Social network analysis of the CaRE² health equity center: Team science in full display

Abstract

Cancer health disparities that exist in the Black or African American and Hispanic or Latino/x communities are scientific challenges, yet there are limited team science approaches to mitigate these challenges. This article's purpose is to evaluate the team science collaborations of the National Institutes of Health‐funded Florida‐California Cancer Research, Education & Engagement (CaRE²) Center partnership underscoring the inclusion of multidisciplinary team members and future under‐represented minority (URM) cancer researchers. To understand our collaborative efforts, we conducted a social network analysis (SNA) of the CaRE² Center partnership among University of Florida, Florida A&M University, and University of Southern California with data collected via the dimensions.ai application programming interface. We downloaded metadata for all publications associated with dimensions.ai IDs. The CaRE² collaboration network increased over time as evidenced by accruing more external collaborators and more publishing of collaborative works. Degree centrality of key personnel was stable in each wave of the networks. CaRE² key personnel averaged a total of 60.8 collaborators in 2018–2019 (SD = 57.4, minimum = 3, maximum = 221), and 65.8 collaborators in 2020–2021 (SD = 56.06, minimum = 4, maximum = 222). Betweenness was largely stable across all groups and waves. We observed a steady decline in transitivity, the probability that a pair of CaRE² co‐authors shared a third co‐author, from 0.74 in 2018 to 0.47 in 2022. The SNA findings suggest that the CaRE² Center partnership's publications show growth in team science collaborations with the inclusion of multidisciplinary team members from the three partner institutions and future URM cancer researchers who were mentored as trainees and early‐stage investigators.

Study Highlights.

• WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

Successes of programs focused on reducing cancer health disparities through team science approaches have not been evaluated with methods such as Social Network Analysis (SNA), an objective approach for ascertaining the connectedness of scientific teams. Such an evaluation could provide evidence for the impact of the National Cancer Institute's Comprehensive Partnerships to Advance Cancer Health Equity (CPACHE) Program.

• WHAT QUESTION DID THIS STUDY ADDRESS?

This study used SNA to evaluate the characteristics and trajectory over time of research publications from the Florida‐California Cancer Research, Education & Engagement (CaRE²) triad partnership with strong emphasis on the inclusion of under‐represented minority trainees and early‐stage investigators within the team.

• WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

The SNA revealed that the partnership increased cohesion and productivity from 2018–2019 to 2020–2021 with similar trends projected for 2022–2023. The CaRE² publication network became more decentralized and less reliant on a small number of highly connected network brokers. CaRE² authors have worked with more unique collaborators and less with their original collaborators, which was expected as the partnership grew and each member expanded their network as a result of the work that was initiated through CaRE.² The partnership also progressed in cross‐institutional scholarship.

• HOW MIGHT THIS CHANGE CLINICAL PHARMACOLOGY OR TRANSLATIONAL SCIENCE?

Findings show that SNA can be used to monitor progress of translational team science efforts and provide evidence of partnership impact and insights to strengthen a partnership's impact through its policies and infrastructure initiatives.

INTRODUCTION

Team science, encouraged and defined by the National Institutes of Health, is “a collaborative effort to address a scientific challenge that leverages the strengths and expertise of professionals, oftentimes trained in different fields.” ¹ Cancer health disparities that exist in the Black or African American (B/AA) and Hispanic or Latino/x (H/L) communities are scientific challenges that must be studied for a clearer understanding of the complex relationships among biological, socio‐demographic, and clinical differences that result in poor health outcomes for individuals in these groups. For current and future authenticity of team science endeavors to address cancer health disparities research, the multidisciplinary research team must include members of the affected communities. ² Further, there must be pathways for developing future under‐represented minority (URM) cancer researchers and integrating them within scientific teams to obtain and hone skills needed for their future roles. ³ An example of a team science initiative to address these scientific challenges of cancer health in the B/AA and H/L communities is the Florida‐California Cancer Research, Education & Engagement (CaRE²) Health Equity Center funded by the National Cancer Institute's Comprehensive Partnerships to Advance Cancer Health Equity (CPACHE) in September 2018.

The CaRE² Center is a bicoastal triad partnership formed among the University of Florida (UF) Cancer Center, Florida A&M University (FAMU), a historically Black university, and the University of Southern California (USC) Norris Comprehensive Cancer Center. The partnership is comprised of six cores, dedicated to administration (AC), community outreach (COC), research education (REC), planning and evaluation (PEC), and two shared resources, statistics and bioinformatics (BSMC) and tissue procurement/repository (TMC).

A key CaRE² Center aim is to track its activities and progress toward benchmarks for continuous quality improvement. To this end, its PEC is solely dedicated to this task to ensure successful achievement of research projects' and cores' aims. As one approach to do so, PEC used a social network analysis (SNA), a powerful and objective approach for ascertaining the connectedness of scientific teams. ⁴ , ⁵ We used SNA to evaluate the characteristics and trajectory of our team science approaches, focusing on the research publications of the center with strong emphasis on the inclusion of the URM trainees and early‐stage investigators (ESIs), within the team. In this article, we present an SNA over time of the partnership's publications to inform evaluation of the team science collaborations underscoring the inclusion of multidisciplinary team members and future URM cancer researchers.

METHODS

Using network methods, we analyzed the CaRE² Center partnership among UF, USC, and FAMU with co‐publication network data collected via the dimensions.ai application programming interface (API), ⁶ which needed no institutional review board approval because the data are publicly available. We identified the dimensions.ai identifier and profile for each of the 98 CaRE² members with at least three publications under the same affiliation, and manually generated additional IDs for the 12 members without an ID and profile – dimensions.ai requires either a minimum of three publications or a user‐connected ORCiD to establish a profile and ID for a researcher. Using the dimensions.ai API, we downloaded metadata (publication ID, title, and concepts, author ID, name, and affiliation) for all peer‐reviewed articles published between January 2018 and December 2022. These dates represent the time period from initial U54 grant submission to renewal submission. The selected articles were associated with one or more of the 98 CaRE² member IDs, then we individually targeted and downloaded the metadata for missing publications associated with the manually generated IDs by following members' curriculum vitae. These metadata were then merged with CaRE² membership data, which includes an indicator whether the contributing researcher(s) are key personnel or trainees. Except for 12 junior CaRE² members, trainees were all prolific authors, averaging 16.34 publications (SD = 18.02) whereas key personnel averaged 38.31 publications (SD = 35.73) over the 5‐year period.

We followed long‐established procedures for constructing co‐authorship networks, ⁷ starting with an edge list where each row represented a unique combination of author and publication, a bipartite network where nodes took on two modes that never directly connected publications and authors. This bipartite network was projected into a one‐mode network where each point (node) was an author, and each connection (edge) represented one or more shared publications. The first set of networks included all CaRE² members and all their external collaborators. We performed a descriptive analysis of these networks, comparing the role of CaRE² members in the 2018–2019 and 2020–2021 co‐authorship networks (Figure 1) with the 2022 co‐authorship network (Figure 2). Using the igraph package ⁸ in the R software environment for statistical computing and graphics, version 4.1.0, ⁹ we calculated a range of centrality measures to assess the involvement of each institution's key personnel and trainees in the network of researchers both directly and indirectly involved in CaRE² research. These measures included:

• Degree: Assuming that nodes with the greatest involvement in a network should be highly connected, degree was calculated by counting the number of edges incident on each node. ¹⁰ Degree represented an investigator's total number of unique co‐authors.

• Betweenness: We identified the middle persons (“brokers”) for information and interactions across the network. Betweenness centrality was calculated by taking the proportion of shortest (geodesic) paths between all possible pairs of investigators that must pass through each target investigator relative to the total number of geodesic paths. ¹⁰

FIGURE 1.

Main components of two bi‐annual CaRE² co‐authorship networks, including trainees, leaders, and investigators as well as their first order neighborhood non‐CaRE² external collaborators, non‐CaRE² researchers with whom CaRE² researchers have co‐authored at least one publication. FAMU, UF, and USC are indicated by their respective institutional colors. CaRE², Florida‐California Cancer Research, Education & Engagement; FAMU, Florida A&M University; UF, University of Florida Cancer Center; USC, University of Southern California Norris Comprehensive Cancer Center.

FIGURE 2.

Main component of the most recent (2022) complete annual CaRE² co‐authorship network, including trainees, leaders, and investigators as well as the first order neighborhood non‐CaRE² external collaborators, non‐CaRE² researchers with whom CaRE² researchers have co‐authored at least one publication. FAMU, UF, and USC are indicated by their respective institutional colors. CaRE², Florida‐California Cancer Research, Education & Engagement; FAMU, Florida A&M University; UF, University of Florida Cancer Center; USC, University of Southern California Norris Comprehensive Cancer Center.

We then focused exclusively on the co‐authorship between CaRE² members, divided into a total of five annual co‐authorship networks (Figure 3). To examine the transformation of these networks between 2018 and 2022, we also calculated annual measures of clustering, homophily, and centralization:

• Clustering coefficient (transitivity): This coefficient was the probability that a given investigator's co‐authors are also co‐authors. ¹¹

• Assortativity coefficient: This coefficient was the tendency of investigators to establish co‐authorship edges within and between both institutions and CaRE² roles, where 1 indicates homophily, and −1 indicates heterophily. ¹²

• Centralization: This measure ascertained whether the CaRE² network was concentrated around a small number of highly central (see Degree and Betweenness) investigators. ⁵

FIGURE 3.

Annual co‐authorship networks of CaRE² trainees, leaders, and investigators. Node size is scaled to represent brokerage (betweenness centrality). Nodes are colored by parent institution. Network union combines the five annual networks. CaRE², Florida‐California Cancer Research, Education & Engagement; FAMU, Florida A&M University; UF, University of Florida Cancer Center; USC, University of Southern California Norris Comprehensive Cancer Center.

To analyze the development of CaRE² over time, we used separable temporal exponential random graph models (STERGMs). ¹³ Specifically, we examined co‐author relationships between the actively publishing members of the CaRE² Center, examining the influence of CaRE² funding, cancer scholarship, institutional affiliation, and role in the CaRE² Center (key personnel and trainee) on the formation and persistence of collaborative relationships. STERGMs are functionally a longitudinal regression that statistically models the formation and persistence of ties in a network, as well as the node and edge characteristics upon which this formation and dissolution is dependent. Exponential random graph (ERG) family models, including STERGMs, iteratively add and remove edges from a network, measuring the change in the network's structure and characteristics, effectively simulating the (non‐)existence of edges in the network. ¹⁴ All of our STERGMs were estimated using conditional maximum likelihood estimation (CMLE).

Generally, ERG model parameter estimates can be interpreted in the same manner as a logit regression, where coefficients are the log‐odds of the existence of an edge in the network (or, in the case of STERGM, the separable log‐odds of tie formation and persistence from wave to wave). By extension, exponentiating ERG model coefficients produce the odds of an edge, and $\text{odds}/\left(1+\text{odds}\right)$ produces the predicted probability of an edge. However, unlike other regression models, independent variables are introduced into an ERG model via a range of different terms.

Our STERGM was specified such that it included overall probability of edge (collaboration and the dependent variable) formation and dissolution (edges, the intercept), and the influence of connectedness, proximity, or similarity between that same dyad in another network or adjacency matrix (edge covariance, the sum of the edge attribute values, $A$, for each edge connecting the ith and jth nodes, or $\text{edgecov}=\sum A_{\mathit{ij}}$); researcher dyad attributes (node covariance, the sum of the nodal attribute value, $A$, for the incident nodes of edge, $E$, summed across all edges, $E_{\mathit{ij}}$, or $\mathit{\text{nodecov}}=\sum _{A\in E_{\mathit{ij}}}\left(A_i+A_j\right)$); differences, and by extension similarities, in dyads on continuous node attributes (absolute difference in the nodal attribute, $A$, between incident nodes of edge, $E$, summed across all edges, $E_{\mathit{ij}}$, or $\mathit{\text{absdiff}}=\sum _{A\in E_{\mathit{ij}}}\left|A_i-A_j\right|$ ); and matching and, by extension, mixing on categorical node attributes (node match, the sum of the number of edges whose incident nodes match on the value of a nodal attribute). We also introduced both geometrically weighted degree (GWD) and geometrically weighted edge‐wise shared partners (GWESP) to respectively account for the tendency of edges to concentrate among a small number of nodes, and triadic closure (A–B–C → A–C). ¹⁵ , ¹⁶

Edge covariance, node covariance, absolute difference, and node match are all generalized ERGM parameters that are used in conjunction with observed independent variables. We specified our STERGM to include the following independent variables: publication count, affiliation (UF, USC, or FAMU), and CaRE² role (trainees, key personnel, and non‐members). Author's publication count was assessed by taking the frequency that each author's ID occurs in the dimensions.ai publication dataset. Both affiliation and CaRE² roles were tracked and reported by CaRE² as part of their membership roster, merged onto the data collected from dimensions.ai. We confirmed the institutional affiliations for all authors by cross‐referencing CaRE² institutional affiliation data with dimensions.ai affiliation data. Publication count was introduced as both node covariance and absolute difference terms, controlling the overall productivity of investigators. Although it may seem counterintuitive, introducing both node and absolute difference terms for the same attribute does not violate independence assumptions or lead to overfitting. ¹⁷ Affiliation and CaRE² roles were both introduced as a node match terms as well as multiple, Boolean node covariance terms, to ascertain their relationship to the development of the CaRE² network. Finally, we introduced two edge covariance terms, the first represented co‐authorship of at least one publication tagged with the “cancer” concept in dimensions.ai, and the second represented co‐authorship of at least one publication that explicitly acknowledged CaRE² funding. Both key concepts and funding were collected by dimensions.ai. The cancer concept is appended to a publication when it evokes the term “cancer,” or some other semantically related term, in the abstract or title. Funding sources are included in the publication metadata indexed by dimensions.ai and are collected directedly from the acknowledgments and funding sections of papers. Given that we controlled productivity, affiliation, and CaRE² role, these edge covariance terms assessed whether collaboration on cancer research and/or CaRE² funding was associated with the formation and persistence of cross‐institutional collaboration between key personnel and trainees – a CaRE² effect.

RESULTS

The 110 CaRE² affiliates authored a total of 2141 publications (indexed by dimensions.ai) between 2018 and 2022 (including journal articles, book chapters, conference proceedings, preprints, monographs, and edited books.). As shown in Table 1, the CaRE² collaboration network grew between the 2018–2019 and 2020–2021 waves, accruing more external collaborators, and publishing more collaborative works, evidenced in the SNA as a denser network with more edges. The 2022–2023 wave is on track to continue this growth trajectory on all three of these measures (nodes, edges, and external collaborators).

TABLE 1.

Collaboration network of CaRE² members and collaborators: number of nodes, edges, and external collaborators across time.

Collaboration network measure	2018–2019	2020–2021	2022 a
Nodes	2646	3274	1811
Edges	18,510	23,622	12,110
External collaborators	2569	3186	1728

^a On track for 2022–2023 to be larger than 2020–2021.

Centrality measure: Degree

Degree centrality of key personnel was stable in each wave of the networks visualized in Figures 1 and 2. CaRE² key personnel averaged a total of 60.8 collaborators in 2018–2019 (SD = 57.4, minimum = 3, maximum = 221), and 65.8 collaborators in 2020–2021 (SD = 56.06, minimum = 4, maximum = 222). Key personnel seem to be on track to continue this trend, averaging a total of 34.05 collaborators in 2022 (SD = 36.35, minimum = 3, maximum = 138). The average degree centrality of trainees increased from 20.9 (SD = 17.9, minimum = 1, maximum = 72) in 2018–2019 to 32.7 (SD = 30.64, minimum = 4, maximum = 158) in 2020–2021. This positive trend in 2022 continued, averaging the same number of unique collaborators in a single year (mean = 20.6, SD = 14.44, minimum = 4, maximum = 55) as they did in 2018–2019. Given that the average number of unique co‐authors increased at similar rate across all three institutions from the 2018–2019 network to the 2020–2021 network (5.7 < δ _degree < 13.85), this growth in the trainees did not appear to be concentrated at any one institution. Although, it should be noted that the relative growth of FAMU was especially pronounced, increasing from 12.55 in 2018–2019 to 18.25 in 2020–2021, a 45.4% increase relative to a 26.3% increase at USC (52.68 → 66.52) and 16.3% at UF (44.59 → 51.87).

Centrality measure: Betweenness

Given that the collaboration networks appeared to be growing from wave‐to‐wave (including in the still‐growing 2022–2023 wave), we calculated normalized betweenness centrality, ensuring that comparisons across networks accounted for the size differential described in Table 1. Betweenness was largely stable across all groups and waves. The only exception was a cross‐institutional comparison among UF, USC, and FAMU. UF and USC averaged between a low of 0.021 (UF 2020–2021 SD = 0.025, minimum = 0, maximum = 0.1) and a high of 0.033 (USC 2020–2021 SD = 0.052, minimum = 0, maximum = 0.21). Generally, USC scored slightly higher on betweenness than the other two institutions, which was not especially surprising as the brokers for west coast collaborators. Surprisingly, despite their clearly central position in Figure 1, FAMU scored much lower on betweenness centrality (mean ≈ 0.006, SD ≈ 0.012, minimum = 0, maximum = 0.046), and the FAMU CaRE² affiliates, on average, boasted fewer collaborators, whereas the UF and USC CaRE² affiliates were disproportionately represented among these collaborators. In this instance, FAMU may have occupied a core position within the network, but the shortest paths across the network would have favored the better connected UF and USC scholars. Therefore, FAMU may have helped broker transitive relationships between UF and USC (i.e., UF–FAMU–USC → UF–USC), then these triadic closures placed both UF and USC on the shortest path(s).

Co‐authorship relationships among CaRE² members

Narrowing focus from CaRE² in the context of its many external collaborators to the co‐author relationships between CaRE² affiliates (Figure 3), we observed a steady decline in transitivity, the probability that a pair of CaRE² co‐authors shared a third co‐author, from 0.74 in 2018 to 0.47 in 2022. This finding implies that there was a decreasing tendency toward triadic closure. Nevertheless, given that no less than half of all triads in the network were closed (i.e., A–B–C → A–C) in any given wave, we deemed it necessary to introduce a GWESP term to our STERGMs to explicitly model and control this type of clustering when analyzing the effect of CaRE² funding on the development of the CaRE² network.

Assortativity by role in the CaRE² center (key personnel and trainee) remained steady, starting at 0.03 in 2018 and ending at 0.08 in 2022, briefly peaking at 0.25 in 2020. Given that values approaching 1 indicate a greater tendency for collaboration between members with the same role, it is likely that this peak was attributable to one or more publications with a large proportion of key personnel contributors. However, the center generally seemed to maintain a reasonably balanced number of intra‐ and inter‐role collaborations (an assortativity of around 0). Assortativity by institution ranged from a minimum of 0.19 in 2020 to 0.92 in 2019, which is indicative of a strong tendency for intra‐institutional collaboration. However, these networks included all co‐authored publications, not just CaRE² funded publications.

Degree centralization peaked at 0.21 in 2020 (min₂₀₂₁ = 0.06), coinciding with the lowest observed institutional assortativity score, whereas betweenness centralization peaked at 0.12 in 2022 (min₂₀₁₉ = 0.02). This finding implies that there was an occasional tendency for the CaRE² network to coalesce around a small number of highly central investigators. The use of STERGMs allowed control of the influence of highly productive, well‐connected investigators who had a disproportionate influence on the network's structure.

Evolution of the CaRE² network and the CaRE² effect

Table 2 presents the STERGM results. Each model consists of two, separate regressions predicting either: Form, as in edge formation (the introduction of a new collaborative edge between the ith and jth researcher when moving from wave $n-1$ to wave $n$); or Persist, as in edge persistence (the continuation of an existing collaborative edge between the ith and jth researcher when moving from wave $n-1$ to wave $n$). Model 1 presents form and persist models specified to include all observed nodal attributes (publication count, institutional affiliation, and grant role). Model 2 introduces network characteristics, specifically GWESP and GWD, to control the influence of centralization (GWD) and triadic closure (GWESP) on our edge formation (form) parameter estimates – these measures resulted in model degeneracy when concurrently introduced into the edge persistence (persist) model, ¹⁸ leading to their exclusion. Nevertheless, we observed a steep decline in both Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) with the introduction of these measures, which capture aspects of the network that we had already observed in the descriptive statistics. Model 3 introduces the first observed edge attribute, a binary indicator as to whether each collaboration between authors is cancer research. The introduction of this measure resulted in a very small reduction in AIC (2144 → 2138), whereas BIC increased slightly (2294 → 2304). This slightly lower AIC but slightly higher BIC is consistent with the marginally significant coefficients reported in Table 2. Finally, model 4 introduces the second observed edge attribute, a binary indicator of CaRE² funding. Unlike model 3, we observed a consistent, marginal reduction in both AIC and BIC upon the introduction of this measure.

TABLE 2.

Separable Temporal Exponential Random Graph Model (STERGM) predicting the formation and persistence of CaRE² co‐authorships. ¹²

	Model 1		Model 2		Model 3		Model 4
	Form	Persist	Form	Persist	Form	Persist	Form	Persist
Edges (intercept)	−6.633*** (0.352)	−3.498** (1.315)	−6.872*** (0.348)	−3.441* (1.338)	−6.888*** (0.353)	−3.429* (1.414)	−6.934*** (0.36)	−3.316* (1.347)
Edge covariance
Cancer collab.					0.781† (0.463)	2.290* (1.117)
CaRE2 funded							2.723*** (0.607)	2.565* (1.047)
Node covariance
Publication count	0.011*** (0.002)	0.02* (0.01)	0.005*** (0.001)	0.02* (0.01)	0.005** (0.001)	0.015 (0.01)	0.005** (0.001)	0.019† (0.01)
UF affiliate	−0.06 (0.12)	−1.125† (0.63)	−0.179* (0.088)	−1.118† (0.629)	−0.171† (0.091)	−1.051† (0.624)	−0.177* (0.09)	−1.149† (0.628)
USC affiliate	−0.443** (0.136)	−1.054 (0.684)	−0.318** (0.104)	−1.048 (0.69)	−0.312** (0.104)	−1.106 (0.703)	−0.319** (0.103)	−1.196† (0.717)
Key personnel	0.852*** (0.182)	−0.644 (0.617)	0.414* (0.163)	−0.637 (0.619)	0.423** (0.163)	−0.475 (0.692)	0.446** (0.164)	−0.663 (0.636)
Trainee	0.376* (0.185)	−0.153 (0.696)	0.202 (0.153)	−0.174 (0.684)	0.199 (0.154)	−0.241 (0.739)	0.227 (0.159)	−0.394 (0.733)
Absolute difference
Publication count	0 (0.002)	−0.003 (0.011)	0.002 (0.002)	−0.003 (0.011)	0.002 (0.002)	0.001 (0.011)	0.002 (0.002)	−0.003 (0.011)
Node match
Institution	1.371*** (0.136)	1.831* (0.725)	1.218*** (0.123)	1.821* (0.726)	1.214*** (0.123)	1.927* (0.764)	1.215*** (0.123)	1.913* (0.759)
Grant role	0.564** (0.171)	0.307 (0.758)	0.516** (0.17)	0.286 (0.765)	0.515** (0.17)	−0.112 (0.837)	0.52** (0.169)	0.191 (0.749)
GWESP (fixed,0.25)			1.696*** (0.131)		1.696*** (0.135)		1.707*** (0.134)
GWD (fixed,0.5)			0.008 (0.185)		0.017 (0.192)		0.03 (0.187)
AIC	2471		2144		2138		2125
BIC	2607		2294		2304		2291

Note: Reported coefficients are log‐odds of the formation and persistence of an edge between the ith and jth node. Standard errors reported in parentheses.

Abbreviations: AIC, Akaike Information Criterion; BIC, Bayesian Information Criteria; CaRE², Florida‐California Cancer Research, Education & Engagement; FAMU, Florida A&M University; GWD, geometrically weighted degree; GWESP, geometrically weighted edge‐wise shared partners; UF, University of Florida Cancer Center; USC, University of Southern California Norris Comprehensive Cancer Center.

^† p < 0.1; *p < 0.05; **p < 0.01; ***p < 0.001.

Following STERGM estimation, we used igraph's goodness‐of‐fit functionality to generate 100 simulated networks for comparison to the observed network. ⁸ Each graph presented in Figure 4 visualizes the extent that the STERGM accurately predicted the observed network's attributes and characteristics by comparing the observed distribution on a set of network properties with the simulated distribution on the same properties. ¹⁹ We observed acceptable, albeit imperfect goodness‐of‐fit (Figure 4). Simulations tended to perform well – indicated by overlap between simulated and observed network(s) – for the middle and upper values of incident edge count (degree), edge‐wise shared partners (ESPs), and minimum geodesic distance. However, the lower bounds of degree and ESP were underestimated, whereas lower bounds of minimum geodesic distance were overestimated. Similarly, observed values on the model parameters generally appeared to be higher than the simulated model parameters. This finding is likely indicative of additional, unobserved variables contributing to investigators' collaboration practices, which is not especially surprising given the limited number of variables available for this analysis.

FIGURE 4.

Goodness‐of‐fit statistics for model 4, Table 2. Observed and simulated distributions are visualized for nodal degree (a), edge‐wise shared partnership (triadic closure) (b), and geodesic distance between the ith and jth nodes (c). Blue rhombi represent simulated expected values, box plots present the full range of simulated values, and solid black lines present the observed distribution. CaRE², Florida‐California Cancer Research, Education & Engagement; FAMU, Florida A&M University; UF, University of Florida Cancer Center; USC, University of Southern California Norris Comprehensive Cancer Center.

Per model 1 (Table 2), the predicted probability of forming a new cross‐institutional co‐authorship between key personnel and trainee was somewhat low at 0.001, whereas the probability of persistence was a moderate 0.03. Contrary to our descriptive analyses, model 2 (Table 2) suggests that both UF and USC affiliates were actually significantly less likely to form new co‐authorships (β _UF = −0.179, p < 0.05; β _USC = −0.318, p < 0.01) compared with FAMU affiliates, after accounting for author productivity (publication count), covariance and matching on grant role (key personnel and trainee), intra‐institutional collaboration, and the networks' tendency for centralization (GWD) and triadic closure (GWESP). This finding supported our hypothesis that FAMU scholars acted as brokers for relationships between UF and USC scholars. Of the three institutions, USC was generally the least likely to form new collaborative ties (−0.443 < β _USC < −0.312). However, curiously enough, there appeared to be a slightly reduced likelihood that co‐authorship with UF affiliates persisted over multiple network waves (−1.149 < β _UF < −1.051, p < 0.1). We observed a very strong tendency for the formation and maintenance of intra‐institutional collaborative ties between investigators (β _form = 1.218 p < 0.001; β _persist = 1.821 p < 0.05). Intra‐institutional co‐authorship was three times more likely than cross‐institutional co‐authorship. Key personnel were more likely to establish new co‐authorship ties in the network (model 1: β _KP = 0.852 p < 0.001). This effect was partially explained by the tendency of key personnel to occupy central positions within the network, controlled via the GWD term (model 2: β _KP = 0.414 p < 0.05).

We observed marginally increased likelihood of tie formation between investigators that share the same role in the CaRE² grant (model 2: β = 0.516 p < 0.01). However, this could be attributable to the on‐boarding and integration of new key personnel and a tendency for trainees to work on the same project(s). We found that collaborations on publications tagged by dimensions.ai with the “cancer” concept were far more likely to persist in subsequent network waves (model 3: β = 2.290, p < 0.05). According to model 3 (Table 2), the baseline‐predicted probability of tie persistence was 0.03. Whereas the predicted probability of tie persistence following cancer research was 0.24. This estimate implies that one‐quarter of all co‐publications tagged by dimensions.ai with the “cancer” concept persisted into a subsequent wave.

However, most importantly, we observed a similarly strong relationship between explicit acknowledgement of the CaRE² grant, tie formation (Table 2; model 4: β = 2.723, p < 0.001), and tie persistence (model 4: β = 2.565, p < 0.05). According to model 4, the probability of tie persistence at the intercept was 0.035. After controlling institutional affiliation, intra‐institutional collaboration, grant role, intra‐role collaboration, triadic closure, and network centralization, the predicted probability of tie persistence in CaRE² funded co‐authorship ties was 0.32. In other words, we estimate that nearly one‐third of CaRE² funded co‐authorship ties followed with co‐authorship in a subsequent network wave.

DISCUSSION

During the project period, the CaRE² Health Equity Center's Planning and Evaluation Core used SNA as one approach to evaluate and characterize team science outcomes. The SNA of publications authored by CaRE² Center's trainees, leaders, and investigators revealed that we have increased cohesion and productivity from 2018–2019 to 2020–2021 with similar trends projected for 2022–2023. The CaRE² network became more decentralized and less reliant on a small number of highly connected network brokers. Center authors have worked with more unique collaborators and less with their original collaborators, which was expected as the CaRE² Center grew and each individual expanded their network as a result of the work that was initiated through the Center. We also have progressed in cross‐institutional scholarship.

The reasons are unclear why the CaRE² external collaborations increased and became denser with more edges. It is possible that as projects and cores focused on initiation of the research and traveled less during the pandemic, the key personnel completed and published work started before the U54 funding and with external collaborators while also integrating trainees into the final work. In addition, it is possible that CaRE² key personnel were recognized for their novel work and sought out by other investigators in the cancer health disparities research space.

The finding that the CaRE² Center's network has become more decentralized and less reliant on a small number of highly connected network brokers suggests growth in new collaborations and indicates reduced risk to the Center's productivity if the highly central scholars move or retire. Therefore, the decentralization increases some degree of resilience when it comes to member turnover within a team science framework.

The fact that URM trainees and ESIs have been well integrated into the “core” of the network, as indicated by the centrality measures, and nearly one‐third of CaRE² funded co‐authorship ties were followed up with co‐authorship in subsequent years are indicators that the CaRE² Center has been successful in stimulating team science supportive of research workforce diversification. The strong CaRE² Center focus on workforce development was evident by the co‐authorship with more trainees/ESIs and the persistence of publications with trainees and center members. Particularly striking was the impact on FAMU trainees and ESIs with a 45% relative increase from 2018–2019 to 2020–2021 at FAMU whereas the relative increase was 26% at USC and 16% at UF. The CaRE² publication policies valuing publishing with trainees and its mission emphasis on enhancing cancer research capacity at FAMU likely contributed to this impact. Furthermore, it is important that nearly one‐quarter of cancer‐related co‐authored publications and nearly one third of CaRE² grant acknowledged co‐authorship ties persisted into a subsequent wave. These increases and persistence were desired, important outcomes of the CaRE² Center's focus on FAMU and creating the cross‐institution infrastructure as well as the research workforce diversity that will be necessary to eliminate cancer health disparities. Therefore, the impact is consistent with the goals of the CPACHE program ²⁰ and the SNA provides evidence of CaRE²'s success toward the goals.

The SNA findings indicated that UF and FAMU appear to be well integrated, but there was a notable division between the Florida institutions and USC, and FAMU brokered the co‐authorship between UF and USC. Of the three institutions, USC was generally the least likely to form new collaborative ties with the Florida institutions, which is likely a result of challenges associated with their physical distance from UF and FAMU, and perhaps a reflection of the fact that UF and FAMU had established ties during the planning grant (P20CA192990) between UF and FAMU, thus USC had overall less time in the partnership than the other institutions. This information suggests that additional incentives and facilitation opportunities should be considered to encourage cross‐institutional publications, especially between California and Florida.

CONCLUSIONS

The SNA findings suggest that the CaRE² Health Equity Center has made significant progress during its first funding cycle to establish a bicoastal, tri‐institutional team science partnership that persisted and integrated URM trainees and ESIs. Specifically, the partnership's publications show growth in team science collaborations with the inclusion of multidisciplinary team members from the three partner institutions and future URM cancer researchers who were mentored as trainees and ESIs. Our findings illustrate the application of SNA approaches to monitor progress of team science efforts and provide insights for strengthening the CaRE² Center's impact through its policies and infrastructure initiatives.

AUTHOR CONTRIBUTIONS

M.O.E., T.B.S., D.J.W., J.R., U.D.S., M.C.S., and R.R.R. wrote the manuscript. D.J.W., M.C.S., and R.R.R. designed the research. M.O.E., T.B.S., D.J.W., J.R., U.D.S., M.C.S., and R.R.R. performed the research. T.B.S. analyzed the data.

FUNDING INFORMATION

This research was made possible by Grant Numbers U54CA233396, U54CA233444, U54CA233465 from the National Institutes of Health (NIH), National Cancer Institute (NCI) and by the University of Florida Clinical and Translational Science Institute, which is supported in part by the NIH National Center for Advancing Translational Sciences under award number UL1TR001427. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the NIH or NCI. The final peer‐reviewed manuscript is subject to the National Institutes of Health Public Access Policy.

CONFLICT OF INTEREST STATEMENT

D.J.W. received a grant from Pfizer for an unrelated study and is Chairman and Founder of eNURSING LLC. All other authors declared no competing interests for this work.

Ezenwa MO, Smith TB, Richey J, et al. Social network analysis of the CaRE² health equity center: Team science in full display. Clin Transl Sci. 2024;17:e13747. doi: 10.1111/cts.13747