Estimation of infections and recovery rates for highly polymorphic parasites when detectability is imperfect, using hidden Markov models

Statistics in Medicine

Volumn 22, Issue 10, 2003, Pages 1709-1724

  Smith, Tom ^a   Vounatsou, Penelope ^a  

^a SWISS TROPICAL AND PUBLIC HEALTH INSTITUTE   (Switzerland)

Author keywords

Bayesian hierarchical model; Hidden Markov process; Imperfect detectbility; Infection rate; Malaria; Markov chain Monte Carlo; Recovery rate

Indexed keywords

MEROZOITE SURFACE PROTEIN 2;

ALLELE; ARTICLE; BED NET; CHILD; CONTROLLED STUDY; CONVALESCENCE; COVARIANCE; DISEASE DURATION; DYNAMICS; FEMALE; GENOTYPE; HUMAN; INFANT; INFECTION RATE; MAJOR CLINICAL STUDY; MALARIA; MALE; MONTE CARLO METHOD; PLASMODIUM FALCIPARUM; POLYMERASE CHAIN REACTION; PROBABILITY; RANDOMIZATION; RESTRICTION FRAGMENT LENGTH POLYMORPHISM; STANDARD; STATISTICAL MODEL; STATISTICAL PARAMETERS; TANZANIA; ALGORITHM; ANIMAL; BAYES THEOREM; BED; CLINICAL TRIAL; CONTROLLED CLINICAL TRIAL; DISEASE TRANSMISSION; GENETICS; MALARIA FALCIPARUM; PRESCHOOL CHILD; RANDOMIZED CONTROLLED TRIAL;

ALGORITHMS; ANIMALS; BAYES THEOREM; BEDDING AND LINENS; CHILD, PRESCHOOL; GENOTYPE; HUMANS; INFANT; MALARIA, FALCIPARUM; MARKOV CHAINS; MONTE CARLO METHOD; PLASMODIUM FALCIPARUM; POLYMERASE CHAIN REACTION; POLYMORPHISM, RESTRICTION FRAGMENT LENGTH; RANDOMIZED CONTROLLED TRIALS; TANZANIA;

EID: 0038025639     PISSN: 02776715     EISSN: None     Source Type: Journal    
DOI: 10.1002/sim.1274     Document Type: Article

References (30)

1. Walter SD, Irwig LM. Estimation of test error rates, disease prevalence and relative risk from misclassified data: a review. Journal of Clinical Epidemiology 1988; 41:923-937.
2. Bekessy A, Molineaux L, Storey J. Estimation of incidence and recovery rates of Plasmodium falciparum parasitaemia from longitudinal data. Bulletin of the WHO 1976; 54:685-691.
3. Muench H. Catalytic Models in Epidemiology. Harvard University Press: Cambridge, Massachusetts, 1959.
4. Cohen JE, Singer B. Malaria in Nigeria: constrained continuous-time Markov models for discrete-time longitudinal data on human mixed-species infections. Lectures on Mathematics in the Life Sciences 1979; 12:69-133.
5. Dietz K, Molineaux L, Thomas A. A malaria model tested in the African savannah. Bulletin of the WHO 1974; 50:347-357.
6. Nedelman J. Inoculation and recovery rates in the malaria model of Dietz, Molineaux and Thomas. Mathematical Biosciences 1984; 69:209-233.
7. Nagelkerke NJ, Chunge RN, Kinoti SN. Estimation of parasitic infection dynamics when detectability is imperfect. Statistics in Medicine 1990; 9:1211-1219.
8. Woolhouse ME, Dye C, Etard JF, Smith T, Charlwood JD, Garnett GP, Hagan P, Hii JL, Ndhlovu PD, Quinnell RJ, Watts CH, Chandiwana SK, Anderson RM. Heterogeneities in the transmission of infectious agents: implications for the design of control programs. Proceedings of the National Academy of Science USA 1997; 94:338-342.
9. Felger I, Irion A, Steiger S, Beck HP. Genotypes of merozoite surface protein 2 of Plasmodium falciparum in Tanzania. Transactions of the Royal Society of Tropical Medicine and Hygiene 1999; 93 (Suppl 1):3-9.
10. Smith T, Felger I, Fraser-Hurt N, Beck HP. Effect of insecticide-treated bed nets on the dynamics of multiple Plasmodium falciparum infections. Transactions of the Royal Society of Tropical Medicine and Hygiene 1999; 93 (Suppl 1):53-57.
11. Bruce MC, Donnelly C, Narara A, Lagog M, Gibson N, Narara A, Walliker D, Alpers MP, Day KP. Age- and species-specific duration of infection in asymptomatic malaria infections in Papua New Guinea. Parasitology 2000; 121:247-256.
12. MacDonald IL, Zucchini W. Hidden Markov and Other Models for Discrete-valued Time Series. Chapman & Hall/CRC: Boca Raton, 1997.
13. Juang BH, Rabiner LR. Hidden Markov models for speech recognition. Technometrics 1991; 33:251-272.
14. Churchill GA, Lazareva B. Bayesian restoration of a hidden Markov chain with applications to DNA sequencing. Journal of Computational Biology 1999; 6:261-277.
15. Chib S. Calculating posterior distributions and modal estimates in Markov mixture models. Journal of Econometrics 1996; 75:79-97.
16. Hughes JP, Guttorp P, Charles SP. A nonhomogeneous hidden Markov model for precipitation. Applied Statistics 1999; 48:15-30.
17. MacDonald IL, Lerer LB. A time-series analysis of trends in firearm-related homicide and suicide. International Journal of Epidemiology 1994; 23:66-72 (erratum 1994; 23:1108).
18. Guihenneuc-Jouyaux C, Richardson S, Longini IM, Jr. Modeling markers of disease progression by a hidden Markov process: application to characterizing CD4 cell decline. Biometrics 2000; 56:733-741.
19. Robert CP, Celeux G, Diebolt J. Bayesian estimation of hidden Markov chains: a stochastic implementation. Statistics and Probability Letters 1993; 16:77-83.
20. Robert CP, Ryden T, Titterington DM. Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method. Applied Statistics 2000; 49:57-75.
21. Gupta S, Day KP. A theoretical framework for the immunoepidemiology of Plasmodium falciparum malaria. Parasite Immunology 1994; 16:361-370.
22. Fraser-Hurt N, Felger I, Edoh D, Steiger S, Mashaka M, Masanja H, Smith T, Mbena F, Beck HP. Effect of insecticide-treated bed nets on haemoglobin values, prevalence and multiplicity of infection with Plasmodium falciparum in a randomized controlled trial in Tanzania. Transactions of the Royal Society of Tropical Medicine aud Hygiene 1999;93 (Suppl 1):47-51.
23. Dempster AN, Laird NM, Rubin DB. Maximum Likelihood estimation from incomplete data via the EM algorithm (with discussion). Journal of Royal Statistical Association, Series B 1977; 39:1-38.
24. Baum LE, Petrie T, Soules G, Weiss N. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Annals of Mathematical Statistics 1970; 37:1554-1563.
25. Gelfand AE, Smith AFM. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 1990; 85:972-985.
26. Spiegelhalter DJ, Thomas A, Best N. WinBUGS. User Manual, version 1.3. Medical Research Council, Cambridge, U.K., 2000.
27. Best N, Cowles MK, Vines K. CODA: Convergence Diagnosis and Output Analysis Software for Gibbs Sampling Output. (0.30). Medical Research Council Cambridge, U.K., 1996.
28. Heidelberger P, Welch P. Simulation run length control in the presence of an initial transient. Operations Research 1983; 31:1109-1144.
29. Nedelman J. Estimation for a model of multiple malaria infections. Biometrics 1985; 41:447-453.
30. Molineaux L, Diebner HH, Eichner M, Collins WE, Jeffery GM, Dietz K. Plasmodium, falciparum parasitaemia described by a new mathematical model. Parasitology 2001; 122:379-391.