Table 1.
Characteristics of malaria forecasting studies included in review (n=29)
| Authors (reference) | Population and setting | Model specifics | Malaria outcome | Number of data points used for training/testing | Evaluation measure |
|---|---|---|---|---|---|
| Regression forecasting studies | |||||
| Adimi et al3 | Community health post data from 2004 to 2007 for 23 provinces in Afghanistan; clinical confirmation | 23 linear regressions (1 for each province); included autoregressive, seasonal and trend parameters | Monthly cases | 31/6 (varied between provinces but last 6 months used only for testing) | Root mean squared error and absolute difference |
| Chatterjee and Sarkar4 | Municipal data for 2002–2005 for Chennai (city), India; microscopic confirmation | Logistic regression; polynominal and autoregressive parameters | Monthly slide positivity rate | 36/1 | 95% CI (for predicted value and compared to observed) |
| Gomez-Elipe et al5 | Health service data from 1997 to 2003 for Karuzi Province, Burundi; clinical confirmation | Linear regression; adjusted for population, lagged weather covariates, autoregressive and seasonal parameters | Monthly incidence | 60/24; 1 month ahead forecasts | 95% CI, correlation, p value trend line of difference (between predicted and observed) |
| Haghdoost et al6 | District health centre data from 1994 to 2001 for Kahnooj District, Iran; microscopic confirmation | Separate Poisson regressions for Plasmodium vivax and Plasmodium falciparum; population offset, lagged weather covariates, seasonality and trend parameters | 10-day cases | 213/73 | Average percent error |
| Rahman et al7 | Hospital data from 1992 to 2001 for all divisions of Bangladesh; clinical confirmation | Four linear regressions (1 for each administrative division and one for all of Bangladesh); environmental covariate for weeks of highest correlation | Yearly cases | 10, 1 year was removed from series at a time | Root mean squared error and relative bias (observed-predicted) |
| Roy et al8 | Municipal data for Chennai (city) (2002–2004) and Mangalore (city) (2003–2007), India; microscopic confirmation | Two linear regressions (one for each city); adjusted for population, lagged weather covariates, autoregressive term, interaction terms, polynomial terms | Monthly SPR (Chennai), monthly cases (Mangalore) | 28/8 (Chennai), 48/12 (Mangalore); 1 month ahead | 95% CI |
| Teklehaimanot et al9 | Health facility data from 1990 to 2000 for all districts in Ethiopia; microscopic confirmation | 10 Poisson regressions (one for each district); lagged weather covariates, autoregressive term, time trend and indicator covariates for week of the year | Weekly cases | 572 (varied between districts, training and testing); 52 weeks (year) were removed from series at a time; 1–4 week ahead forecasts | Compared performance of alerts from predicted versus observed cases (using potentially prevented cases) |
| Xiao et al10 | Medical and health unit data from 1995 to 2007 for Hainan Province, China; microscopic confirmation | Poisson regression; lagged weather covariates, autoregressive term | Monthly incidence | 144/12 | T-test (predictive value significantly different than actual) |
| Yacob and Swaroop11 | Medical data from 1944 to 1996 for all health districts in Punjab; clinical confirmation | 19 linear regressions (1 for each district); include coefficients of correlation between rainfall and epidemic figures from 1914 to 1943 | Seasonal epidemic figure* | Coefficient of correlation (between actual and predicted epidemic figure) | |
| Yan et al12 | Municipal data from 1951 to 2001 for Chongquin (city), China | Linear regression; logarithm curve | Yearly cases | 50/1 | Visual inspection of predicted within range of actual values |
| ARIMA forecasting studies | |||||
| Abeku et al13 | Health clinics data from 1986 to 1999 for 20 areas in Ethiopia; mixture of microscopic and clinical confirmed | 20 models (1 for each area) compared approaches: Overall average, seasonal average, seasonal adjustment, ARIMA | Monthly cases | 168/12 (varied between areas but last 12 months only used for testing); 1–12 month ahead forecasts | Average forecast error |
| Briët et al14 | Health facility data from 1972 to 2005 for all districts in Sri Lanka; microscopic confirmation | 25 models (1 for each district) compared approaches: Holt-Winters, ARIMA (seasonality assessed with fixed effects or harmonics) and SARIMA; lagged weather covariates | Monthly cases of malaria slide positives | 180/204 (varied between districts but approximately 50% of series reserved for testing); 1–4 month ahead forecasts | Mean absolute relative error |
| Liu et al15 | Data from 2004 to 2010 for China | SARIMA | Monthly incidence | 72/12 | Visual (plot of predicted vs observed) |
| Wangdi et al16 | Health centre data from 1994 to 2008 for seven districts in Bhutan; microscopic and antigen confirmation | Seven models (one for each district): SARIMA and ARIMAX; lagged weather covariates | Monthly cases | 144/24 | Mean average percent error |
| Wen et al17 | Data from 1991 to 2002 for Wanning County, China | SARIMA | Monthly incidence | 252/12 | 95% CI |
| Zhang et al18 | CDC data from 1959 to 1979 for Jinan (city) China; clinical confirmation | SARIMA; lagged weather covariates | Monthly cases | 84/120 (removed 1967 and 1968 from series) | Visual (plot of predicted vs observed) |
| Zhou et al19 | Data from 1996 to 2007 for Huaiyuan County, China; microscopic and clinical confirmation | SARIMA | Monthly incidence | 108/12 | Average error |
| Zhu et al20 | Data from 1998 to 2007 for Huaiyuan and Tongbai counties, China | SARIMA | Monthly incidence rates | 84/24; 1–12 month ahead forecasts | 95% CI and error |
| Mathematical forecasting studies | |||||
| Gaudart et al21 | Data from cohort of children from 1996 to 2000 in Bancoumana (municipality), Mali from 1996 to 2006; microscopic confirmation | VSEIRS model | Monthly incidence rate | 60 (training and testing); 15 day, 1 month, 2 month, seasonal forecasts | Mean absolute percentage error and root mean squared error |
| Laneri et al22 | Health centre data (passive and active surveillance) for Kutch (1987–2007) and Balmer (1985–2005) Districts, India; microscopic confirmation | 2 models (one for each district); compared two types of VSEIRS model to linear and negative binominal regressions | Monthly incidence for parameter estimation; seasonal totals (Sept−Dec) for epidemic forecasting | 240 (training and testing); 1 to 4 months ahead forecasts | Weighted mean square error and prediction likelihood |
| Neural network forecast studies | |||||
| Cunha et al23 | Ministry of Health data from 2003 to 2009 for Cornwall (City), Brazil; microscopic confirmation | Compared neural network to linear regression | Monthly cases | 72/12; 3, 6 and 12 months forecasts | Absolute error and mean square error |
| Gao et al24 | Data from 1994 to 1999 for Honghe State, China | Neural network | Monthly incidence | 48/12 | Percent error |
| Kiang et al25 | Hospital and clinic data from 1994 to 2001 for 19 provinces, Thailand; microscopic confirmation | 19 neural networks (1 for each province); various architectures used (varied by province) | Monthly incidence | 84/12 | Root mean square error |
| Other forecasting methods | |||||
| Fang et al26 | Data from 1956 to 1988 for Xuzhou (City), China | Grey and Grey Verhulst models (1,1) | Yearly incidence | 30/2 | Percent error |
| Gao et al27 | Data from 1998 to 2005 for Longgang District, China | Grey model (1,1) | Yearly incidence | 6/1 | Error and percent error |
| Guo et al28 | Data from 1988 to 2010 China | Grey model (1,1) | Yearly incidence | 21/2 | Visual (plot of predicted vs observed) |
| Gill29 | Medical data from 1925 to 1926 for health districts in Punjab; clinical confirmation | 29 forecasts consisting of visual inspection of rainfall, spleen rates and epidemic potential† | Seasonal epidemic (yes/no) | Qualitative comparison of prediction (presence of epidemic) to epidemic figure | |
| Medina et al30 | Community health centre data from 1996 to 2004 (14 centres) for Niono District, Mali; clinical confirmation | Multiplicative Holt-Winters model, age-specific rates (three age groups); compared to seasonal adjustment method | Monthly malaria consultation rates | 36/72; 2 and 3-month ahead forecasts; one step ahead forecasts | Mean absolute percentage error and 95% CI |
| Xu and Jin31 | Data from 2000 to 2005 for Jiangsu Province, China | Grey model | Yearly cases | 4/1 | Visual (plot of predicted vs observed number of cases) |
*Seasonal epidemic figure is the ratio of October incidence to mean spring incidence.
†Epidemic potential is the coefficient of variability of fevers during the month of October for the periods of 1868–1921.
ARIMA, auto-regressive integrated moving average; ARIMAX, auto-regressive integrated moving average with exogenous input; SARIMA, seasonal auto-regressive integrated moving average; SPR, slide positivity rate; VSEIRS, vector-susceptible-exposed-infected-recovered-susceptible model.