39Diredawa 0.61 25.2 0.61 26.6 0.82 26.9 0.82 26.9 1.1 31 1.1 31.1Hosana 0.35 25.6 0.62 32.6 0.71 33.5 0.8 34.3 0.97 28 0.97 28Jimma 0.39 24.9 0.39 24.9 0.78 31.8 0.87 33.1 0.97 32.1 0.87 31.9Nazareth 0.54 33.9 0.54 33.9 0.86 34 0.86 34 1.1 18.7 1.2 19.7Wolayita 0.54 24.8 0.54 24.8 0.86 30.5 0.86 30.5 0.97 29.9 1.1 29.9Zeway 0.36 30.2 0.36 30.2 0.84 37.2 0.84 37.2 0.84 36.4 0.84 28.5Total 0.46 25.9 0.53 27.8 0.72 31.9 0.79 32.6 0.9 31.2 0.97 29.7

average, similar alerts per year. Figure 3 shows that alertthreshold methods based on weekly data perform muchbetter than those based on monthly data.Discussion

We have described a novel method for evaluating theperformance of malaria early detection systems for theirability to trigger alerts of unusually high malaria casenumbers with sufficient notice so that control measurescan be implemented in time to have an effect on the epi-demic. By defining the performance of an algorithm interms of the potentially prevented cases falling in a giventime window after the alerts are generated, we attemptedto capture the public health value of an alert system,which is its ability to predict excess malaria cases. Giventhe same number of alerts triggered by different potentialdetection algorithms, the objective is to identify an alertthreshold algorithm that triggers alerts at the beginning ofunusually high transmission periods, on the assumptionthat such periods are the ones in which interventions arelikely to prevent the most cases.

Given the wide variations in malaria transmission, nostandard expectation exists about what proportion of casescan be averted with what intervention. With the assumptionthat the magnitude of the effect of an intervention would berelated to the difference between the observed number ofcases and size of the long-term seasonal mean and SD, wecalculated PPC. In other words, we assumed that an inter-vention would lower the number of cases towards theunderlying seasonal mean or, if very effective, to I SDbelow the underlying mean. Th e sensitivity of the relativeperformance of the different algorithms wa s tested by usingdifferent window periods (8 or 24 weeks) of effectivenessof possible intervention methods. These window periodsare based on the duration of effects of common interven-tions, such as insecticide spraying, which have residual

activity of 8 to 24 weeks (18-20), and other emergencmalaria epidemic control measures such as mass druadministration that could lower the incidence of malariwithin an 8- to 24-week range (21). Unlike the compledetection algorithms tested for other diseases (22-26), thalgorithms compared in this study are simple to implemenwithout the use of computers, which are currently unavailable to malaria control efforts in most parts of Africa.

At relatively smaller number of alerts triggered, threshold algorithms based on percentile anticipated the highespercentage of the potentially preventable malaria cases- oall approaches. Th e percentile algorithm's good performance relative to the optimally timed alerts indicates thattriggers alerts at the beginning of epidemics rather than ithe middle of ongoing epidemics. Given the attractivcharacteristics of the percentile algorithm, a further ques

35-

'K30-30C:

a)25-co0

20-

- Weekly -h Monthly0.4 0.5 0.6 0.7 0.8No. of alerts per y 0.9 1.0

Figure 3. Percent of potentially preventable cases (PPC) obtaineusing weekly and monthly data with an 8-week window.

1R 1 . . . . . ,_ I


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tion is what percentile level one should use. Beyond 0.4 to0.6 alerts/year, the %PPC leveled off because most of thepeaks with higher numbers of cases, possibly epidemicperiods, were detected with fewer alerts by using 85th to90th percentiles. The leveling off of %PPC occurs becausewe assume that an alert triggered at week t, which leads toapplication of intervention measures, will prevent anotheralert until week t + 24. In practical terms, an interventioninitiated after an alert was triggered by a less-specific alertthreshold during relatively lower transmission might pro-vide little benefit for a community in reducing malariatransmission, especially if it consumed scarce resourcesthat would then be unavailable during periods of highertransmission.In situations in which cost is no t an issue and yearlyapplication of preventive measures is possible, slide posi-tivity proportion could be recommended. It performed aswell as or better than all other types of algorithms when allalgorithms were set to trigger an average of one alert pe ryear. During malaria epidemics, the slide positivity propor-tion becomes very high (16,17), and the rise in the propor-tion of positive slides may begin at the onset of theepidemic to give an early warning, as our data showed. Theinterannual variation in the time and intensity of the peak ofmalaria transmission impacts the effectiveness of the annu-al alert with interventions at a fixed week every year; usingthe slide positivity proportion would identify the right timefor intervention. The limitation for using slide positivityproportion is that it requires evaluating the cut-off level inindividual health facilities and revising the baseline with achange of health personnel because the baseline slide posi-tivity proportion may vary due to differences in epidemio-logic patterns of malaria and other causes of fever. Thus,although slide positivity proportion thresholds could bedefined in the absence of historical data, our results suggestthat such data would be required to calibrate the thresholdproperly for any given locality. The slope on log scale algo-rithm performed poorly because the largest proportionalrate-of-change for the number of cases tended to occur dur-ing periods of very low case numbers (perhaps reflectingchance fluctuations).

Comparative performance of different alert thresholdswas insensitive to the length of the window and the choiceof function to define potentially prevented cases. Thisstudy indicated the use of weekly data rather than monthlydata in constructing threshold methods and in follow-upprevented more cases, consistent with the World HealthOrganization's recommendations (5).

A key limitation of our study w as that the use of a long-term measure of disease frequency from a retrospectivedataset assumes that the long-term trend did not changesignificantly and that the method of data collectionremained the same. Factors such as change of laboratory

technician affect the number of slides that are judged pos-itive for malaria parasites. Such changes should be consid-ered, and revising the threshold values frequently with themost recent data and standardized training of laboratorytechnicians are advisable. Moreover, existing interventions(which may, in some places, have been based in part onalgorithms of the sort we considered) could also interferewith the trend. In this analysis, we did not exclude epidem-ic years from the data since, on the one hand, we do nothave a standard definition of malaria epidemics and, on theother hand, all possible data points should be used to cal-culate measures of disease frequency and scatter to comeup with potential threshold levels unless the data pointswere considered as outliers.

We deliberately chose to evaluate only simple, earlydetection algorithms, rather than more complex ones thatmight require climate or weather data or complicated sta-tistical models. In the dataset we considered, the best ofthese simple algorithms performed quite well relative tothe best possible algorithm, which suggests that they maybe adequate for many purposes. In principle, the methodwe propose could easily be applied to evaluate more com-plex, early warning algorithm s and to test whether theiradded complexity results in substantially better perform-ance. It is an open question whether the same methodswould work as well in localities (or for diseases) with dif-ferent patterns of variation in incidence, for example, inthose with less pronounced seasonal peaks in incidence.In conclusion, we have shown that simple weekly per-centile cutoffs appear to perform well for detecting malar-ia epidemics in Ethiopia. The ability to identify periodswith a higher number of malaria cases by using an earlydetection method will enable the more rational applicationof malaria control methods. The comparative techniquedeveloped in this study may be useful for testing other pro-posed alert threshold methods and for application in otherpopulations and other diseases.Acknowledgments

We thank the Ministry of Health of Ethiopia for allowing usto access the information, and Andrew Spielman and ChristinaMills for comments.

The Fogarty International Center of the National Institutesof Health funded (grant number 5D43TW000918) this study.Financial support for data collection was provided by WorldHealth Organization/RBM. The Ellison Medical Foundation gavesupport to M.L.

Dr. Teklehaimanot worked as a medical director and zonalmalaria control program officer in Ethiopia for 4 years. Since2001, he has been enrolled in the doctoral program in epidemiol-ogy at the Harvard School of Public Health. His primary researchinterest is in early warning of malaria epidemics.


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Address for correspondence: Hailay D. Teklehaimanot, Department oEpidemiology, Harvard School of Public Health, 677 Huntington AveBoston, MA 02115, USA; fax: 617-566-7805; email: [email protected]

i .I *i

EMERGING INFECTIM OISEWS- --------- auau f Mw.de go vedcdTo receive tables ofcontents oFnew isues send a;n emailto l:[email protected] with subsrib eid-toc n he bo*dyofyor ss .


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TITLE: Alert Threshold Algorithms and Malaria Epidemic

Detection

SOURCE: Emerging Infect Dis 10 no7 Jl 2004

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