Vol.:(0123456789) 1 3 Social Network Analysis and Mining (2018) 8:35 https://doi.org/10.1007/s13278-018-0513-2 ORIGINAL ARTICLE Effect of estimation method, definition of ratio, and the plausible range in estimating social network size Maryam Zamanian 1  · Farzaneh Zolala 2  · Ali Akbar Haghdoost 3  · Mohammad Reza Baneshi 4 Received: 6 January 2018 / Revised: 13 April 2018 / Accepted: 18 April 2018 © Springer-Verlag GmbH Austria, part of Springer Nature 2018 Abstract A prime for network scale-up studies is the calculation of network size (C). To estimate C, respondents are asked about the number of their acquaintances belonging to specific reference groups with known sizes. The aim of this manuscript is to address influence of method of estimation and exclusion of unreliable reference groups on C. Recruiting 1275 women and using 25 reference groups, C was calculated applying traditional and Means of Sums (MoS) estimators. This C is applied to back-calculate the size of reference groups. To assess the closeness of back-calculated and real size, two types of ratio were calculated: back-calculated over real size, and its reverse. The tolerable range for ratio was defined as (0.5, 1.5), (0.5, 2), and < 1 based on the absolute logarithmic scale. The reference group corresponding to the poorest ratio was omitted. New C was estimated based on the remainder of the reference groups. The whole process continued in an iterative fashion until all ratios fall within the plausible range. In the traditional approach, C was robust with respect to definition of ratio and its tolerable range. Minimum and maximum C were 174 and 186. In the MoS analysis, C values hugely diverse ranged 185–557. This might partially be due to small number of eligible reference groups contributing in the estimation of C. As C is used to estimate size of hidden groups, its calculation needs careful plan. We recommend authors to provide a range of values for C. Keywords Network size · Estimator · Bias · Means of sums 1 Introduction Estimating the size of hidden subpopulations is an important issue in public health (Bernard et al. 2010). For example, understanding and measuring the burden of HIV remains facing several challenges around the globe. However, HIV prevention, care, and treatment efforts including advocacy for populations at risk of HIV, design and implementation of national guidelines, and HIV program evaluations are not feasible without relatively precise estimates of the impact and magnitude of HIV among most-at-risk subpopulations (for example, sex workers). Given the importance of inform- ing public health policy makers with reliable information about the number of people at risk of HIV, it is crucial to quantify the population size of these key subpopulations. Population size estimation (PSE) methods are divided into direct and indirect methods. Direct PSE methods, such as enumeration and survey, are prone to different biases (Shokoohi et al. 2012). Using direct estimation technique of population size has various challenges such as hallmark and discrimination. In addition, survey for direct population size estimation (according to the relatively small population size) requires a large sample size, and it is not often feasible. Network scale-up (NSU) is an indirect PSE method which is implemented in general population. While in direct survey, respondents are asked to provide information about them- selves, in NSU method respondents are asked to concentrate on their network (shown by C) and to provide the number of their acquaintances who belong to the subpopulation * Mohammad Reza Baneshi rbaneshi2@gmail.com 1 Department of Epidemiology, School of Health, Arak University of Medical Sciences, Arak, Iran 2 Social Determinants of Health Research Center, Institute for Futures Studies in Health, Kerman University of Medical Sciences, Kerman, Iran 3 HIV/STI Surveillance Research Center, and WHO Collaborating Center for HIV Surveillance, Institute for Futures Studies in Health, Kerman University of Medical Sciences, Kerman, Iran 4 Modeling in Health Research Center, Institute for Futures Studies in Health, Kerman University of Medical Sciences, Kerman, Iran