Using temporary marking of owned dogs to estimate numbers of owned and unowned dogs

If owned dogs are brought to clinics for veterinary treatment, vaccination or sterilisation a proportion of owners may be willing to have a simple collar fitted to the dog to provide a visible mark, lasting for at least a few days. In that case it may be possible to use subsequent street surveys and a survey of dog-owning households to estimate the number of owned and unowned dogs, as detailed for example by Kayali et al in the Bulletin of the World Health Organisation, 2003, 81 (10). Estimates of the numbers of owned and unowned dogs are required to evaluate the likely effect of the existing intervention effort and suggest required changes in its design.

The following downloads provide a modified version of the published method that can be be used to estimate the number of owned and unowned dogs and to run simulation trials of the estimation method. The basic idea is simple. A known number of owned dogs are marked. Using information from the owners that number is split into the number of "confined" dogs and the number of "unconfined" dogs, i.e. those with access to public areas. Assuming the unconfined marked dogs are as likely to be seen on the street as unmarked dogs (some of which will be unowned, others unmarked unconfined owned dogs) the number of marked dogs seen on the street surveys allows the number of unmarked dogs on the street to be estimated. For example, if about a third of the unconfined marked dogs were seen on a street survey we would estimate that the total number of unmarked dogs on the street is about three times the number of unmarked dogs seen. At the same time a survey of dog-owning households should reveal the total number of owned dogs (for example, if about half of the dogs encountered on the household survey are marked we would estimate the total number of owned dogs is about twice the number that were marked). The household survey will also reveal what fraction of unmarked owned dogs are confined and hence suggest what fraction of our estimate of unmarked dogs on the street are unconfined owned dogs as opposed to unowned dogs.

The "temporary_mark_population" program differs from the published method in that, for simplicity, the data on confinement is incorporated as a term in the likelihood rather then being used to provide Bayesian prior probabilities. It is not necessary to be familiar with either Bayesian statistics or likelihood to use the program. The marking, street survey and household survey data can be typed into a text file using the comma-separated format shown in the "datafile.txt" download. The data required are of three types. During intervention owners who agree to have their dog marked are asked whether or not the dog is confined and the number of confined and unconfined marked dogs recorded. During each of up to four street surveys of the intervention area the numbers of marked and unmarked dogs seen are recorded. And in each of the dog-owning households randomly selected during the household survey the dogs are classified as marked, unmarked confined and unmarked unconfined and the totals recorded. The program can then be run by clicking on the "estimate" command button. The parameter estimates will be shown in the textboxes grouped into the "parameters" section of the form. An initial, default guess at the parameter value appears in each upper box and the final "maximum likelihood" estimate in the textbox below. To the right of that lower textbox a checkbox is checked if the corresponding parameter is to be set "free" during the estimation, otherwise the initial value in the upper textbox will be used. By default all parameters are "free". To obtain confidence limits on any of the parameter estimates (for example on the number of unowned dogs) fix that parameter by unchecking its checkbox and set its value above or below the estimate generated when it was set "free". Run the estimation program again and check by how much the "negLL" value reported near the top of the form changes. 95% confidence limits on a parameter are values at which the negLL value is increased by 1.92. Changing the number of unowned dogs will effect the owned dogs estimate and hence the estimated percentage of dogs that are unowned, an important statistic for planning and evaluating intervention. Thus establishing confidence limits on the number of unowned dogs will, at the same time, establish the confidence limits on the percentage of dogs that are unowned.

If the textbox showing the path to the data file is cleared the program changes to a simulation mode. The parameter values in the upper textboxes are then used to simulate data ,displayed in the "data" section of the form. That data is used in place of data read from the data file to estimate the parameter values. The parameter estimates, expressed as percentages of the values used to drive the simulation, are displayed graphically at the bottom of the form. The textbox to the right of the "Run simulation" command button can be set to the required number of repeat simulations (eg. 100). The graphs then show the parameter estimates averaged over the number of runs completed, to indicate any bias in the estimates - the averaged parameter estimates should converge to 100% of the parameter value used to drive the simulation if the estimator is unbiased.

A critical assumption of the published method is that unconfined owned dogs are as likely to be seen on the street as unowned dogs. In a fully urban environment an unconfined owned dog may well be hidden within the house at the time of the street survey, even though it has the option to roam on the street. A textbox at the top of the form can be used to set the visibility of an unconfined owned dog as a percentage of the visibility of an unowned dog (which has to spend all of its time in public areas). Running a simulation with that value set at less than 100% shows that the visibility of unowned dogs will be underestimated and hence the number of unowned dogs overestimated if unconfined owned dogs are less visible.

In the "temporary_mark_population1" program the data collected during the household survey is extended to allow the assumption to be relaxed. The idea is that the household survey is conducted at the same time of day as the street surveys in order to observe the status of the unconfined owned dogs at that time. The number of categories recorded is increased from three to six: marked dogs are recorded as confined, unconfined and on the street, and unconfined but still within the house; and unmarked dogs are split into the same three catagories. A multinomial distribution for the six recorded frequencies is incorporated into the likelihood to allow unbiased estaimtion of the number of owned and unowned dogs even if unconfined owned dogs are less likely to be seen during the street surveys than unowned dogs.

Experimentation with the simulation will show that it is not essential to run more than one street survey. Successive surveys are not used as a way of detecting dogs marked on earlier surveys (though such marking or identification by natural marks could be incorporated). However repeating the street surveys will increase the total sample sizes of marked and unmarked dogs seen, thus avoiding small-sample bias and reducing the width of the confidence intervals.

Download the following files to the same temporary folder to try out the temporary_mark_population and temporary_mark_population1 programs:

either:

or:

and:

LIST OF ADDITIONAL PROGRAMS

- Sterilisation rates required to stabilise a population
- A regression estimator for a roaming dog population
- An estimator for total roaming dogs in a city block using sight-resight data (allowing for possible emigration)
- An estimator for total roaming dogs in a city block using sight-resight data (allowing for possible heterogeneity)
- A program for using temporary marking of owned dogs to estimate numbers of owned and unowned dogs
- A program for using permanent marking of roaming dogs to estimate their survival
- Population dynamics

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