Estimating the impact of physician risky-prescribing on the network structure underlying physician shared-patient relationships

Abstract

Social network analysis and shared-patient physician networks have become effective ways of studying physician collaborations. Assortative mixing or "homophily" is the network phenomenon whereby the propensity for similar individuals to form ties is greater than for dissimilar individuals. Motivated by the public health concern of risky-prescribing among older patients in the United States, we develop network models and tests involving novel network measures to study whether there is evidence of geographic homophily in prescribing and deprescribing in the specific shared-patient network of physicians linked to the US state of Ohio in 2014. Evidence of homophily in risky-prescribing would imply that prescribing behaviors help shape physician networks and could inform interventions to reduce risky-prescribing (e.g., should interventions target groups of physicians or select physicians at random). Furthermore, if such effects varied depending on the structural features of a physician's position in the network (e.g., by whether or not they are involved in cliques - groups of actors that are fully connected to each other - such as closed triangles in the case of three actors), this would further strengthen the case for targeting of select physicians for interventions. Using accompanying Medicare Part D data, we converted patient longitudinal prescription receipts into novel measures of the intensity of each physician's risky-prescribing. Exponential random graph models were used to simultaneously estimate the importance of homophily in prescribing and deprescribing in the network beyond the characteristics of physician specialty (or other metadata) and network-derived features. In addition, novel network measures were introduced to allow homophily to be characterized in relation to specific triadic (three-actor) structural configurations in the network with associated non-parametric randomization tests to evaluate their statistical significance in the network against the null hypothesis of no such phenomena. We found physician homophily in prescribing and deprescribing in both the state-wide and multiple HRR sub-networks, and that the level of homophily varied across HRRs. We also found that physicians exhibited within-triad homophily in risky-prescribing, with the prevalence of homophilic triads significantly higher than expected by chance absent homophily. These results may explain why communities of prescribers emerge and evolve, helping to justify group-level prescriber interventions. The methodology could be applied to arbitrary shared-patient networks and even more generally to other kinds of network data that underlies other kinds of social phenomena.

Keywords: Deprescribing; Homophily; Quantifying polypharmacy; Risky prescribing; Shared-patient physician network; State-space; Transition matrix.

Fig. 1

Study cohort definition and workflow. Note: Beneficiaries were included in the study if they had at least 3 months of continuous coverage of Medicare Parts A, B, and D, and 2 years of continuous parts A and B coverage prior to cohort entry. LCC = largest connected component.

Fig. 2

Illustrative computation of triadic homophily statistics ${Tri}_1(\mathbf{a},\mathbf{x})$ and ${Tri}_2(\mathbf{a},\mathbf{x})$. Suppose nodes A, B, C, and D are physicians who have contributed to risky prescribing, and nodes E and F are non-risky-prescribing physicians. The number of risky 2-stars with nodes A, B, C, and D being the center vertex is 1, 3, 1, and 0, respectively. Therefore, the total number of 2-stars among risky prescribing physicians is five.

Fig. 3

Workflow of modeling patient prescription states. Note: The left-hand panel (L) shows a made-up example of a patient’s sequence of prescription fills with their corresponding drug class. The center panel (C) shows the counting process to split the sequence of prescription fills into discrete exposure time intervals that reflect the initialization and the discontinuation of a prescription fill. The red line indicates the prescription fill length of the opioid in panel (L), and the blue line indicates the benzodiazepine (BZD) fill length. The right-hand panel (R) shows the corresponding prescription state during each time interval in panel (C) and the transition between them, forming a trajectory of prescription states across time. “O” stands for filling an opioid, “B” stands for filling a BZD, and “OB” stands for filling an opioid and a BZD concurrently.

Fig. 4

Prescribing measures by specialty of physicians in the largest connected component of the shared-patient prescribing physician Ohio network in 2014. Specialists are medical specialists other than surgeons. Hospital-based services include anesthesiology, radiology, and pathology. PCP denotes primary care physicians. $I_{OBS}$ is the prescribing index based on a physician’s contribution to bringing patients to prescription state $OBS$, $I_{\mathit{presc}2mr}\left(I_{\mathit{depresc2mr}}\right)$ is the prescribing index based on a physician’s contribution to prescribing (deprescribing) two or more drug types to patients. Error bars show the standard errors of the respective measures.

Fig. 5

Egocentric network of the physician with maximum node degree (N = 276) in the LCC of the prescribing network. The ego physician was removed from the plot for the clarity of presentation. The ties shown in the plots are among the peers of the ego physician. The nodes are sized by physician annual volume (the number of distinct patients treated throughout the year). The colors of nodes correspond to their prescribing behavior or specialties. A) The connections among physicians are distinguished by whether they have ever contributed to bringing patients to the riskiest prescription state (the $OBS$ state). B) The connections among physicians where the node color represents the value of $I_{OBS}$, the proportion of times they bring their patients to prescription state $OBS$. C) The connections among physicians where the node color represents $I_{\mathit{pres}{\mathit{c}}_{2}mr}$, the proportion of prescribing events when two or more drugs are prescribed at once to the patients. D) The connections among physicians where the node color represents $I_{\mathit{depres}{\mathit{c}}_2\mathit{mr}}$, the proportion of deprescribing events at which two or more drugs are deprescribed at once to the patients. E) The connections among physicians are colored by their specialties.

Fig. 6

Histogram of triadic homophily network statistics generated by the non-parametric test for triadic homophily. The triadic homophily statistic ${Tri}_1(\mathbf{a},\mathbf{x})$ is the proportion of closed triangles in the network in which each node has the $I_{\mathit{ever}OBS}$ node attribute, reflecting whether a physician has ever contributed to bringing patients to the riskiest prescription state $OBS$. The triadic homophily statistic ${Tri}_2(\mathbf{a},\mathbf{x})$ is the proportion of open two-paths with all nodes having the same attribute that are closed in the network. Panel (a) is the histogram of ${Tri}_1(\mathbf{a},\mathbf{x})$ and panel (b) is the histogram of ${Tri}_2(\mathbf{a},\mathbf{x})$ calculated from 30 networks with randomly shuffled node attributes under the null hypothesis of no homophily with respect to the given prescribing index. The red vertical lines denote the values in the observed network.