Parameters - Centers for Disease Control and Prevention
Goodreau SM, Hamilton DT, Jenness SM, Sullivan PS, Valencia RK, Wang LY, Dunville RL, Barrios LC, Rosenberg, ES. Targeting strategies for pre-exposure prophylaxis (PrEP) among adolescent sexual minority males (ASMM) in the United States: a modeling study.ParametersAll parameters are taken directly from Jenness et al. 2016 ADDIN EN.CITE <EndNote><Cite><Author>Jenness</Author><Year>2016</Year><RecNum>13</RecNum><DisplayText>(1)</DisplayText><record><rec-number>13</rec-number><foreign-keys><key app="EN" db-id="xvdv2sspezx5x4ew22qv2waqev0p25tsetrx" timestamp="0">13</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Jenness, S. M.</author><author>Goodreau, S. M.</author><author>Rosenberg, E.</author><author>Beylerian, E. N.</author><author>Hoover, K. W.</author><author>Smith, D. K.</author><author>Sullivan, P.</author></authors></contributors><auth-address>Department of Epidemiology.
Department of Anthropology.
Center for Studies in Demography and Ecology, University of Washington, Seattle.
Division of HIV/AIDS Prevention, Centers for Disease Control and Prevention, Atlanta, Georgia.
Department of Epidemiology Department of Global Health, Emory University.</auth-address><titles><title>Impact of the Centers for Disease Control's HIV Preexposure Prophylaxis Guidelines for Men Who Have Sex With Men in the United States</title><secondary-title>J Infect Dis</secondary-title><alt-title>The Journal of infectious diseases</alt-title></titles><periodical><full-title>J Infect Dis</full-title></periodical><dates><year>2016</year><pub-dates><date>Jul 14</date></pub-dates></dates><isbn>1537-6613 (Electronic)
0022-1899 (Linking)</isbn><accession-num>27418048</accession-num><urls><related-urls><url>;(1), unless noted below.Entry and debutIndividuals are able to enter the population at multiple ages (13-18), and to experience anal intercourse (AI) debut either upon entry into the population, or sometime thereafter. This is because our population definition consists of those who have begun to identify as gay/bisexual, or who have begun sexual activity with males. That is, an individual need not have sexually debuted to fall within our population definition.The probability of each age at entry is given by: Age at EntryProbability1344%1413%1512%1611%1710%1810%These numbers were derived through back-calculation from the size of the respondent pool in the Youth Risk Behavioral Surveillance System, or YRBSS ADDIN EN.CITE <EndNote><Cite><Author>Sharma</Author><Year>2016</Year><RecNum>23</RecNum><DisplayText>(2)</DisplayText><record><rec-number>23</rec-number><foreign-keys><key app="EN" db-id="xvdv2sspezx5x4ew22qv2waqev0p25tsetrx" timestamp="0">23</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Sharma, Akshay</author><author>Wang, Li Yan</author><author>Dunville, Richard</author><author>Kearns, Rachel</author><author>Rosenberg, Eli</author><author>Sullivan, Patrick</author></authors></contributors><titles><title>HIV and STD Testing Behavior among Young Men Who Have Sex With Men: Analysis of Pooled Youth Risk Behavior Survey Data, 2005-2013</title><secondary-title>Journal of Adolescent Health</secondary-title></titles><pages>S80</pages><volume>58</volume><number>2</number><dates><year>2016</year></dates><isbn>1054-139X</isbn><urls></urls></record></Cite></EndNote>(2), which began with:Current ageWeighted # ASMMWeighted # malesEst. % ASMM146,648141,9754.7%1514,789310,3814.8%1620,566309,4896.6%1717,957280,3136.4%18+14,658181,3638.1%We excluded ages below 14 since the numbers of adolescent sexual minority males (ASMM) were small and the estimates highly variable. We then fit a logarithmic curve to these five numbers:We selected a logarithmic curve over a linear one since the former recognizes that the proportion of ASMM should asymptote at some older age. We used the resulting equation to develop predicted proportions for each age (13-18) in our model. We then converted these into the proportions entering our model at each age listed above.For debut, we then derive two parameters: one for the probability of debuting at entry (i.e. first meeting the definition of ASMM because of sexual activity) and, for those not debuting at entry, at weekly probability of debuting thereafter. We then used the data from the same adolescents about their reported age of first anal intercourse, given their current age:AI debut ageCurrent age131415161718No AI1365%35%1439%14%47%1532%15%10%43%1632%13%13%11%31%1727%11%13%14%6%29%1833%10%11%15%17%0%14%We used approximate Bayesian computation (ABC) to find the values of our two parameters that, when simulated with the selected population entry rates above, would come closest to generating this matrix of retrospective debut times in a population interviewed at these ages. We used the Beaumont method for sequential ABC, as implemented in the R package EasyABC, with uniform priors on the range (0,1) and (0, 0.002) for our two parameters, and tolerance levels 1000, 100, and 75. We used the mean of all non-rejected parameters values as our final estimate, yielding a probability of AI debut at population entry of 50.6%, and a weekly probability of debut thereafter at 0.34%.Sexual networksWe reduced the number of different relational networks being modeled from three to one. Sections 1.2.1 – 1.2.3 describe specific features and parameters pertaining to the structure of this network.1.2.1 Momentary degreeThe model is expressed in terms of momentary degrees (number of ASMM partners per person at a given point in time). Based on reports from Halkitis 2013 PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5IYWxraXRpczwvQXV0aG9yPjxZZWFyPjIwMTM8L1llYXI+
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ADDIN EN.CITE.DATA (3), 27% of sexually active ASMM are in a male-male relationships at any given time. The 0.27 mean degree set the target mean degree for sexually active ASMM. In this model of adolescents not all members of the population are active (see section 1.1). Thus, at the population level, including the proportion of ASMM that are not sexually active, the adjusted mean degree is 0.162. In order to account for heterogeneity in sexual activity, we model five risk groups, consistent with our previously published adult model ADDIN EN.CITE <EndNote><Cite><Author>Jenness</Author><Year>2016</Year><RecNum>13</RecNum><DisplayText>(1)</DisplayText><record><rec-number>13</rec-number><foreign-keys><key app="EN" db-id="xvdv2sspezx5x4ew22qv2waqev0p25tsetrx" timestamp="0">13</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Jenness, S. M.</author><author>Goodreau, S. M.</author><author>Rosenberg, E.</author><author>Beylerian, E. N.</author><author>Hoover, K. W.</author><author>Smith, D. K.</author><author>Sullivan, P.</author></authors></contributors><auth-address>Department of Epidemiology.
Department of Anthropology.
Center for Studies in Demography and Ecology, University of Washington, Seattle.
Division of HIV/AIDS Prevention, Centers for Disease Control and Prevention, Atlanta, Georgia.
Department of Epidemiology Department of Global Health, Emory University.</auth-address><titles><title>Impact of the Centers for Disease Control's HIV Preexposure Prophylaxis Guidelines for Men Who Have Sex With Men in the United States</title><secondary-title>J Infect Dis</secondary-title><alt-title>The Journal of infectious diseases</alt-title></titles><periodical><full-title>J Infect Dis</full-title></periodical><dates><year>2016</year><pub-dates><date>Jul 14</date></pub-dates></dates><isbn>1537-6613 (Electronic)
0022-1899 (Linking)</isbn><accession-num>27418048</accession-num><urls><related-urls><url>;(1). For these, the propensity to form partnerships was weighted by the quintile distribution of the number of anal sex partners reported in the last year by ASMM in the American Men’s Internet Survey, or AMIS ADDIN EN.CITE <EndNote><Cite><Author>Sanchez</Author><Year>2016</Year><RecNum>21</RecNum><DisplayText>(4)</DisplayText><record><rec-number>21</rec-number><foreign-keys><key app="EN" db-id="xvdv2sspezx5x4ew22qv2waqev0p25tsetrx" timestamp="0">21</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Sanchez, T.</author><author>Zlotorzynska, M.</author><author>Sineath, C.</author><author>Kahle, E.</author><author>Sullivan, P.</author></authors></contributors><auth-address>Emory University, Rollins School of Public Health, Atlanta, GA, United States. Travis.Sanchez@emory.edu.</auth-address><titles><title>The Annual American Men's Internet Survey of Behaviors of Men Who have Sex with Men in the United States: 2014 Key Indicators Report</title><secondary-title>JMIR Public Health Surveill</secondary-title></titles><periodical><full-title>JMIR Public Health Surveill</full-title></periodical><pages>e23</pages><volume>2</volume><number>1</number><keywords><keyword>Hiv</keyword><keyword>Internet</keyword><keyword>Msm</keyword><keyword>Std</keyword><keyword>bisexual</keyword><keyword>gay</keyword><keyword>homosexual</keyword><keyword>surveillance</keyword><keyword>survey</keyword></keywords><dates><year>2016</year></dates><isbn>2369-2960 (Electronic)
2369-2960 (Linking)</isbn><accession-num>27244770</accession-num><urls><related-urls><url>;(4), The parameters for momentary degree among sexually active ASMM guiding this model are:QuintileMean momentary degreeLowest quintile0.054Second quintile0.106Third quintile0.161Fourth quintile0.247Highest quintile0.782Mean0.2701.2.2. Age mixingAge mixing within the cohort of interest was not explicitly included in the model. However, the likelihood of entering the ASMM population and the likelihood of sexual debut were both a function of age, resulting in a strong increase in sexual activity with age and ensuring that most contacts were between two males both 16-18.1.2.3. Relational durationsFollowing previous methods [cite to be inserted when available], we matched the median duration of ongoing relationships from source data. We examined data from AMIS ADDIN EN.CITE <EndNote><Cite><Author>Sanchez</Author><Year>2016</Year><RecNum>21</RecNum><DisplayText>(4)</DisplayText><record><rec-number>21</rec-number><foreign-keys><key app="EN" db-id="xvdv2sspezx5x4ew22qv2waqev0p25tsetrx" timestamp="0">21</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Sanchez, T.</author><author>Zlotorzynska, M.</author><author>Sineath, C.</author><author>Kahle, E.</author><author>Sullivan, P.</author></authors></contributors><auth-address>Emory University, Rollins School of Public Health, Atlanta, GA, United States. Travis.Sanchez@emory.edu.</auth-address><titles><title>The Annual American Men's Internet Survey of Behaviors of Men Who have Sex with Men in the United States: 2014 Key Indicators Report</title><secondary-title>JMIR Public Health Surveill</secondary-title></titles><periodical><full-title>JMIR Public Health Surveill</full-title></periodical><pages>e23</pages><volume>2</volume><number>1</number><keywords><keyword>Hiv</keyword><keyword>Internet</keyword><keyword>Msm</keyword><keyword>Std</keyword><keyword>bisexual</keyword><keyword>gay</keyword><keyword>homosexual</keyword><keyword>surveillance</keyword><keyword>survey</keyword></keywords><dates><year>2016</year></dates><isbn>2369-2960 (Electronic)
2369-2960 (Linking)</isbn><accession-num>27244770</accession-num><urls><related-urls><url>;(4), limiting to respondents 18 or younger led to an estimate of 14 days. Our model structure implies that relational dissolution follows a memoryless process, and thus relational durations follow a geometric distribution. Converting our median to the corresponding mean for the geometric distrubition yielded average relational durations of 20.2 days (2.89 weeks). The adopted values for momentary degree and relational durations together imply a mean number of partners per year of 4.9, qualitatively similar to the value of 4.2 found in AMIS.Anal intercourse (AI) frequenciesThe baseline frequency of AI within ongoing relationships was derived from Rotheram-Borus et al. 1994 ADDIN EN.CITE <EndNote><Cite><Author>Rotheram-Borus</Author><Year>1994</Year><RecNum>15</RecNum><DisplayText>(5)</DisplayText><record><rec-number>15</rec-number><foreign-keys><key app="EN" db-id="xvdv2sspezx5x4ew22qv2waqev0p25tsetrx" timestamp="0">15</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Rotheram-Borus, M. J.</author><author>Reid, H.</author><author>Rosario, M.</author></authors></contributors><auth-address>HIV Center for Clinical and Behavioral Studies, Columbia-Presbyterian Medical Center, New York State Psychiatric Institute, NY.</auth-address><titles><title>Factors mediating changes in sexual HIV risk behaviors among gay and bisexual male adolescents</title><secondary-title>Am J Public Health</secondary-title></titles><periodical><full-title>Am J Public Health</full-title></periodical><pages>1938-46</pages><volume>84</volume><number>12</number><keywords><keyword>Adolescent</keyword><keyword>*Bisexuality</keyword><keyword>HIV Infections/*prevention & control/transmission</keyword><keyword>*Homosexuality, Male</keyword><keyword>Humans</keyword><keyword>Male</keyword><keyword>Risk-Taking</keyword><keyword>Sexual Behavior</keyword></keywords><dates><year>1994</year><pub-dates><date>Dec</date></pub-dates></dates><isbn>0090-0036 (Print)
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ADDIN EN.CITE.DATA (7-9). The condom use rate applied to the entire population; no fixed proportion of the population always used condoms. RoleBased on estimates from the American Men’s Internet Survey (AMIS), 14.5% of the population were exclusively insertive, 28.2% were exclusively receptive and 57.3% were versatile (both insertive and receptive). Partnering between two ASMM who were exclusively receptive or exclusively insertive was forbidden in the relational model. TestingSharma et al. ADDIN EN.CITE <EndNote><Cite><Author>Sharma</Author><Year>2016</Year><RecNum>23</RecNum><DisplayText>(2)</DisplayText><record><rec-number>23</rec-number><foreign-keys><key app="EN" db-id="xvdv2sspezx5x4ew22qv2waqev0p25tsetrx" timestamp="0">23</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Sharma, Akshay</author><author>Wang, Li Yan</author><author>Dunville, Richard</author><author>Kearns, Rachel</author><author>Rosenberg, Eli</author><author>Sullivan, Patrick</author></authors></contributors><titles><title>HIV and STD Testing Behavior among Young Men Who Have Sex With Men: Analysis of Pooled Youth Risk Behavior Survey Data, 2005-2013</title><secondary-title>Journal of Adolescent Health</secondary-title></titles><pages>S80</pages><volume>58</volume><number>2</number><dates><year>2016</year></dates><isbn>1054-139X</isbn><urls></urls></record></Cite></EndNote>(2) explore HIV testing among ASMM. In an additional unpublished analysis for this model, they found that 29.2% of sexually experience 18-year-old ASMM had tested for HIV at least once in their lifetime. We simulated multiple weekly testing hazards until obtaining a value that yielded this outcome. This final selection was for a constant weekly hazard for testing of 0.00238, which corresponds to a mean test interval of 2,900 days.Rates for progression through the care cascade conditional on testing were carried over from the adult model ADDIN EN.CITE <EndNote><Cite><Author>Jenness</Author><Year>2016</Year><RecNum>13</RecNum><DisplayText>(1)</DisplayText><record><rec-number>13</rec-number><foreign-keys><key app="EN" db-id="xvdv2sspezx5x4ew22qv2waqev0p25tsetrx" timestamp="0">13</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Jenness, S. M.</author><author>Goodreau, S. M.</author><author>Rosenberg, E.</author><author>Beylerian, E. N.</author><author>Hoover, K. W.</author><author>Smith, D. K.</author><author>Sullivan, P.</author></authors></contributors><auth-address>Department of Epidemiology.
Department of Anthropology.
Center for Studies in Demography and Ecology, University of Washington, Seattle.
Division of HIV/AIDS Prevention, Centers for Disease Control and Prevention, Atlanta, Georgia.
Department of Epidemiology Department of Global Health, Emory University.</auth-address><titles><title>Impact of the Centers for Disease Control's HIV Preexposure Prophylaxis Guidelines for Men Who Have Sex With Men in the United States</title><secondary-title>J Infect Dis</secondary-title><alt-title>The Journal of infectious diseases</alt-title></titles><periodical><full-title>J Infect Dis</full-title></periodical><dates><year>2016</year><pub-dates><date>Jul 14</date></pub-dates></dates><isbn>1537-6613 (Electronic)
0022-1899 (Linking)</isbn><accession-num>27418048</accession-num><urls><related-urls><url>;(1), in the absence of large-scale ASMM-specific data parametrized as needed for the model. However, given the very low rate of testing in this population, treatment is not widespread, so that the exact details of treatment uptake and adherence given testing are unlikely to have a large effect on our model.Contact outside the populationTransmission of HIV from partners outside the modeled population was modeled using a weekly hazard, which varied as a function of age and risk quintile. The first component of this hazard was the probability of contact outside the explicitly modeled population:Risk QuintileAge131415161718Risk q1.0022.0046.0068.0092.0114.0136Risk q2.0046.0092.0136.0182.0228.0274Risk q3.0068.0136.0206.0274.0342.0410Risk q4.0106.0212.0318.0424.0530.0636Risk q5.0334.0666.1000.1334.1666.2000These were derived by first calculating the overall mean contact rate, via back-calculation from data collected from 19-24 year-old young adult MSM (YAMSM). We began by estimating a mean of 6.3 AI partners in the last year for this YAMSM population, derived from analyses of data from InvolveMENt PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5TdWxsaXZhbjwvQXV0aG9yPjxZZWFyPjIwMTU8L1llYXI+
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ADDIN EN.CITE.DATA (10) and the MAN Project ADDIN EN.CITE <EndNote><Cite><Author>Hernandez-Romieu</Author><Year>2015</Year><RecNum>24</RecNum><DisplayText>(11)</DisplayText><record><rec-number>24</rec-number><foreign-keys><key app="EN" db-id="xvdv2sspezx5x4ew22qv2waqev0p25tsetrx" timestamp="0">24</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hernandez-Romieu, A. C.</author><author>Sullivan, P. S.</author><author>Rothenberg, R.</author><author>Grey, J.</author><author>Luisi, N.</author><author>Kelley, C. F.</author><author>Rosenberg, E. S.</author></authors></contributors><auth-address>From the *Department of Epidemiology, Rollins School of Public Health, Emory University, Atlanta, GA; daggerDepartment of Epidemiology and Biostatistics, School of Public Health, Georgia State University, Atlanta, GA; and double daggerDivision of Infectious Diseases, School of Medicine, Emory University, Atlanta, GA.</auth-address><titles><title>Heterogeneity of HIV Prevalence Among the Sexual Networks of Black and White Men Who Have Sex With Men in Atlanta: Illuminating a Mechanism for Increased HIV Risk for Young Black Men Who Have Sex With Men</title><secondary-title>Sex Transm Dis</secondary-title><alt-title>Sexually transmitted diseases</alt-title></titles><pages>505-12</pages><volume>42</volume><number>9</number><dates><year>2015</year><pub-dates><date>Sep</date></pub-dates></dates><isbn>1537-4521 (Electronic)
0148-5717 (Linking)</isbn><accession-num>26267877</accession-num><urls><related-urls><url>;(11). We then derived an estimate (6.67%) of the proportion of YAMSM aged 19-25 who report their last AI act as being with a partner aged 18 years or younger, from the Checking In study ADDIN EN.CITE <EndNote><Cite><Author>Khosropour</Author><Year>2011</Year><RecNum>36</RecNum><DisplayText>(12)</DisplayText><record><rec-number>36</rec-number><foreign-keys><key app="EN" db-id="xvdv2sspezx5x4ew22qv2waqev0p25tsetrx" timestamp="0">36</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Khosropour, C. M.</author><author>Sullivan, P. S.</author></authors></contributors><auth-address>Rollins School of Public Health, Department of Epidemiology, Emory University, Atlanta, GA, USA.</auth-address><titles><title>Predictors of retention in an online follow-up study of men who have sex with men</title><secondary-title>J Med Internet Res</secondary-title></titles><pages>e47</pages><volume>13</volume><number>3</number><keywords><keyword>Adult</keyword><keyword>Confidence Intervals</keyword><keyword>Ethnic Groups/*statistics & numerical data</keyword><keyword>Follow-Up Studies</keyword><keyword>HIV Infections/*prevention & control/transmission</keyword><keyword>Health Promotion/*organization & administration</keyword><keyword>Homosexuality, Male/psychology/*statistics & numerical data</keyword><keyword>Humans</keyword><keyword>Internet/*organization & administration</keyword><keyword>Male</keyword><keyword>Multivariate Analysis</keyword><keyword>Odds Ratio</keyword><keyword>Prospective Studies</keyword><keyword>Risk-Taking</keyword><keyword>Sex Education/*organization & administration</keyword><keyword>Sexual Partners/*classification/psychology</keyword><keyword>United States</keyword><keyword>Young Adult</keyword></keywords><dates><year>2011</year></dates><isbn>1438-8871 (Electronic)
1438-8871 (Linking)</isbn><accession-num>21745792</accession-num><urls><related-urls><url>;(12). We focus on this study since it was conducted online (as opposed to in-person for InvolveMENt and the MAN Project), which we suspect will reduce the quite strong desirability working against reporting adolescent partners by this age group. To reverse these rates from contacts per YAMSM to contacts per sexually debuted ASMM, we then adjust by the relative sizes of those two cohorts (7 birth-years for YAMSM aged 19-25 vs. 6 birth-years for ASMM aged 13-18), and based on the proportion of adolescent ASMM who have sexually debuted (60%). We also converted from a yearly to a weekly rate, and converted from an incidence of new relationships to the prevalence of relationship by multiplying by relationship length in weeks (2.89). Together this yields:6.3 ×0.0667 ×76×0.6 × 152×2.89=0.0454To convert from this grand mean to the age-by-risk-quintile matrix above, we assumed a linear decrease in contact rates down to 0 as age declined, and applied the same relative contact rates for the risk quintiles found in the table in Section 1.2.1 to the risk quintiles here, but fixing the grand mean.With weekly contact rates set, we then calculate a rough initial estimate of HIV infection given contact. We set these as 10% probability of the partner being HIV+ (given estimates of HIV prevalence in the 19-25 age range from the National HIV Behavioral Surveillance PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5XZWpuZXJ0PC9BdXRob3I+PFllYXI+MjAxMzwvWWVhcj48
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ADDIN EN.CITE.DATA (13, 14) a 46% probability of not using condoms (see Section 1.4), and a 1% chance of transmission given an act with an HIV+ partner (meant as an approximate weighted average across all condomless AI acts regardless of stage). The resulting estimates then entered into the Approximate Bayesian Computation (see Section 2). Pre-Exposure Prophylaxis (PrEP)We adopted the same four levels of per-act transmission reduction by adherence level from Jenness et al. ADDIN EN.CITE <EndNote><Cite><Author>Jenness</Author><Year>2016</Year><RecNum>13</RecNum><DisplayText>(1)</DisplayText><record><rec-number>13</rec-number><foreign-keys><key app="EN" db-id="xvdv2sspezx5x4ew22qv2waqev0p25tsetrx" timestamp="0">13</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Jenness, S. M.</author><author>Goodreau, S. M.</author><author>Rosenberg, E.</author><author>Beylerian, E. N.</author><author>Hoover, K. W.</author><author>Smith, D. K.</author><author>Sullivan, P.</author></authors></contributors><auth-address>Department of Epidemiology.
Department of Anthropology.
Center for Studies in Demography and Ecology, University of Washington, Seattle.
Division of HIV/AIDS Prevention, Centers for Disease Control and Prevention, Atlanta, Georgia.
Department of Epidemiology Department of Global Health, Emory University.</auth-address><titles><title>Impact of the Centers for Disease Control's HIV Preexposure Prophylaxis Guidelines for Men Who Have Sex With Men in the United States</title><secondary-title>J Infect Dis</secondary-title><alt-title>The Journal of infectious diseases</alt-title></titles><periodical><full-title>J Infect Dis</full-title></periodical><dates><year>2016</year><pub-dates><date>Jul 14</date></pub-dates></dates><isbn>1537-6613 (Electronic)
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ADDIN EN.CITE.DATA (15) These values are 0%, 31%, 81%, and 95%, for the four adherence categories. We derived our base levels of the four adherence categories among ASMM from the preliminary data reported from the ATN113 trial ADDIN EN.CITE <EndNote><Cite ExcludeYear="1"><Author>Hosek</Author><RecNum>22</RecNum><DisplayText>(16)</DisplayText><record><rec-number>22</rec-number><foreign-keys><key app="EN" db-id="xvdv2sspezx5x4ew22qv2waqev0p25tsetrx" timestamp="0">22</key></foreign-keys><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Hosek, S.</author><author>Landovitz, R.</author><author>Rudy, B.</author><author>Kapogiannis, B. </author><author>Siberry, G.</author><author>Rutledge, B.</author><author>Liu, N.</author><author>Brothers, J.</author><author>Rooney, J.</author><author>Wilson C.M.</author><author>ATN 110/113 study team,</author></authors></contributors><titles><title>An HIV Pre-Exposure Prophylaxis Demonstration Project and Safety Study for Adolescent MSM ages 15-17 in the US (ATN 113)</title><secondary-title>AIDS 2016: 21st International AIDS Conference</secondary-title></titles><dates></dates><pub-location>Durban</pub-location><urls></urls></record></Cite></EndNote>(16), averaged across each of the follow-up timepoints, yielding 20.9%, 24.4%, 13.1% and 41.6% of ASMM in each adherence category, from low to high. Taking a weighted average across these categories means that the average ASMM currently prescribed PrEP experiences a 58% reduction in HIV acquisition per act. We also considered an optimistic and a pessimistic adherence scenarios, derived from the first (4 week) and last (48 week) study visit.For discontinuation, we also used the preliminary data from ATN113, considering that those who showed 0 adherence by week 48 could effectively be considered withdrawn from active PrEP use and discontinued. We then set a constant weekly probability of discontinuation (1.43%) such that 50% of those initiating had discontinued by Week 48. Model calibrationSelection of parametersTwo parameters were used for model calibration: a multiplier applied to the frequency of AI and a multiplier applied to the transmission probability from an MSM outside the age range of the simulation. For the former, the only data identified were from a small study more than 20 years old ADDIN EN.CITE <EndNote><Cite><Author>Rotheram-Borus</Author><Year>1994</Year><RecNum>15</RecNum><DisplayText>(5)</DisplayText><record><rec-number>15</rec-number><foreign-keys><key app="EN" db-id="xvdv2sspezx5x4ew22qv2waqev0p25tsetrx" timestamp="0">15</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Rotheram-Borus, M. J.</author><author>Reid, H.</author><author>Rosario, M.</author></authors></contributors><auth-address>HIV Center for Clinical and Behavioral Studies, Columbia-Presbyterian Medical Center, New York State Psychiatric Institute, NY.</auth-address><titles><title>Factors mediating changes in sexual HIV risk behaviors among gay and bisexual male adolescents</title><secondary-title>Am J Public Health</secondary-title></titles><periodical><full-title>Am J Public Health</full-title></periodical><pages>1938-46</pages><volume>84</volume><number>12</number><keywords><keyword>Adolescent</keyword><keyword>*Bisexuality</keyword><keyword>HIV Infections/*prevention & control/transmission</keyword><keyword>*Homosexuality, Male</keyword><keyword>Humans</keyword><keyword>Male</keyword><keyword>Risk-Taking</keyword><keyword>Sexual Behavior</keyword></keywords><dates><year>1994</year><pub-dates><date>Dec</date></pub-dates></dates><isbn>0090-0036 (Print)
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ADDIN EN.CITE.DATA (6). This more recent study did not provide a measure of AI frequency in the form we needed, but did suggest that the AI rates reported in the older study are likely underestimates. For the latter metric (transmission from outside the age range), we had no direct measure of the quantity of interest, and needed to back-calculate it from reports form young adult MSM 19-25 years old (see Section 1.7); we further assumed that this metric would be subject to a particularly high level of desirability bias.Approximate Bayesian Computation (ABC) procedureWe used Approximate Bayesian Computation, with our calibration outcome being 7% HIV prevalence among 18-year-old ASMM. Our inputs were multiplication factors on the two tuning parameters, each given a uniform prior from 1 to 10. For each of the 100 parameter combinations we conducted 16 simulations, and retained those parameter combinations that yielded epidemics with HIV prevalence among 18-year-olds between 6% and 8%. We then used two-dimensional kernel density estimation to determine a final mean value for each of our multipliers. This was implemented in the R package MASS using the kde2d algorithm.ResultsThe final two-dimensional kernel density plot is shown below, and the final selected values for the two multipliers were 3.6 (for frequency of AI with other ASMM) and 8.2 (for contact outside the modeled population).Final set of parametersThe various derivations above led to the following final set of parameters that are common to all modeled scenarios. For parameters than vary between runs, see Table 1 in the body of the manuscript.ParameterValue(s)Prob. of age at entry into ASMM population13: 44%14: 13%15: 12%16: 11%17: 10%18: 10%Prob. of AI debut at population entry50.6%Prob. of debut (per week) if not at population entry0.34%Expected momentary degree (number of partnerships ongoing), in quintiles0.054, 0.106, 0.161, 0.247, 0.782 (grand mean = 0.270)Mean relational duration2.89 weeksMean weekly number of AI acts within ongoing relationships0.96Prob. condom use per Ai act54%Sexual role14.5% exclusively insertive28.2% exclusively receptive57.3% versatileWeekly probably of testing for HIV0.00238%Weekly probability of acquiring HIV from MSM above modeled age rangeRisk QuintileAge131415161718Risk q18.30E-061.74E-052.56E-053.47E-054.30E-055.13E-05Risk q21.74E-053.47E-055.13E-056.87E-058.60E-051.03E-04Risk q32.56E-055.13E-057.77E-051.03E-041.29E-041.55E-04Risk q44.00E-058.00E-051.20E-041.60E-042.00E-042.40E-04Risk q51.26E-042.51E-043.77E-045.03E-046.28E-047.54E-044 References ADDIN EN.REFLIST [1] Jenness SM, Goodreau SM, Rosenberg E, et al. Impact of the Centers for Disease Control's HIV Preexposure Prophylaxis Guidelines for Men Who Have Sex With Men in the United States. J Infect Dis 2016.[2] Sharma A, Wang LY, Dunville R, et al. HIV and STD Testing Behavior among Young Men Who Have Sex With Men: Analysis of Pooled Youth Risk Behavior Survey Data, 2005-2013. Journal of Adolescent Health 2016;58:S80.[3] Halkitis PN, Kapadia F, Siconolfi DE, et al. Individual, psychosocial, and social correlates of unprotected anal intercourse in a new generation of young men who have sex with men in New York City. Am J Public Health 2013;103:889-895.[4] Sanchez T, Zlotorzynska M, Sineath C, et al. The Annual American Men's Internet Survey of Behaviors of Men Who have Sex with Men in the United States: 2014 Key Indicators Report. JMIR Public Health Surveill 2016;2:e23.[5] Rotheram-Borus MJ, Reid H, Rosario M. Factors mediating changes in sexual HIV risk behaviors among gay and bisexual male adolescents. Am J Public Health 1994;84:1938-1946.[6] Hidalgo MA, Kuhns LM, Hotton AL, et al. The MyPEEPS randomized controlled trial: a pilot of preliminary efficacy, feasibility, and acceptability of a group-level, HIV risk reduction intervention for young men who have sex with men. Arch Sex Behav 2015;44:475-485.[7] Sifakis F, Hylton JB, Flynn C, et al. Racial disparities in HIV incidence among young men who have sex with men: the Baltimore Young Men's Survey. J Acquir Immune Defic Syndr 2007;46:343-348.[8] Pathela P, Schillinger JA. Sexual behaviors and sexual violence: adolescents with opposite-, same-, or both-sex partners. Pediatrics 2010;126:879-886.[9] Everett BG, Schnarrs PW, Rosario M, et al. Sexual orientation disparities in sexually transmitted infection risk behaviors and risk determinants among sexually active adolescent males: results from a school-based sample. Am J Public Health 2014;104:1107-1112.[10] Sullivan PS, Rosenberg ES, Sanchez TH, et al. Explaining racial disparities in HIV incidence in black and white men who have sex with men in Atlanta, GA: a prospective observational cohort study. Ann Epidemiol 2015;25:445-454.[11] Hernandez-Romieu AC, Sullivan PS, Rothenberg R, et al. Heterogeneity of HIV Prevalence Among the Sexual Networks of Black and White Men Who Have Sex With Men in Atlanta: Illuminating a Mechanism for Increased HIV Risk for Young Black Men Who Have Sex With Men. Sex Transm Dis 2015;42:505-512.[12] Khosropour CM, Sullivan PS. Predictors of retention in an online follow-up study of men who have sex with men. J Med Internet Res 2011;13:e47.[13] Wejnert C, Le B, Rose CE, et al. HIV infection and awareness among men who have sex with men-20 cities, United States, 2008 and 2011. PLoS One 2013;8:e76878.[14] Wejnert C, Hess KL, Rose CE, et al. Age-Specific Race and Ethnicity Disparities in HIV Infection and Awareness Among Men Who Have Sex With Men--20 US Cities, 2008-2014. J Infect Dis 2016;213:776-783.[15] Grant RM, Anderson PL, McMahan V, et al. Uptake of pre-exposure prophylaxis, sexual practices, and HIV incidence in men and transgender women who have sex with men: a cohort study. Lancet Infect Dis 2014;14:820-829.[16] Hosek S, Landovitz R, Rudy B, et al. An HIV Pre-Exposure Prophylaxis Demonstration Project and Safety Study for Adolescent MSM ages 15-17 in the US (ATN 113). AIDS 2016: 21st International AIDS Conference. Durban. ................
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