Application of the Capture-Recapture Method in Estimating the Size of the Active Homosexual Male Population in Hangzhou City of China

Abstract

The homosexual population is particularly susceptible to sexually transmitted disease because of various high-risk sexual behaviors among them. The authors explored the application of capture-recapture methods in estimating the size of the sexually active homosexual male population in Hangzhou. Homosexual men at 9 activity sites were investigated in Hangzhou, Zhejiang. The total active homosexual male population of Hangzhou estimated by the capture-recapture method and multiplier method was 2014 (95% confidence interval [CI] = 1899-2129) and 2012.5 (95% CI 1925 to 2101), respectively. This study shows that the capture-recapture method can be used to enumerate and provide accurate and reliable estimates of the active homosexual population in any area, provided that certain conditions are controlled.

Keywords

homosexual male population size capture-recapture methods

Introduction

The prevalence of various high-risk sexual behaviors among homosexuals is increasing. These activities include early onset of sexual life, multiple sex partners, specific sexual activities such as oral or anal sex, fist sex, unprotected intercourse, and involvement in the sex trade.¹ These practices lead to the homosexual population as a whole becoming particularly susceptible to various sexually transmitted diseases, especially AIDS.

In 1981, the first case of HIV infection in the homosexual population was confirmed,² and during the past 2 decades, the homosexual population represents an expanded pool of HIV infection in many countries.³ Estimation of the epidemic situation in China in 2001 and 2010 showed that several regions of the country were encountering a peak period of AIDS morbidity and mortality at the same time.^4,5

It is difficult to accurately estimate the prevalence of homosexuality because of social stigma associated with identifying people as gay.⁶ The capture-recapture method, derived from a method developed for studies of animal populations, is commonly used for estimating the size of rare and elusive populations, which are difficult to find and count or are highly mobile and cannot be counted at one time.⁷ The method was first introduced in 1889 and is still widely used in wildlife science to estimate the size of closed animal populations.^8,9 The principal of the method consists of cross-linking information from different monitoring systems, estimate specific cases and the common cases from each source, and identify the number of cases not found in any of the sources. Fixed-spot observation has also been used for such studies. These methods were originally derived for the survey of the activity of particular living beings in a specific ecosystem.^9,10

The capture-recapture method can be basically divided into 2 groups: one uses a 2-source method, and the other one involves 3 or more sources.¹¹ The procedure is that at one time as many animals as possible in an area are captured, tagged, and released; this is called the capture stage. At a later time, this is repeated (ie, the recapture stage). The number of animals in each sample, n_A and n_B, and the number common to both, n₁₁, are used to estimate the number in the total population. This method is also referred to as the capture-mark-recapture method. The capture-recapture method makes the following assumptions: that during the investigation, the population is closed; that no identifiers are lost, so that individuals can be matched from capture to recapture; that all individuals have the same probability of being captured; and that there is no dependence between capture and recapture.¹²

Many researchers have successfully used the capture-recapture method in epidemiological studies to estimate the prevalence of diseases and health-related problems,¹³ including childhood diabetes,¹⁴ parasitic diseases,¹⁵ substance abuse,¹⁶ cancer,¹⁷ and dementia.¹⁸ The present study was undertaken using a 2-source method to estimate the size of the homosexual male population in Hangzhou city of China. Highly sexually active homosexual men are a specific group of people that are elusive, highly mobile, and difficult to count. Several places, such as bars, parks, and bathhouses, in Hangzhou are considered possible activity sites for this population of males.

Hangzhou is a city in the middle stage of socioeconomic development. It is neither a crowded metropolis nor an underdeveloped rural area but a medium sized city with generally educated residents. As a result, Hangzhou may reflect the current situation in regard to the prevalence of male homosexuality for the Chinese population as a whole.

Methods

Procedures of Investigation

A total of 9 homosexual male activity sites in Hangzhou, considered as possible activity sites for homosexual men, were verified and confirmed as suitable places for the investigation; these included 2 bars, 4 parks, 1 bathhouse, 1 public latrine, and 1 public arena. Prior to the investigation, homosexual men at the activity sites were informed of the study and their consent was obtained. Permission and assistance was also obtained from the hosts of selected sites prior to the investigation.

A total of 20 homosexual male volunteers were recruited as helpers. They were given detailed information about the objective and the process of the study as well as the future use of the data obtained from the present investigation. They also helped the researchers explain the contents of the survey to homosexual men and promised to keep it secret. Moreover, several pilot studies were performed prior to the main study to assess the feasibility and reliability of the present investigation. Most homosexual men understood the content of the present investigation. Nobody refused to participate in the investigation.

An initial investigation was undertaken between October 23 and 27, 2000, using a fixed-spot observation method—the multiplier method. This method is a kind of indirect method for estimation of the size of a particular population. The basic principle of this method is that the number of people belonging to the estimated population who appear at selected institutions or services during a certain period is equal to the total size of the estimated population multiplied by the reciprocal of the population who attended the selected institutions or services during the same period. During this investigation, 2 homosexual male volunteers counted the number of participants at a single site every half hour. In addition, 2 homosexual male volunteers and the researcher made an inspection tour among the 9 sites to identify repeated counts caused by the floating population. Estimates in this study were based on the time when the sum of the numbers of homosexual men from 9 different sites was the highest for each day.

A second investigation was undertaken at the same 9 sites between December 2007 and January 2008. The capture-recapture method was used in this study. All homosexual men who participated in the activities at the 9 sites were interviewed face-to-face and asked to complete a questionnaire. A well-trained investigator provided a detailed introduction and explanation of the questionnaire prior to it being completed. The questionnaire obtained information on demographics (age, education level, marriage status, and occupation), frequency of participation at the activity sites, and the number of homosexual men known by the participant who never visited the activity site. In this study, homosexual men moving from one site to another could be easily identified by duplicate information obtained in the questionnaire. In addition, a suitable and effective special key ring tag was made for each of the homosexual men during the interview; they were asked to carry this about for the purpose of recapture. This method estimated the number of active homosexual men in the region.

Statistical Analysis

The 2-source method is the simplest capture-recapture method and is used to estimate the unknown population size of a group of people. The first source provides individuals for tagging, whereas the second source provides individuals for recapture. We assumed that there are 2 sources in the study, with n₁₁, n₁₀, n₀₁, and n₀₀ representing the number of individuals captured in both sources, the number of individuals captured in source A only, the number of individuals captured in source B only, and the number of individuals missed in both sources, respectively. So, the number of individuals in the first source (n_A) is given as (n₁₁ + n₁₀), and the number of individuals in second source (n_B) is given as (n₁₁ + n₀₁). N was defined as the total population in question. It was assumed that if r = n₁₁ + n₁₀ + n₀₁, then n₀₀ = N − r. If this assumption is true, then the ratio of tagged individuals to the number of individuals in the second source should approximate to the ratio of total tagged individuals to the total population; that is,

\frac{n_{11}}{n_{B}} = \frac{n_{A}}{N} .

Rearranging the equation above produces a point estimate value of the total population:

N = \frac{n_{A} n_{B}}{n_{11}} .

And the estimate for the 95% confidence interval (CI) of the total population will be

N \pm 1.96 \sqrt{Var(N)} .

In the equation above, Var(N) is the variance of the total population N:

Var (N) = \frac{n_{A} n_{B} (n_{A} - n_{11}) (n_{B} - n_{11})}{{n_{11}}^{2} (n_{11} - 1)} .

From the equation above, it can be seen that the value of the variance of the total population is greatly influenced by the number of individuals common to both sources (n₁₁). When n₁₁ = 1, because (n₁₁ − 1) = 0 and the denominator also becomes 0, the variance becomes arbitrarily great, and the total population N will also become very large; however, this is apparently illogical. Thus, when n₁₁ is very small, especially when n₁₁ < 5, the total population and the variance ought to be calculated as follows:

N = \frac{(n_{A} + 1) (n_{B} + 1)}{n_{11} + 1} - 1,

Var (N) = \frac{(n_{A} + 1) (n_{B} + 1) (n_{A} - n_{11}) (n_{B} - n_{11})}{{(n_{11} + 1)}^{2} (n_{11} + 2)} .

And the coincident rate of the sample of each source can be calculated accordingly as follows:

\frac{n_{A}}{N} \times 100 %

and

\frac{n_{B}}{N} \times 100 % .

Then, the coincident rate of 2 sources is given by

\frac{[n_{A} + (n_{B} - n_{11})]}{N} \times 100 %,

and the mutual coincident rate of 2 sources is given by^19,20

\frac{n_{11}}{n_{A}} \times \frac{n_{B}}{n_{11}} \times 100 % .

Data obtained at the bars were assigned to the first source (A) and the remainder (parks, bathhouse, public latrine, and public arena) to the second source (B). By comparing the data from 2 sources, targets that were captured repeatedly were identified and the number of repeats counted.

The equations shown were used to estimate the total population and other related data and to rectify the error of data obtained from only a single source. Because the frequency of participation at the sites for every single homosexual man in a given week was different, the data were stratified by frequency of participation at the sites.

All data were entered into a computerized database using the Epidata 3.0 software and analyzed using the Epi Info 6.04 for DOS and SPSS 11.0 software.

Results

Demographic Data

Homosexual men were investigated in the 9 venues in 2000, 2007, and 2008. Their mean ages were 31.63 ± 10.28, 34.17 ± 9.21, and 35.25 ± 10.23 years, respectively, ranging from 18 to 62 years (Table 1). The majority (78.9% to 81.9%) were 25 to 45 years old. Students occupied the proportion from 28.6% to 36.6%, and the most common occupations were trade workers and technicians. The proportion of homosexual men engaged in trade, art, and freelance work have increased from 2000 to 2008.

Table 1.

The Demographic General Characteristics of Homosexual Men.

	Number of Homosexual Men
	2000 (%)	2007 (%)	2008 (%)
Age (years)
<25	232 (18.6)	203 (15.3)	241 (17.1)
25-45	989 (79.1)	1084 (81.9)	1113 (78.9)
>45	29 (2.3)	37 (2.8)	57 (4)
Total	1250 (100)	1324 (100)	1411 (100)
Occupation
Worker	127 (10.2)	114 (8.6)	116 (8.2)
Occupations in trade	235 (18.8)	324 (24.5)	361 (25.6)
Farmer	77 (6.2)	34 (2.6)	42 (3)
Student	458 (36.6)	415 (31.3)	404 (28.6)
Technician	223 (17.8)	254 (19.2)	259 (18.4)
Occupations in art, culture, recreation, and sport	46 (3.7)	74 (5.6)	81 (5.7)
Unemployed person	30 (2.4)	23 (1.7)	44 (3.1)
Others	54 (4.3)	86 (6.5)	104 (7.4)
Total	1250 (100)	1324 (100)	1411 (100)

Population Estimated With the Multiplier Method

Data obtained in December 2007 show that 1250 homosexual men gathered at the sites and participated in activities in 1 week (Table 2). The mean number of homosexual men participating in activities each day was 178.6 persons.

Table 2.

The Number of Homosexual Men Participating in the Activity at 9 Active Sites in 1 Week.^a

Time	Site 1	Site 2	Site 3	Site 4	Site 5	Site 6	Site 7	Site 8	Site 9	Total
Day 1	27	30	8	20	14	8	12	6	8	133
Day 2	30	19	7	22	20	6	17	6	8	135
Day 3	36	28	10	18	13	10	20	8	7	150
Day 4	25	35	12	17	19	7	16	7	8	146
Day 5	62	56	16	32	36	18	25	12	12	269
Day 6	65	42	13	24	32	17	23	9	10	235
Day 7	45	35	9	19	24	12	18	10	10	182
Total	290	245	75	152	158	78	131	58	63	1250

Sites 1and 2, bar; site 3, bathhouse; sites 4-7, parks; site 8, public latrine; site 9, public arena. Dates: October 23, 2000, to October 29, 2000.

According to the face-to-face interviews with all 1250 homosexual men, the interval between the 2 visits to the activity sites ranged from 3 to 15 days, with a mean of 11.27 ± 2.74 days. The total number of homosexual men was calculated as (1250/7) × 11.27 = 2012.5. The approximate 95% CI calculated by assuming a Poisson distribution was between 1925 and 2101.

Population Estimated With the Capture-Recapture Method

Estimation of the population of homosexual men in December 2007

Table 3 shows the number of homosexual men seen at 2 sources in Hangzhou in 1 week in December 2007. Source A comprised 2 bars, and source B was composed of 1 bathhouse, 4 parks, 1 public latrine, and 1 public arena. The data indicated that 91.7% (1214/1324) of them had participated 1 or 2 times in sexual behavior at 1 or both sources in 1 week. About one third of them (382/1324) had participated in sexual behavior more than once at both sources in 1 week.

Table 3.

The Number of Homosexual Men Observed at 2 Sources in December 2007 Analyzed by Frequency.

		Number of Times in 1 Week
Source A	Source B	1	2	3	4	Total
Present	Present	237	128	12	5	382
Present	Absent	321	175	23	3	522
Absent	Present	112	241	55	12	420

Table 4 shows the results of estimation of the number of homosexual men in December 2007 by using the capture-recapture model. The total number of homosexual men was 1896 (95% CI = 1792-2000). The coincident rate for source A was 47.7% (95% CI = 45.2-50.5). The coincident rate for source B was 42.3% (95% CI = 40.1-44.8). The coincident rate for the 2 sources was 69.8% (95% CI = 66.2-73.9; P = .7667).

Table 4.

Estimate of the Number of Homosexual Men by Using Capture-Recapture Model (December 2007).^a

Frequency	n₁	n₂	n₁₂	n	N	Se1	CI	Se2	CI
1	558	349	237	670	821	68%	64-72	43%	40-45
2	303	369	128	544	871	35%	31-39	42%	38-47
3	35	67	12	90	187	19%	14-30	36%	26-58
4	8	17	5	20	26	31%	23-48	65%	48-103
Total	904	802	382	1324		47.7%	45.2-50.5	42.3%	40.1-44.8

Abbreviation: CI, confidence interval.

n₁, n₂, n₁₂, n, Are the numbers of homosexual men from source A, source B, sources A and B, and observed at A and B, respectively. N is the estimation of the total number of homosexual men. Se1 and Se2 are the coincidences of sources A and B, respectively.

Estimation of the population of homosexual men in January 2008

Table 5 shows the number of homosexual men seen at 2 sources in Hangzhou in 1 week in January 2008, analyzed by number of times that the homosexual man participated in the activity. In total, 93.3% (1316/1411) of them had participated in sexual activities nearly 1 or 2 times at 1 or 2 sources in 1 week. In addition, 26.2% of them had participated in sexual behavior more than once at both sources in 1 week.

Table 5.

The Number of Homosexual Men Observed at 2 Sources in January 2008 Analyzed by Frequency.

		Number of Times in 1 Week
Source A	Source B	1	2	3	4	Total
Present	Present	241	112	10	7	370
Present	Absent	353	195	31	3	582
Absent	Present	132	283	35	9	459

Similarly, Table 6 lists the results of estimation of number of homosexual men using the capture-recapture model. As a result, the number of homosexual men observed at A and B was 1411. Estimation of the total number of homosexual men was 2131 (95% CI = 2005-2257). The coincident rate was 44.7% (95% CI = 42.2-47.5) for source A, 38.9% (95% CI = 36.7-41.3) for source B, and 66.2% (95% CI = 62.5-70.4; P = .4428) for both sources.

Table 6.

Estimation of the Number of Homosexual Men by Using the Capture-Recapture Model (January 2009).^a

Frequency	n₁	n₂	n₁₂	n	N	Se1	CI	Se2	CI
1	594	373	241	726	919	65%	61-69	41%	38-43
2	307	395	112	590	1078	28%	25-32	37%	33-42
3	41	45	10	76	175	23%	16-41	26%	18-45
4	10	16	7	19	22	45%	36-62	73%	58-99
Total	952	829	370	1411		44.7%	42.2-47.5	38.9	36.7-41.3

Abbreviation: CI, confidence interval.

Comparison of the investigations in December 2007 and January 2008 found no significant difference between the results. This allowed an estimation to be made of the mean value across both investigations. From the results of this calculation, we found that the total number of homosexual men was 2014 (95% CI = 1899-2129). The combined coincident rate for source A was 46.2% (95% CI = 43.7-49.0), and for source B it was 40.6% (95% CI = 38.4-43.1). The coincident rate for both the sources was 68.0% (95% CI = 66.4-72.2).

Discussion

The number of high-activity homosexual men in Hangzhou was 2014 when estimated with the capture-recapture method and was 2013 when estimated with the multiplier method. The results obtained by the 2 methods are very close; thus, it is reasonable to conclude that the number of homosexual men who gathered at the activity sites and who participated in the activities in Hangzhou was 2014 persons, with 95% CI = 1899 to 2129.

Reliable use of the 2-source method requires that the coincident rates of each source are greater than 40% and the coincident rate for both the sources is greater than 60%. In the first investigation, the coincident rates of each source were 47.7% (45.2%-50.5%) and 42.3% (40.1%-44.8%), respectively, and the coincident rate of 2 sources was 69.8% (66.2%-73.9%). Thus, estimation of the population size was trustworthy. In the second investigation, the coincident rates of each source were 44.7% (42.2%-47.5%) and 38.9% (36.7%-41.3%), respectively, and the coincident rate of 2 sources was 66.2% (62.5%-70.4%). Because the coincident rate of source B (38.9%) in this investigation was less than 40%, the estimation of population size may have greater potential for error. However, in our case, the results of the second investigation were close to those of the first investigation, and using mean values across both studies compensated for any possible error. In addition, the coincident rates across both the sources were greater than 60% in both investigations. We therefore conclude that the combination of data from 2 sources greatly increases the validity, completeness, and reliability of our data. The P values of the results of the 2 investigations were .7667 and .4428, respectively, indicating that the 2 sources were generally independent of one another.

It should be noted that there were several limitations to the investigation in our study. In the investigation using the fixed-spot observation method, several homosexual male volunteers were recruited to help count and identify the homosexual men gathered at the activity sites and to obtain identification criteria.²¹ However, because of the dark and crowded environment, miscounting and misidentification of homosexual men could not always be prevented. It was also recognized that the floating population of homosexual men could result in either overestimation or underestimation of the true population. An attempt to control for repeated counts of the floating population was made by inspecting each of the activity sites, but the problem was not completely avoided as there was no way of accurately estimating this fluid population of homosexual men. The third area of limitation is related to cultural and geographic issues. Homosexual men are discriminated against in China, and to avoid this, they gather together in concealed and fixed sites where gate crashers are usually unwelcome. These factors may have resulted in an underestimation of the true population in our study and may explain why the findings obtained by the 2 methods were so close.

Homosexual male health is a legitimate focus for scientific study but is one that has generally been neglected by public health research. Only 3027 articles, the equivalent of 0.08% of the MEDLINE database, focused on homosexual male individuals over the past 2 decades. Moreover, most studies that addressed homosexual male populations focused on sexually transmitted diseases or on mental disorders.²² Our study focused on the prevalence of male homosexuality in a medium-sized city in China, which is in the eastern part of the country with the greatest population in the world. A number of articles concerning the same topic have been published previously, but most of them were simply based on a combination of face-to-face interviews and/or self-completion questionnaires.^23,24 Such studies may have failed to identify some of the true homosexual population because of the social stigma associated with being gay.

Our approach was to try to apply the capture-recapture method to estimate the size of a specific group of homosexual men. This method has been advocated for use in estimating the completeness of a register,²⁵ and many researchers have used this method to estimate the true population size from existing data sources that provide incomplete lists of cases.^26,27 Unfortunately, monitoring systems that collect reports of diseases or records of specific groups of people are not well established in many developing countries. Thus, there were no lists of homosexual men that could have been used for the capture-recapture method generated by any agency or organization in Hangzhou. Therefore, we ourselves had to generate the lists by administering face-to-face interviews to the homosexual men at each activity site, and we made a specific tag for the purpose of recapture of every homosexual man during the interview. Lists generated in this way were then used for the capture-recapture model.

We found that the results obtained by using the capture-recapture method were consistent with the results obtained by using the combination of fixed-spot observation and the multiplier method. For this reason, we can conclude that the study has demonstrated the accuracy of the capture-recapture method for estimating the population of active homosexual men, It also shows the usefulness and feasibility of such a method because the costs in time and labor involved in carrying out an investigation of population size using the capture-recapture method are much lower when compared with the costs using the multiplier method.

Data from active homosexual men were obtained from 2 different sources by the same researcher, which means that the range of the population may have been diminished and the total population of homosexual men underestimated. Therefore, multiple active surveillance systems need to be set up to enhance the accuracy of estimation and help establish a health policy and program.

Homosexual men are not only highly susceptible to sexually transmitted diseases because of risky sexual behaviors existing among them,²⁸ but because they live in a heterosexist society, homosexual men have to also deal with harmful psychological stress and are susceptible to mental health problems and suicidal tendencies because of the lack of social support.²⁹ Moreover, some of the men also have associated substance abuse or alcohol dependence.³⁰

Estimating the homosexual male population is necessary because it helps in planning for health care needs and developing relevant research programs within the population. We found that most of the homosexual men surveyed were students, technicians, businessmen, and workers. They had a comfortable professional environment and/or a high income. About 80% of them were 25 to 45 years old. The results of this study will allow us to know which homosexual men are in need of health care services and health promotion programs.

It should be noted that the present study only shows the population size of homosexual men who participated in homosexual activities. The hidden population of homosexual men remains to be investigated. Greater efforts should be devoted to this, and new methodology that is cost-effective should be introduced to the research on the homosexual population.

An interesting question for future research concerns the psychological and physiological differences between homosexual men and men in general. Another question is how we are going to prevent this specific population from HIV infection and mental problems.

Footnotes

Acknowledgements

We would like to thank Professor Yi Shen for his helpful suggestions and comments on statistical analyses. We would also like to thank the hosts who kindly agreed to allow this investigation to be carried out at their sites and all the anonymous homosexual men who gave us their warmest hands in this study.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by a grant from the Zhejiang Natural Science Foundation (399139) and the fund from Health Bureau of Zhejiang Province.

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