- Volume 21 Issue 6
DOI QR Code
Estimating the Transmittable Prevalence of Infectious Diseases Using a Back-Calculation Approach
- Lee, Youngsaeng (ICT Convergence Research Center for Smart Appliances, Chonnam National University) ;
- Jang, Hyun Gap (JW LEE Center for Global Medicine, College of Medicine, Seoul National University) ;
- Kim, Tae Yoon (Department of Statistics, Kyemyong University) ;
- Park, Jeong-Soo (Department of Statistics, Chonnam National University)
- Received : 2014.05.20
- Accepted : 2014.08.24
- Published : 2014.11.30
A new method to calculate the transmittable prevalence of an epidemic disease is proposed based on a back-calculation formula. We calculated the probabilities of reactivation and of parasitemia as well as transmittable prevalence (the number of persons with parasitemia in the incubation period) of malaria in South Korea using incidence of 12 years(2001-2012). For this computation, a new probability function of transmittable condition is obtained. The probability of reactivation is estimated by the least squares method for the back-calculated longterm incubation period. The probability of parasitemia is calculated by a convolution of the survival function of the short-term incubation function and the probability of reactivation. Transmittable prevalence is computed by a convolution of the infected numbers and the probabilities of transmission. Confidence intervals are calculated using the parametric bootstrap method. The method proposed is applicable to other epidemic diseases in other countries where incidence and a long incubation period are available. We found the estimated transmittable prevalence in South Korea was concentrated in the summer with 276 cases on a peak at the
Supported by : National Research Foundation of Korea (NRF)
- Adak, T., Sharma, V. P. and Orlov, V. S. (1998). Studies on the Plasmodium vivax relapse pattern in India, American Journal of Tropical Medicine and Hygiene, 59, 175-179. https://doi.org/10.4269/ajtmh.1998.59.175
- Bacchetti, P., Segal, M. and Jewell, N. P. (1993). Back-calculation of HIV infection rate (with discussion), Statistical Science, 8, 82-119. https://doi.org/10.1214/ss/1177010994
- Brookmeyer, R. and Gail, M. H. (1988). A method of obtaining short-term projections and lower bounds on the size of the AIDS epidemic, Journal of the American Statistical Association, 83, 301-308. https://doi.org/10.1080/01621459.1988.10478599
- Burket, D. A., Lee, W. J., Lee, K. W., Kim, H. C., Lee, H. I., Lee, J. S., Shin, E. H., Wirtz, R. A., Cho, H. W., Claborn, D. M., Coleman, R. E., Kim, W. Y. and Klein, T. A. (2002). Late season commercial mosquito trap and host seeking activity evaluation against mosquitoes in a malarious area of the Republic of Korea, Korean Journal of Parasitology, 40, 45-54. https://doi.org/10.3347/kjp.2002.40.1.45
- Centers for Disease Control and Prevention; CDC (2006). Available from: http://www.cdc.gov/malaria/
- Cogswell, F. B. (1992). The hypnozoite and relapse in primate malaria, Clinical Microbiology Reviews, 5, 26-35. https://doi.org/10.1128/CMR.5.1.26
- Contacos, P. G., Collins, W. E., Jeffery, G. M., Krotoski, W. A. and Howard, W. A. (1972). Studies on the characterization of Plasmodium vivax strains from Central America, American Journal of Tropical Medicine and Hygiene, 21, 707-712. https://doi.org/10.4269/ajtmh.1972.21.707
- De Angelis, D., Hickman, M. and Yang, S. (2004). Estimating long-term trends in the incidence and prevalence of opiate use/injecting drug use and the number of former users: Back-calculation methods and opiate overdose deaths, American Journal of Epidemiology, 160, 994-1004. https://doi.org/10.1093/aje/kwh306
- Friedman, J. H. (1984). A Variable Span Scatterplot Smoother, Technical Report No.5, Laboratory for computational statistics, Stanford University.
- Garnham, P. C. C., Bray, R. S., Bruce-Chwatt, L. J., Draper, C. C., Killick-Kendrick, R., Sergiev, P. G., Tiburskaja, N. A., Shute, P. G. and Maryon, M. (1975). A strain of Plasmodium vivax characterized by prolonged incubation: Morphological and biological characteristics, Bulletin of the World Health Organization, 52, 21-32.
- Goubar, A., Bitar, D., Cao, W. C., Feng, D., Fang, L. Q. and Desenclos, J. C. (2009). An approach to estimate the number of SARS cases imported by international air travel, Epidemiology & Infection, 137, 1019-1031. https://doi.org/10.1017/S0950268808001635
- Greenwood, B. and Mutabingwa, T. (2002). Malaria in 2002, Nature, 415, 670-672. https://doi.org/10.1038/415670a
- Hall, H. I., Song, R., Rhodes, P., Prejean, J., An, Q., Lee, L. M., Karon, J., Brookmeyer, B., Kaplan, E. H., McKenna, M. T., Janssen, R. S. and for the HIV Incidence Surveillance Group (2008). Estimation of HIV incidence in the United States, Journal of the American Medical Association, 300, 520-529. https://doi.org/10.1001/jama.300.5.520
- Kim, J. H. (2011). Semi-parametric bootstrap confidence intervals for high-quantiles of heavy-tailed distributions, Communications for Statistical Applications and Methods, 18, 717-732. https://doi.org/10.5351/CKSS.2011.18.6.717
- Kim, S. J., Kim, S. H., Jo, S. N., Gwack, J., Youn, S. K. and Jang, J. Y. (2013). The long and short incubation periods of plasmodium vivax malaria in Korea: The characteristics and relating factors, Infection & Chemotherapy, 45, 184-193. https://doi.org/10.3947/ic.2013.45.2.184
- Kitchen, A. and Chiodini, P. (2006). Malaria and blood transfusion, Vox Sanguinis, 90, 77-84. https://doi.org/10.1111/j.1423-0410.2006.00733.x
- Korean Center for Disease Control (2007). Malaria Infection Control and Management Policy, KCDC, Seoul.
- Korean Center for Disease Control (2008). Statistics of Communicable Diseases, Seoul: KCDC, Available from: http://stat.cdc.go.kr.
- Law, M., Lynskey, M., Ross, J. and Hall, W. (2001). Back-projection estimates of the number of dependent heroin users in Australia, Addiction, 96, 433-443. https://doi.org/10.1046/j.1360-0443.2001.9634337.x
- Lee, J. S., Lee, W. J., Cho, S. H. and Ree, H. I. (2002). Outbreak of vivax malaria in areas adjacent to the demilitarized zone, South Korea, American Journal of Tropical Medicine and Hygiene, 66, 13-17. https://doi.org/10.4269/ajtmh.2002.66.13
- Lee, Y., Jang, H., Rhee, J. A. and Park, J. S. (2014). Statistical estimations for Plasmodium vivax malaria in South Korea, Asia Pacific Journal of Tropical Medicine, in press.
- Mangoni, E. D., Severini, C., Menegon, M., Romi, R., Ruggiero, G. and Majori, G. (2003). Case report: An unusual late relapse of Plasmodium vivax malaria, American Journal of Tropical Medicine and Hygiene, 68, 159-160.
- Mary, M., Gary, T., Mary, C. and Monica, P. (2001). Transfusion-transmitted malaria in the United States from 1963 through 1999, New England Journal of Medicine, 344, 1973-1978. https://doi.org/10.1056/NEJM200106283442603
- Mezzetti, M. and Robertson, C. (1999). A hierarchical Bayesian approach to age-specific backcalculation of cancer incidence rates, Statistics in Medicine, 18, 919-933. https://doi.org/10.1002/(SICI)1097-0258(19990430)18:8<919::AID-SIM89>3.0.CO;2-7
- Nishiura, H., Lee, H. W., Cho, S. H., Lee, W. G., In, T. S., Moon, S. U., Chung, G. T. and Kim, T. S. (2007). Estimates of short- and long-term incubation periods of Plasmodium vivax malaria in the Republic of Korea, Transactions of the Royal Society of Tropical Medicine and Hygiene, 101, 338-343. https://doi.org/10.1016/j.trstmh.2006.11.002
- Park, J. W., Klein, T. A., Lee, H. C., Pacha, L. A., Ryu, S. H., Yeom, J. S., Moon, S. H., Kim, T. S., Chai, J. Y., Oh, M. D. and Choe, K. W. (2005). Vivax malaria: A continuing health threat to the Republic of Korea, American Journal of Tropical Medicine and Hygiene, 69, 159-167.
- Punyacharoesin, N. and Viwatwongkasem, C. (2009). Trends in three decades of HIV/AIDS epidemic in Thailand by nonparametric backcalculation method, AIDS, 23, 1143-1152. https://doi.org/10.1097/QAD.0b013e32832baa1c
- R-CRAN (2014). R program, Available from: http://www.r-project.org
- Ree, H. I., Hwang, U. W., Lee, I. Y. and Kim, T. E. (2001). Daily survival and human blood index of Anopheles sinensis, the vector species of malaria in Korea, American Mosquito Control Association, 17, 67-72.
- Rogers, D. J. and Randolph, S. E. (2000). The global spread of malaria in a future, warmer world, Science, 289, 1763-1766.
- WHO (2005). World Malaria Report.