The count of blood films examined for malaria as well as those positive for malaria per month reported by government health facilities and aggregated by medical officer of health (MOH) area (which represent sub district health administrative divisions) were provided by the Anti Malaria Campaign of Sri Lanka for the period 1972 – 2003. In addition, data aggregated by district were available for the years 2004 – 2005. For some of the records, the number of blood films examined was marked as "not received" (and therefore classified as missing). For 14.90% of the MOH area level records, the value was zero, or left blank. For the latter records, there was ambiguity as to whether the data value could be missing due to problems in data recording, or genuinely zero if no patients presented themselves for examination in that particular area in that particular month. As such, in a data cleaning procedure (see section on statistical methods), 1.4% of the records was declared as not available (NA) if the number of blood films examined was marked as "not received" (0.95%), or if the number of blood films could be classified as a lower additive outlier (0.44%). The data from districts in the north and east, where data gathering and reporting was affected by the armed conflict, had the largest percentage of data labelled not available: Jaffna (5.4%), Mannar (26.1%), Vavuniya (8.9%), Kilinochchi (2%), Trincomalee (2%) and Ampara (5.4%). After imputation, MOH area level data for positive cases were aggregated to district resolution and combined with the district level data (for the period 2004 – 005).

Records of precipitation (rain fall) collected by 342 stations across the island were purchased from the Meteorological Department of Sri Lanka (see Figure 1). This consisted mostly of monthly aggregate data, but for an area in the south (Ruhuna), daily rainfall data were also available for 57 stations covering partly the districts of Ratnapura, Hambantota, Badulla and Moneragala, for the period January 1972 – March 2003. Three stations with consistently aberrant rainfall, detected through cross validation using kriging 19, were removed from the dataset. Monthly rainfall surfaces were created through spatial prediction using kriging 19. From the daily data available, the monthly "rainy day index" was calculated for each station by dividing the number of days per month that rainfall was larger than zero by the number of days that a reading for rainfall was available. Monthly rainy day index surfaces were generated following the same procedure as for the total monthly rainfall. From each monthly rainfall surface, the average value of rainfall/rainy day index was extracted for each district.

The monthly count of malaria positive blood slides in each district y_t were transformed to normality via the logarithmic transformation z_t = log (y_t + 1). The models tested included exponentially smoothing and auto-regressive integrated moving average (ARIMA) models 20. As some of the district malaria count time series showed strong seasonality, seasonality was also modelled. In models using exponential smoothing, seasonality was included using the Holt-Winters procedure 20. In ARIMA models, seasonality was included via three different approaches which are all widely used in literature: seasonality through fixed (monthly) effects; seasonality through harmonics; and through random effects using seasonal mixed auto-regressive integrated moving average (SARIMA) models. Whether or not covariates such as rainfall and concurrent malaria case counts in neighbouring areas improved the predictive ability of the models was also tested. In addition, the seasonal adjustment method used by Abeku and colleagues 16, was tested.

The additive Holt-Winters prediction function (for time series with period length s) at time t+h is given by the following equation:

z ˆ t + h = m t , h + S t , h MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGafmOEaONbaKaadaWgaaWcbaGaemiDaqNaey4kaSIaemiAaGgabeaakiabg2da9iabd2gaTnaaBaaaleaacqWG0baDcqGGSaalcqWGObaAaeqaaOGaey4kaSIaem4uam1aaSbaaSqaaiabdsha0jabcYcaSiabdIgaObqabaaaaa@3DC2@

where m_t,h is the average number of cases at time t+h expressed as a trend r_t,h and an overall mean term a_t, that is m_t,h = r_t,h + a_t. S_t,h is a seasonality term at time t+h, such that S_t,h = S_{t-s+1+(h-1)mod s} where (h - 1) mod s is the remainder of h-1 after division by s (e.g. 14mod12 = 2). Thus

z ˆ t + h = a t + h r t + S t − s + 1 + ( h − 1 ) mod ⁡ s MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGafmOEaONbaKaadaWgaaWcbaGaemiDaqNaey4kaSIaemiAaGgabeaakiabg2da9iabdggaHnaaBaaaleaacqWG0baDaeqaaOGaey4kaSIaemiAaGMaemOCai3aaSbaaSqaaiabdsha0bqabaGccqGHRaWkcqWGtbWudaWgaaWcbaGaemiDaqNaeyOeI0Iaem4CamNaey4kaSIaeGymaeJaey4kaSIaeiikaGIaemiAaGMaeyOeI0IaeGymaeJaeiykaKIagiyBa0Maei4Ba8MaeiizaqMaem4Camhabeaaaaa@4E08@

where a_t, r_t and S_t are calculated by the following recursive functions:

a_t = α(z_t - S_t-s) + (1 - α)(a_t-1 + r_t-1);

r_t = β(a_t - a_t-1) + (1 - β)r_t-1;

S_t = γ(z_t - a_t) + (1 - γ)S_t-s.

Both seasonal and non-seasonal (with γ fixed to 0) models were tested using the function "HoltWinters" in the package "stats" of the statistical software package "R".

It was assumed that z_t is Gaussian distributed, z_t ~ N (μ_t, σ²), with mean μ_t and variance σ². Further, it was assumed that

μ_t = f(z_t, d, p, x_t) + g(u_t, q)

where f(z_t, d, p, x_t) and g(u_t, q) model the temporal correlation as

f(z_t, d, p, x_t) = Φ_p(B)(1 - B)^d(x_t - z_t) + z_t and g(u_t, q) = Θ_q(B)u_t - u_t

where

Φ_p(B) = 1 - φ₁B - ... - φ_pB^p;

Θ_q(B) = 1 - θ₁B - ... - θ_qB^q;

u_t is Gaussian white noise;

x_t = m_t + S_t;

S_t models the seasonal process;

m_t models the mean of z_t

B is a backshift operator with B^d(z_t) = z_t-d.

The seasonality in the ARIMA models of equation 2 was modelled by fixed effects. In particular it was assumed:

• S_t = 0 (A non seasonal model),

• St=∑12(αkδk,t)whereδk,t={1if t=nk0if t≠nk MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqbaeqabeWaaaqaaiabdofatnaaBaaaleaacqWG0baDaeqaaOGaeyypa0ZaaabCaeaadaqadaqaaiabeg7aHnaaBaaaleaacqWGRbWAaeqaaOGaeqiTdq2aaSbaaSqaaiabdUgaRjabcYcaSiabdsha0bqabaaakiaawIcacaGLPaaaaSqaaaqaaiabigdaXiabikdaYaqdcqGHris5aaGcbaGaee4DaCNaeeiAaGMaeeyzauMaeeOCaiNaeeyzaugabaGaeqiTdq2aaSbaaSqaaiabdUgaRjabcYcaSiabdsha0bqabaGccqGH9aqpdaGabaqaauaabaqaciaaaeaacqaIXaqmaeaacqqGPbqAcqqGMbGzcqqGGaaicqqG0baDcqGH9aqpcqqGUbGBcqqGRbWAaeaacqaIWaamaeaacqqGPbqAcqqGMbGzcqqGGaaicqqG0baDcqGHGjsUcqqGUbGBcqqGRbWAaaaacaGL7baaaaaaaa@60B8@

(Seasonality through fixed effects for months: Note that in this model m_t does not contain an intercept to avoid over parameterisation),

• St=∑i2Aisin⁡(2πfit+2πϕi) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaem4uam1aaSbaaSqaaiabdsha0bqabaGccqGH9aqpdaaeWbqaaiabdgeabnaaBaaaleaacqWGPbqAaeqaaOGagi4CamNaeiyAaKMaeiOBa4MaeiikaGIaeGOmaiJaeqiWdaNaemOzay2aaSbaaSqaaiabdMgaPbqabaGccqWG0baDcqGHRaWkcqaIYaGmcqaHapaCcqaHvpGAdaWgaaWcbaGaemyAaKgabeaakiabcMcaPaWcbaGaemyAaKgabaGaeGOmaidaniabggHiLdaaaa@4AB0@

a second order harmonic component where A_i is the amplitude of harmonic i; f_i is the frequency of harmonic i, with f₁ = 1/s, f₂ = 2/s; and ϕ_i is the phase shift (in units of time) of harmonic i.

Also, a multiplicative seasonal ARIMA(p,d,q)*(P,D,Q) model (henceforth SARIMA) was considered with period s, obtained by modifying equation 2 into

μ = f(z_t, d, p, D, P, s, m_t) + g(u_t, q, Q, s)

where

f ( z t , d , p , D , P , s , m t ) = Φ p ( B ) ( 1 − B ) d ( 1 − B s ) D Φ P ∗ ( B s ) ( m t − z t ) + z t ; MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@6B86@

g ( u t , q , Q , s ) = Θ q ( B ) Θ Q ∗ ( B s ) u t − t t ; MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaem4zaCMaeiikaGIaemyDau3aaSbaaSqaaiabdsha0bqabaGccqGGSaalcqWGXbqCcqGGSaalcqWGrbqucqGGSaalcqWGZbWCcqGGPaqkcqGH9aqpcqqHyoqudaWgaaWcbaGaemyCaehabeaakiabcIcaOiabdkeacjabcMcaPiabfI5arnaaDaaaleaacqWGrbquaeaacqGHxiIkaaGccqGGOaakcqWGcbGqdaahaaWcbeqaaiabdohaZbaakiabcMcaPiabdwha1naaBaaaleaacqWG0baDaeqaaOGaeyOeI0IaemiDaq3aaSbaaSqaaiabdsha0bqabaGccqGG7aWoaaa@5012@

Φ P ∗ ( B s ) = 1 − φ 1 ∗ B s − … − φ P ∗ B s P ; MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaeuOPdy0aa0baaSqaaiabdcfaqbqaaiabgEHiQaaakiabcIcaOiabdkeacnaaCaaaleqabaGaem4CamhaaOGaeiykaKIaeyypa0JaeGymaeJaeyOeI0IaeqOXdy2aa0baaSqaaiabigdaXaqaaiabgEHiQaaakiabdkeacnaaCaaaleqabaGaem4CamhaaOGaeyOeI0IaeSOjGSKaeyOeI0IaeqOXdy2aa0baaSqaaiabdcfaqbqaaiabgEHiQaaakiabdkeacnaaCaaaleqabaGaem4CamNaemiuaafaaOGaei4oaSdaaa@4994@

Θ Q ∗ ( B s ) = 1 − θ 1 ∗ B s − … − θ Q ∗ B s Q ; MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaeuiMde1aa0baaSqaaiabdgfarbqaaiabgEHiQaaakiabcIcaOiabdkeacnaaCaaaleqabaGaem4CamhaaOGaeiykaKIaeyypa0JaeGymaeJaeyOeI0IaeqiUde3aa0baaSqaaiabigdaXaqaaiabgEHiQaaakiabdkeacnaaCaaaleqabaGaem4CamhaaOGaeyOeI0IaeSOjGSKaeyOeI0IaeqiUde3aa0baaSqaaiabdgfarbqaaiabgEHiQaaakiabdkeacnaaCaaaleqabaGaem4CamNaemyuaefaaOGaei4oaSdaaa@4991@

and Φ_p(B), Θ_q(B), u_t, m_t and B as explained above.

The function "arima" in the package "stats" of the statistical software "R" was used to calculate the prediction criterion. Tested models included all (Gaussian) ARIMA models possible with combinations of parameters (p, d, q) with p, q ∈ {0,1,2} and with d = 1, without explanatory variables, and all (Gaussian) SARIMA models possible with combinations of parameters (p, d, q, P, D, Q) with p, q ∈ {0,1,2} and d = 1 and P, D, Q ∈ {0,1}, also without explanatory variables. An intercept was not included in the mean as it drops out of the equation due to differencing (d = 1). The differencing also removes effects of trends such as potentially caused by population growth.

Covariates were included in the term m_t. In particular, 1) mt=∑jβjzj,t−1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyBa02aaSbaaSqaaiabdsha0bqabaGccqGH9aqpdaaeqbqaaiabek7aInaaBaaaleaacqWGQbGAaeqaaOGaemOEaO3aaSbaaSqaaiabdQgaQjabcYcaSiabdsha0jabgkHiTiabigdaXaqabaaabaGaemOAaOgabeqdcqGHris5aaaa@3DC2@ where z_j,t-1 is the transformed malaria count at month t - 1 in neighbour j; 2) m_t = βχ_t-l where χ_t is the rainfall parameter in month t-l with l = lag. Rainfall was considered at lags of one to four months preceding malaria and in the following forms: untransformed monthly rainfall, logarithmically transformed monthly rainfall, rainy day index (for those districts appropriate), monthly rainfall factored into quintiles (in case of non-linear relationships), and rainfall with a separate coefficient for each of the twelve months, i.e. a coefficient for January rainfall, one for February, etc., in order to allow for seasonally varying effects. For each district, covariates were tested by including them into the (S)ARIMA model that performed best for the respective district and lag.

In a data cleaning procedure, the time series of blood film counts in MOH areas were logarithmically transformed to normality (after the value one was added to the data). Under the null hypothesis, each observation was assumed to be part of a seasonal autoregressive integrated moving average (SARIMA) process with parameters p = 0, d = 1, q = 1, P = 0, D = 1, and Q = 1. Observations were marked as additive outlier if the likelihood ratio test statistic (for an additive outlier) for the observation was below a threshold of -6 21. For those observations classified as not available or as a lower additive outlier that were not at the beginning or end of a series, values for the number of malaria positive blood films were estimated through a one-step-ahead SARIMA forecasting model on both the original series and on the reversed series, and the two estimates were averaged. This approach has been discussed by Mwaniki and colleagues 22. Finally, the MOH area data series were aggregated to district resolution before analysis, as these spatial units remained constant over the study period, whereas for many MOH areas boundaries changed (within district boundaries) over the study period.

Abeku and colleagues 16 tested a seasonal adjustment method on malaria data in Ethiopia and found that it performed better in comparison to SARIMA models. They obtained best results when using a three year "training" time series. The prediction formula used is as follows:

z ˆ t = 1 3 ∑ k = 1 k = 3 { z t − 12 k } = 1 3 ∑ l = 1 l = 3 { z t − l − 1 3 ∑ k = 1 k = 3 { z t − 12 k − l } } . MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=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@745F@

For each district, model parameters were estimated on approximately the first half of the malaria case time series (January 1972 – December 1987), and one to four step ahead (out of sample) predictions were made on the second half (January 1988 – December 2005) with the parameters fixed.

For selection of the best predictive models, all models tested were evaluated on the prediction criterion which was defined as the mean absolute relative error (mare) of back transformed out of sample predictions:

( m a r e ) = 1 N ∑ i = 1 N | y t − y ^ t y t + 1 | MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaeiikaGIaemyBa0MaemyyaeMaemOCaiNaemyzauMaeiykaKIaeyypa0ZaaSaaaeaacqaIXaqmaeaacqWGobGtaaWaaabCaeaadaabdaqcfayaamaalaaabaGaemyEaK3aaSbaaeaacqWG0baDaeqaaiabgkHiTiqbdMha5zaajaWaaSbaaeaacqWG0baDaeqaaaqaaiabdMha5naaBaaabaGaemiDaqhabeaacqGHRaWkcqaIXaqmaaaakiaawEa7caGLiWoaaSqaaiabdMgaPjabg2da9iabigdaXaqaaiabd6eaobqdcqGHris5aaaa@4CE6@

where yˆt MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGafmyEaKNbaKaadaWgaaWcbaGaemiDaqhabeaaaaa@2EFD@ is the predicted number of malaria positive cases at time t, and N is the number of predictions. Predictions needed to be genuinely out of sample in order to prevent bias towards more parameter models. The (mare) was used rather than mean square error, as the malaria count time series show widely differing variances across the series 20. The best model was that with the lowest prediction criterion for a given time series.

The mean absolute relative prediction error calculated by the best model (without extrinsic explanatory variables) tested was quite large for many districts. However, as the models were fitted to only half of the length of the time-series available for the purpose of model testing (out of sample predictions are required), it is expected that for application in a forecasting system where the full series are used for fitting, the error will be reduced. For some districts in the north, the forecasting error was particularly large. For these districts, a relatively large proportion of the data had been imputed, and the quality of the existing data is likely compromised by the armed conflict in this region. General issues related to data quality are discussed elsewhere 23. In this (primarily) temporal study, issues relating to spatial variation in data quality (e.g. through access to health facilities for sampling) are of less importance than those pertaining to temporal aspects, such as the deployment of mobile clinics during specific periods. Despite the sometimes large prediction errors, especially for larger forecasting horizons, prediction intervals yielded by these models (albeit less accurate for low predicted mean counts due to the Gaussian approximation used) could aid the AMC in assessing the risk of malaria in the near future, and adjust resources for preparedness accordingly. Although the best model selected varied among districts and over forecasting horizons, the difference between models was often small. Instead of specifying a different model for each situation, for practical implementation, it may be worth selecting for each district (or even group of districts) one model that performs well on average over a range of forecasting horizons (and districts within the group), provided that the prediction quality does not deteriorate more than a set percentage. A pilot forecasting system using district specific SARIMA models is currently being tested by the AMC in Sri Lanka (the system currently uses models without explanatory variables because a system to incorporate newly observed data is not yet in place). As the spatial resolution of the forecasting models presented is at district level, predictions will not help spatially targeted control at sub district level. For this, regional malaria control officers will have to rely on their experience of where within the district cases tend to occur if they occur, possibly aided by existing malaria maps at sub district level 23.

It should be kept in mind that the malaria count data are not a direct proxy of new malaria infections or even infective bites. Recrudescent and relapsing cases (mostly due to ineffective drugs) occur multiple times in the malaria dataset, and immunity may play a role during periods of higher