Maximum likelihood estimation of the negative binomial dispersion parameter for highly overdispersed data, with applications to infectious diseases

PLoS ONE

Volumn 2, Issue 2, 2007, Pages

  Lloyd Smith, James O ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCURACY; ARTICLE; BINOMIAL DISTRIBUTION; CONFIDENCE INTERVAL; CONTROLLED STUDY; DISEASE TRANSMISSION; EPIDEMIC; HUMAN; INFECTION; INTERNAL BIAS; MATHEMATICAL COMPUTING; MAXIMUM LIKELIHOOD METHOD; STATISTICAL ANALYSIS; STATISTICAL MODEL; COMPUTER SIMULATION; EPIDEMIOLOGY; HEALTH SURVEY; INFECTIOUS DISEASE MEDICINE; STATISTICS;

BINOMIAL DISTRIBUTION; COMPUTER SIMULATION; CONFIDENCE INTERVALS; DISEASE OUTBREAKS; DISEASE TRANSMISSION, INFECTIOUS; HUMANS; INFECTIOUS DISEASE MEDICINE; LIKELIHOOD FUNCTIONS; POPULATION SURVEILLANCE; SELECTION BIAS;

EID: 34250370287     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0000180     Document Type: Article

References (29)

1. Bliss CI, Fisher RA (1953) Fitting the negative binomial distribution to biological data - note on the efficient fitting of the negative binomial. Biometrics 9: 176-200.
2. Pielou EC (1977) Mathematical Ecology. New York: Wiley.
3. White GC, Bennetts RE (1996) Analysis of frequency count data using the negative binomial distribution. Ecology 77: 2549-2557.
4. Shaw DJ, Grenfell BT, Dobson AP (1998) Patterns of macroparasite aggregation in wildlife host populations. Parasitology 117: 597-610.
5. Walther BA, Morand S (1998) Comparative performance of species richness estimation methods. Parasitology 116: 395-405.
6. Power JH, Moser EB (1999) Linear model analysis of net catch data using the negative binomial distribution. Can J Fish Aq Sci 56: 191-200.
7. Alexander N, Moyeed R, Stander J (2000) Spatial modelling of individual-level parasite counts using the negative binomial distribution. Biostatistics 1: 453-463.
8. Lloyd-Smith JO, Schreiber SJ, Kopp PE, Getz WM (2005) Superspreading and the effect of individual variation on disease emergence. Nature 438: 355-359.
9. Harris TE (1989) The Theory of Branching Processes. New York: Dover.
10. Anscombe FJ (1950) Sampling theory of the negative binomial and logarithmic series distributions. Biometrika 37: 358-382.
11. Pieters EP, Gates CE, Matis JH, Sterling WL (1977) Small sample comparison of different estimators of negative binomial parameters. Biometrics 33: 718-723.
12. Wilson K, Bjornstad ON, Dobson AP, Merler S, Poglayen G, et al. (2001) Heterogeneities in macroparasite infections: patterns and processes. In: Hudson PJ, Rizzoli A, Grenfell BT, Heesterbeek H, Dobson AP, eds. The Ecology of Wildlife Diseases. Oxford: Oxford University Press. pp. 6-44.
13. Ross GJS, Preece DA (1985) The negative binomial distribution. Statistician 34: 323-336.
14. Clark SJ, Perry JN (1989) Estimation of the negative binomial parameter kappa by maximum quasi-likelihood. Biometrics 45: 309-316.
15. Piegorsch WW (1990) Maximum-likelihood estimation for the negative binomial dispersion parameter. Biometrics 46: 863-867.
16. Gregory RD, Woolhouse MEJ (1993) Quantification of parasite aggregation - a simulation study. Acta Trop 54: 131-139.
17. Saha K, Paul S (2005) Bias-corrected maximum likelihood estimator of the negative binomial dispersion parameter. Biometrics 61: 179-185.
18. Thompson WL (2002) Towards reliable bird surveys: Accounting for individuals present but not detected. Auk 119: 18-25.
19. Wallinga J, Teunis P (2004) Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures. Am J Epidemiol 160: 509-516.
20. Gray BR (2005) Selecting a distributional assumption for modelling relative densities of benthic macroinvertebrates. Ecol Model 185: 10-12.
21. Donnelly CA, Fisher MC, Fraser C, Ghani AC, Riley S, et al. (2004) Epidemiological and genetic analysis of severe acute respiratory syndrome. Lancet Infect Dis 4: 672-683.
22. Diekmann O, Heesterbeek JAP (2000) Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis, and Interpretation. Chichester: John Wiley & Sons.
23. Boswell MT, Patil GP (1970) Chance mechanisms generating the negative binomial distribution. In: Patil GP, ed. Random Counts in Scientific Work. University ParkPA: Pennsylvania State University Press. pp. 3-22.
24. Rice JA (1995) Mathematical statistics and data analysis. Belmont, CA: Duxbury Press.
25. Willson LJ, Folks JL, Young JH (1984) Multistage estimation compared with fixed-sample-size estimation of the negative binomial parameter κ. Biometrics 40: 109-117.
26. Blaker H (2000) Confidence curves and improved exact confidence intervals for discrete distributions. Can J Stat 28: 783-798.
27. Ridout MS, Demetrio CGB, Hinde JP (1998) Models for counts data with many zeros. Proceedings of the XIXth International Biometric Conference. pp. 179-192.
28. Anderson RM, May RM (1991) Infectious Diseases of Humans: Dynamics and Control: Oxford University Press.
29. 0 of an infectious pathogen by a removal method. Math Biosci 198: 14-26.