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Frequentist and Bayesian approaches to prevalence estimation using examples from Johne's disease

Published online by Cambridge University Press:  17 March 2008

Locksley L. McV. Messam ,
Adam J. Branscum ,
Michael T. Collins  and
Ian A. Gardner
Locksley L. McV. Messam
Affiliation:
Department of Medicine and Epidemiology, School of Veterinary Medicine, University of California, One Shields Avenue, Davis, CA, USA
Adam J. Branscum
Affiliation:
Department of Biostatistics, College of Public Health, University of Kentucky, Lexington, KY, USA
Michael T. Collins
Affiliation:
Department of Pathobiological Sciences, School of Veterinary Medicine, University of Wisconsin-Madison, Madison, WI, USA
Ian A. Gardner*
Affiliation:
Department of Medicine and Epidemiology, School of Veterinary Medicine, University of California, One Shields Avenue, Davis, CA, USA
*
*Corresponding author. E-mail: [email protected]
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Abstract

Although frequentist approaches to prevalence estimation are simple to apply, there are circumstances where it is difficult to satisfy assumptions of asymptotic normality and nonsensical point estimates (greater than 1 or less than 0) may result. This is particularly true when sample sizes are small, test prevalences are low and imperfect sensitivity and specificity of diagnostic tests need to be incorporated into calculations of true prevalence. Bayesian approaches offer several advantages including direct computation of range-respecting interval estimates (e.g. intervals between 0 and 1 for prevalence) without the requirement of transformations or large-sample approximations. They also allow direct probabilistic interpretation, and the flexibility to model in a straightforward manner the probability of zero prevalence. In this review, we present frequentist and Bayesian methods for animal- and herd-level true prevalence estimation based on individual and pooled samples. We provide statistical methods for detecting differences between population prevalence and frequentist methods for sample size and power calculations. All examples are motivated using Mycobacterium avium subspecies paratuberculosis infection and we provide WinBUGS code for all examples of Bayesian estimation.

Keywords

prevalence estimationBayesian methodsfrequentist methodspooled testingMycobacterium avium subspecies paratuberculosis
Type
Review Article
Information
Animal Health Research Reviews , Volume 9 , Issue 1 , June 2008 , pp. 1 - 23
Copyright
Copyright © 2008 Cambridge University Press

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References

Adcock, CJ (1997). Sample size determination: a review. Statistician 46: 261–283.CrossRefGoogle Scholar
Agresti, A (1996). An Introduction to Categorical Data Analysis. New York: Wiley-Interscience.Google Scholar
Agresti, A and Coull, BA (1998). Approximate is better than ‘exact’ for interval estimation of binomial proportions. The American Statistician 52: 119–126.Google Scholar
Altman, DG (1991). Practical Statistics for Medical Research. London and New York: Chapman and Hall.Google Scholar
Baggesen, DL, Wegener, HC, Bager, F, Stege, H and Christensen, J (1996). Herd prevalence of Salmonella enterica infections in Danish slaughter pigs determined by microbiological testing. Preventive Veterinary Medicine 26: 201–213.CrossRefGoogle Scholar
Benito, A, Carmena, D, Joseph, L, Martinez, J and Guisantes, JA (2006). Dog echinococcosis in Northern Spain: comparison of coproantigen and serum antibody assays with coprological exam. Veterinary Parasitology 142: 102–111.CrossRefGoogle ScholarPubMed
Berry, DA (1996). Statistics: A Bayesian Perspective. Belmont, CA: Duxbury Press.Google Scholar
Berry, DA and Lindgren, BW (1996). Statistics: Theory and Methods. Belmont, CA: Duxbury Press.Google Scholar
Bland, JM and Altman, DG (1998). Bayesians and frequentists. British Medical Journal 317: 1151–1160.CrossRefGoogle ScholarPubMed
Boelaert, F, Walravens, K, Biront, P, Vermeersch, JP, Berkvens, D and Godfroid, J (2000). Prevalence of paratuberculosis (Johne's disease) in the Belgian cattle population. Veterinary Microbiology 77: 269–281.CrossRefGoogle ScholarPubMed
Borel, N, Doherr, MG, Vretou, E, Psarrou, E, Thoma, R and Pospischil, A (2004). Seroprevalences for ovine enzootic abortion in Switzerland. Preventive Veterinary Medicine 65: 205–216.CrossRefGoogle ScholarPubMed
Branscum, AJ, Gardner, IA and Johnson, WO (2004). Bayesian modeling of animal- and herd-level prevalences. Preventive Veterinary Medicine 66: 101–112.CrossRefGoogle ScholarPubMed
Branscum, AJ, Gardner, IA and Johnson, WO (2005a). Estimation of diagnostic-test sensitivity and specificity through Bayesian modeling. Preventive Veterinary Medicine 68: 145–163.CrossRefGoogle ScholarPubMed
Branscum, AJ, Gardner, IA, Wagner, BA, McInturff, PS and Salman, MD (2005b). Effect of diagnostic testing error on intracluster correlation coefficient estimation. Preventive Veterinary Medicine 69: 63–75.CrossRefGoogle ScholarPubMed
Branscum, AJ, Johnson, WO and Gardner, IA (2006). Sample size calculations for disease freedom and prevalence estimation surveys. Statistics in Medicine 25: 2658–2674.CrossRefGoogle ScholarPubMed
Brinkhof, JMA, Houwers, DJ and van Maanen, C (2006). Development of a sample pooling strategy for the serodiagnosis of small ruminant lentiviral infections using the ELITEST-MVV ELISA. Small Ruminant Research, doi:10.1016/j.smallrumres.2006.03.003Google Scholar
Cameron, AR and Baldock, FC (1998). Two-stage sampling in surveys to substantiate freedom from disease. Preventive Veterinary Medicine 34: 19–30.CrossRefGoogle ScholarPubMed
Carabin, H, Balolong, E, Joseph, L, McGarvey, ST, Johansen, MV, Fernandez, T, Willingham, AL and Olveda, R (2005). Estimating sensitivity and specificity of a faecal examination method for Schistosoma japonicum infection in cats, dogs, water buffaloes, pigs, and rats in Western Samar and Sorsogon Provinces, The Philippines. International Journal for Parasitology 35: 1517–1524.CrossRefGoogle ScholarPubMed
Christensen, J and Gardner, IA (2000). Herd-level interpretation of test results for epidemiologic studies of animal diseases. Preventive Veterinary Medicine 45: 83–106.CrossRefGoogle ScholarPubMed
Christensen, J, Baggesen, DL, Nielsen, B and Stryhn, H (2002). Herd prevalence of Salmonella spp. in Danish pig herds after implementation of the Danish Salmonella Control Program with reference to a pre-implementation study. Veterinary Microbiology 88: 175–188.CrossRefGoogle ScholarPubMed
Clough, HE, Clancy, D, O'Neill, PD and French, NP (2003). Bayesian methods for estimating pathogen prevalence within groups of animals from faecal-pat sampling. Preventive Veterinary Medicine 58: 145–169.CrossRefGoogle ScholarPubMed
Collins, MT, Wells, SJ, Petrini, KR, Collins, JE, Schultz, RD and Whitlock, RH (2005). Evaluation of five antibody detection tests for diagnosis of bovine paratuberculosis. Clinical and Diagnostic Laboratory Immunology 12: 685–692.Google ScholarPubMed
Collins, MT, Gardner, IA, Garry, FB, Roussel, AJ and Wells, SJ (2006). Consensus recommendations on diagnostic testing for the detection of paratuberculosis in cattle in the United States. Journal of the American Veterinary Medical Association 229: 1912–1919.CrossRefGoogle ScholarPubMed
Cowling, DW, Gardner, IA and Johnson, WO (1999). Comparison of methods for estimation of individual-level prevalence based on pooled samples. Preventive Veterinary Medicine 39: 211–225.CrossRefGoogle ScholarPubMed
Delafosse, A, Castro-Hermida, JA, Baudry, C, Ares-Mazas, E and Chartier, C (2006). Herd-level risk factors for Cryptosporidium infection in dairy-goat kids in western France. Preventive Veterinary Medicine 77: 109–121.CrossRefGoogle ScholarPubMed
Donald, AW, Gardner, IA and Wiggins, AD (1994). Cut-off points for aggregate herd testing in the presence of disease clustering and correlation of test errors. Preventive Veterinary Medicine 19: 167–187.CrossRefGoogle Scholar
Dorny, P, Phiri, IK, Vercruysse, J, Gabriel, S, Willingham, IAL, Brandt, J, Victor, B, Speybroeck, N and Berkvens, D (2004). A Bayesian approach for estimating values for prevalence and diagnostic test characteristics of porcine cysticercosis. International Journal for Parasitology 34: 569–576.CrossRefGoogle ScholarPubMed
Dunson, DB (2001). Commentary: Practical advantages of Bayesian analysis of epidemiologic data. American Journal of Epidemiology 153: 1222–1226.CrossRefGoogle ScholarPubMed
Durr, PA, Tait, N and Lawson, AB (2005). Bayesian hierarchical modelling to enhance the epidemiological value of abattoir surveys for bovine fasciolosis. Preventive Veterinary Medicine 71: 157–172.CrossRefGoogle ScholarPubMed
Enoe, C, Georgiadis, MP and Johnson, WO (2000). Estimation of sensitivity and specificity of diagnostic tests and disease prevalence when the true disease state is unknown. Preventive Veterinary Medicine 45: 61–81.CrossRefGoogle ScholarPubMed
Fleiss, JL (1981). Statistical Methods for Rates and Proportions. New York: Wiley.Google Scholar
Gardner, IA (2002). The utility of Bayes' theorem and Bayesian inference in veterinary clinical practice and research. Australian Veterinary Journal 80: 758–761.CrossRefGoogle ScholarPubMed
Geurden, T, Claerebout, E, Vercruysse, J and Berkvens, D (2004). Estimation of diagnostic test characteristics and prevalence of Giardia duodenalis in dairy calves in Belgium using a Bayesian approach. International Journal for Parasitology 34: 1121–1127.CrossRefGoogle ScholarPubMed
Goodman, SN and Berlin, JA (1994). The use of predicted confidence intervals when planning experiments and the misuse of power when interpreting results. Annals of Internal Medicine 121: 200–206.CrossRefGoogle ScholarPubMed
Greenland, S (1990). Randomization, statistics, and causal inference. Epidemiology 1: 421–429.CrossRefGoogle ScholarPubMed
Greiner, M and Gardner, IA (2000a). Application of diagnostic tests in veterinary epidemiologic studies. Preventive Veterinary Medicine 45: 43–59.CrossRefGoogle ScholarPubMed
Greiner, M and Gardner, IA (2000b). Epidemiologic issues in the validation of veterinary diagnostic tests. Preventive Veterinary Medicine 45: 3–22.CrossRefGoogle ScholarPubMed
Hanson, T, Johnson, WO and Gardner, IA (2003a). Hierarchical models for estimating herd prevalence and test accuracy in the absence of a gold standard. Journal of Agricultural Biological and Environmental Statistics 8: 223–239.CrossRefGoogle Scholar
Hanson, TE, Johnson, WO, Gardner, IA and Georgiadis, MP (2003b). Determining the infection status of a herd. Journal of Agricultural Biological and Environmental Statistics 8: 469–485.CrossRefGoogle Scholar
Hui, SL and Walter, SD (1980). Estimating the error rates of diagnostic tests. Biometrics 36: 167–171.CrossRefGoogle ScholarPubMed
Humphry, RW, Cameron, A and Gunn, GJ (2004). A practical approach to calculate sample size for herd prevalence surveys. Preventive Veterinary Medicine 65: 173–188.CrossRefGoogle ScholarPubMed
Johnson, WO, Gastwirth, JL and Pearson, LM (2001). Screening without a ‘gold standard’: the Hui–Walter paradigm revisited. American Journal of Epidemiology 153: 921–924.CrossRefGoogle Scholar
Johnson, WO, Su, CL, Gardner, IA and Christensen, R (2004). Sample size calculations for surveys to substantiate freedom of populations from infectious agents. Biometrics 60: 165–171.CrossRefGoogle ScholarPubMed
Jovanovic, BD and Levy, PS (1997). A look at the Rule of Three. The American Statistician 51: 137–139.CrossRefGoogle Scholar
Kalis, CHJ, Collins, MT, Barkema, HW and Hesselink, JW (2004). Certification of herds as free of Mycobacterium paratuberculosis infection: actual pooled faecal results versus certification model predictions. Preventive Veterinary Medicine 65: 189–204.CrossRefGoogle ScholarPubMed
Kalis, CHJ, Hesselink, JW, Barkema, HW and Collins, MT (2000). Culture of strategically pooled bovine fecal samples as a method to screen herds for paratuberculosis. Journal of Veterinary Diagnostic Investigation 12: 547–551.CrossRefGoogle ScholarPubMed
Kline, RL, Brothers, TA, Brookmeyer, R, Zeger, S and Quinn, TC (1989). Evaluation of human immunodeficiency virus seroprevalence in population surveys using pooled sera. Journal of Clinical Microbiology 27: 1449–1452.CrossRefGoogle ScholarPubMed
Lachin, JM (1981). Introduction to sample size determination and power analysis for clinical trials. Controlled Clinical Trials 2: 93–113.CrossRefGoogle ScholarPubMed
Lachin, JM (1992). Power and sample size evaluation for the McNemar test with application to matched case-control studies. Statistics in Medicine 11: 1239–1251.CrossRefGoogle ScholarPubMed
Leemis, LM and Trivedi, KS (1996). A comparison of approximate interval estimators for the Bernoulli parameter. The American Statistician 50: 63–68.CrossRefGoogle Scholar
Letellier, C, De Meulemeester, L, Lomba, M, Mijten, E and Kerkhofs, P (2005). Detection of BVDV persistently infected animals in Belgium: evaluation of the strategy implemented. Preventive Veterinary Medicine 72: 121–125.CrossRefGoogle ScholarPubMed
Louis, TA (1981). Confidence intervals for a binomial parameter after observing no successes. The American Statistician 35: 154–154.CrossRefGoogle Scholar
Lui, K-J (2004). Statistical Estimation of Epidemiological Risk. Chichester, UK and Hoboken, NJ: Wiley.CrossRefGoogle Scholar
Manning, EJB and Collins, MT (2001). Mycobacterium avium subsp. paratuberculosis: pathogen, pathogenesis and diagnosis. Revue Scientifique et Technique de l'Office International des Epizooties 20: 133–150.CrossRefGoogle ScholarPubMed
Martin, SW, Shoukri, M and Thorburn, MA (1992). Evaluating the health-status of herds based on tests applied to individuals. Preventive Veterinary Medicine 14: 33–43.CrossRefGoogle Scholar
Munoz-Zanzi, C, Thurmond, M, Hietala, S and Johnson, W (2006). Factors affecting sensitivity and specificity of pooled-sample testing for diagnosis of low prevalence infections. Preventive Veterinary Medicine 74: 309–322.CrossRefGoogle ScholarPubMed
Ngowi, HA, Kassuku, AA, Maeda, GEM, Boa, ME, Carabin, H and Willingham, IAL (2004). Risk factors for the prevalence of porcine cysticercosis in Mbulu District, Tanzania. Veterinary Parasitology 120: 275–283.CrossRefGoogle ScholarPubMed
Nielsen, SS, Thamsborg, SM, Houe, H and Bitsch, V (2000). Bulk-tank milk ELISA antibodies for estimating the prevalence of paratuberculosis in Danish dairy herds. Preventive Veterinary Medicine 44: 1–7.CrossRefGoogle ScholarPubMed
Nielsen, SS, Enevoldsen, C and Grohn, YT (2002a). The Mycobacterium avium subsp. paratuberculosis ELISA response by parity and stage of lactation. Preventive Veterinary Medicine 54: 1–10.CrossRefGoogle ScholarPubMed
Nielsen, SS, Grohn, YT and Enevoldsen, C (2002b). Variation of the milk antibody response to paratuberculosis in naturally infected dairy cows. Journal of Dairy Science 85: 2795–2802.CrossRefGoogle ScholarPubMed
Rahme, E, Joseph, L and Gyorkos, TW (2000). Bayesian sample size determination for estimating binomial parameters from data subject to misclassification. Journal of the Royal Statistical Society Series C – Applied Statistics 49: 119–128.CrossRefGoogle Scholar
Rapsch, C, Schweizer, G, Grimm, F, Kohler, L, Bauer, C, Deplazes, P, Braun, U and Torgerson, PR (2006). Estimating the true prevalence of Fasciola hepatica in cattle slaughtered in Switzerland in the absence of an absolute diagnostic test. International Journal for Parasitology 36: 1153–1158.CrossRefGoogle ScholarPubMed
Rogan, WJ and Gladen, B (1978). Estimating prevalence from the results of a screening test. American Journal of Epidemiology 107: 71–76.CrossRefGoogle ScholarPubMed
Rosner, B (2000). Fundamentals of Biostatistics. Pacific Grove, CA: Duxbury.Google Scholar
Rothman, KJ and Greenland, S (1998). Measures of disease frequency. In: Rothman, KJ and Greenland, S (eds) Modern Epidemiology. Philadelphia, PA: Lippincott-Raven, pp. 29–46.Google Scholar
Roussas, GG (2003). Introduction to Probability and Statistical Inference. Amsterdam, Boston: Academic Press.Google Scholar
Sacks, JM, Bolin, SR and Crowder, SV (1989). Prevalence estimation from pooled samples. American Journal of Veterinary Research 50: 205–206.Google ScholarPubMed
Scheaffer, RL, Mendenhall, W and Ott, L (1995). Elementary Survey Sampling. Belmont, CA: Duxbury Press.Google Scholar
Schenker, N and Gentleman, JF (2001). On judging the significance of differences by examining the overlap between confidence intervals. The American Statistician 55: 182–186.CrossRefGoogle Scholar
Sergeant, ESG, Whittington, RJ and More, SJ (2002). Sensitivity and specificity of pooled faecal culture and serology as flock-screening tests for detection of ovine paratuberculosis in Australia. Preventive Veterinary Medicine 52: 199–211.CrossRefGoogle ScholarPubMed
Sockett, DC, Carr, DJ and Collins, MT (1992). Evaluation of conventional and radiometric fecal culture and a commercial DNA probe for diagnosis of Mycobacterium paratuberculosis infections in cattle. Canadian Journal of Veterinary Research 56: 148–153.Google Scholar
Staubach, C, Schmid, V, Knorr-Held, L and Ziller, M (2002). A Bayesian model for spatial wildlife disease prevalence data. Preventive Veterinary Medicine 56: 75–87.CrossRefGoogle ScholarPubMed
Su, CL, Gardner, IA and Johnson, WO (2004). Diagnostic test accuracy and prevalence inferences based on joint and sequential testing with finite population sampling. Statistics in Medicine 23: 2237–2255.CrossRefGoogle ScholarPubMed
Tavornpanich, S, Gardner, IA, Anderson, RJ, Shin, S, Whitlock, RH, Fyock, T, Adaska, JM, Walker, RL and Hietala, SK (2004). Evaluation of microbial culture of pooled fecal samples for detection of Mycobacterium avium subsp paratuberculosis in large dairy herds. American Journal of Veterinary Research 65: 1061–1070.CrossRefGoogle ScholarPubMed
Tavornpanich, S, Gardner, IA, Carpenter, TE, Johnson, WO and Anderson, RJ (2006). Evaluation of cost-effectiveness of targeted sampling methods for detection of Mycobacterium avium subsp paratuberculosis infection in dairy herds. American Journal of Veterinary Research 67: 821–828.CrossRefGoogle ScholarPubMed
Tu, XM, Litvak, E and Pagano, M (1994). Screening tests – can we get more by doing less? Statistics in Medicine 13: 1905–1919.CrossRefGoogle ScholarPubMed
Tu, XM, Litvak, E and Pagano, M (1995). On the informativeness and accuracy of pooled testing in estimating prevalence of a rare disease – application to HIV screening. Biometrika 82: 287–297.CrossRefGoogle Scholar
Turnquist, SE, Snider, TG, Kreeger, JM, Miller, JE, Hagstad, HV and Olcott, BM (1991). Serologic evidence of paratuberculosis in Louisiana beef-cattle herds as detected by ELISA. Preventive Veterinary Medicine 11: 125–130.CrossRefGoogle Scholar
van Schaik, G, Schukken, YH, Crainiceanu, C, Muskens, J and VanLeeuwen, JA (2003). Prevalence estimates for paratuberculosis adjusted for test variability using Bayesian analysis. Preventive Veterinary Medicine 60: 281–295.CrossRefGoogle ScholarPubMed
Vose, D (2000). Risk Analysis: A Quantitative Guide. Chichester, UK and New York: Wiley.Google Scholar
Wagner, B and Salman, MD (2004). Strategies for two-stage sampling designs for estimating herd-level prevalence. Preventive Veterinary Medicine 66: 1–17.CrossRefGoogle ScholarPubMed
Wang, X-H, Wu, X-H and Zhou, X-N (2006). Bayesian estimation of community prevalences of Schistosoma japonicum infection in China. International Journal for Parasitology 36: 895–902.CrossRefGoogle ScholarPubMed
Wells, SJ, Whitlock, RH and Lindeman, CJ (2002). Evaluation of bacteriologic culture of pooled fecal samples for detection of Mycobacterium paratuberculosis. American Journal of Veterinary Research 63: 1207–1211.CrossRefGoogle ScholarPubMed
Wells, SJ, Godden, SM, Lindeman, CJ and Collins, JE (2003). Evaluation of bacteriologic culture of individual and pooled fecal samples for detection of Mycobacterium paratuberculosis in dairy cattle herds. Journal of the American Veterinary Medical Association 223: 1022–1025.CrossRefGoogle ScholarPubMed
Wittes, J (2002). Sample size calculations for randomized controlled trials. Epidemiologic Reviews 24: 39–53.CrossRefGoogle ScholarPubMed
Worlund, DD and Taylor, G (1983). Estimation of disease incidence in fish populations. Canadian Journal of Fisheries and Aquatic Sciences 40: 2194–2197.CrossRefGoogle Scholar
Youden, WJ (1950). Index for rating diagnostic tests. Cancer 3: 32–35.3.0.CO;2-3>CrossRefGoogle ScholarPubMed