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# Table 1 Summary of size estimation methods. The continuity of this table is across four pages

Sampling method | Description | Assumption | Strength | Weakness |
---|---|---|---|---|

Capture-recapture [15] | Assesses the overlaps between incomplete case lists from multiple independent data sets |
1) the selected sampled population is a good representation of the whole population 2) the sample is a closed population 3) able to match individuals in both datasets; 4) individuals have an equal likelihood of being captured | Simple and easy to use for researchers |
Capture biases: not everyone has an equal chance of being captured; Estimates would be too high if matches were not identified or too low if recaptures were matched incorrectly |

Multiplier [16] | Two independent sources of data are used to make the estimation, including an authentic count or list of the population whose size is being estimated and a survey of the populations whose size is being estimated | There is accurate demographic and geographic information of the key population | Simple and easy to use | The quality of the data can cause bias; the resulting survey samples may not be fully representative of the key population |

Delphi [17] | Estimating the size of key populations by the individual judgment of several experts | The estimation from an expert team could accurately reflect the reality | Low cost with high efficiency | The estimation may be subjective and not reliable because of the quality of the expert team; Lack of strategies to deal with the disparity between the experts |

Mapping [18] | The locations of the key population are systematically identified and mapped to estimate the size of the key population | The quality of the data can be guaranteed by the full involvement of the key populations | The estimate is made with transparency | The missing of some geographical locations may underestimate the size of key populations; overestimation may happen if the key population frequently attend multiple locations |

Workbook [19] | The key population is identified first and then the estimates are combined with the total population to calculate the proportion of the key population in a specific region | Typically used in countries or regions where the epidemic is low and concentrated | The estimate is made with transparency; errors can be prevented by automatic consistency and audit check | In some countries, data may be limited because of stigma and discrimination among the key populations and legal issues, which may make data unreliable or of poor quality |

Network scale-up [20] | Respondents are asked about the behaviors of acquaintances from their social network to estimate the number of key populations from the social network of each respondent |
The average size of personal networks of key populations and the population as a whole are the same; People can accurately report the behaviors of acquaintances from their social networks | The privacy of the key populations is protected because the researchers do not directly contact them | The respondents may ignore key populations among their acquaintances (transmission error); Obtaining a representative sample is challenging because of stigma and discrimination |

Respondent Driven Sampling [21] |
A sample from the key population is selected purposively and then these selected individuals are given coupons to recruit other key populations from their social network |
Recruiters randomly pass coupons to their social network members who are members of the key populations; Every participant has only one chance to receive the coupon and is equally likely to be recruited; | The Respondent-Driven Sampling method is an effective sampling method for estimating hard-to-reach networked populations with no sampling frames | Limited recruitment within the key populations may lead to biased estimates |

Bayesian Estimation [22] | The key population size is estimated following Bayes' theorem, which is based on a prior probability distribution | If there exists some prior knowledge, like prior probability, the Bayesian method is suitable | It can solve the problem when there is no direct data to estimate the population size for a specified geographical area through survey sampling studies by utilizing empirical data | Bayesian methods might be subjective, due to different researchers with different prior beliefs |

Stochastic Simulation [23] | Estimating the size of a certain population (e.g., HIV-positive) using epidemiologic data using the Monte Carlo method | Parameters are based on the data from representative clinical trials or observational cohort studies | Stochastic simulation makes it possible to naturally produce plausibility intervals for estimates in the face of uncertainty | First, some complex simulation process is quite time-consuming. Second, thanks to different kinds of parameters setting and the unknown quality of observed data, the robustness of some simulation model estimates is not stable |

Laska-Meisner-Siegel Estimation [24] | Based on a single sample and in a single venue, it is an unbiased estimator for the size of a population | This method assumes that we only have a one-time sampling | This estimation method is time- and resources- saving, when comparing with capture-recapture | This method only requires one single sample, thus its estimation accuracy might be lower than other several times sampling estimation methods |