Dynamic social network analysis of a brief alcohol intervention trial in heavy-drinking college students shows spillover effects

Abstract

Background:

Heavy drinking college students tend to have close social networks, and there is theoretical and empirical support for the idea that behavior change can spread through those networks via close ties. The objective of this research was to determine whether intervention-induced behavior change in a subset of heavy drinkers in a sociometric (whole) college class-year social network is transmitted to other heavy drinkers in the network, resulting in reduced behavioral risk and change in network ties.

Methods:

We conducted a controlled trial in which most of a first-year college class (N = 1,236; 56.9% female) was enrolled, with alcohol use and social network ties measured early in each of three semesters. Following baseline assessment, the network was divided into two groups, brief motivational intervention (BMI) and natural history control (NHC) according to dormitory residence location. A subset of heavy drinkers in each group was selected, and those in the BMI group received an in-person intervention.

Results:

Using Stochastic Actor-Oriented Modeling, we found a significant tendency for participants in the BMI group to shed ties with individuals with similar drinking behaviors between the first and second semesters, relative to the NHC group. Furthermore, heavy drinkers with reciprocal ties to intervention recipients in the BMI group showed a significant reduction in drinks per week.

Conclusions:

Individual alcohol interventions appear to have effects both on behavior and network connections among individuals who did not receive the intervention. Continued research is needed to identify the optimal conditions for diffusion of behavior change.

Introduction

Hazardous alcohol use and its consequences are a serious problem in young adulthood, with hazardous drinking historically higher among college students relative to noncollege youth (Schulenberg et al., 2021). The first year of college in particular is associated with increases in excessive drinking and alcohol-related consequences (Del Boca et al., 2004, Tremblay et al., 2010), with residential colleges (Presley et al., 2002) and coeducational college residences showing the highest risk for first years (Weitzman et al., 2003). Indeed, the transition to college is a NIAAA-identified “critical period” for alcohol risk (National Institute on Alcohol Abuse and Alcoholism, 2002). Risky drinking early in the first year may negatively affect a student’s transition, and hazardous drinking patterns may persist beyond the first year (Schulenberg and Maggs, 2002).

Peer social relationships play an important role in young adult drinking behaviors; in young adulthood the proportion of alcohol-consuming friends is associated concurrently and prospectively with an individual’s drinking (DeMartini et al., 2013, Talbott et al., 2012). Peer affiliations in the first semester of college may be particularly important as they set the stage for later behavior (Talbott et al., 2012). In addition, college and university residential housing creates a peer-intensive environment that may magnify peer influences, with alcohol use higher among college students who live in residence halls compared to those who live at home with parents (Harford et al., 2002, O’Hare, 1990). There is evidence also that undergraduate dormitory residents show network clustering on alcohol use (Barnett et al., 2014), and shared attitudes about alcohol use are organized by dormitory and by floor (Bourgeois and Bowen, 2001).

Alcohol Interventions with College Students

Brief Motivational Interview (BMI) interventions with heavy drinkers are known to be effective in reducing alcohol use (Samson and Tanner-Smith, 2015, Mun et al., 2022). One of the most effective components of BMIs is personalized normative feedback, whereby participants are provided correct information about the drinking behaviors of their peers in order to correct misperceptions of social norms (which appear to drive heavier drinking; Carey et al., 2010, Reid and Carey, 2015). While this component of BMI addresses an element of peer influence (i.e., the perception of others’ drinking influences one’s own), it does not address behavioral influence or the selection of peers as friends in naturally occurring peer social ecologies.

There is theoretical and empirical support for the idea that the interdependence among individuals and specifically the embeddedness of individuals in a social network can be important for behavior change (Valente, 2010). For example, Reid et al., (2015) found that college drinkers who received a brief alcohol intervention initiated less behavior change (regardless of their intervention condition) if they were embedded in a heavy drinking peer network. This reflects a primary mechanism of behavior change, i.e., behavioral influence from others who are proximal in the network, which theoretically could enhance or suppress behavior change. A related body of research indicates that activating high-status peer leaders in school (Gottfredson and Wilson, 2003, Mellanby et al., 2000, Paluck and Shepherd, 2012) and community settings (Kelly et al., 1991, Soumerai et al., 1998) to deliver harm-reduction messages is effective in changing collective norms (Paluck and Shepherd, 2012) and in reducing health-risk behaviors among network members (Rulison et al., 2015, Valente et al., 2003, White et al., 2020).

Thus, there is evidence that the behavior of network ties can suppress behavior change and that specific network members can support behavior change. In addition, the behavior change in one person or group can be transmitted or transferred to others through their network ties. These effects have been called collateral health consequences or “spillover” effects (Shakya et al., 2012). For example, researchers have suggested that interventions administered to some heavy drinkers in a social ecosystem can have indirect (“spillover”) effects on other heavy drinkers’ behavior (Conrod et al., 2013, Hallgren et al., 2021), and there is evidence that change in drinking behaviors of youth has a meaningful effect on the drinking of their close peers (Ali and Dwyer, 2010, Eisenberg et al., 2014). Though theoretically supported, to our knowledge there have been no investigations that have attempted to modify the alcohol use among some network members to stimulate a spillover effect (i.e., indirect intervention effect) among close network ties, or to evaluate whether the spillover effect influences the network ties themselves.

Social learning theory provides a theoretical basis for understanding the processes through which such behavior and network change may occur (Bandura, 1977). These primary processes are selection, defined as the tendency to attach to others (i.e., form social relationships) who show similar behavioral patterns, and influence, defined as the tendency for an individual to behave similarly to others. These processes are reciprocally related in any social network, in that both behavior and ties change over time; changes in an individual’s behavior may affect who they are connected to within a network, and vice versa. They are also both fundamentally important processes to study in an effort to understand whether or how behavior change that is stimulated by an intervention diffuses through a population (Valente, 2012).

Relationship Type and Behavioral Transmission

The types of ties that are more likely to transmit effects are critical to understanding spillover. That behavior is diffused across relatively close ties has been established in studies of substance use among early adolescents and young adults (Ali et al., 2011, Cassidy et al., 2018). In the case of alcohol use, close ties provide more frequent opportunities to observe another’s drinking and so provide the opportunity for direct influence, including being offered a drink or being encouraged to drink (Borsari and Carey, 2001, Read et al., 2005). Close ties can be defined in various ways, including living proximity (e.g., roommates; Eisenberg et al., 2014), self-report of best friend status (Cruz et al., 2012), emotional closeness (Duncan et al., 2005), and reciprocal network relationships (i.e., both network members select the other as an important tie; Tucker et al., 2014, Zhu et al., 2014).

Objective

The purpose of this investigation was to determine whether changes in alcohol use produced by an individual BMI administered to a small set of heavy drinking students were transmitted through the college class social network to other heavy drinkers, such that heavy drinkers who had not received the intervention showed reduced alcohol use and reduced contact with other heavy drinkers. To investigate these effects, we enrolled a complete social network of one first-year college class early in the first semester. After separating the class into two groups (BMI and Natural History Control; NHC), we selected a subset of heavy drinkers in each group who were optimally tied to other heavy drinkers (Ott et al., 2018) to serve as intervention recipients. Intervention recipients in the BMI group received an in-person BMI and those in the NHC group receiving no contact. All participants in both groups completed follow-up assessments conducted 5 and 12 months after baseline. We expected that heavy drinkers in the BMI group who did not receive any intervention would show (a) greater reduction in alcohol use (reflecting an influence effect) and (b) reduction in ties to other heavy drinkers (reflecting a selection effect) compared to their counterparts in the natural history control (NHC) group. In addition, we examined the subset of participants who selected an intervention recipient as an important network tie (i.e., an out-tie), and we examined different types of relationships to intervention recipients, including roommates, best friends, and reciprocated ties, as well as degree of self-reported closeness, to determine if these types or qualities of ties were more likely to transmit the hypothesized influence effect of reduced alcohol use. We hypothesized a moderating effect of relationship closeness such that participants who had close relationships with BMI intervention recipients would show greater effects on alcohol use, but the most relevant type of closeness was not clear a priori so we examined several possibilities.

Design

The study design was a two-group controlled trial starting in the fall 2016 semester of the first year of college at a private university in the northeast with follow-up observations 5 and 12 months later. All procedures were approved by the university Institutional Review Board and the trial was preregistered (clinicaltrials.gov NCT02895984)

Participants.

All first-year students were eligible to participate, except older returning undergraduates (n = 11; M age = 28.1), and students in a dual program with another college (n = 18). All first-year students at this institution are required to live in on-campus first-year dormitories and do not select their roommates. Of the 1,660 eligible students, 1,342 (80.8%) enrolled and completed the time 1 (T1) survey (see Figure 1). We allowed students to “opt-out;” if they did not want to be included on the list of network members for others to select (described further below); these students were removed from the network list (n = 39; 2.3%). Descriptive information about participants are in Tables 1 and 2.

Figure 1: Participant Flow Diagram;

Note. HED = Heavy Episodic Drinking; BMI = Brief Motivational Intervention; NHC = Natural History Control

Table 1.

Descriptive Statistics of Participants (N = 1,236)

Variable	N (%) or M(SD)
Age at T1	18.63 (0.51)
Birth sex
Female	703 (56.9)
Male	533 (43.1)
Hispanic/Latino/a Ethnicity	192 (15.5)
Race
American Indian/Alaskan Native	10 (0.8)
Asian	285 (23.1)
Black/African American	86 (7.0)
More than one race	126 (10.2)
Native Hawaiian or other Pacific Islander	3 (0.2)
White	694 (56.1)
Other	4 (0.3)
Prefer not to answer	7 (0.6)

Table 2.

Network Dependent Variable Categories and Descriptive Statistics of the Social Network Variables Over Time

	Time 1	Time 2	Time 3
Past month drinks per week N (%) - Categories
0	330 (26.7)	308 (34.0)	265 (29.2)
>0 to .99	143 (15.8)	140 (15.5)	154 (17.0)
1 to 4.9	332 (36.6)	415 (45.8)	430 (47.5)
5 to 9.9	256 (28.3)	205 (22.6)	264 (29.1)
10 to 70	173 (19.1)	165 (18.2)	122 (13.5)
Missing	2 (0.2)	3 (0.3)	1 (0.1)
Past month drinks per week M (SD)	4.7 (6.2)	4.4 (5.7)	4.3 (5.3)
Network variables
Total number of ties	6,456	4,804	4,213
Network Density	0.004	0.003	0.003
Average Degree M (SD)	5.4 (2.9)	3.9 (2.6)	3.4 (2.4)
Average Jaccard Index1 M (SD)		0.32 (.18)	0.38 (.22)

¹The Jaccard Index is calculated as the number of consistently present ties across each two-wave period, divided by the number of unique (i.e., not duplicated) ties that exist in either of the respective two waves. The index ranges from 0 to 1. Scores close to one indicate more consistency in a participant’s ties between two waves, and scores close to zero indicate inconsistency or greater change from one wave to the next.

Enrollment.

In the late summer/early fall we used multiple methods to provide information about the study to students, including social media, posters, table slips in campus food venues, emails, and staff attendance at campus activity fairs and events. Informed consent was conducted online, with parental consent for minors facilitated using a custom-programmed personalized email from minor to parent. Additional details about the design and procedures can be found in Barnett et al. (2019).

Procedures

The T1, time 2 (T2), and time 3 (T3) surveys were open for two weeks, in mid-October and mid-March of the first year and mid-October of the sophomore year, conducted at the same time of the semester for each observation. At each observation, participants were emailed a link to the online survey. Follow-up rates were 97.8% at T2 and 95.2% at T3. Participants were compensated $50, $55, and $60 at T1, T2, and T3, respectively, with a $20 bonus for completing all three surveys.

Measures

Demographics.

At baseline, participants provided information about age, sex assigned at birth, and race/ethnicity. The university provided dormitory information.

Alcohol use.

Alcohol use was measured at each observation. Average number of drinks per week (DPW) was calculated by multiplying participants’ drinking frequency (“In the past 30 days on how many days did you have at least one drink of any alcoholic beverage?”) by number of drinks per drinking day (“In the past 30 days, on the days when you drank, how many drinks did you drink on average?”), a Quantity-Frequency Index adapted from the Behavioral Risk Factor Surveillance System Questionnaire (Centers for Disease Control and Prevention, 2021). Since it is a technical requirement of Stochastic Actor-Oriented Modeling (see data analysis below) that ordinal categories be used (Ripley et al., 2021), we categorized DPW into five categories based on the variable distribution and reasonable divisions: 0, >0-.99, 1.0-4.9, 5.0-9.9, 10.0 or more (see Table 2 for distributions at each time point). To measure heavy drinking we asked participants, “Considering all types of alcoholic beverages, how many times during the past 30 days did you have four (five) or more drinks in one occasion?” Four or more was presented for women, five or more for men (National Institute on Alcohol Abuse and Alcoholism, 2015).

Network survey.

Using data provided by the university, we prepopulated the network survey with all members of the class who had not opted out of participating. At each observation, participants were asked to identify up to 10 individuals in the first-year class who had been important to them in the past 30 days by selecting their classmates’ names on a list containing all the students. We adapted the Important People and Activities measure for this purpose (Longabaugh and Zywiak, 2002). We programmed an auto-complete function in the list; as participants typed a name, the field jumped to names that matched what they were typing, allowing them to rapidly select classmates. For each person they selected, participants indicated the degree of closeness to that individual: “How close do you feel to this person?” from (0) Not at all close to (5) Extremely close. They were also asked to “Select up to 3 best friend(s) in this group.” Roommate status was derived from the dormitory information provided by the university. A reciprocated tie was defined as present if two individuals in the network nominated one another.

Intervention Procedures

Participants lived in one of 15 first-year residence halls, with numbers of participants in each ranging from 2-162 (Median = 72; Mean = 82.4, SD = 40.7). First-year residence halls on the campus are grouped in two locations, about a 10-minute walk apart. Prior to the first survey, the first author randomly assigned these two groups to conditions to localize the transmission of intervention effects within BMI as much as practicable. The seven BMI halls had 585 participants and the eight NHC dorms had 757, with no difference in percent of students enrolled by condition. The different group sizes were not a concern because the modeling approach used to evaluate intervention effects does not require balanced group sizes.

Identifying intervention recipients.

In the baseline (T1) data, we identified participants who reported heavy drinking two or more times in the past month (N = 530; 39.6%). We modified Borgatti’s Key Player approach (Borgatti, 2006) to identify heavy drinkers who, as a set, were maximally connected to other heavy drinkers within their respective groups (BMI or NHC), but minimally connected to heavy drinkers in the other group (for details see Ott et al., 2018). We called these individuals “Strategic Players” (SPs). The SPs (25% of heavy drinkers in each group: 71 in BMI; 74 in NHC) were selected immediately after T1 survey closure, and SPs in the BMI group were scheduled for intervention. There were no demographic (race or birth sex) differences between those who were selected as SPs and the heavy drinking group from which they were chosen, and SPs did not differ on DPW from other heavy drinkers in their group. In addition, there was no difference on DPW between the SPs in the BMI and NHC groups (Ott et al., 2020).

Intervention administration, fidelity, and outcomes with SPs.

Information about the intervention administration and outcomes is presented in detail elsewhere (Barnett et al., in preparation) but is explained briefly here. Five counselors (two men, three women) experienced with MI administered the BMIs (61 BMIs were delivered out of 71 cases in the BMI condition; 86%), which incorporated personalized normative feedback produced from the baseline data. The first author provided intensive training in the intervention, weekly group supervision, and individual counselor feedback using recordings of sessions throughout the intervention period. All sessions were coded using the MITI (Moyers et al., 2010) by a team at our research center. Using a recommended standard (Madson et al., 2016, Moyers et al., 2010), we selected random 20-minute segments of session recordings (N = 58; 3 declined audio), with 20% (N = 12) randomly selected for double coding. Coder reliability averaged ICC = .71, and global scores were at or above the competency level of 4.0, with the exception of Autonomy (3.8). Behavior counts also showed scores at competency levels (67% complex reflections [competency is 50%]; 97% MI Adherent [competency is 100%]). NHC SPs received no intervention.

Significant changes in alcohol use for multiple outcomes were found for SPs in the BMI group compared to NHC SPs. Specifically, past-month average number of drinks per week, number of heavy drinking days, estimated peak Blood Alcohol Concentration, and number of alcohol-related consequences were all significantly lower at the 12-month follow up in the BMI SPs group relative to the NHC SPs, with small to medium effect sizes (Barnett et al., in preparation). We present these findings as evidence there was a direct effect of the intervention but limit our presentation given space limitations and our interest in the present analysis in focusing on the indirect effect of this intervention.

Data Analyses

Analysis sample.

This sample included only individuals who completed all three surveys (N = 1,236; 92.1% of those who enrolled at T1). This approach avoids confounding changes in sample composition with actual substantive changes in networks and drinking behavior over time. There was no difference between BMI and NHC in the proportion of participants who completed all three surveys (p = .205; see Figure 1). Individuals excluded from the analytic sample did not differ on race/ethnicity (non-Hispanic white vs. other) or DPW. Women were more likely to complete surveys than men at all three time points (p < .05 to p < .001). However, subsequent analysis determined that there were no significant sex differences in the modeled effects of substantive interest.

Modeling approach.

We used the Stochastic Actor-Oriented Modeling (SAOM) framework (Snijders et al., 2010), implemented with the R package RSiena (v.1.3.0) to model the co-evolution of relationships (among network members) and drinking behavior. The SAOM framework is based on an underlying stochastic (probabilistic) process wherein individual-level discrete state variables change in continuous time at a rate commensurate with the observed change, and with each successive change dependent only on the current state of the system. For the present study, state is represented by the social network of important person ties (1 if present, 0 if absent) among participants, and by the drinking behavior of each, measured as categorized drinks per week (DPW). These state variables are hypothesized to change interdependently based on selection and influence mechanisms, the former for relationships and the latter for drinking. The SAOM framework allows for the estimation of these two separate sets of parameters (selection and influence) simultaneously. One equation (selection) predicts changes in network ties from the existing structure and other factors such as individual or dyadic characteristics. The other equation (influence) models changes in behavior based on current individual characteristics as well as various measures of network embedding (e.g. exposure to heavy drinkers). SAOM thus provides a plausible framework for investigating how a behavior (DPW in this study) might change as a result of exposure to intervention recipients (SPs), under circumstances where a participant’s drinking behavior and relationships (i.e., self-reported network ties) are interdependent.

In practice, a SAOM is specified as a multivariate multinomial logistic equation for each state variable (here, the network of ties denoted by participants and DPW), each predicting the probabilities of possible one-step changes. An iterative process is employed to find the parameter values that best explain the observed aggregate change in the system from one survey time to another. Moment, maximum likelihood and Bayesian criteria are available to evaluate fit; our analyses used the moment approach, as it is much faster than alternatives, with little disadvantage in efficiency when applied to large networks (Snijders et al., 2010). A bootstrapping approach is used to calculate standard errors for effect coefficients, which in turn are used to obtain statistical significance estimates (Ripley et al., 2021). A parameter can be interpreted as the predicted change in log-odds of the endogenous variable with a one-unit change in the predictor. Normally such effects are assumed to be symmetrical, i.e., the same amount up or down with a unit change, plus or minus, in the predictor (a so-called evaluation effect). However, in some cases predictors operate differently depending on whether they are predicting an increase or decrease in a state variable. SAOM allows this by splitting a covariate effect into a term that captures only increases in a state variable (creation effect) and another capturing only maintenance or decrease (maintenance effect). For instance, in this study there was no basis to predict whether the intervention would equally affect creation of new ties vs. maintenance of old ones, so models had to examine all such possibilities. Note as well that quantitative predictors were centered at their time-period-specific means, which affects interpretation.

Defining contrasts.

First, we define contrasts for the network part of the model. As for any linear model, the contrast is achieved with two indicator (0-1) variables. The first contrast variable, HD.BMI.NSP was set to 1 for all heavy drinkers in the BMI group who were not Strategic Players (shown in green in Figure 2), and zero otherwise. The second contrast, OTHER.0, was 1 for all of the comparison-irrelevant members of the zero category of HD.BMI.NSP (i.e., non-drinkers and non-heavy-drinkers, including SPs in either the BMI or NHC groups); these individuals are shown in white in Figure 2. The 0 value for OTHER.0 (shown in blue in Figure 2) is the reference category for HD.BMI.NSP; thus, the parameter of HD.BMI.NSP shows the difference between the green and blue-shaded subgroups, which is the comparison of substantive interest. Because OTHER.0 is only present to control out individuals who are not relevant for indirect intervention effects (i.e., non-drinkers, non-heavy drinkers, and SPs), we refer to it as a “control” indicator. Its parameter is of no substantive interest, even though such effects need to be included so that HD.BMI.NSP gives the difference between the target populations for indirect effects in each group (i.e. the green and blue subgroups in Figure 2).

Figure 2: Study Design and Contrast Variable Definitions (Time 1; N = 1,236);

Note: For the network portion of the model, the contrast variable HD.BMI.NSP was set to 1 for all heavy drinkers in the BMI group who were not direct intervention recipients (shown in green), and 0 otherwise. The second contrast, OTHER.0, was 1 for all of the comparison-irrelevant members of the 0 category of HD.BMI.NSP (i.e., non-drinkers, non-heavy-drinkers and Strategic Players in either the BMI or NHC groups); these individuals are shown in white. The 0 value for OTHER.0 (shown in blue) is thus the reference category for HD.BMI.NSP; thus, the parameter of HD.BMI.NSP shows the difference between the green and blue-shaded subgroups, which is the comparison of substantive interest.

For the behavior (i.e., alcohol use) model, a conceptually similar approach was taken, although different because of the need to identify effects of affiliating with SPs in the BMI or NHC group. Three indicator variables were defined: HD.NSP was set to 1 for non-SP heavy drinkers in both BMI and NHC groups, and 0 otherwise; this indicator is identified by the green and blue-shaded groups in Figure 2. This indicator controlled for the higher drinking among heavy drinkers, so that other effects could be interpreted net of that predefined difference. Additionally, to examine intervention transmission through reciprocal relationships (i.e., each participant nominated the other as important), we created two more contrasts: RECIP.BMI.SP was set to 1 for individuals who had a reciprocal relationship with an SP in the BMI group, and RECIP.NHC.SP was set to 1 for individuals who had a reciprocated relationship with an SP in the NHC group. When all are included in the behavior (i.e., drinking) model, these contrasts can be used to compare the effects of exposure to BMI (the RECIP.BMI.SP parameter) and NHC (the RECIP.NHC.SP parameter) SPs in the population as a whole. Importantly, HD.NSP x RECIP.BMI.SP and HD.NSP x RECIP.NHC.SP interactions narrow this difference to heavy drinkers only, which was the comparison of primary substantive interest (see Figure 3).

Figure 3: Study Design and Contrast Variable Definitions for the Behavior Portion of the Model (Time 1; N = 1,236);

Note. For the behavior portion of the model HD.NSP was set to 1 for targeted heavy drinkers in both intervention and control groups (identified by the green and blue-shaded groups), and 0 otherwise. RECIP.BMI.SP was set to 1 for individuals who had a reciprocal relationship with an SP in the BMI group (noted by the solid bidirectional arrows), and RECIP.NHC.SP was set to 1 for individuals who had a reciprocated relationship with an SP in the NHC group (dashed bidirectional arrows). These contrasts are used to compare the effects of exposure to BMI and NHC SPs in the population as a whole. Interaction terms with HD.NSP (denoted by green and blue groups) narrow this difference to heavy drinkers only, which was the comparison of primary substantive interest.

Model Specification

Our primary goal was to determine whether the intervention had the broadest possible beneficial effects on the behavior of heavy drinkers in the BMI group who did not receive any intervention; the first comparison then was differential change in amount of drinking between BMI and NHC subgroups (in green and blue in Figure 2). We then followed this model with one that evaluated whether participants who had selected an SP in the network survey (i.e., had an out-tie to an SP) showed change in DPW in BMI vs. NHC. We then proceeded to evaluate moderation of the indirect effect according to tie closeness, best friend status, roommate status, and reciprocated ties with BMI SPs.

Our analysis strategy differs somewhat from a more traditional randomized trial analysis in that we do not directly compare intervention and control groups. This is because we could not avoid overlap in network nominations between these groups, which inevitably led to individuals in the NHC condition being exposed to BMI-SPs. Such contamination is not uncommon in experiments in natural settings, where control individuals may avail themselves of the treatment of interest regardless of experimenter efforts to prevent this (Imbens and Rubin, 2015). But unlike traditional designs, our study measured such contamination using network data, explicitly controlled for exposure regardless of initially-assigned study group, and utilized the ties in the behavior portion of the model (as shown in Figure 3).

Network model.

A number of effects were included in the model to predict network evolution.

(a). Control effects (Table 3, rows 1-6).

Control variables were not of substantive importance but are required to capture network evolution properly. Outdegree acts like an intercept in standard regression, giving a kind of unconditional value of tie density in the network, but otherwise is only of descriptive value. Reciprocity, transitivity, and 3-cycles (see Table S1 in supplemental materials for definitions) reflect network closure tendencies (Block, 2015). For example, transitivity is the tendency for a person to attract a new tie from the friend of a friend. These controls needed to be included because their effects could otherwise be confounded with important effects such as preference for friends whose drinking patterns are similar to one’s own. Covariates were added to control for physical proximity (living in the same dormitory at baseline), and for the typical tendency for individuals to affiliate with others of the same sex.

(b). Variables related to drinking (Table 3, rows 7-10).

These predictors focused on drinking behavior (DPW) as a basis for tie formation and maintenance. In directed network models, effects may be associated with the choices one makes as a function of drinking (“ego” effects), or of another individual’s drinking (“alter” effects), or of the similarity between ego and alter drinking. Thus, the DPW ego effect reflects the relationship between drinking and making ties to others (i.e., out-ties), with a positive coefficient; meaning that people who drink more tend to nominate more alters. Likewise, the DPW alter effect reflects the relationship between drinking and receiving more incoming ties from others. A positive similarity effect (“sim” in tables) implies that individuals are more likely to nominate someone whose DPW is similar to their own.

(c). Contrasts involving HD.BMI.NSP and OTHER.0 (Table 3, rows 11-20).

Any term with HD.BMI.NSP in it can be interpreted as a comparison between the BMI target and NHC target groups (i.e., heavy drinkers who did not receive the intervention). Thus, the network part of the model contains main effects of these indicators (rows 11-14), which capture any differences in tendencies to create or receive nominations among the contrast groups. HD.BMI.NSP and OTHER.0 were also interacted with similarity in DPW (rows 15-18). Some exploration (see next section) revealed that similarity effects differed according to whether they predicted creation of new ties (rows 16 and 18 of Table 3) or maintenance of existing ties (rows 15 and 17), so these effects were estimated separately for the HD.BMI.NSP and OTHER.0 contrasts. Indicator variables were also examined to test for time heterogeneity (Table 3, rows 19 and 20). These variables identified effects specific to changes from time periods 1-2 or 2-3 but not both, as is generally recommended (Ripley et al., 2021).

Table 3.

Stochastic Actor Model: Group Comparison of Friendship Tie Formation and Drinks Per Week Among Heavy Drinkers with a Reciprocal Tie to a Strategic Player

	Effect	Type1	β	SE	t-ratio(p)	95% CI
	Network Model
1	Outdegree	eval	−4.17	0.09	46.30(.001)	−4.35, −4.00
2	Reciprocity	eval	3.07	0.04	76.80(.001)	3.00, 3.15
3	Transitivity	eval	1.37	0.04	34.30(.001)	1.29, 1.45
4	3-Cycles	eval	−0.48	0.03	16.00(.001)	−0.54, −0.42
5	Same Dorm	eval	0.36	0.03	12.00(.001)	0.30, 0.42
6	Same Sex	eval	0.35	0.02	17.50(.001)	0.31, 0.39
7	DPW ego	eval	−0.15	0.02	7.50(.001)	−0.19, −0.11
8	DPW alter	eval	0.17	0.02	8.50(.001)	0.13, 0.21
9	DPW sim	endow	−0.81	0.66	−1.20(.22)	−2.10, 0.49
10	DPW sim	creat	3.50	0.88	3.98(.001)	1.78, 5.22
11	HD.BMI.NSP ego	eval	−0.08	0.10	0.80(.42)	−0.28, 0.12
12	HD.BMI.NSP2 alter	eval	0.00	0.04	--	--
13	OTHER.0 ego	eval	−0.06	0.10	0.60(.55)	−0.26, 0.14
14	OTHER.03 alter	eval	0.07	0.04	1.75(.08)	−0.01, 0.15
15	HD.BMI.NSP ego x DPW sim	endow	0.46	1.28	0.36(.72)	−2.05, 2.97
16	HD.BMI.NSP ego x DPW sim	creat	−0.31	1.19	0.26(.79)	−2.64, 2.02
17	OTHER.0 ego x DPW sim	endow	1.26	0.73	1.72(.08)	−0.17, 2.69
18	OTHER.0 ego x DPW sim	creat	−0.70	0.95	0.74(.46)	−2.56, 1.16
19	HD.BMI.NSP ego x DPW sim x time 1-2	endow	−2.57	0.86	2.98(.003)	−4.26, −0.88
20	OTHER.0 ego x DPW sim x time 1-2	endow	−0.17	0.29	0.58(.56)	−0.74, 0.40
	Behavior Model
21	DPW linear shape	eval	−0.19	0.03	6.33(.001)	−0.25, −0.13
22	DPW quadratic shape	eval	−0.16	0.03	2.00(.046)	−0.32, 0.00
23	DPW average alter	eval	0.46	0.08	5.75(.001)	0.30, 0.62
24	DPW effect from HD.NSP4	eval	0.29	0.08	3.63(.001)	0.13, 0.45
25	DPW effect from RECIP.BMI.SP5: reciprocated relationship with BMI intervention recipient	eval	0.05	0.12	0.42(.68)	−0.19, 0.29
26	DPW effect from RECIP.NHC.SP6: reciprocated relationship with NHC intervention recipient	eval	0.11	0.11	1.00(.32)	−0.11, 0.33
27	DPW effect from HD.NSP x RECIP.BMI.SP: heavy drinkers x BMI intervention recipients with reciprocated alters	eval	−0.36	0.17	2.11(.034)	−0.69, −0.03
28	DPW effect from HD.NSP x RECIP.NHC.SP: heavy drinkers x NHC intervention recipients with reciprocated alters	eval	−0.20	0.16	−1.25(.21)	−0.51, 0.11

Notes. Rate effects not shown (see Table S4 for all effects).

DPW = drinks per week; BMI = Brief Motivational Intervention; NHC = Natural History Control

¹eval: evaluation type effect is symmetric for increases or decreases in the dependent variable endow: endowment type effect predicts tendency to:

- drop or maintain ties for variables in the network model

- stay the same or decline for variables in the behavior model

- creat: creation type effect predicts tendency to:

- add new ties for variables in the network model

- increase in value (by 1 unit) for variables in the behavior model

²HD.BMI.NSP = 1 for heavy drinkers in the BMI group who were not strategic players (green subgroup in Figure 2), 0 otherwise

³OTHER.0 = 1 if not a heavy drinker (so includes non-drinkers and non-heavy drinkers) or a Strategic Player in either BMI or NHC (white groups in Figure 2)

⁴HD.NSP = 1 for heavy drinkers were not Strategic Players in either the BMI or NHC group.

⁵RECIP.BMI.SP = 1 for participants who had a reciprocal relationship with one or more Strategic Players in the BMI group.

⁶RECIP.NHC.SP) = 1 for participants who had a reciprocal relationship with one or more Strategic Players in the NHC group.

Behavior model.

Control effects included linear and quadratic shape, which specify the shape of the preference function for change in drinking behavior. The substantively important effects focused on the influence of directly-connected peer drinking, specifically the influence of the average DPW of alters for any given individual (Table 3, line 23), and the effects of having a reciprocal relationship with an SP in either BMI or NHC conditions (Table 3, lines 25-28). The comparisons of interest were the interaction between HD.NSP and RECIP.BMI.SP, which reflects the effect for heavy drinkers of a reciprocated relationship with an SP in the BMI group (line 27), and the interaction between HD.NSP and RECIP.NHC.SP, which reflects the effect for heavy drinkers of a reciprocated relationship with an SP in the NHC group (line 28). Effects in lines 24-26 ensure that interaction effects in lines 27-28 do not simply reflect lower-order main or interaction effects.

Model Building

To provide the best possible start values for iterative estimation, models were built using the recommended forward-selection approach (Ripley et al., 2021). First, control parameters were modeled, followed by first-order effects, then relevant two-way and three-way interactions. SAOMs with statistically significant higher-order effects always include their lower-order components, whether the latter were statistically significant or not, for the sake of interpretational clarity. It was not necessary to test for time heterogeneity of effects by including them in models, however, because RSiena includes a time test that allows such effects to be identified (Lospinoso et al., 2011).

Results

From this point forward, we report only on participants who were used in analyses (N = 1,236; 56.9% female). The two largest racial groups were White (56.1%) and Asian (23.1%); Latinx ethnicity was 15.5%. At T1, 651 participants (52.6%) reported one or more days of heavy drinking in the past 30 days, 255 (20.6%) reported drinking but no heavy drinking days, and 330 (26.7%) reported no drinking. The participants selected as intervention recipients (the SPs) comprised 20.0% of all heavy drinkers, 14.3% of all drinkers, and 10.5% of all participants.

At T1, the total number of network nominations made was 8,614, for an average per participant of 6.97 (SD = 2.96; Median = 7). The average percent of ties that were reciprocated was 36.9% (SD = 22.2). Considering only those who were targets for the indirect intervention effect (i.e., those with 1 or more heavy drinking days who were not SPs), 75.6% had one or more ties to a SP (33.2% to BMI; 35.7% to NHC, and 6.7% to both), for an average of 1.07 ties (SD = 0.84; range 0-5) per person. Of heavy drinkers with ties to BMI SPs, 52.4% of those ties were reciprocated; this proportion was 48.9% for heavy drinkers with ties to NHC SPs, χ²(1, N = 429) = .53, p = 0.46).

Model of Intervention Effects

Network model.

All the control effects (outdegree, reciprocity, transitive triplets, 3-cycles, same dorm, and same sex) were statistically significant (Table 3) and can be interpreted as follows: outdegree was negative, meaning there was a tendency for individuals to nominate less than (in this case, much less than) half of the available population (a not particularly useful value given the size of the network), ignoring all other predictors (outdegree acts like an intercept term in ordinary regression). Reciprocity was positive, reflecting that individuals tended to reciprocate nominations; transitivity was positive, indicating that friends of friends tended to become friends over time; the negative 3-cycles effect indicated a tendency towards local status hierarchies (Block, 2015); same dorm was positive, indicating that relationships were more likely between students in the same dorm; and same sex was positive, indicating that same-sex friends were more likely to be selected. We do not present rate parameters (estimates of rates of change in ties and drinking between study waves), as they are not of substantive interest. Full model results are available in Supplemental materials.

The model also shows significant effects in the class as a whole for DPW alter (β = 0.17, p < .001) and DPW ego (β = −0.15, p < .001), indicating that participants who drank more (relative to those who drank less) were more likely to be chosen by others, but were less likely to choose others, respectively. There was also a strong DPW similarity effect (β = 3.50, p < .001); individuals tended to choose others whose drinking quantity was similar to their own. However, this effect applied only to tie creation (as noted in the “type” column of Table 3). Tie maintenance (referred to as an endowment effect), in contrast, was not significantly related to DPW similarity (β = −0.81, p > 0.22). This suggests that participants were more likely to form new ties with other students whose drinking was similar, but maintaining ties did not depend on drinking similarity (suggesting maintenance of ties depended on other factors).

Turning now to the part of the network model addressing the indirect intervention hypothesis, the effect of DPW similarity on tie maintenance was significantly lower for the BMI target group (heavy drinkers who did not receive intervention) compared to the NHC target subgroup (β = −2.57, p < .003), but only for the T1-T2 interval. That is, although tie maintenance did not depend on drinking similarity in the first-year class as a whole (DPW similarity effect described above), there was a significant tendency for BMI target heavy drinkers to shed ties or not to form new ties to individuals whose drinking was similar to their own, compared to NHC target heavy drinkers, but only across the first two time periods.

Drinking model.

The average alter effect was positive (β = 0.46, p < .001), showing that there was a tendency for students who nominated heavier drinkers (i.e., higher DPW) to drink more themselves. Additionally, the HD.NSP parameter was positive and significant (β = 0.29, p < .001), indicating that drinking was more likely to increase over time among heavy drinkers compared to non-heavy drinkers. Our analyses tested first whether there was an indirect effect among all heavy drinkers, but did not find significant group differences in DPW (see Table S2 in supplemental materials). We next evaluated whether heavy drinkers with out-ties to SPs showed the indirect effect; this model also did not find significant between-group differences in DPW (see Table S3 in supplemental materials). We next tested moderated effects of different indicators of closeness; only reciprocated ties with BMI recipients (SPs) were found to predict spillover, and hence this model results are presented in Table 3 and interpreted below (see also Table S4 in supplemental materials). Models testing relationship closeness alternatives (best friend, roommate, reported closeness) are available on request.

Indicators RECIP.BMI.SP and RECIP.NHC.SP were not significant by themselves; that is, there was no differential effect on alcohol use of a reciprocated relationship to SPs in the NHC vs. BMI groups in the first-year class when all participants were considered. However, when this comparison was narrowed to just heavy drinkers, both interactions (HD.NSP x RECIP.BMI.SP and HD.NSP x RECIP.NHC.SP) were negative, indicating that a reciprocal relationship with an SP was negatively related to alcohol use for heavy drinkers. However, only the HD.NSP x RECIP.BMI.SP interaction (i.e., the BMI group) was statistically significant (β = −0.36, p = .034). These results suggest that the effect of exposure to SPs in the BMI group (via a reciprocated tie) was associated with a significant reduction in alcohol use across the entire study period relative to heavy drinkers without reciprocal ties to BMI SPs.

Discussion

In this investigation, we enrolled a high proportion of students in one college class and administered a brief motivational intervention to a subset of heavy drinkers. We found that both selection and influence effects were present across subsequent observations among heavy drinking participants who did not receive the intervention. Specifically, heavy drinking participants who had a reciprocal network tie to a BMI intervention recipient (SP) showed lower drinks per week in the 12 months after the BMI intervention relative to those who did not have reciprocal ties to BMI SPs, while similar reduction in heavy drinkers with reciprocal ties to NHC SP’s was not found, supporting our hypothesis that there would be an influence effect from the BMI, albeit found only among heavy drinkers who had a mutual relationship with an SP in BMI. Somewhat different circumstances were found for the selection effect, in that we found a differential tendency for participants in the BMI group to shed ties to those who drink similarly to them, relative to the NHC group. Supporting our hypothesis, this selection effect was found when all participants were considered (i.e., not just among those with a close relationship), but was found only in our early observations (T1 to T2).

The influence finding was specific to reciprocated relationships, that is, relationships where both the BMI SP and the targeted heavy drinker selected each other in their network survey as important in the fall of their first college year. We were hoping that that this effect would be propagated more broadly (i.e., such that all heavy drinkers might be influenced), but did not find a general transmission across the network; we found it only among participants who had a mutual relationship with a BMI intervention recipient. We considered other relationship characteristics as possibly important in the transmission of behavior change, including evaluating heavy drinkers with out-ties to an SP and indicators of relationship closeness, including roommate, best friend, and closeness self-report of participants, but the reciprocal relationship was the only significant finding to emerge. This finding is consistent with other work that indicates that agreed-upon relationship status suggests greater potential for influence (McMillan et al., 2018, Valente, 2010, Zhu et al., 2014). It implies that relationships in which both individuals indicate the relationship is present (and presumably important) are a potentially good target for intervention in which spillover effects are desired. Importantly, behavior change was not evaluated only among heavy drinkers in the BMI group; as shown in Figure 3 the analytic approach allowed all reciprocal ties to BMI SPs to be included, regardless of the other drinker’s group. Moreover, reciprocal ties were more prevalent among heavy drinkers with ties to intervention recipients (49% for NHC and 52% for BMI) than among members of the whole network (37%), suggesting a greater potential for transmission across these ties.

The general similarity effect for DPW was found to be positive, but much smaller across the first two waves for BMI group targets relative to NHC. In other words, the tendency for individuals to form relationships with those who had similar drinking behaviors (i.e., the similarity effect) was attenuated by our intervention. This could be interpreted to mean that participants (our interest is heavy drinkers) in the BMI group show a lower tendency to form ties or a greater tendency to shed ties to other heavy drinkers. This finding differentiated the (non-SP) heavy drinkers in the BMI and NHC groups according to their original assigned group, although the ties they formed or shed could have been to members of either group. We conclude that the difference in this similarity effect was most likely a function of the heavy drinkers having a closer proximity (in the network sense and in the physical sense) to BMI intervention recipients.

The timing of the effects seems important to reflect on, as they differed, with the selection effect found in the first two waves (from early to midway through the first year of college), whereas the influence effect was found throughout the three waves. Apparently, the indirect effect of the intervention appeared to affect selection broadly (i.e., not just among special types of ties) but only in the first part of the follow-up period, while influence, which was specifically found among heavy drinkers with reciprocal ties to intervention recipients, was omnipresent. This difference in timing and specificity of effects seems important to study further, as it could have implications for social network intervention targets.

Strengths and Limitations

Strengths of this investigation include high enrollment, indicating the network was well represented in the data, and retention, which exceeded 95% at both follow-up observations and allowed for 92% of those enrolled at baseline to be included in the complete case analysis. The BMI was administered to a high proportion of the targeted individuals with high intervention fidelity. Balance on sex and racial/ethnic representation were good. Similar to intent-to-treat approaches, all SPs (and their relationship ties) were included in analyses, regardless of whether they received the intervention. Our single network tie generator (“Who is important to you?”) was defined for participants quite broadly with a range of relationship types included. Finally, SAOMs are multivariate, i.e., contain numerous controls which address the complexity of full networks and provide more confident interpretation of effects as both causal and independent. In particular, in the influence model we were able to include all reciprocal ties to intervention recipients regardless of the original (BMI or NHC) group of the other heavy drinkers, essentially incorporating cross-group influences; this cross-group connection would otherwise have been considered a contamination but in this study became a strength.

Limitations include the baseline drinking differences between intervention groups, with higher drinks per week in the BMI group. It is possible that transmission of intervention effects could differ as a function of this higher drinking in the BMI group. Also, randomized trials typically control for intervention exposure differences. In this study, participants indirectly chose exposure to the intervention through their choice of network members. However, this exposure (or contamination in the case of NHC participants with ties to a BMI SP) was measured directly through network ties and thus controlled for in a manner analogous to a propensity score.

We paid participants to complete assessments and the intervention which raises the issues of ecological validity and generalizability. It was essential to have high participation of the network members to test our hypotheses, and we believe our methods, including compensation, resulted in the very high enrollment and retention rates. Finally, the results do not attempt to correct for the possible underestimation of Type I error that may result from exploratory analysis, but we believe that the modest amount of exploratory work leading to the eventual models described were appropriate to the knowledge currently available about social ecological effects on drinking.

Future Directions

Many aspects of this research area warrant further investigation. First, we identified behavioral spillover effects for reciprocally connected peers of intervention recipients, indicating that behavior change occurred in a subgroup of heavy drinkers. Additional investigation of close relationships and the characteristics of those relationships that optimize spillover is warranted. For example, individuals have multiplex relationships with others (e.g., work, school, social, sexual activity), and these different types of relationships or combination of relationships may be meaningful for behavioral diffusion. Second, it is critical to understand the mechanisms through which those effects were transmitted. In other words, how were these effects transmitted through the reciprocal friend relationship? Good candidates for investigation are perceived norms (Borsari and Carey, 2003), and (changed) modeling of heavy drinking. Third, there has been some evidence of spillover of intervention effects in other ages and subgroups including adolescents (Ali and Dwyer, 2010, Shakya et al., 2012), but more research is needed on the diffusion of behavior change into different and diverse networks, such as other educational or work contexts. This should include understanding what characteristics of the network itself (e.g., density) are important for this effect. Finally, longitudinal network modeling is quite challenging, as it requires considerable computing power and data analytic expertise. Cross-sectional network analysis approaches are commonly used but are not sufficient for research investigating adoption or maintenance of behaviors and social influences, and can be misleading if over-interpreted (van den Ende et al., 2022). Development of user-friendly approaches that allow for different types of outcome variables are needed.

Conclusions

This controlled trial determined that a brief alcohol intervention conducted on a set of optimally positioned heavy drinkers in a first-year college class resulted in reduced alcohol use and reduced risky social ties among heavy drinkers who received no intervention, indicating both behavioral and network spillover effects of a relatively small scope intervention.