Methods

Our analysis was based on a fine-grained dataset we assembled on operations at the University of Iowa Hospitals and Clinics (or UIHC, a 700-bed comprehensive academic medical and regional referral center in Iowa City) from January 2005 through December 2011. The dataset contains both architectural and in-patient data: admission, discharge, and transfer records; diagnostic codes; and clinical test results. We constructed the set of CDI cases for in-patients by extracting (1) the date of positive CDI diagnosis and (2) the patient’s room in the hospital at the time of positive CDI test. CDI diagnosis was determined via laboratory test. A C. difficile toxin test was used during January 2005–April 2008; a C. difficile toxin A and B test was used during May 2008–December 2009, and a C. difficile toxin PCR test was used thereafter. Formally, a CDI case can be viewed as a triple (p, r, d) where p is a patient, r is a room in the hospital, and d is a day in the period (January 2005–December 2011) such that patient p tested positive for CDI on day d while occupying room r. Our dataset included 1,963 total CDI cases.

To determine whether these CDI cases exhibited spatiotemporal interaction and clustering, we sought to accurately estimate the distance between pairs of rooms in the hospital. Starting with architectural drawings, we “discretized” the UIHC hospital space and constructed a hospital graph. The results from this discretization process have also been reported elsewhere.Reference Curtis, Hlady, Kanade, Pemmaraju, Polgreen and Segre²⁵ Each room in the hospital is represented by a node (larger spaces, such as hallways, are subdivided into smaller room-sized polygons represented as individual nodes), and edges (or hops) are added between pairs of nodes corresponding to spatial units between which direct physical passage is possible. Each edge (hop) corresponds to a walking distance of 5–6 m. Edges respect architectural barriers (eg, walls), so 2 adjacent rooms that do not share a doorway are not connected by an edge. The hospital graph comprised 18,961 nodes and 23,442 edges. The hospital graph imposes a distance metric on the UIHC space, and distances along the shortest paths in this graph correspond to the shortest walking distances in the UIHC space (Fig. 1).

Fig. 1.

Each path in the hospital graph from a node s to a node t corresponds to a valid walking route in the hospital from the spatial unit corresponding to node s to the spatial unit corresponding to node t. For example, the top figure shows 2 rooms, 4082-A and 4049, whose shortest path distance in the UIHC graph is 11 hops (a hop is an edge in the hospital graph). The bottom figure shows rooms 4082-A and 4084, whose shortest path distance in the UIHC is 3 hops.

Our analysis was based on spatiotemporal interaction and clustering tests, all of which correct for solely spatial or solely temporal effects. Among these tests, 3 were performed using a CDI case proximity graph, consisting of nodes representing CDI cases and edges connecting 2 nodes if they occurred within T days and within distance D in the hospital graph of each other, where T ≥ 0 and D ≥ 0 were integer parameters (Fig. 2).

Fig. 2.

$CPG_{(14,5)}^{CDI,obs}$: CDI case proximity graph for T = 14 days and path length of D = 5 ($\le 30$ m). The graph contains 1,963 nodes, corresponding to CDI cases at the UIHC during January 2005– December 2011. Its 682 edges correspond to pairs of cases occurring with 14 days and distances of no more than 5 hops ($ \le 30$ m) from one another. The resulting CDI case proximity graph contains 1,519 components, 1,229 of which are single nodes. The mean component size is 1.29 and the maximum component size is 11. A component of size 11 is enlarged and shown on the left. The CDI cases in this component occurred over a roughly 2-month period (April 30–June 21, 2010) in the GMed (4JPE) unit; 9 of these cases occurred in a “pod” of 7 adjacent patient rooms, whereas 2 occurred in a single-patient room in a separate “pod.”

We used the Knox test to compare the observed number of pairs of CDI cases that occurred both within T days and within distance D of each other to the distribution of the number of pairs of cases within these time and distance thresholds of each other, conditioned on the absence of spatiotemporal interaction.Reference Knox²⁶ In other words, we compared the number of edges in the observed CDI case proximity graph, denoted $CPG_{(T,D)}^{CDI,obs}$, to the distribution of the number of edges in a random CDI case proximity graph denoted $CPG_{(T,D)}^{CDI,rand}$. To calculate this distribution, we ran Monte Carlo simulations with the time stamps of cases randomly permuted. Notably, permuting the time stamps left purely spatial correlations and purely temporal correlations intact while disrupting the joint spatiotemporal structure. We used extensions of the Knox test to explicitly test for other aspects of spatiotemporal structure. To test for burstiness, an important facet of infection diffusion involving periods of significant activity followed by periods of inactivity, we implemented the mean component size test.Reference Takaguchi, Masuda and Holme^{27,Reference Akbarpour and Jackson28} A component in the CDI case proximity graph is a maximal set of cases that are all reachable from each other via paths composed of edges in the graph. A graph can have many components, and in the mean component size test, we compared the mean size of components in $CPG_{(T,D)}^{CDI,obs}$ to the distribution of mean component size of $CPG_{(T,D)}^{CDI,rand}$. As in the Knox test, we used Monte Carlo simulations with the time stamps randomly permuted to calculate these expectations. The maximum component size test was similar (see Appendix A online). Finally, we also performed the Mantel test,Reference Mantel³⁰ in which we computed the Pearson correlation between the spatial and temporal distance matrices of the CDI cases and compared this with the correlation between a randomly permuted spatial distance matrix and the (unpermuted) temporal distance matrix. If the 2 observed distance matrices had high correlation, then randomization would result in correlation that was consistently smaller.

As a counterfactual experiment, and as a “stress test” for our approach, we repeated all of the tests just described on aspiration pneumonia, a complication that occurs when food, stomach acid, or saliva are inhaled into the lungs. Because aspiration pneumonia is not infectious, we expected to see very different results for aspiration pneumonia than for CDI. For the 6-year period between January 2007 and December 2013, 790 aspiration pneumonia cases were reported at UIHC. Unlike CDI, however, hospital records associate aspiration pneumonia with a hospitalization rather than a precise date of onset. Therefore, we used hospital prescription data to yield a proxy for an onset date. Starting from the list of antibiotics commonly used to treat aspiration pneumonia,Reference Bartlett^31–Reference Bowerman, Zhang and Waite³³ we defined the onset of aspiration pneumonia as the first time one of these antibiotics (Table 1) was prescribed for a patient diagnosed with aspiration pneumonia. This method yielded a total of 535 distinct aspiration pneumonia cases with associated time stamps; patient rooms were then determined based on the time stamps and were used to construct the observed aspiration pneumonia case proximity graph $CPG_{(T,D)}^{AP,obs}$.

Table 1.

Most Frequently Prescribed Antibiotics, Sorted by Frequency, for Patient Visit Records Marked with the Aspiration Pneumonia Complication Code During 2007–2013^a

^a A total of 790 patient visits were coded with aspiration pneumonia. Because some patients were prescribed >1 antibiotic from the list, the sum of the prescriptions (996) exceeds the number of aspiration pneumonia codes.