Article
Estimation of the population size of Canadian commercial poultry farms by log-linear capture-recapture analysis Farouk El Allaki, Jette Christensen, André Vallières, Julie Paré
Abstract The objective of this study was to estimate the population size of Canadian poultry farms in 3 subpopulations (British Columbia, Ontario, and Other) by poultry category. We used data for 2008 to 2011 from the Canadian Notifiable Avian Influenza (NAI) Surveillance System (CanNAISS). Log-linear capture-recapture models were applied to estimate the number of commercial chicken and turkey farms. The estimated size of farm populations was validated by comparing sizes to data provided by the Canadian poultry industry in 2007, which were assumed to be complete and exhaustive. Our results showed that the log-linear modelling approach was an appropriate tool to estimate the population size of Canadian commercial chicken and turkey farms. The 2007 farm population size for each poultry category was included in the 95% confidence intervals of the farm population size estimates. Log-linear capture-recapture modelling might be useful for estimating the number of farms using surveillance data when no comprehensive registry exists.
Résumé L’objectif de cette étude était d’estimer le nombre de ferme de volaille au Canada dans trois sous-populations (Colombie-Britannique, Ontario et Autre) par catégorie de volaille. Nous avons utilisé des données du Système canadien de surveillance de l’influenza aviaire à déclaration obligatoire (SCSIADO) de 2008 à 2011. Nous avons utilisé des modèles log-linéaires pour estimer le nombre de fermes commerciales de poulets et de dindons. Nous avons validé les tailles des populations de fermes en les comparants aux données de 2007 fournies par l’industrie canadienne de la volaille (prétendues complètes et exhaustives). Nos résultats ont démontré que l’approche de modélisation log-linéaire était un outil approprié pour estimer les tailles des populations de fermes de poulets et dindons au Canada. Pour chaque catégorie de volaille, la taille de la population de fermes de 2007 était incluse dans l’intervalle de confiance des tailles estimées des populations de fermes avec un niveau de confiance de 95 %. La modélisation log-linéaire de type capture-recapture pourrait être utile pour estimer le nombre de fermes en utilisant des données de surveillance en particulier lorsqu’il n’existe aucun registre exhaustif. (Traduit par les auteurs)
Introduction Capture-recapture (or mark-recapture) was initially used in ecology to estimate the size of wild animal populations. Basically, a sample of animals is captured, marked, and then returned to the population. Later, a new sample of animals is captured and the number of marked individuals in this sample is counted. The population size is estimated based on the relative number of marked and unmarked animals in subsequent samples. The simplest capture-recapture model is the 2-sample Lincoln-Petersen model for a closed population (1). Other capture-recapture methods have been proposed for estimating the population size using more than 2 samples (2–4). The method was first introduced by Petersen in 1896 to estimate the size of fish populations and Lincoln used it in 1930 to estimate the size of duck populations (5,6). Its use has since been extended to study the dynamics of wild populations (7).
In public health, capture-recapture methods have been used to estimate the completeness of a register (8) and to estimate the prevalence or the incidence of diseases and health-related problems such as diabetes (9), mental illness (10), cancer (11,12), and malaria (13). The application of capture-recapture methods in veterinary epidemiology dates back to the work of Cameron in 1997, which estimated the number of outbreaks of foot-and-mouth disease in northern Thailand (14). These methods were subsequently applied to estimate the number of units, e.g., animals, farms, districts, affected by specific animal health issues such as scrapie (15–17), East-Coast fever (18), and highly pathogenic avian influenza (19). Capture-recapture methods were used to assess the sensitivity of veterinary surveillance systems such as the scrapie surveillance in Great Britain (16) and the mandatory bovine abortion notification system in France (20). In 2008, the Canadian Notifiable Avian Influenza (NAI) Surveillance System (CanNAISS) was designed and implemented to detect NAI in domestic poultry in Canada (21). In CanNAISS,
Canadian Food Inspection Agency, Epidemiology and Surveillance Section, Saint-Hyacinthe, Quebec (El Allaki, Vallières, Paré); Canadian Food Inspection Agency, Epidemiology and Surveillance Section, Atlantic Veterinary College, Department of Health Management, Charlottetown, Prince Edward Island (Christensen). Address all correspondence to Dr. Farouk El Allaki; telephone: 450-773-8421, ext. 0096; fax: 450-768-0064; e-mail: [email protected] Received December 10, 2013. Accepted January 28, 2014. 2014;78:267–273
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Table I. Applied definitions and acronyms Word/Expression Definition Notifiable Avian Influenza (NAI) “… an infection of poultry caused by any influenza A virus of the H5 or H7 subtypes or by any AI virus with an intravenous pathogenicity index (IVPI) greater than 1.2 (or as an alternative at least 75% mortality) as described below. NAI viruses can be divided into highly pathogenic notifiable avian influenza (HPNAI) and low pathogenicity notifiable avian influenza (LPNAI)…’’ OIE, Terrestrial Animal Health Code, 2011 (Chapter 10.4; Article 10.4.1.1) Subpopulation Refers to a subset of the Canadian commercial farm population in one of the following three regions: British Columbia, Ontario, and Other. Therefore three mutually exclusive subpopulations were defined. Farm Physical location where the poultry are kept and raised Poultry “All domesticated birds, including backyard poultry, used for the production of meat or eggs for consumption, for the production of other commercial products, for restocking supplies of game, or for breeding these categories of birds, as well as fighting cocks used for any purpose.’’ OIE, Terrestrial Animal Health Code, 2011 (Chapter 10.4; Article 10.4.1.2) Poultry category: Broiler breeder chicken Parent stock producing hatching eggs/day olds for the chicken broiler production Roaster Chicken for meat . 3.7 kg live of weight Table-egg layer breeder chicken Great grandparent, grandparent and parent stock producing hatching eggs/day olds for the chicken egg production for human consumption Table-egg layer chicken Chicken layers producing eggs for human consumption Turkey breeder Great grandparent, grandparent and parent stock producing hatching eggs/day olds for the turkey meat production for human consumption Turkey for meat Turkey raised for meat production slaughter schedules, hatchery supply flock lists, and registries are used as a sampling frame. This includes population sizes for different categories of poultry from 2007, but not a national population registry stratified by category. We hypothesize that the log-linear capture-recapture method applied to data from repeated veterinary surveys or ongoing surveillance may (1) provide appropriate estimates of farm population size and (2) help to assess the completeness of a list of farms, e.g., a farm registry. The objectives of this study were to estimate the population size of Canadian commercial poultry farms in 3 subpopulations (British Columbia, Ontario, and Other) by poultry categories using CanNAISS surveillance data and to compare the estimates with the population sizes obtained from the 2007 data, which were assumed to be complete and comprehensive.
Materials and methods The definitions for “notifiable avian influenza (NAI)” and “poultry” used in this paper are those of the World Organisation for Animal Health (OIE). These and other terms are defined in Table I.
Surveillance components, subpopulations, and poultry categories From 2008 to 2011, sampling and testing for CanNAISS were conducted in 5 surveillance components: pre-slaughter (Pre-S) surveillance; hatchery supply flock (HSF) surveillance; voluntary enhanced NAI surveillance (VENAIS); post-outbreak surveillance in British Columbia in 2009 (POSBC 2009); and surveillance of NAI in table-egg layer farms in Manitoba in 2011 (TEL-MB 2011) (Table II).
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The Pre-S and HSF components were mandatory, ongoing, n-farm surveillance activities. Farms were sampled from slaugho ter schedules or lists of hatchery supply flocks. In the voluntary enhanced NAI surveillance (VENAIS) component, poultry farms were sampled as required for export or as part of the company’s health strategy. For the POSBC 2009 component, poultry farms were sampled from the provincial poultry farm registry in 2009. For the TEL-MB 2011 component, in addition to the farms sampled as part of the Pre-S and HSF components, all table-egg layer farms in Manitoba coming to the end of a production cycle during a 3-mo surveillance period (February 1 to May 1, 2011) were sampled, based on the provincial poultry registry data. The Canadian poultry population was divided into 3 mutually exclusive subpopulations based on historical evidence, geography, and epidemiology of NAI (21). These 3 subpopulations were British Columbia (BC), Ontario (ON), and Other (Alberta, Saskatchewan, Manitoba, Quebec, New Brunswick, Nova Scotia, Prince Edward Island, and Newfoundland & Labrador). The Canadian Notifiable Avian Influenza (NAI) Surveillance System targeted healthy chickens and turkeys approaching the end of their production cycle. More specifically, 5 poultry categories were targeted by this surveillance system: roasters, broiler breeder chickens, table-egg layers (including breeders), turkey breeders, and turkeys for meat. We targeted long-lived poultry and therefore excluded chicken broiler farms (birds , 3.7 kg live weight). In BC, we collapsed the 2 turkey categories (meat-type and breeder) into 1 because the number of turkey farms sampled in each turkey category was low.
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As NAI is a contagious disease that is controlled at the farm level (not at the individual bird level), the farm was our unit of interest. Therefore, each farm sampled as part of CanNAISS had 1 farm unique identifier (Farm Id) corresponding to 1 physical location where the tested birds were located (see online Supplementary Material). The distribution of tested farms by year, subpopulation, and CanNAISS component is presented in Table II. A farm already sampled in one CanNAISS component was not eligible for sampling in another component during the next 6 months. The lists of farms sampled by the CanNAISS in each year (2008, 2009, 2010, and 2011) were considered as 4 different (but potentially overlapping) lists of farms present in Canada (Table II).
Log-linear modelling approach and data To estimate the total number of commercial poultry farms in Canada, a 4-list capture-recapture analysis was used based on 4 sampling lists (lists of farms sampled by the CanNAISS in 2008, 2009, 2010, and 2011). We conducted a separate analysis for each poultry category and subpopulation. For clarity, we present the analytical framework for a 3-list capture-recapture approach, which can be easily extended to a 4-list capture-recapture analysis (8). Mathematically, the log-linear approach models the logarithm of the expected value of each observable category. The fully saturated model for sampling lists 1, 2, and 3 is: Log E(mijk) = u 1 u1I(i = 1) 1 u2I(j = 1) 1 u3I(k = 1) 1 u12I(i = j = 1) 1 u13I(i = k = 1) 1 u23I(j = k = 1) 1 u123I(i = j = k = 1)
(1)
where: I(A) is an indicator function for an event A (e.g., I = 1; j = 1); u is the intercept; u1, u2, and u3 are 3 main effects for the log odds of appearing in sampling list 1, 2, and 3, respectively; u12, u13, and u23 are 3 first-order interactions (each corresponding to the interaction between pairs of lists); and u123 is a second-order interaction term (corresponding to the interaction effect among 3 lists) (2,22). Equation 1 uses a log link function and assumes a Poisson distribution of the dependent variable. There are 7 observed cells in a 3-list log-linear model but 8 different possible models (22). Therefore, it is not possible to construct a fully saturated model and t is generally assumed that the secondorder interaction term is null, i.e., u123 = 0 (8,22). The underlying assumptions of the capture-recapture approach are that: i) the farm population was closed, that is, no new farm appeared and no existing farm disappeared during the study period (2008 to 2011); ii) all farms have the same ‘capture/sampling’ probability within each year (equal catchability of farms). Dependence among the 4 sampling lists (i.e., the presence of a farm in a sampling list is influenced by the presence of the same farm in a previous sampling list) was modelled by adding interaction terms to the model. To identify relevant parameters, we used a forward selection process starting with the intercept and main effects parameters (u, u1, u2, u3, u4) and then added successively first-order interactions, and so on, until no further significant improvement of the goodnessof-fit of the model was obtained. Deviance was used to assess the goodness-of-fit of the model. Model selection was based on the Akaike Information Criterion (AIC) (23). The log-linear model with the lowest AIC was selected as the best model. The 95% confidence
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Table II. Distribution of tested farms by year, subpopulation, and CanNAISS component CanNAISS component POSBC TEL-MB Year Subpopulation Pre-S HSF VENAIS 2009 2011 2008 British Columbia 74 — — — — Ontario 245 — 45 — — Other 282 — — — — Canada 601 — 45 — — 2009
British Columbia 38 Ontario 110 Other 163 Canada 311
— — — 44 — — — 44
220 — — 220
— — — —
2010
British Columbia Ontario Other Canada
104 41 — 108 7 45 200 87 — 412 135 45
— — — —
— — — —
2011 British Columbia 70 10 — — — Ontario 147 41 48 — — Other 251 86 — — 53 Canada 468 137 48 — 53 CanNAISS: Canadian Notifiable Avian Influenza Surveillance System; Pre-S: Pre-slaughter surveillance component; HSF: Hatchery Supply Flock surveillance component; VENAIS: Voluntary Enhanced Notifiable Avian Influenza Surveillance; POSBC 2009: Post-outbreak surveillance in British Columbia in 2009; TEL-MB 2011: Surveillance of Notifiable Avian Influenza in table-egg layer farms in Manitoba in 2011; (2) No farm s ampled.
intervals (95% CI) of the estimated population sizes were calculated in statistical analysis software (SAS, Version 9.1; Microsoft, Redmond, Washington, USA) using the profile likelihood method. The log-linear modelling approach is appropriate for multi-list capture-recapture data using different detection protocols, selection methods, or data sources and when there is overlapping among sampling lists (15,16). An alternative approach uses uni-list capture-recapture methods such as Zero-Truncated Poisson or negative binomial models, in which the data are generated by a single detection protocol. In our case, multi-list capture-recapture analyses were more appropriate for analyzing CanNAISS data for the following reasons: (1) different detection protocols, i.e., the different years when CanNAISS was implemented, during the reference period 2008 to 2011 were used in CanNAISS with a perfect identification system of the sampled farms and (2) the overlapping fractions over the years were not too small (15,24,25). The data for our analysis were extracted from the CanNAISS database and formatted to include the farm unique identifier (Farm Id), sampled poultry category, sampling year, and subpopulation (BC, Ontario, and Other). Four sampling lists were created, one for each year (2008, 2009, 2010, 2011). The data were transferred into SAS (Version 9.1, Microsoft) for analysis. In 2007, representatives of the Canadian poultry industry provided data on the number of poultry farms. The data were compiled and stored in a spreadsheet
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Turkey
Turkey for meat
Turkey breeder
Table-egg layer
Turkey
Turkey breeder
0.960
—
20 (7–58)
65 (33–141) 0.0922 360 (256–587)
8.498 10 0.5803 211.5017
u 1 u 2 u 3 u 4
75.0
10.939 8 0.2052 25.0612
308
24
na
84
226
73
11.733 7 0.1097 22.2671 510 (252–1.076) 579
232 (143–412)
68 (33–153)
na
u 1 u 2 u 3 u 4 u 1u 2 u 1u 3 u 2u 3
23.501
21.322
160 (88–299)
13.263 10 0.2093 26.7365 120 (71–205)
0.499 2 0.779
12.678 7 0.080
98
60
199
2007 data 66
401 (163–1,197) 369
—
44 (22–91)
223 (137–383)
Population size estimate (95% CI) 73 (40–139)
u 1 u 2 u 3 u 4
u 1 u 2 u 3 u 4 u 1u 3 u 2u 3 u 1u 2u 4 u 1u 3u 4
u 1 u 2 u 3 u 4 u 1u 2 u 2u 3 u 3u 4
0.052
—
— u 1 u 2 u 3 u 4 u 2u 3 u 3u 4
19.7
155.9
95.6
86.3
5
—
22.444
24.682
3.167 8 0.923 212.833
10.960
—
15.556 9 0.077
9.318 7 0.231
Turkey for meat 83.1 u 1 u 2 u 3 u 4 u 1u 2 u 1u 3 u 1u 4 u 2u 3 u 2u 4 8.099 4 0.0880 u3u4 u1, u2, u3, u4 are main effects for sampling lists for 2008, 2009, 2010 and 2011 respectively. a Akaike Information Criterion. b The BC turkey farm population was small therefore we collapsed the two turkey categories. c No broiler breeder farm was tested in Ontario in 2009 and no model fitted the data using the 2008, 2010, and 2011 sampling lists. na: not available; (—): not applicable.
Roaster
Other Chicken Broiler breeder chicken
Roaster
u 1 u 2 u 3 u 4 u 1u 2 u 1u 4 u 2u 3 u 2u 4 u 3u 4
—
u1 u2 u3 u4 u34
u 1 u 2 u 3 u 4 u 1u 4 u 2u 3 u 3u 4
— u 1 u 2 u 3 u 4 u 1u 2 u 2u 4
35.2
Table-egg layer
70.0 14.3
Turkey breeder and turkey for meatb
Turkey
76.4
Sampling fraction (%) Model Deviance df P-value AICa 100.0 u 1 u 2 u 3 u 4 u 1u 2 u 3u 4 15.173 8 0.056 20.827
Ontario Chicken Broiler breeder chickenc
Table-egg layer
Poultry Poultry farm Subpopulation species category British Columbia (BC) Chicken Broiler breeder chicken
Table III. Sampling fractions, farm population size estimates, and the 2007 data for each subpopulation by poultry category
Broiler breeder chicken (BC)
Table-egg layer (BC)
Turkey breeder and turkey for meat (BC)
Table-egg layer (Ontario)
Turkey breeder (Ontario)
Turkey for meat (Ontario)
Broiler breeder chicken (Other)
Table-egg layer (Other)
Turkey breeder (Other)
Turkey for meat (Other)
Figure 1. Relationship between capture-recapture relative difference and sampling fraction by poultry category and subpopulation.
(Microsoft Excel 2002). These are referred to as the 2007 data and it was assumed that they were complete and comprehensive. Thus, a capture-recapture estimate of farm population size was considered valid if its 95% CI contained the 2007 data population size for the same poultry category and subpopulation. We used a scatter plot diagram, made in Microsoft Excel 2010, to explore the relationship between the capture-recapture relative difference (RD) for a given poultry category and its related sampling fraction (Equations 2 to 3) between 2008 and 2011. ˆ 2N Relative difference (a, b) = (N ab ab(2007))/Nab(2007)
(2)
Sampling fraction (a, b) = Number of farms sampled (a, b)/ Nab(2007)
(3)
ˆ is the number of farms in poultry category a in subpopuwhere: N ab lation b estimated using capture-recapture methods and Nab(2007) refers to the number of farms in poultry category a and subpopulaˆ tion b in the 2007 data. By substituting 95% confidence limits of N ab in equation 2, the bounds of the 95% CI of the RD were calculated. We plotted RD estimates against the sampling fraction for a given poultry category.
Results All the 95% CI of the farm population size estimates in the 3 subpopulations (BC, Ontario, and Other) included the 2007 data population size (Table III). The capture-recapture relative difference (point estimate) was close to zero (Figure 1). Only in Ontario was the range of capture-recapture relative difference wider for low sampling fractions than for larger sampling fractions (Figure 1).
Discussion In this study, the log-linear modelling approach provided reasonable point estimates of population sizes given the proportion of farms sampled for each subpopulation because the 95% CI included the 2007 data. Sampling fractions exceeding 100% were observed
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for broiler breeder chicken farms in the “Other” category. Although this may be explained by an increased number of farms, this seems unlikely because the industry is supply managed to ensure that the supply of a product matches the demand. The more likely explanation is that the 2007 data were incomplete. Our results (data not shown) were consistent with the principle of the capture-recapture analysis itself, in that when the recapture rate among sampling lists is low as a result of a low sampling fraction, we expect that estimates will be less accurate (2). This study illustrated that uncertainty about the capture-recapture estimates is not only affected by the sampling fraction. In BC and Other subpopulations, we were not able to see a decrease in the capture-recapture relative difference ranges as the sampling fraction increased. These results may suggest that the overlapping rate among sampling lists might influence the accuracy of the estimates. The assumption of a closed population is rarely truly satisfied in biological applications (26). We assumed that the number and distribution of chicken and turkey farms did not change from 2007 to 2011 and that no new farm appeared or existing farm disappeared. Based on Statistics Canada’s Census of Agriculture, there were 4578 poultry farms in 2006 and 4484 farms in 2011 (27). The commercial poultry industry in Canada is supply managed, which means that Canadian production and imports are regulated to ensure that the supply of a product matches the demand for it. For the turkey population, the number of birds slaughtered in Canada was reasonably stable during the study period, ranging from 20 454 572 to 22 750 170 birds per year (28). For the chicken population (including mature chickens), the total number of birds slaughtered per year in Canada remained relatively stable during the study period, ranging from 636 872 749 to 639 616 479 (28). With respect to the equicatchability assumption, we stratified the data by poultry category and subpopulation to address the impact of variable catchability of the farms, as suggested by several authors (3,9,29–32). The log-linear capture-recapture method may be particularly relevant for repeated surveys or ongoing surveillance systems when poultry farms are sampled on a continuous basis and when
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little or incomplete information is available on the total number of poultry farms in a specific area. This method does not replace a census or the results of a valid survey for the purpose of creating a poultry farm registry, however, because of the uncertainty related to the model outcome and the possible violation of the underlying assumptions. In future studies, there may be a need to better understand the effect of the recapture (overlapping) rate and the sampling fraction on the accuracy of the capture-recapture estimates. Applying capture-recapture methods to surveillance data and comparing to a complete farm registry may help to better understand the effect of these factors and to validate the actual log-linear capture-recapture estimates. Comparing results from various capture-recapture methods such as 2-list capture-recapture methods, e.g., Bailey, Chapman, and Chao estimators, and log-linear modelling and understanding their limitations will help in selecting the most appropriate capturerecapture analysis to use for future animal surveillance.
Acknowledgments The authors thank all Canadian chicken and turkey feather boards for their support and for providing the 2007 reference farm population data to make this study possible.
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Estimation of the population size of Canadian commercial poultry farms by log-linear capture-recapture analysis Farouk El Allaki, Jette Christensen, André Vallières, Julie Paré
Abstract The objective of this study was to estimate the population size of Canadian poultry farms in 3 subpopulations (British Columbia, Ontario, and Other) by poultry category. We used data for 2008 to 2011 from the Canadian Notifiable Avian Influenza (NAI) Surveillance System (CanNAISS). Log-linear capture-recapture models were applied to estimate the number of commercial chicken and turkey farms. The estimated size of farm populations was validated by comparing sizes to data provided by the Canadian poultry industry in 2007, which were assumed to be complete and exhaustive. Our results showed that the log-linear modelling approach was an appropriate tool to estimate the population size of Canadian commercial chicken and turkey farms. The 2007 farm population size for each poultry category was included in the 95% confidence intervals of the farm population size estimates. Log-linear capture-recapture modelling might be useful for estimating the number of farms using surveillance data when no comprehensive registry exists.
Résumé L’objectif de cette étude était d’estimer le nombre de ferme de volaille au Canada dans trois sous-populations (Colombie-Britannique, Ontario et Autre) par catégorie de volaille. Nous avons utilisé des données du Système canadien de surveillance de l’influenza aviaire à déclaration obligatoire (SCSIADO) de 2008 à 2011. Nous avons utilisé des modèles log-linéaires pour estimer le nombre de fermes commerciales de poulets et de dindons. Nous avons validé les tailles des populations de fermes en les comparants aux données de 2007 fournies par l’industrie canadienne de la volaille (prétendues complètes et exhaustives). Nos résultats ont démontré que l’approche de modélisation log-linéaire était un outil approprié pour estimer les tailles des populations de fermes de poulets et dindons au Canada. Pour chaque catégorie de volaille, la taille de la population de fermes de 2007 était incluse dans l’intervalle de confiance des tailles estimées des populations de fermes avec un niveau de confiance de 95 %. La modélisation log-linéaire de type capture-recapture pourrait être utile pour estimer le nombre de fermes en utilisant des données de surveillance en particulier lorsqu’il n’existe aucun registre exhaustif. (Traduit par les auteurs)
Introduction Capture-recapture (or mark-recapture) was initially used in ecology to estimate the size of wild animal populations. Basically, a sample of animals is captured, marked, and then returned to the population. Later, a new sample of animals is captured and the number of marked individuals in this sample is counted. The population size is estimated based on the relative number of marked and unmarked animals in subsequent samples. The simplest capture-recapture model is the 2-sample Lincoln-Petersen model for a closed population (1). Other capture-recapture methods have been proposed for estimating the population size using more than 2 samples (2–4). The method was first introduced by Petersen in 1896 to estimate the size of fish populations and Lincoln used it in 1930 to estimate the size of duck populations (5,6). Its use has since been extended to study the dynamics of wild populations (7).
In public health, capture-recapture methods have been used to estimate the completeness of a register (8) and to estimate the prevalence or the incidence of diseases and health-related problems such as diabetes (9), mental illness (10), cancer (11,12), and malaria (13). The application of capture-recapture methods in veterinary epidemiology dates back to the work of Cameron in 1997, which estimated the number of outbreaks of foot-and-mouth disease in northern Thailand (14). These methods were subsequently applied to estimate the number of units, e.g., animals, farms, districts, affected by specific animal health issues such as scrapie (15–17), East-Coast fever (18), and highly pathogenic avian influenza (19). Capture-recapture methods were used to assess the sensitivity of veterinary surveillance systems such as the scrapie surveillance in Great Britain (16) and the mandatory bovine abortion notification system in France (20). In 2008, the Canadian Notifiable Avian Influenza (NAI) Surveillance System (CanNAISS) was designed and implemented to detect NAI in domestic poultry in Canada (21). In CanNAISS,
Canadian Food Inspection Agency, Epidemiology and Surveillance Section, Saint-Hyacinthe, Quebec (El Allaki, Vallières, Paré); Canadian Food Inspection Agency, Epidemiology and Surveillance Section, Atlantic Veterinary College, Department of Health Management, Charlottetown, Prince Edward Island (Christensen). Address all correspondence to Dr. Farouk El Allaki; telephone: 450-773-8421, ext. 0096; fax: 450-768-0064; e-mail: [email protected] Received December 10, 2013. Accepted January 28, 2014. 2014;78:267–273
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Table I. Applied definitions and acronyms Word/Expression Definition Notifiable Avian Influenza (NAI) “… an infection of poultry caused by any influenza A virus of the H5 or H7 subtypes or by any AI virus with an intravenous pathogenicity index (IVPI) greater than 1.2 (or as an alternative at least 75% mortality) as described below. NAI viruses can be divided into highly pathogenic notifiable avian influenza (HPNAI) and low pathogenicity notifiable avian influenza (LPNAI)…’’ OIE, Terrestrial Animal Health Code, 2011 (Chapter 10.4; Article 10.4.1.1) Subpopulation Refers to a subset of the Canadian commercial farm population in one of the following three regions: British Columbia, Ontario, and Other. Therefore three mutually exclusive subpopulations were defined. Farm Physical location where the poultry are kept and raised Poultry “All domesticated birds, including backyard poultry, used for the production of meat or eggs for consumption, for the production of other commercial products, for restocking supplies of game, or for breeding these categories of birds, as well as fighting cocks used for any purpose.’’ OIE, Terrestrial Animal Health Code, 2011 (Chapter 10.4; Article 10.4.1.2) Poultry category: Broiler breeder chicken Parent stock producing hatching eggs/day olds for the chicken broiler production Roaster Chicken for meat . 3.7 kg live of weight Table-egg layer breeder chicken Great grandparent, grandparent and parent stock producing hatching eggs/day olds for the chicken egg production for human consumption Table-egg layer chicken Chicken layers producing eggs for human consumption Turkey breeder Great grandparent, grandparent and parent stock producing hatching eggs/day olds for the turkey meat production for human consumption Turkey for meat Turkey raised for meat production slaughter schedules, hatchery supply flock lists, and registries are used as a sampling frame. This includes population sizes for different categories of poultry from 2007, but not a national population registry stratified by category. We hypothesize that the log-linear capture-recapture method applied to data from repeated veterinary surveys or ongoing surveillance may (1) provide appropriate estimates of farm population size and (2) help to assess the completeness of a list of farms, e.g., a farm registry. The objectives of this study were to estimate the population size of Canadian commercial poultry farms in 3 subpopulations (British Columbia, Ontario, and Other) by poultry categories using CanNAISS surveillance data and to compare the estimates with the population sizes obtained from the 2007 data, which were assumed to be complete and comprehensive.
Materials and methods The definitions for “notifiable avian influenza (NAI)” and “poultry” used in this paper are those of the World Organisation for Animal Health (OIE). These and other terms are defined in Table I.
Surveillance components, subpopulations, and poultry categories From 2008 to 2011, sampling and testing for CanNAISS were conducted in 5 surveillance components: pre-slaughter (Pre-S) surveillance; hatchery supply flock (HSF) surveillance; voluntary enhanced NAI surveillance (VENAIS); post-outbreak surveillance in British Columbia in 2009 (POSBC 2009); and surveillance of NAI in table-egg layer farms in Manitoba in 2011 (TEL-MB 2011) (Table II).
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The Pre-S and HSF components were mandatory, ongoing, n-farm surveillance activities. Farms were sampled from slaugho ter schedules or lists of hatchery supply flocks. In the voluntary enhanced NAI surveillance (VENAIS) component, poultry farms were sampled as required for export or as part of the company’s health strategy. For the POSBC 2009 component, poultry farms were sampled from the provincial poultry farm registry in 2009. For the TEL-MB 2011 component, in addition to the farms sampled as part of the Pre-S and HSF components, all table-egg layer farms in Manitoba coming to the end of a production cycle during a 3-mo surveillance period (February 1 to May 1, 2011) were sampled, based on the provincial poultry registry data. The Canadian poultry population was divided into 3 mutually exclusive subpopulations based on historical evidence, geography, and epidemiology of NAI (21). These 3 subpopulations were British Columbia (BC), Ontario (ON), and Other (Alberta, Saskatchewan, Manitoba, Quebec, New Brunswick, Nova Scotia, Prince Edward Island, and Newfoundland & Labrador). The Canadian Notifiable Avian Influenza (NAI) Surveillance System targeted healthy chickens and turkeys approaching the end of their production cycle. More specifically, 5 poultry categories were targeted by this surveillance system: roasters, broiler breeder chickens, table-egg layers (including breeders), turkey breeders, and turkeys for meat. We targeted long-lived poultry and therefore excluded chicken broiler farms (birds , 3.7 kg live weight). In BC, we collapsed the 2 turkey categories (meat-type and breeder) into 1 because the number of turkey farms sampled in each turkey category was low.
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As NAI is a contagious disease that is controlled at the farm level (not at the individual bird level), the farm was our unit of interest. Therefore, each farm sampled as part of CanNAISS had 1 farm unique identifier (Farm Id) corresponding to 1 physical location where the tested birds were located (see online Supplementary Material). The distribution of tested farms by year, subpopulation, and CanNAISS component is presented in Table II. A farm already sampled in one CanNAISS component was not eligible for sampling in another component during the next 6 months. The lists of farms sampled by the CanNAISS in each year (2008, 2009, 2010, and 2011) were considered as 4 different (but potentially overlapping) lists of farms present in Canada (Table II).
Log-linear modelling approach and data To estimate the total number of commercial poultry farms in Canada, a 4-list capture-recapture analysis was used based on 4 sampling lists (lists of farms sampled by the CanNAISS in 2008, 2009, 2010, and 2011). We conducted a separate analysis for each poultry category and subpopulation. For clarity, we present the analytical framework for a 3-list capture-recapture approach, which can be easily extended to a 4-list capture-recapture analysis (8). Mathematically, the log-linear approach models the logarithm of the expected value of each observable category. The fully saturated model for sampling lists 1, 2, and 3 is: Log E(mijk) = u 1 u1I(i = 1) 1 u2I(j = 1) 1 u3I(k = 1) 1 u12I(i = j = 1) 1 u13I(i = k = 1) 1 u23I(j = k = 1) 1 u123I(i = j = k = 1)
(1)
where: I(A) is an indicator function for an event A (e.g., I = 1; j = 1); u is the intercept; u1, u2, and u3 are 3 main effects for the log odds of appearing in sampling list 1, 2, and 3, respectively; u12, u13, and u23 are 3 first-order interactions (each corresponding to the interaction between pairs of lists); and u123 is a second-order interaction term (corresponding to the interaction effect among 3 lists) (2,22). Equation 1 uses a log link function and assumes a Poisson distribution of the dependent variable. There are 7 observed cells in a 3-list log-linear model but 8 different possible models (22). Therefore, it is not possible to construct a fully saturated model and t is generally assumed that the secondorder interaction term is null, i.e., u123 = 0 (8,22). The underlying assumptions of the capture-recapture approach are that: i) the farm population was closed, that is, no new farm appeared and no existing farm disappeared during the study period (2008 to 2011); ii) all farms have the same ‘capture/sampling’ probability within each year (equal catchability of farms). Dependence among the 4 sampling lists (i.e., the presence of a farm in a sampling list is influenced by the presence of the same farm in a previous sampling list) was modelled by adding interaction terms to the model. To identify relevant parameters, we used a forward selection process starting with the intercept and main effects parameters (u, u1, u2, u3, u4) and then added successively first-order interactions, and so on, until no further significant improvement of the goodnessof-fit of the model was obtained. Deviance was used to assess the goodness-of-fit of the model. Model selection was based on the Akaike Information Criterion (AIC) (23). The log-linear model with the lowest AIC was selected as the best model. The 95% confidence
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Table II. Distribution of tested farms by year, subpopulation, and CanNAISS component CanNAISS component POSBC TEL-MB Year Subpopulation Pre-S HSF VENAIS 2009 2011 2008 British Columbia 74 — — — — Ontario 245 — 45 — — Other 282 — — — — Canada 601 — 45 — — 2009
British Columbia 38 Ontario 110 Other 163 Canada 311
— — — 44 — — — 44
220 — — 220
— — — —
2010
British Columbia Ontario Other Canada
104 41 — 108 7 45 200 87 — 412 135 45
— — — —
— — — —
2011 British Columbia 70 10 — — — Ontario 147 41 48 — — Other 251 86 — — 53 Canada 468 137 48 — 53 CanNAISS: Canadian Notifiable Avian Influenza Surveillance System; Pre-S: Pre-slaughter surveillance component; HSF: Hatchery Supply Flock surveillance component; VENAIS: Voluntary Enhanced Notifiable Avian Influenza Surveillance; POSBC 2009: Post-outbreak surveillance in British Columbia in 2009; TEL-MB 2011: Surveillance of Notifiable Avian Influenza in table-egg layer farms in Manitoba in 2011; (2) No farm s ampled.
intervals (95% CI) of the estimated population sizes were calculated in statistical analysis software (SAS, Version 9.1; Microsoft, Redmond, Washington, USA) using the profile likelihood method. The log-linear modelling approach is appropriate for multi-list capture-recapture data using different detection protocols, selection methods, or data sources and when there is overlapping among sampling lists (15,16). An alternative approach uses uni-list capture-recapture methods such as Zero-Truncated Poisson or negative binomial models, in which the data are generated by a single detection protocol. In our case, multi-list capture-recapture analyses were more appropriate for analyzing CanNAISS data for the following reasons: (1) different detection protocols, i.e., the different years when CanNAISS was implemented, during the reference period 2008 to 2011 were used in CanNAISS with a perfect identification system of the sampled farms and (2) the overlapping fractions over the years were not too small (15,24,25). The data for our analysis were extracted from the CanNAISS database and formatted to include the farm unique identifier (Farm Id), sampled poultry category, sampling year, and subpopulation (BC, Ontario, and Other). Four sampling lists were created, one for each year (2008, 2009, 2010, 2011). The data were transferred into SAS (Version 9.1, Microsoft) for analysis. In 2007, representatives of the Canadian poultry industry provided data on the number of poultry farms. The data were compiled and stored in a spreadsheet
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Turkey
Turkey for meat
Turkey breeder
Table-egg layer
Turkey
Turkey breeder
0.960
—
20 (7–58)
65 (33–141) 0.0922 360 (256–587)
8.498 10 0.5803 211.5017
u 1 u 2 u 3 u 4
75.0
10.939 8 0.2052 25.0612
308
24
na
84
226
73
11.733 7 0.1097 22.2671 510 (252–1.076) 579
232 (143–412)
68 (33–153)
na
u 1 u 2 u 3 u 4 u 1u 2 u 1u 3 u 2u 3
23.501
21.322
160 (88–299)
13.263 10 0.2093 26.7365 120 (71–205)
0.499 2 0.779
12.678 7 0.080
98
60
199
2007 data 66
401 (163–1,197) 369
—
44 (22–91)
223 (137–383)
Population size estimate (95% CI) 73 (40–139)
u 1 u 2 u 3 u 4
u 1 u 2 u 3 u 4 u 1u 3 u 2u 3 u 1u 2u 4 u 1u 3u 4
u 1 u 2 u 3 u 4 u 1u 2 u 2u 3 u 3u 4
0.052
—
— u 1 u 2 u 3 u 4 u 2u 3 u 3u 4
19.7
155.9
95.6
86.3
5
—
22.444
24.682
3.167 8 0.923 212.833
10.960
—
15.556 9 0.077
9.318 7 0.231
Turkey for meat 83.1 u 1 u 2 u 3 u 4 u 1u 2 u 1u 3 u 1u 4 u 2u 3 u 2u 4 8.099 4 0.0880 u3u4 u1, u2, u3, u4 are main effects for sampling lists for 2008, 2009, 2010 and 2011 respectively. a Akaike Information Criterion. b The BC turkey farm population was small therefore we collapsed the two turkey categories. c No broiler breeder farm was tested in Ontario in 2009 and no model fitted the data using the 2008, 2010, and 2011 sampling lists. na: not available; (—): not applicable.
Roaster
Other Chicken Broiler breeder chicken
Roaster
u 1 u 2 u 3 u 4 u 1u 2 u 1u 4 u 2u 3 u 2u 4 u 3u 4
—
u1 u2 u3 u4 u34
u 1 u 2 u 3 u 4 u 1u 4 u 2u 3 u 3u 4
— u 1 u 2 u 3 u 4 u 1u 2 u 2u 4
35.2
Table-egg layer
70.0 14.3
Turkey breeder and turkey for meatb
Turkey
76.4
Sampling fraction (%) Model Deviance df P-value AICa 100.0 u 1 u 2 u 3 u 4 u 1u 2 u 3u 4 15.173 8 0.056 20.827
Ontario Chicken Broiler breeder chickenc
Table-egg layer
Poultry Poultry farm Subpopulation species category British Columbia (BC) Chicken Broiler breeder chicken
Table III. Sampling fractions, farm population size estimates, and the 2007 data for each subpopulation by poultry category
Broiler breeder chicken (BC)
Table-egg layer (BC)
Turkey breeder and turkey for meat (BC)
Table-egg layer (Ontario)
Turkey breeder (Ontario)
Turkey for meat (Ontario)
Broiler breeder chicken (Other)
Table-egg layer (Other)
Turkey breeder (Other)
Turkey for meat (Other)
Figure 1. Relationship between capture-recapture relative difference and sampling fraction by poultry category and subpopulation.
(Microsoft Excel 2002). These are referred to as the 2007 data and it was assumed that they were complete and comprehensive. Thus, a capture-recapture estimate of farm population size was considered valid if its 95% CI contained the 2007 data population size for the same poultry category and subpopulation. We used a scatter plot diagram, made in Microsoft Excel 2010, to explore the relationship between the capture-recapture relative difference (RD) for a given poultry category and its related sampling fraction (Equations 2 to 3) between 2008 and 2011. ˆ 2N Relative difference (a, b) = (N ab ab(2007))/Nab(2007)
(2)
Sampling fraction (a, b) = Number of farms sampled (a, b)/ Nab(2007)
(3)
ˆ is the number of farms in poultry category a in subpopuwhere: N ab lation b estimated using capture-recapture methods and Nab(2007) refers to the number of farms in poultry category a and subpopulaˆ tion b in the 2007 data. By substituting 95% confidence limits of N ab in equation 2, the bounds of the 95% CI of the RD were calculated. We plotted RD estimates against the sampling fraction for a given poultry category.
Results All the 95% CI of the farm population size estimates in the 3 subpopulations (BC, Ontario, and Other) included the 2007 data population size (Table III). The capture-recapture relative difference (point estimate) was close to zero (Figure 1). Only in Ontario was the range of capture-recapture relative difference wider for low sampling fractions than for larger sampling fractions (Figure 1).
Discussion In this study, the log-linear modelling approach provided reasonable point estimates of population sizes given the proportion of farms sampled for each subpopulation because the 95% CI included the 2007 data. Sampling fractions exceeding 100% were observed
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for broiler breeder chicken farms in the “Other” category. Although this may be explained by an increased number of farms, this seems unlikely because the industry is supply managed to ensure that the supply of a product matches the demand. The more likely explanation is that the 2007 data were incomplete. Our results (data not shown) were consistent with the principle of the capture-recapture analysis itself, in that when the recapture rate among sampling lists is low as a result of a low sampling fraction, we expect that estimates will be less accurate (2). This study illustrated that uncertainty about the capture-recapture estimates is not only affected by the sampling fraction. In BC and Other subpopulations, we were not able to see a decrease in the capture-recapture relative difference ranges as the sampling fraction increased. These results may suggest that the overlapping rate among sampling lists might influence the accuracy of the estimates. The assumption of a closed population is rarely truly satisfied in biological applications (26). We assumed that the number and distribution of chicken and turkey farms did not change from 2007 to 2011 and that no new farm appeared or existing farm disappeared. Based on Statistics Canada’s Census of Agriculture, there were 4578 poultry farms in 2006 and 4484 farms in 2011 (27). The commercial poultry industry in Canada is supply managed, which means that Canadian production and imports are regulated to ensure that the supply of a product matches the demand for it. For the turkey population, the number of birds slaughtered in Canada was reasonably stable during the study period, ranging from 20 454 572 to 22 750 170 birds per year (28). For the chicken population (including mature chickens), the total number of birds slaughtered per year in Canada remained relatively stable during the study period, ranging from 636 872 749 to 639 616 479 (28). With respect to the equicatchability assumption, we stratified the data by poultry category and subpopulation to address the impact of variable catchability of the farms, as suggested by several authors (3,9,29–32). The log-linear capture-recapture method may be particularly relevant for repeated surveys or ongoing surveillance systems when poultry farms are sampled on a continuous basis and when
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little or incomplete information is available on the total number of poultry farms in a specific area. This method does not replace a census or the results of a valid survey for the purpose of creating a poultry farm registry, however, because of the uncertainty related to the model outcome and the possible violation of the underlying assumptions. In future studies, there may be a need to better understand the effect of the recapture (overlapping) rate and the sampling fraction on the accuracy of the capture-recapture estimates. Applying capture-recapture methods to surveillance data and comparing to a complete farm registry may help to better understand the effect of these factors and to validate the actual log-linear capture-recapture estimates. Comparing results from various capture-recapture methods such as 2-list capture-recapture methods, e.g., Bailey, Chapman, and Chao estimators, and log-linear modelling and understanding their limitations will help in selecting the most appropriate capturerecapture analysis to use for future animal surveillance.
Acknowledgments The authors thank all Canadian chicken and turkey feather boards for their support and for providing the 2007 reference farm population data to make this study possible.
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