The Disaggregated Repeated Measures Design: A Novel Approach to Assess Sexual Risk Behaviors

Abstract

Although numerous studies have examined sexual and substance use behaviors that put people at risk for sexually transmitted infections (STI) including HIV, most focus on an overall measure of aggregate risk or a few simple and particular subtypes of sexual acts assessed in separate analyses. In this article, we introduce a more sensitive approach to assess how the relative characteristics of sex acts may determine the level of risk in which an individual chooses to engage. Project AWARE, a randomized clinical trial conducted among 5012 patients in 9 STD clinics across the US, is used to illustrate the approach. Our study was guided by two aims: (1) describe a new approach to examine the count of sexual acts using a disaggregated repeated measures design, and (2) show how this new approach can be used to evaluate interactions among different categories of sexual risk behaviors and other predictors of interest (such as gender/sexual orientation). Profiles of different subtypes of sexual acts in the past 6 months were assessed. Potential interactions of the characteristics associated with each subtype which resulted in up to 48 distinct subtypes of sexual risk behaviors — sex with a primary/non-primary partner; partner’s HIV status; vaginal/anal sex; condom use, and substance use before or during sex act — can be examined. Specifically, we chose condom use, and primary and non-primary status of partner as an application in this paper to illustrate our method. There are significantly more condomless sex acts (M=23, s.e.=0.9) and sex acts with primary partners (M=27.1, s.e.=0.9) compared to sex acts with condoms (M=10.9, s.e.=0.4, IRR=2.10, 95% CI=1.91–2.32, p<.001) and sex acts with non-primary partner (M=10.9, s.e.=0.5, IRR=2.5, 95% CI=2.33–2.78, p<.001). In addition, there are significant differences for the count of sexual risk behaviors among women who have sex with men (WSM), men who have sex with women (MSW) and men who have sex with men (MSM) for sex acts with and without condom use, primary and non-primary partner, and their interaction (ps=.03, <.0001 and .001, respectively). This approach extends our understanding of how people make choices among sexual behaviors and may be useful in future research on disaggregated characteristics of sex acts.

1. Introduction

Sexual risk behaviors play a major role in HIV/AIDS transmission, as well as the spread of other sexually transmitted infections (STIs). In 2016, gay and bisexual men accounted for 67% of new diagnoses and heterosexuals accounted for approximately 24% of HIV diagnoses (Hess et al., 2017). Historically, the most effective approach to reducing HIV and other STI risk among sexually active persons is the correct and consistent use of condoms (Weller & Davis, 2002). Pre-exposure prophylaxis (PrEP) has recently introduced another potent approach to reducing HIV; however, its use is only beginning to grow and has not been recommended except for those at very high levels of risk. Further, PrEP does not protect against STIs other than HIV and requires taking the medicine every day. For people living with HIV, active antiretroviral therapy (ART) can reduce the viral load to a very low or undetectable level, greatly decreasing the chance of transmitting HIV. However, decreased risk of transmission is achievable only if PLHA stay virally suppressed. Overall, approximately 60% of PLHA in the US are not well engaged in care and not taking ART (Bradley et al., 2014). In addition, virally suppressed individuals who believe they are unlikely to transmit the virus might increase risk for acquiring new sexually transmitted disease and other comorbidities (e.g., through condomless sex or increased drug use including injection). Therefore, research on sexual risk behaviors remains important in evaluating educational, clinical, and public health prevention interventions, as well as public policy.

Despite numerous studies having measured self-reported sexual activities, no gold standard method for assessing sexual risk behavior and condom use exists. Measures of condom use are widely inconsistent across studies (Fonner, Kennedy, O’Reilly, & Sweat, 2014; Noar, Cole, & Carlyle, 2006). Noar et al. (2006) conducted a systematic review of 56 studies conducted between 1989 and 2003 for measures of self-reported condom use within correlational studies of sexual risk behavior and evaluated them on the basis of suggestions from the methodological literature. Recently, Fonner et al. (2014) also conducted a systematic assessment of condom use measurement in evaluation of HIV prevention and interventions in 215 studies since 1990. Both studies note that number of response categories, recall or temporal period, sex partner specificity, and sex act specificity represent important factors affecting our ability to evaluate the efficacy of behavioral interventions on sexual risk behaviors (Fonner et al., 2014; Noar et al., 2006).

At present, there are two options for categorizing sexual risk behaviors: relative frequency measures and count measures (Schroder, Carey, & Vanable, 2003). Relative frequencies of condomless intercourse can be further divided into four kinds of measures: proportions, percentage ratings, categorical measures, and dichotomies, all measuring frequency of condomless intercourse relative to the total number of intercourse occasions. In contrast to relative frequency measures, count measures represent risk in terms of the number of discrete events on a ratio scale. Usually, participants are asked the number of times they engaged in a particular type of sexual risk behavior during a specific period of time. Because relative frequency measures suffer from imprecision with respect to HIV contraction risk and non-generalizable results from limited information, Schroder et al. (2003) suggests that count data are more appropriate for intervention studies. Count data for sexual behavior not only yield important and non-redundant information, but they also can be used to determine whether the intervention succeeded in reducing the absolute number of participants’ high-risk encounters.

However, there are methodological challenges involved in using count measures of sexual behavior, including (1) how to assess sexual behavior and (2) how to analyze the resulting data (Fonner et al., 2014; Noar et al., 2006; Schroder et al., 2003). The goal of this article is to propose a new way to analyze sexual behaviors as a repeated count variable. Sexual episodes with differing attributes are disaggregated and treated as repeated measures at a single point at time. For example, over any period of time, we can determine the count of sexual episodes that involve anal penetration, substance use, condom use, and overall episodes with an HIV-negative, non-primary partner. Across these dimensions, we can create 48 distinct subtypes of sexual risk behaviors if we fully disaggregate and analyze them using a generalized estimating equation (GEE) model. We describe the application of the method to evaluate interactions among characteristics of sexual behavior and other risk predictors, such as gender/sexual orientation, using data from Project AWARE (Metsch et al., 2013), a randomized clinical trial conducted among 5012 patients in 9 STD clinics across the US. We provide a non-technical description of how our approach can easily be implemented in standard software packages and how the output can be interpreted.

2. Methods

2.1. Parent Study

The parent study, Project AWARE, is described elsewhere in detail (Metsch et al., 2013). In Project AWARE, individuals seeking services at STD clinics were recruited between April and December 2010. We use data on cumulative STI incidence and sexual risk behaviors during the 6 months after participants were randomized to either (1) on-site rapid HIV testing with brief, patient-centered risk-reduction counseling or (2) on-site rapid HIV testing with information only. After providing written informed consent, participants were tested for STIs, completed a risk-behavior assessment using audio computer-assisted self-interview (ACASI) and were randomized to one of the two study groups. At 6 months after randomization, participants were tested for STIs and completed a follow-up ACASI assessing changes in their self-reported sexual risk. Medical records were abstracted to document any STIs and associated treatment that occurred between the baseline and 6-month assessments. Inclusion criteria were (1) currently seeking services at the STD clinic, (2) >=18 years of age, (3) reported negative or unknown HIV status, (4) can communicate in English, (5) agreed to be tested for STIs including HIV; (6) signed a medical record release to permit abstraction of STI tests, results, and treatment; and (7) lived in the vicinity of the clinic. Participants were reimbursed for their time and effort up to a maximum of $90. Oral informed consent was obtained for screening; eligible individuals provided written informed consent to enroll in the trial. All study procedures were reviewed, approved and overseen by multiple institutional review boards.

2.2. Assessment of Sexual Risk Behaviors

It is essential to create a balanced measure that can both capture all the dimensions of sexual behaviors recommended from previous studies and literature reviews (Fonner et al., 2014; Noar et al., 2006; Schroder et al., 2003), and use a count data format to best capture variability in sexual activity. In the absence of a gold standard method for assessing sexual risk behavior and condom use, and in light of recommendations from the literature summarized from previous systematic studies and reviews (Fonner et al., 2014; Noar et al., 2006; Schroder et al., 2003), Project AWARE (Metsch et al., 2013), adapted questions used in project EXPLORE that correlate with HIV seroconversion and are well-accepted by participants (Koblin et al., 2006). These questions were asked using ACASIs. Questions about sexual behaviors were asked hierarchically for women who have sex with men (WSM), men who have sex with women (MSW), and men who have sex with men (MSM). Project AWARE did not include behaviors of women when having sex with women because these behaviors are much less likely to transmit HIV. For the “count” of sex behaviors, we asked participants to separately count each sex act in the past 6 months. For example, if on one occasion they had both vaginal and anal sex, this would count as two acts. As another example, if on one occasion the participant was involved in repeated sex acts (say three acts of vaginal sex) with the same partner or with different partners, this would be counted as three times. Questions were first targeted toward the participants’ partner types, i.e. most recent primary partner or non-primary partner. Second, the partner’s HIV status was solicited, including HIV-positive, HIV-negative or HIV-unknown status. Third, the site of penetration was solicited, i.e., vaginal or anal sex (insertive or receptive for MSM), respectively. Fourth, protection/condom use information, whether a condom was used with those sex acts was solicited. Fifth, whether the person or her/his partner was on drugs, or drunk or buzzed on alcohol within 2 hours before or during sex were solicited. Profiles of up to 48 (2×3×2×2×2) different subtypes of sexual acts can be created and assessed using this approach. We can extract specific information, and select different levels of sexual behaviors depending on the research questions. For example, we can aggregate the count of all types of condomless sex behaviors, or we may be interested in more detailed information, such as one or a few of the 48 subtypes - the count of condomless vaginal sex acts with non-primary partners of unknown HIV status and where substances were used. Whenever more than two subtypes are examined, analyzing them in a disaggregated repeated measures framework allows comparison across subtypes, complete with statistical tests of differences.

2.3. Generalized Estimation Equation Analyses (GEE) and Negative Binomial Model

In 1986, Liang and Zeger proposed the GEE approach, which does not make full distributional assumptions of a probability model, but rather requires specification of only the statistical distribution of the mean and a guess of a “working” correlation structure of the responses (Zeger & Liang, 1986). GEE provides a robust general framework to account for possible correlations among continuous, ordinal, dichotomous, and count outcome data, as well as to account for the variance-covariance structure of repeated-measures data. The GEE approach has been increasingly used to analyze data from behavioral intervention trials as a means of assessing change over time with extremely skewed sexual behavior data (Carey et al., 2004; “Efficacy of voluntary HIV-1 counselling and testing in individuals and couples in Kenya, Tanzania, and Trinidad: a randomised trial. The Voluntary HIV-1 Counseling and Testing Efficacy Study Group,” 2000; Kamb et al., 1998; “The NIMH Multisite HIV Prevention Trial: reducing HIV sexual risk behavior. The National Institute of Mental Health (NIMH) Multisite HIV Prevention Trial Group,” 1998; Otto-Salaj, Kelly, Stevenson, Hoffmann, & Kalichman, 2001). GEE is a particularly useful tool for data with group comparisons with non-normal outcomes, as is the case in research focused on the count of sexual risk behaviors. GEE assumes that a known transformation of the marginal distribution of the outcome is a linear function of the predictors of interest. Compared to the common fixed effects ANOVA (which assumes normally distributed outcomes), GEE estimates “population-averaged” models using an extension of the quasi-likelihood approach, which requires few assumptions about the full distribution of the dependent variable (Zeger & Liang, 1986). Therefore, GEE is applicable to a wide variety of non-normally distributed outcome variables. In GEE, the data are modeled by specifying the appropriate distribution family for the mean of the dependent variable, such as negative binomial or Poisson, for count variables outcomes.

Negative binomial regression can be used for over-dispersed count data; that is when the conditional variance exceeds the conditional mean (SAS, 2009). It can be considered as a generalization of Poisson regression since it has the same mean structure as Poisson regression, while it has an extra parameter to model the over-dispersion. If the conditional distribution of the outcome variable is over-dispersed, the confidence intervals for the Negative binomial regression are likely to be narrower as compared to those from a Poisson regression model (Hilbe, 1994; SAS, 2009; Lawless, 1987; McCullagh & Nelder, 1989). In SAS GENMOD procedure for using negative binomial models, there is an estimate of the dispersion coefficient (often called alpha) by maximum likelihood. If the alpha value is constrained to zero, then a Poisson model is suggested. Otherwise, if the estimated alpha has a 95% confidence interval that does not include zero, then a negative binomial model form is more appropriate over the Poisson model. An estimate greater than zero suggests over-dispersion (variance greater than mean). An estimate less than zero suggests under-dispersion, which is very rare (SAS, 2009).

Mixed models or hierarchical linear modeling with specified fixed and random effects can also be used to model the covariance structure of the repeated measures and applied to non-normally distributed data by specifying the correct distribution family. The main difference between GEE and mixed models is that GEE provides estimates using the population-averaged method, whereas mixed modeling provides estimates conditional on random factors (Schroder et al., 2003). In practice, both estimates tend to deliver similar results. A more detailed discussion of differences between population-averaged models and mixed models can be found in Neuhaus et al. (J. M. Neuhaus, 1992; John M Neuhaus, Kalbfleisch, & Hauck, 1991). Therefore, we have used GEE in our analysis as a population-averaged model to measure the count of sexual behaviors due to their ease of implementation and lower likelihood of estimation difficulties.

2.4. Data Structure

Data indexing the count of different sexual behaviors need to be appropriately formatted to use a fully disaggregated repeated measures design. Frequently, data are held in a wide format, where, for a given participant, each of the different categories of sexual behaviors are listed in a single row, and the participant’s count for different sexual risk behavior categories appears in a separate column. Our approach requires a data restructure from this wide format to a long format where each different risk behavior appears on a new row with additional variables describing the context of the data. In the long format, each row has one particular type of sexual risk behavior and their count for a given participant. Each participant will have multiple rows – one for each different type of sexual behavior. In our example, a total of five variables describing the risk context will be created: X₁=condom use (condom use=0, condomless=1); X₂=site of penetration (vaginal=0, anal=1); X₃=substance use before or during sex (No=0, Yes=1); X₄=partner’s HIV status (HIV negative=0, unknown HIV status=1, HIV positive=2); X₅=primary partner (No=0, Yes=1). “Counts” will be created from the transformed data as the dependent variable indicating the count of the particular type of sexual risk behavior described by the risk context variables. Depending on the research question, we can select one or more of the five variables for the data restructure and model fit. For example, if we select X₁=condom use (condom use=0, condomless=1), then there are two rows per person. If X₁=0, then “count” indicates the count of sex acts with a condom, whereas if X₁=1, then the “count” indicates the count of condomless sex acts. Similarly, if we add X₂, site of penetration to the model, then there will be four rows per person, each of which will have the count of different types of sexual risk behaviors. In our current data sample, up to 48 count variables for sexual risk behaviors can be identified through different combinations of the five variables available in project AWARE (2×2×2×3×2). A sample data example of the original data set of 48 variables of count of different types of sex acts, and the restructured data with count variable and five corresponding indicators can be found in Appendix 1.

2.5. Statistical Analysis

Repeated-measures negative binomial regression with the GEE approach was used. To analyze the condomless sexual risk behaviors as a count variable, the following models were used to examine 1) main effects of risk characteristic; 2) interactions among subtypes of risk characteristics; and 3) interactions among subtypes of risk characteristic with other factor (e.g. gender/sexual orientation).

2.5.1. Model for a risk characteristic on a single dimension

To assess how a single risk characteristic relates to the count of sexual acts, we can assume the following regression model:

$$\log (Y)={\beta }_0+{\beta }_i{X}_i$$ (model 1)

where Y=count of sex acts; β₀=intercept of Y; β_i=regression coefficient; X_i=characteristics of sex acts.

Particularly, X_i can be chosen from different dimensions of sexual behavior, including i=1: condom use (condom use=0, condomless=1); i=2: site of penetration (Vaginal=0, Anal=1); i=3: substance use before or during sex (No=0, Yes=1); i=4: partner’s HIV status (HIV negative=0, unknown HIV status=1, HIV positive=2); and i=5: sex acts with primary partner (No=0, Yes=1). In model 1, if i=1, then we can estimate the mean count of particular categories of sex acts (e.g., mean count of condom use sex acts and mean count of condomless sex acts), and also compare the risk ratio within the particular categories of sex acts (e.g., compare the count of condomless sex acts against the count of condom use sex acts).

We can also use two or more subtypes of count of sex behaviors in the model, depending on the research question. For example:

$$\log \left(Y\right)={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2$$ (model 2)

Similarly, through model 2, we can estimate the mean counts of particular categories of sex acts combining across dimensions (e.g., mean count of condom use sex acts, mean count of condomless sex acts, mean count of vaginal sex acts, and mean count of anal sex acts, respectively) and compare the risk ratio within each sex act dimension (e.g., compare count of condomless sex acts with condom use sex acts, and compare count of anal sex acts with vaginal sex acts).

2.5.2. Interactions among Subtypes of Count of Sexual Acts

Subtypes of sexual acts can be examined by adding two-way or more-way interaction terms to the model, depending on how many risk characteristics are needed to answer the research question. For example:

$$\log (Y)={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+{\beta }_3{X}_1{X}_2$$ (model 3)

or

$$\log (Y)={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+{\beta }_3{X}_3+{\beta }_4{X}_1{X}_2+{\beta }_5{X}_1{X}_3+{\beta }_6{X}_2{X}_3+{\beta }_7{X}_1{X}_2{X}_3$$ (model 4)

Compared to model 2, by adding a two-way interaction X₁X₂ between X₁ = condom use and X₂= site of penetration in model 3, we can additionally estimate the mean count of particular subtypes of sex acts (e.g., mean count of condom use vaginal sex, mean count of condomless vaginal sex, mean count of condom use anal sex, and mean count of condomless anal sex, respectively) and additionally compare the risk ratio among the four particular subtypes of sex acts (e.g., compare count of condomless vaginal sex with count of condom use vaginal sex). Similarly, we can include three types and three way-interactions in model 4.

2.5.3. Examining Interactions of Risk Characteristics with Other Factors

We can also include additional factors of interest in the model. For example, we could include gender/sexual orientation (women, MSW, and MSM) as an additional predictor. We can use the model to estimate 1) the mean count of different subtypes of sexual risk behaviors across gender/sexual orientation; 2) compare the risk ratio across gender/sexual orientation categories within a category of sexual risk behaviors; and 3) compare the risk ratio among categories of sexual risk behaviors within a given gender/sexual orientation. Several options within the correlation matrix structure among observations drawn from the same participants are available to choose. For example, one could use the identity matrix, which assumes that repeated observations are uncorrelated, the exchangeable correlation matrix, which assumes that repeated observations for a subject are equally correlated, or a number of other matrices. The quasi-likelihood information criterion (QIC), a modification of the Akaike information criterion (AIC), was used to compare and select GEE models with appropriate working correlations where the model with the smaller statistic is preferred (Pan, 2001). A thorough discussion concerning the properties of various working correlations can be found in Liang and Zeger (Zeger & Liang, 1986). The corresponding SAS syntax (SAS Version 9.4) can be found in Appendix 2.

2.5.4. Application

To illustrate the approach we are introducing, we used X₁=: condom use (condom use=0, condomless=1) and X₅= sex acts with primary partner (No=0, Yes=1). First, we examined condom use as a main effect in the model for count of sex acts (model 5).

$$\log (Y)={\beta }_0+{\beta }_1{X}_1$$ (model 5)

In this case, mean count of sex acts with condom use and count of condomless sex acts were estimated. Risk ratios comparing rate (count) of condomless sex acts and rate (count) of sex acts with condoms used was also calculated. The same procedure was applied to sex acts with primary versus non-primary partners in model 6.

$$\log (Y)={\beta }_0+{\beta }_1{X}_5$$ (model 6)

Second, interactions between condom use and partner type were examined by including both of the main effects and the interaction between condom use and partner type in the model model 7.

$$\log (Y)={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_5+{\beta }_3{X}_1{X}_5$$ (model 7)

Specifically, four potential subtypes of sexual risk behaviors (condom use with primary partner, condom use with non-primary partner, condomless sex acts with primary partner, and condomless sex acts with non-primary partner) were examined using the permutation of the two variables. Similarly, the estimated count and the risk ratios among the four subtypes of sexual risk behaviors were calculated.

Third, we controlled the gender/sexual orientation in the model, in addition to the effects of condom use and partner type (models 8, 9, and 10).

$$\log (Y)={\beta }_0+{\beta }_1{X}_1+{\beta }_2\ast gender+{\beta }_3{X}_1\ast gender$$ (model 8)

$$\log (Y)={\beta }_0+{\beta }_1{X}_5+{\beta }_2\ast gender+{\beta }_3{X}_5\ast gender$$ (model 9)

$$\begin{gathered} \log (Y)={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_5+{\beta }_3\ast gender+{\beta }_4{X}_1{X}_5+{\beta }_5{X}_1\ast gender+{\beta }_6{X}_5\ast gender+ \\ {\beta }_7{X}_1{X}_5\ast gender \end{gathered}$$ (model 10)

Specifically, 1) we estimated the mean count of four subtypes of sexual risk behaviors stratified by gender/sexual orientation (women MSW, MSM); 2) compared risk ratios within two main effects and four subtypes of sexual acts among gender/sexual orientation; and 3) compare risk ratios among two main effects and four subtypes of sexual acts within each gender/sexual orientation.

2.5.5. Sensitivity Analysis

A sensitivity analysis using bootstrap with different sample sizes for a demonstration was conducted to compare a negative binomial GEE model with sexual risk behaviors as count measures with the traditional method using a logistic GEE model with sexual risk behaviors as binary outcomes. A random subset of the data was sampled out at differing sample sizes and then the bootstrap confidence interval was calculated via 1000 replicates. The randomly drawn subset was the same for both methods and all bootstrap replicates to minimize the Monte Carlo variability to only that of the bootstrap procedure. Both GEE models were set to unstructured correlations.

3. Results

Table 1 provides a summary of the count of subtypes of sexual risk behaviors from the GEE models. The mean estimates created by the negative binomial model will be the same as the simple means of the counts, however, the model-based means utilize the appropriate variance function, providing accurate standard errors and confidence intervals. The estimated mean count of sex acts with condom use is 10.9 (SE=0.4, range 0–503), and the mean count of condomless sex is 23.0 (SE=0.9, range 0–1838). The estimated mean count of sex acts with primary partners is 27.1 (SE=0.9, range 0–1182), and the mean count of sex acts with non-primary partner is 10.9 (SE=0.5, range 0–999). The category with the most reported sex acts, count of condomless sex acts with primary partner (M=20.6, SE=0.9, range 0–1182), has a mean count that is four times that in the category with the fewest reported sex acts, condom use with non-primary partner (M=5.0, SE=0.3, range 0–499).

Table 1.

Estimated Count of Sexual Risk Behaviors from GEE Negative Binomial

				From GEE model					From Observed
	Condom	Partner	N	Mean	SE	95% CI		Model	Mean	SD	Min	Max
Main effects
	condom use		4912	10.9	0.4	10.2	11.7	(5)	10.9	26.9	0	503
	condomless		4912	23.0	0.9	21.2	24.8		23.0	64.2	0	1838
		primary	4157	27.1	0.9	25.8	29.5	(6)	27.1	60.0	0	1182
		non-primary	4906	10.9	0.5	10.0	11.9		10.9	33.5	0	999
Interactions								(7)
	condom use	primary	3159	9.2	0.4	8.4	10.0		9.2	22.9	0	300
	condom use	non-primary	4904	5.0	0.3	4.5	5.5		5.0	17.6	0	499
	condomless	primary	4157	20.6	0.9	19.0	22.4		20.1	55.3	0	1182
	condomless	non-primary	4906	5.9	0.4	5.2	6.7		5.9	26.3	0	949

Table 2 provides selected comparisons of risk ratios and their 95% confidence intervals for count of sexual risk behaviors. For example, participants reported more condomless sex (IRR=2.1, 95% CI=1.91–2.32, p<.0001) compared to sex acts with condom use; and fewer sex acts with non-primary partners (IRR=0.4, 95% CI=0.36–0.43, p<.0001) compared to sex acts with primary partners. As for the two-way interaction results, there are six potential pair-wise comparisons among the four subtypes of count of sexual risk behaviors. Note that there are 15% fewer sex acts involving condom use with non-primary partners compared to condomless sex acts with non-primary partners (IRR=0.85, 95% CI=0.73–0.98, p=.029).

Table 2.

Comparison of Risk Ratio for Count of Sexual Risk Behaviors.

	Study interest		Reference type		GEE-Negative binomial
	Condom	Partner	Condom	Partner	IRR	95% CI		P-value
Main effects
	condomless		condom use		2.10	1.91	2.32	<.0001
		non-primary		primary	0.40	0.36	0.43	<.0001
Interactions
	condom use	non-primary	condom use	primary	0.56	0.49	0.64	<.0001
	condom use	non-primary	condomless	non-primary	0.85	0.73	0.98	0.029
	condom use	non-primary	condomless	primary	0.25	0.22	0.28	<.0001
	condom use	primary	condomless	non-primary	1.51	1.29	1.76	<.0001
	condom use	primary	condomless	primary	0.44	0.39	0.50	<.0001
	condomless	non-primary	condomless	primary	0.29	0.26	0.33	<.0001

Tables 3, 4 and 5 illustrate the impact of sexual risk behaviors and gender/sexual orientation. Table 3 contains the estimated count of sexual risk behavior subtypes stratified by gender/sexual orientation. There are significant differences in the count of sexual risk behaviors among WSM, MSM and MSW for main effects of condom use, partner type, and their interaction (ps=.03, <.0001, and .001, respectively). With respect to partner type, MSM reported the fewest sex acts with primary partners (M=17.0, SE=0.9), but the highest count of sex acts with non-primary partners (M=13.4, SE=1.3). Corresponding numbers for WSM and MSW were M=33.7, SE=0.8 for primary partner; M=9.3, M=1.8 for non-primary partner and M=32.8, SE=0.8 for primary partner; M=10.6, SE=1.6 for non-primary partner, respectively.

Table 3.

Estimated Count of Sexual Risk Behaviors from GEE Negative Binomial by Gender/Sexual Orientation

			WSM		MSM		MSW		Model	p*
	Condom	Partner	Mean	SE	Mean	SE	Mean	SE
Main effects
	condom use		11.7	0.8	11.0	0.6	10.2	0.6	(8)	0.03
	condomless		24.7	1.6	19.0	1.7	24.4	1.5
		primary	33.7	0.8	17.0	0.9	32.8	0.8	(9)	<.0001
		non-primary	9.3	1.8	13.4	1.3	10.6	1.6
Interactions									(10)	0.001
	condom use	primary	9.1	0.7	7.6	0.8	9.6	0.7
	condom use	non-primary	4.9	0.6	6.6	0.4	4.0	0.3
	condomless	primary	25.1	1.7	12.4	1.2	24.1	1.5
	condomless	non-primary	4.4	0.4	6.8	0.7	6.6	0.7

^*type 3 gee p-value for X1*gender/sexual orientation in model 8, and X5*gender/sexual orientation in model in model 9 and X1*X5*gender/sexual orientation in model in model 10

Table 4.

Comparison and Associated Risk Ratio among Gender/Sexual Orientation within Categories of Sexual Risk Behaviors

	Study interest			Reference type			GEE-Negative binomial
	Condom	Partner	Gender	Condom	Partner	Gender	IRR	95% CI		P-value
Main effects
	condom use		WSM	condom use		MSM	1.06	0.89	1.26	0.496
	condom use		WSM	condom use		MSW	1.15	0.97	1.37	0.109
	condom use		MSM	condom use		MSW	1.08	0.93	1.26	0.306
	condomless		WSM	condomless		MSM	1.30	1.05	1.62	0.018
	condomless		WSM	condomless		MSW	1.02	0.85	1.21	0.861
	condomless		MSM	condomless		MSW	0.78	0.63	0.96	0.022
		primary	WSM		primary	MSM	1.99	1.65	2.39	<.0001
		primary	WSM		primary	MSW	1.03	0.89	1.19	0.728
		primary	MSM		primary	MSW	0.52	0.43	0.62	<.0001
		non-primary	WSM		non-primary	MSM	0.69	0.56	0.85	0.001
		non-primary	WSM		non-primary	MSW	0.87	0.70	1.09	0.232
		non-primary	MSM		non-primary	MSW	1.26	1.03	1.54	0.024
Interactions
	condom use	primary	WSM	condom use	primary	MSM	1.19	0.93	1.52	0.159
	condom use	primary	WSM	condom use	primary	MSW	0.94	0.77	1.15	0.567
	condom use	primary	MSM	condom use	primary	MSW	0.79	0.62	1.01	0.063
	condom use	non-primary	WSM	condom use	non-primary	MSM	0.74	0.57	0.96	0.026
	condom use	non-primary	WSM	condom use	non-primary	MSW	1.22	0.94	1.60	0.140
	condom use	non-primary	MSM	condom use	non-primary	MSW	1.65	1.36	2.00	<.0001
	condomless	primary	WSM	condomless	primary	MSM	2.02	1.60	2.56	<.0001
	condomless	primary	WSM	condomless	primary	MSW	1.04	0.87	1.25	0.647
	condomless	primary	MSM	condomless	primary	MSW	0.51	0.41	0.65	<.0001
	condomless	non-primary	WSM	condomless	non-primary	MSM	0.64	0.48	0.86	0.003
	condomless	non-primary	WSM	condomless	non-primary	MSW	0.66	0.49	0.89	0.006
	condomless	non-primary	MSM	condomless	non-primary	MSW	1.03	0.76	1.39	0.859

Table 5.

Comparison and Associated Risk Ratio among Categories of Sexual Risk Behaviors within Gender/Sexual Orientation

	Study interest			Reference type			GEE-Negative binomial
	Condom	Partner	Gender	Condom	Partner	Gender	IRR	95% CI		P-value
Main effects
	condom use		WSM	condomless		WSM	0.47	0.40	0.56	<.0001
	condom use		MSM	condomless		MSM	0.58	0.47	0.71	<.0001
	condom use		MSW	condomless		MSW	0.42	0.36	0.48	<.0001
		non-primary	WSM		primary	WSM	0.28	0.23	0.33	<.0001
		non-primary	MSM		primary	MSM	0.79	0.68	0.91	0.001
		non-primary	MSW		primary	MSW	0.32	0.28	0.37	<.0001
Interactions
	condom use	non-primary	WSM	condom use	primary	WSM	0.54	0.42	0.70	<.0001
	condom use	non-primary	WSM	condomless	non-primary	WSM	1.12	0.84	1.48	0.444
	condom use	non-primary	WSM	condomless	primary	WSM	0.19	0.15	0.25	<.0001
	condom use	primary	WSM	condomless	non-primary	WSM	2.07	1.62	2.65	<.0001
	condom use	primary	WSM	condomless	primary	WSM	0.36	0.30	0.43	<.0001
	condomless	non-primary	WSM	condomless	primary	WSM	0.17	0.14	0.21	<.0001
	condom use	non-primary	MSM	condom use	primary	MSM	0.87	0.69	1.09	0.224
	condom use	non-primary	MSM	condomless	non-primary	MSM	0.97	0.77	1.22	0.781
	condom use	non-primary	MSM	condomless	primary	MSM	0.53	0.42	0.66	<.0001
	condom use	primary	MSM	condomless	non-primary	MSM	1.12	0.82	1.52	0.475
	condom use	primary	MSM	condomless	primary	MSM	0.61	0.45	0.83	0.001
	condomless	non-primary	MSM	condomless	primary	MSM	0.55	0.46	0.66	<.0001
	condom use	non-primary	MSW	condom use	primary	MSW	0.42	0.34	0.51	<.0001
	condom use	non-primary	MSW	condomless	non-primary	MSW	0.60	0.48	0.76	<.0001
	condom use	non-primary	MSW	condomless	primary	MSW	0.17	0.14	0.19	<.0001
	condom use	primary	MSW	condomless	non-primary	MSW	1.45	1.13	1.87	0.004
	condom use	primary	MSW	condomless	primary	MSW	0.40	0.33	0.48	<.0001
	condomless	non-primary	MSW	condomless	primary	MSW	0.27	0.22	0.34	<.0001

Table 4 provides the results of pairwise comparisons and associated risk ratios among WSM, MSW, and MSM within categories of sexual risk behaviors. There are no significant differences in mean counts of sex acts with condom use among WSM, MSW, and MSM. However, WSM reported 30% more condomless sex acts compared to MSM (IRR=1.3, 95% CI=1.05–1.62, p=.018) whereas MSM reported 22% fewer condomless sex acts compared to MSW (IRR=0.78, 95% CI=0.63–0.96, p=.022). As for sex acts with non-primary partners, WSM reported 31% fewer acts compared to MSM (IRR=0.69, 95% CI=0.56–0.85, p=.001), whereas MSM reported 26% more acts with non-primary partner compared to MSW (IRR=1.26, 95% CI=1.03–1.54, p=.024).

Overall, WSM reported fewer sex acts (with or without condoms) with non-primary partners compared to MSM. A closer look indicates that WSM reported 26% fewer sex acts with condoms with non-primary partners compared to MSM (IRR=0.74, 95% CI=0.57–0.96, p=.026). The corresponding mean of sex acts with condoms with non-primary partner for WSM was 4.9 vs 6.6 for MSM (Table 3). Whereas MSM reported more sex acts with condoms with non-primary partners compared to MSW (IRR=1.65, 95% CI=1.36–2.00, p<.0001). The corresponding mean of sex acts with condoms with non-primary partner for MSM was 6.6 vs 4.0 for MSW (Table 3). WSM reported 36% fewer condomless sex acts with non-primary partners compared to MSM (IRR=0.64, 95% CI=0.48–0.86, p=.003) and 34% fewer compared to MSW (IRR=0.66, 95% CI=0.49–0.89, p=.006). No significant difference was found between MSM and MSW for condomless sex acts with non-primary partners. The corresponding mean of condomless sex acts with non-primary partners were 4.4, 6.8, and 6.6 for WSM, MSM and MSW, respectively (Table 3).

Table 5 provides pairwise comparisons and associated risk ratios between different categories of sexual risk behaviors within WSM, MSW, and MSM. WSM, MSW, and MSM all reported fewer sex acts with condom use compared to condomless sex acts, and fewer sex acts with non-primary partners than with primary partners. There was no difference between rates of sex acts with versus without condoms with non-primary partners for WSM (IRR=1.12, 95% CI=0.84–1.48, p=.444). Similarly, no difference was observed for MSM (IRR=0.97, 95% CI=0.77–1.22, p=.781). However, MSW reported 40% lower rate of sex acts with condoms with non-primary partners compared to condomless sex acts with non-primary partners (IRR=0.60, 95% CI=0.48–0.76, p<.0001). WSM, MSW, and MSM all reported fewer sex acts with condoms with primary partners compared to condomless sex acts with primary partners.

The results from the sensitivity analysis were mixed (Figure 1). Both negative binomial GEE model with sexual risk behaviors as count measures and the traditional method using a logistic GEE model with sexual risk behaviors as binary outcomes showed consistent directions for different types of the sexual risk behaviors. Although logistic regression seems to be more sensitive to have a narrower confidence interval compared to our approach, we provides better predictions to exclude zero for small sample sizes. This may be because the inference is different between the two methods; one is looking for number of acts while the other is simple presence or absence binary. The simpler outcome will show narrower confidence intervals since it trains on a more granular outcome.

Figure 1.

Sensitivity analysis using bootstrap comparing GEE negative binomial model and GEE logistic regression with sexual risk behaviors outcomes

* X1=condom use (condom use=0, condomless=1); X2=site of penetration (vaginal=0, anal=1); X3=substance use before or during sex (No=0, Yes=1); X4=partner’s HIV status (HIV negative=0, unknown HIV status=1, HIV positive=2); X5=primary partner (No=0, Yes=1)

4. Discussion

In this article, we proposed a GEE approach for analyzing sexual risk behaviors as a count variable. Specifically, depending on the goals of a particular study, we can select one or more categories of sexual risk behaviors for inclusion in a model. Up to 48 mutually exclusive categories of sexual risk behaviors can be created and analyzed using the disaggregated repeated measures design. We included all of the potential sex act dimensions suggested by previous reviews (Fonner et al., 2014; Noar et al., 2006; Schroder et al., 2003). For example, recommendations from prior reviews include 1) differentiating between primary and non-primary partners; 2) differentiating among vaginal, and anal sex; 3) whether condoms were used during the most recent sexual encounter or during a clearly defined time frame; and 4) actual number of protected versus unprotected sex acts. We used condom use and partner relationship to illustrate our methods. Researchers interested in using counts of sexual risk behaviors as study outcomes and who are familiar with the interpretation of GEE parameters may find this a useful way to perform their analysis.

Our approach has several advantages and some disadvantages. On the positive side, first, we proposed a method that can examine sexual risk behaviors as count measures. Research has shown that count data is preferred for intervention studies on sexual risk behaviors because these models provide the precise extent of reduction in participants’ high risk encounters (Schroder et al., 2003). Second, by using restructured data and measures with long format data, our method allows the researcher to include different categories of sexual risk behaviors in one model instead of repeatedly testing separate models that may increase Type I error risk. Note that GEE can be applied whenever a marginal model is sensible for correlated multinomial responses, such as a wide variety of forms of clustered data. Researchers can select different categories of sexual risk behaviors based on their study hypotheses and interests. Third, GEE also allows one to test interactions in the model so that differences across subtypes of sexual risk behaviors can be examined. For example, we examined the interactions of condom use and partner type in our application. Fourth, covariates not related to the characteristics of sexual risks can also be added to the model. For example, we used gender/sexual orientation in our application. Other potential factors, such as different types of substance use and treatment effects, can also be included in the model depending on the study goals. Fifth, because the count of sexual risk behaviors is likely characterized by over-dispersion and is non-normally distributed, GEE is ideally suited to this type of data. It is difficult to compare the results presented in this study with other studies. We used a new technique to estimate the count of the sexual risk behaviors, whereas most other studies have reported the proportion of sexual risk behaviors (Fonner et al., 2014; Marks, Crepaz, Senterfitt, & Janssen, 2005; Owen et al., 2015), or used assumptions to calculate total number of sex acts (Attia, Egger, Müller, Zwahlen, & Low, 2009; Downs & De Vincenzi, 1996). However, the counts of sexual risk behaviors were reported directly by participants, and further, our approach provides estimated mean counts, incidence rate ratios, and 95% CI. These tools facilitate precision and ease of interpretation. Sixth, a large, geographically, and ethnically diverse sample from nine STD clinics in the US was included.

In spite of several strengths, these methods do have limitations. Although count data for sexual risk behaviors provide better and more precise indicators of HIV acquisition risk and sufficient information about the absolute frequencies of sexual intercourse, these data do carry some drawbacks. Count data for sexual risk behaviors require sophisticated data preparation and analytic methods (Schroder et al., 2003). Compared to dichotomous measures, collecting and analyzing count data can be more time-consuming and expensive. Additionally, sexual intercourse is a sensitive topic (perhaps leading to over-reporting or under-reporting), and count measures also require the participant to recall the number of sexual occasions over a specific time period, including partner type, whether a condom was used, and methods of penetration. It should be noted that ACASI methods are known to reduce social desirability biases (Ghanem, Hutton, Zenilman, Zimba, & Erbelding, 2005). Before asking the participant to report engagement in sexual risk behaviors, a short instrument was provided to facilitate accurate responding. Second, we noticed that, as more interaction terms were included in the model, counts for each specific sexual risk behavior were more likely to be zero-inflated because the number of occasions was being divided more finely. For example, if we were to include all five variables and their interactions in the model, the estimated mean count of condomless anal sex acts with HIV-positive non-primary partners and without substance use is .015, which indicates that very few participants reported this particular type of sex act. As the number of interaction terms increases, a zero-inflated negative binomial model might be more appropriate to use, and doing so considerably increases the modeling complexity. Finally, we used data from a randomized controlled trial to demonstrate the approach. Despite the multi-site design and large sample size, individual characteristics were determined on the basis of self-report, and responses to questions related to sensitive topics, which may be subject to response bias and social desirability bias, and may not be generalizable to other populations or other settings. However, such limitation can only have an impact on the associations detected and is more related to experimental design, but should not be viewed as a limitation of the proposed approach.

In our application, we observed differences in condom use behaviors between primary and non-primary partner types. Of the expected 10.9 sex acts with non-primary partners, 5 of these acts would be expected to involve condoms and 5.9 would not, suggesting a 15% difference between counts for these two types of behaviors. Further analysis of interactions among gender/sexual orientation, condom use, and partner type indicated that MSW reported 40% fewer sex acts with than without condoms with non-primary partners. This finding implies that, for MSW, the majority of sex acts are performed without condoms. Although several studies showed that higher percentages of MSM engaged in inconsistent condom use and were more likely to engage in condomless sex or have multiple sex partners compared to MSW (Browne, Clubb, Wang, & Wagner, 2009; Mattson et al., 2014), our analysis suggested the opposite, and the numbers of condomless sex acts with non-primary partners were roughly the same between MSM and MSW. Given the high infection rate among MSM compared to MSW, our results indicate that the vulnerability to HIV/STI among MSM may be more complicated and may involve additional factors not considered in our analyses. There were no significant differences between sex acts with and without condom use with non-primary partners between WSM or MSM, which indicates that MSM and WSM are equally likely to either use or not use condom with non-primary partners. Results for MSM were inconsistent with previously reported findings indicating that consistent condom use was significantly higher within non-primary partnerships (Azariah & Perkins, 2010; D’Anna et al., 2012; Franssens, Hospers, & Kok, 2009). In our analysis, mean estimates of count of sex acts with non-primary partners and count of condomless sex acts with non-primary partners were 6.6 and 6.8, respectively. The results indicate that MSM have not perceived the heightened risk for HIV/STIs in less steady partnerships. The difference between the present study and previous studies may also involve differences between prevalence and count measures. Previous studies on partner relationship and condom use among women indicated similar results as ours (Macaluso, Demand, Artz, & Hook III, 2000). For example, consistency of condom use was higher with non-primary or new/casual partners than with primary or regular partners.

In summary, we have described an alternative approach to examine the count of sexual risk behaviors using a fully disaggregated repeated measures design and illustrated how this approach can evaluate sexual risk behaviors and other related risk factors or interesting covariates. The measures and approach may serve as a useful tool in future research on disaggregated characteristics of sex acts.