Inference of R0 and Transmission Heterogeneity from the Size Distribution of Stuttering Chains
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{"title"=>"Inference of R0 and Transmission Heterogeneity from the Size Distribution of Stuttering Chains", "type"=>"journal", "authors"=>[{"first_name"=>"Seth", "last_name"=>"Blumberg", "scopus_author_id"=>"9639027000"}, {"first_name"=>"James O.", "last_name"=>"Lloyd-Smith", "scopus_author_id"=>"6602998795"}], "year"=>2013, "source"=>"PLoS Computational Biology", "identifiers"=>{"pmid"=>"23658504", "sgr"=>"84878503913", "doi"=>"10.1371/journal.pcbi.1002993", "scopus"=>"2-s2.0-84878503913", "pui"=>"369039757", "isbn"=>"1553-7358 (Electronic) 1553-734X (Linking)", "issn"=>"1553734X"}, "id"=>"6c7782d7-902a-36bd-b507-524dd1a1cab6", "abstract"=>"This paper focuses on infectious diseases such as monkeypox, Nipah virus and avian influenza that transmit weakly from human to human. These pathogens cannot cause self-sustaining epidemics in the human population, but instead cause limited transmission chains that stutter to extinction. Such pathogens would go extinct if they were confined to humans, but they persist because of continual introduction from an external reservoir (such as animals, for the zoonotic diseases mentioned above). They are important to study because they pose a risk of emerging if they become more transmissible, or conversely to monitor the success of efforts to locally eliminate a pathogen by vaccination. A crucial challenge for these ‘stuttering’ pathogens is to quantify their transmissibility, in terms of the intensity and heterogeneity of disease transmission by infected individuals. In this paper, we use monkeypox as an example to show how these transmission properties can be estimated from commonly available data describing the size of observed stuttering chains. These results make it easier to monitor diseases that pose a risk of emerging (or re-emerging) as self-sustaining human pathogens, or to decide whether a seemingly large chain may signal a worrisome change in transmissibility.", "link"=>"http://www.mendeley.com/research/inference-r0-transmission-heterogeneity-size-distribution-stuttering-chains", "reader_count"=>79, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>5, "Researcher"=>27, "Student > Doctoral Student"=>4, "Student > Ph. D. Student"=>19, "Student > Postgraduate"=>1, "Student > Master"=>12, "Other"=>1, "Student > Bachelor"=>4, "Lecturer"=>3, "Professor"=>2}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>5, "Researcher"=>27, "Student > Doctoral Student"=>4, "Student > Ph. D. Student"=>19, "Student > Postgraduate"=>1, "Student > Master"=>12, "Other"=>1, "Student > Bachelor"=>4, "Lecturer"=>3, "Professor"=>2}, "reader_count_by_subject_area"=>{"Unspecified"=>6, "Agricultural and Biological Sciences"=>31, "Computer Science"=>3, "Earth and Planetary Sciences"=>2, "Economics, Econometrics and Finance"=>1, "Engineering"=>1, "Environmental Science"=>4, "Nursing and Health Professions"=>1, "Biochemistry, Genetics and Molecular Biology"=>1, "Mathematics"=>11, "Medicine and Dentistry"=>16, "Psychology"=>1, "Social Sciences"=>1}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>16}, "Social Sciences"=>{"Social Sciences"=>1}, "Psychology"=>{"Psychology"=>1}, "Mathematics"=>{"Mathematics"=>11}, "Unspecified"=>{"Unspecified"=>6}, "Environmental Science"=>{"Environmental Science"=>4}, "Engineering"=>{"Engineering"=>1}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>2}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>31}, "Computer Science"=>{"Computer Science"=>3}, "Nursing and Health Professions"=>{"Nursing and Health Professions"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}}, "reader_count_by_country"=>{"Netherlands"=>1, "Belgium"=>1, "United States"=>7, "United Kingdom"=>4, "Australia"=>1}, "group_count"=>1}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1051535"], "description"=>"<p>A) Ninety percent confidence regions for and inference are shown for monkeypox data gathered between 1980 and 1984 in the Democratic Republic of Congo <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002993#pcbi.1002993-Fine1\" target=\"_blank\">[26]</a>, <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002993#pcbi.1002993-Jezek2\" target=\"_blank\">[27]</a>. The two confidence regions are based on the same set of data. The chain size analysis is based on the number of cases in isolated outbreaks of monkeypox, whereas the contact tracing data are based on the number of transmission events caused by each case. The black cross hairs indicate the previously reported 90% confidence intervals for monkeypox transmission parameters based on the first generation of transmission in this data set [, ] <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002993#pcbi.1002993-LloydSmith2\" target=\"_blank\">[24]</a>. B) Model predictions for the chain size distribution based on three different values of , including the ML value of that is based on contact tracing data. A subset of the chain size data consisting of only those chains having exactly one identified primary infection is shown for comparison to model predictions. When the two-parameter ML value for the contact tracing data is compared to the likelihoods of the and models, the scores for the latter models are 4.3 and 23.3 respectively.</p>", "links"=>[], "tags"=>["Theoretical biology", "statistics", "Biostatistics", "epidemiology", "Epidemiological methods", "Infectious disease epidemiology", "Infectious diseases", "Infectious disease modeling", "Zoonoses", "Public health", "disease ecology", "tracing", "monkeypox"], "article_id"=>696202, "categories"=>["Mathematics", "Medicine", "Biological Sciences"], "users"=>["Seth Blumberg", "James O. Lloyd-Smith"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002993.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Contact_tracing_and_chain_size_analysis_of_monkeypox_data_/696202", "title"=>"Contact tracing and chain size analysis of monkeypox data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-05-02 01:43:22"}
  • {"files"=>["https://ndownloader.figshare.com/files/1051536"], "description"=>"<p>A) Applying maximum likelihood estimation to simulated data shows the sensitivity of chain size analysis and contact tracing analysis for detecting a change in . Results show the probability of detecting a significant change between the monkeypox data from the 1980s and a simulated data set with (equal to the ML value for the 1980s data) and specified along the x-axis. Statistical significance was determined by setting a 95% confidence threshold on the likelihood ratio test (details provided in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002993#s3\" target=\"_blank\">methods</a> section). Curves represent different values for the number of simulated chains, . Results are depicted for inference from detailed contact tracing data (dashed line) or more readily available chain size data (solid line). B) The specificity for detecting a statistically significant change in (as compared to 1980s monkeypox contact tracing data) is shown when various values of are assumed during chain size analysis (as applied to the same chain size data simulated for panel A). The specificity is defined as the probability that a change is not detected for an assumed value of conditioned on our gold standard for a lack of change (e.g. a change is not detected when is allowed to be a free parameter during inference). The solid line corresponds to chains and the dashed line to .</p>", "links"=>[], "tags"=>["Theoretical biology", "statistics", "Biostatistics", "epidemiology", "Epidemiological methods", "Infectious disease epidemiology", "Infectious diseases", "Infectious disease modeling", "Zoonoses", "Public health", "disease ecology", "clarifies"], "article_id"=>696203, "categories"=>["Mathematics", "Medicine", "Biological Sciences"], "users"=>["Seth Blumberg", "James O. Lloyd-Smith"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002993.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Chain_size_analysis_clarifies_surveillance_needs_/696203", "title"=>"Chain size analysis clarifies surveillance needs.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-05-02 01:43:23"}
  • {"files"=>["https://ndownloader.figshare.com/files/1051537"], "description"=>"<p>A) Size of an observed chain that is anomalously large as a function of and . The cumulative distribution threshold indicated in the legend denotes the chosen cutoff for the cumulative chain size distribution that determines when an observed chain is anomalously large. B) Analogous to panel A, but results are based on the largest observed chain for a group of 100 observed chains.</p>", "links"=>[], "tags"=>["Theoretical biology", "statistics", "Biostatistics", "epidemiology", "Epidemiological methods", "Infectious disease epidemiology", "Infectious diseases", "Infectious disease modeling", "Zoonoses", "Public health", "disease ecology", "anomalously"], "article_id"=>696204, "categories"=>["Mathematics", "Medicine", "Biological Sciences"], "users"=>["Seth Blumberg", "James O. Lloyd-Smith"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002993.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Size_of_anomalously_large_chains_/696204", "title"=>"Size of anomalously large chains.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-05-02 01:43:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/1051538"], "description"=>"<p>The axes represent the true , and inputs for the simulations. A) Root mean square relative error for ML inference of (). B) Root mean square absolute error for ML inference of (). C) Bias of inference (). D) Fraction of the absolute error that is attributable to bias (). The contour plots were generated based on a lattice of simulation results for linearly spaced values of and logarithmically spaced values of or . The values for each lattice point were computed by averaging the results of 2,000 simulations. For visualization purposes, simulation results were smoothed by a one-neighbor moving average.</p>", "links"=>[], "tags"=>["Theoretical biology", "statistics", "Biostatistics", "epidemiology", "Epidemiological methods", "Infectious disease epidemiology", "Infectious diseases", "Infectious disease modeling", "Zoonoses", "Public health", "disease ecology", "inference"], "article_id"=>696205, "categories"=>["Mathematics", "Medicine", "Biological Sciences"], "users"=>["Seth Blumberg", "James O. Lloyd-Smith"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002993.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Characterization_of_inference_as_a_function_of_and_with_left_column_and_as_a_function_of_and_with_right_column_/696205", "title"=>"Characterization of inference as a function of and with (left column) and as a function of and with (right column).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-05-02 01:43:25"}
  • {"files"=>["https://ndownloader.figshare.com/files/1051540"], "description"=>"<p>A) Error of inference as quantified by the root mean square of the absolute differences between the reciprocals of the inferred and true value of for simulated data (). The contour plot was generated based on the same simulations and inference procedure that was used to produce the panels of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002993#pcbi-1002993-g004\" target=\"_blank\">figure 4</a>. B) Same as panel A except that for all simulations and now the number of simulated chains varies. C) Summary of how well inference works when and . The dashed black line represents a perfect match between the true and inferred values. The magenta line shows the median value of ML inference of . The dashed blue lines show the median values of the upper and lower limits of the 90% confidence intervals for . For visualization purposes and because is essentially a Poisson distribution, the upper confidence intervals were bounded at . The green line shows the median estimate for inference based solely on the first and second moments of the simulated data, (<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002993#pcbi.1002993.e381\" target=\"_blank\">equation 7</a>). All curves were determined from the results of one thousand simulations for logarithmically distributed values of the true . D–F) Same as panel C, but for different and pairs.</p>", "links"=>[], "tags"=>["Theoretical biology", "statistics", "Biostatistics", "epidemiology", "Epidemiological methods", "Infectious disease epidemiology", "Infectious diseases", "Infectious disease modeling", "Zoonoses", "Public health", "disease ecology"], "article_id"=>696207, "categories"=>["Mathematics", "Medicine", "Biological Sciences"], "users"=>["Seth Blumberg", "James O. Lloyd-Smith"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002993.g005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Characterization_of_inference_/696207", "title"=>"Characterization of inference.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-05-02 01:43:27"}
  • {"files"=>["https://ndownloader.figshare.com/files/1051541"], "description"=>"<p>A) The inferred value of is plotted as a function of the two probabilities we use to model surveillance. Results are based on a simulation of 10,000 chains for a lattice of and pairs. For visualization purposes, simulation results were smoothed by a one-neighbor moving average. B) Analogous to panel A but for the dispersion parameter.</p>", "links"=>[], "tags"=>["Theoretical biology", "statistics", "Biostatistics", "epidemiology", "Epidemiological methods", "Infectious disease epidemiology", "Infectious diseases", "Infectious disease modeling", "Zoonoses", "Public health", "disease ecology", "imperfect"], "article_id"=>696208, "categories"=>["Mathematics", "Medicine", "Biological Sciences"], "users"=>["Seth Blumberg", "James O. Lloyd-Smith"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002993.g006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Influence_of_imperfect_observation_on_and_inference_/696208", "title"=>"Influence of imperfect observation on and inference.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-05-02 01:43:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1051542"], "description"=>"<p>ML estimates of and and corresponding 90% confidence regions are when all clusters are treated as chains, and for two approaches to assigning constituent chain sizes for clusters with more than one primary case (details provided in the text). For visual comparison, the contour corresponding to the chain size analysis from <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002993#pcbi-1002993-g001\" target=\"_blank\">figure 1</a> is replicated.</p>", "links"=>[], "tags"=>["Theoretical biology", "statistics", "Biostatistics", "epidemiology", "Epidemiological methods", "Infectious disease epidemiology", "Infectious diseases", "Infectious disease modeling", "Zoonoses", "Public health", "disease ecology", "entangled", "chains"], "article_id"=>696209, "categories"=>["Mathematics", "Medicine", "Biological Sciences"], "users"=>["Seth Blumberg", "James O. Lloyd-Smith"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002993.g007"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Complications_of_entangled_chains_can_affect_inference_/696209", "title"=>"Complications of entangled chains can affect inference.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-05-02 01:43:29"}
  • {"files"=>["https://ndownloader.figshare.com/files/1051543"], "description"=>"<p>The COV for the offspring distribution (i.e. the distribution for the number of transmission events caused by each case, panel A) and chain size distribution (panel B) are both a function of and .</p>", "links"=>[], "tags"=>["Theoretical biology", "statistics", "Biostatistics", "epidemiology", "Epidemiological methods", "Infectious disease epidemiology", "Infectious diseases", "Infectious disease modeling", "Zoonoses", "Public health", "disease ecology", "offspring"], "article_id"=>696210, "categories"=>["Mathematics", "Medicine", "Biological Sciences"], "users"=>["Seth Blumberg", "James O. Lloyd-Smith"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002993.g008"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Coefficient_of_variation_for_offspring_and_chain_size_distribution_/696210", "title"=>"Coefficient of variation for offspring and chain size distribution.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-05-02 01:43:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/1051544"], "description"=>"<p>A) The probability distribution for chain sizes for various parameter choices, when transmission is described by a negative binomial offspring distribution. B) Same as panel A but with logarithmically scaled axes, to highlight lower frequencies and larger chain sizes. C) The weighted probability density for the same and pairs given in panel A. D) Same as C with logarithmically scaled axes. The legend in panel A applies to all panels.</p>", "links"=>[], "tags"=>["Theoretical biology", "statistics", "Biostatistics", "epidemiology", "Epidemiological methods", "Infectious disease epidemiology", "Infectious diseases", "Infectious disease modeling", "Zoonoses", "Public health", "disease ecology", "stuttering", "chains", "varies"], "article_id"=>696211, "categories"=>["Mathematics", "Medicine", "Biological Sciences"], "users"=>["Seth Blumberg", "James O. Lloyd-Smith"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002993.g009"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_size_distribution_of_stuttering_chains_varies_as_a_function_of_and_/696211", "title"=>"The size distribution of stuttering chains varies as a function of and .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-05-02 01:43:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/1051545"], "description"=>"<p>As detailed in the methods section, a statistical difference was determined by using the likelihood ratio test to compare two transmission models. The first model assigns separate values of to the 1980s monkeypox data and the simulated data, while the second model assigns a single to both data sets. Both models assign a single value of to both data sets. Since the second model is nested in the first, statistical significance was determined by setting a 95% confidence threshold on the likelihood ratio test. Probability values that exceed 5% indicate an over-abundance of false positive detections of change in . Each result was based on 10,000 simulations.</p>", "links"=>[], "tags"=>["Theoretical biology", "statistics", "Biostatistics", "epidemiology", "Epidemiological methods", "Infectious disease epidemiology", "Infectious diseases", "Infectious disease modeling", "Zoonoses", "Public health", "disease ecology", "falsely", "detecting"], "article_id"=>696212, "categories"=>["Mathematics", "Medicine", "Biological Sciences"], "users"=>["Seth Blumberg", "James O. Lloyd-Smith"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002993.t002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Probability_of_falsely_detecting_a_change_in_/696212", "title"=>"Probability of falsely detecting a change in .", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-05-02 01:43:32"}
  • {"files"=>["https://ndownloader.figshare.com/files/1051546"], "description"=>"<p>The cutoff for a chain sizes that are considered anomalously large was determined by when the cumulative chain size probability exceed the cumulative distribution threshold for (ML value for 1980s monkeypox data) and as indicated in the table. The frequency of outlier detection was then determined according to the probability that chain sizes would exceed the chain size cutoff as predicted by the ML values of and for monkeypox.</p>", "links"=>[], "tags"=>["Theoretical biology", "statistics", "Biostatistics", "epidemiology", "Epidemiological methods", "Infectious disease epidemiology", "Infectious diseases", "Infectious disease modeling", "Zoonoses", "Public health", "disease ecology", "anomalously"], "article_id"=>696213, "categories"=>["Mathematics", "Medicine", "Biological Sciences"], "users"=>["Seth Blumberg", "James O. Lloyd-Smith"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002993.t003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Frequency_of_anomalously_large_chains_/696213", "title"=>"Frequency of anomalously large chains.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-05-02 01:43:33"}
  • {"files"=>["https://ndownloader.figshare.com/files/1051547"], "description"=>"<p>Inference results for monkeypox data.</p>", "links"=>[], "tags"=>["Theoretical biology", "statistics", "Biostatistics", "epidemiology", "Epidemiological methods", "Infectious disease epidemiology", "Infectious diseases", "Infectious disease modeling", "Zoonoses", "Public health", "disease ecology", "monkeypox"], "article_id"=>696214, "categories"=>["Mathematics", "Medicine", "Biological Sciences"], "users"=>["Seth Blumberg", "James O. Lloyd-Smith"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002993.t001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Inference_results_for_monkeypox_data_/696214", "title"=>"Inference results for monkeypox data.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-05-02 01:43:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/1051548"], "description"=>"<p>The number of transmission chains tabulated by size (i.e. total number of cases) for three different assignment algorithms.</p>", "links"=>[], "tags"=>["Theoretical biology", "statistics", "Biostatistics", "epidemiology", "Epidemiological methods", "Infectious disease epidemiology", "Infectious diseases", "Infectious disease modeling", "Zoonoses", "Public health", "disease ecology", "chains", "tabulated"], "article_id"=>696215, "categories"=>["Mathematics", "Medicine", "Biological Sciences"], "users"=>["Seth Blumberg", "James O. Lloyd-Smith"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002993.t004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_number_of_transmission_chains_tabulated_by_size_i_e_total_number_of_cases_for_three_different_assignment_algorithms_/696215", "title"=>"The number of transmission chains tabulated by size (i.e. total number of cases) for three different assignment algorithms.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-05-02 01:43:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/1051549", "https://ndownloader.figshare.com/files/1051550", "https://ndownloader.figshare.com/files/1051552"], "description"=>"<div><p>For many infectious disease processes such as emerging zoonoses and vaccine-preventable diseases, and infections occur as self-limited stuttering transmission chains. A mechanistic understanding of transmission is essential for characterizing the risk of emerging diseases and monitoring spatio-temporal dynamics. Thus methods for inferring and the degree of heterogeneity in transmission from stuttering chain data have important applications in disease surveillance and management. Previous researchers have used chain size distributions to infer , but estimation of the degree of individual-level variation in infectiousness (as quantified by the dispersion parameter, ) has typically required contact tracing data. Utilizing branching process theory along with a negative binomial offspring distribution, we demonstrate how maximum likelihood estimation can be applied to chain size data to infer both and the dispersion parameter that characterizes heterogeneity. While the maximum likelihood value for is a simple function of the average chain size, the associated confidence intervals are dependent on the inferred degree of transmission heterogeneity. As demonstrated for monkeypox data from the Democratic Republic of Congo, this impacts when a statistically significant change in is detectable. In addition, by allowing for superspreading events, inference of shifts the threshold above which a transmission chain should be considered anomalously large for a given value of (thus reducing the probability of false alarms about pathogen adaptation). Our analysis of monkeypox also clarifies the various ways that imperfect observation can impact inference of transmission parameters, and highlights the need to quantitatively evaluate whether observation is likely to significantly bias results.</p></div>", "links"=>[], "tags"=>["Theoretical biology", "statistics", "Biostatistics", "epidemiology", "Epidemiological methods", "Infectious disease epidemiology", "Infectious diseases", "Infectious disease modeling", "Zoonoses", "Public health", "disease ecology", "inference", "heterogeneity", "stuttering", "chains"], "article_id"=>696216, "categories"=>["Mathematics", "Medicine", "Biological Sciences"], "users"=>["Seth Blumberg", "James O. Lloyd-Smith"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002993.s001", "https://dx.doi.org/10.1371/journal.pcbi.1002993.s002", "https://dx.doi.org/10.1371/journal.pcbi.1002993.s003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Inference_of_R_0_and_Transmission_Heterogeneity_from_the_Size_Distribution_of_Stuttering_Chains/696216", "title"=>"Inference of <i>R</i><sub>0</sub> and Transmission Heterogeneity from the Size Distribution of Stuttering Chains", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2013-05-02 01:43:36"}

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Relative Metric

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