Appendix

Appendix A: Decision Tree for classifying HCFO-CDIs

Figure A1 displays the decision tree used to classify patient visits. Since only admission month, discharge month, length of stay and time between visits are given, visits with a length of stay (LOS) greater than 30 days made it too uncertain whether the time at which the patient was infected with C. difficile overlapped with other patient visits, and hence we excluded such patients. Following [Reference Gupta and Khanna25–27], any CDI visits with a LOS of 3 days or fewer were considered community acquired and were not included as cases (HCFO-CDIs) in our analysis; we therefore also excluded non-CDI visits with LOS ≤3. Any CDI visits which had either a primary CDI diagnosis or a present on admission tag associated with the CDI diagnosis were also considered to be community acquired, unless the patient had another hospital visit within the past 4 weeks, in which case they were considered to have a community-onset healthcare-associated CDI [Reference Gupta and Khanna25]; both types of patient visits were excluded from our cohort. We defined a readmission to be a CDI visit which had a previous CDI visit within the last 12 weeks. We did not include readmissions as cases in our statistical analysis, and hence we also excluded from our set of potential matched controls those non-CDI visits which had a previous CDI visit within the last 12 weeks. However, we treated CDI visits which were patient transfers specially, where a patient transfer was defined to be a visit with an admission date equal to a discharge date of a previous visit; see Appendix B for more details on transfer patients.

Fig. A1.

A tree illustrating how inpatient visits were classified in the study. LOS, length of stay; POA, present on admission tag or CDI was primary diagnosis; HCFO-CDI, healthcare-associated infection.

Appendix B: Constructing the CDI potential transmission networks

By looking at the location and time of each patient's visit, we constructed a network that corresponds to potential transmission events between patients. The exact time of each inpatient visit is not included in the HCUP SID due to privacy concerns. The information available for each visit includes the admission month, discharge month and length of stay. From these data, we computed the probability of each pair of inpatient visits being coincident in time and location. Let a _i and d _i denote the admission and discharge month, respectively, for the i ^th inpatient visit. For a pair of visits i and j which occurred at the same hospital facility, we considered the following eight scenarios:

1. 1. a _i = d _i = a _j = d _j, i.e. the i ^th and j ^th visits took place entirely within the same month.

2. 2. a _i  + 1 =  d _i  =  a _j  =  d _j, i.e. i's visit spanned two distinct months, while j's visit spanned only the month in which i was discharged.

3. 3. a _i = d _i − 1 = a _j = d _j, i.e. i's visit spanned two distinct months, while j's visit spanned only the month in which i was admitted.

4. 4. a _i = d _i = a _j + 1 = d _j, i.e. j's visit spanned two distinct months, while i's visit spanned only the month in which j was discharged.

5. 5. a _i = d _i = a _j = d _j − 1, i.e. j's visit spanned two distinct months, while i's visit spanned only the month in which j was admitted.

6. 6. a _i + 1 = d _i = a _j + 1 = d _j, i.e. both i's and j's visits spanned two distinct months, and both visits were admitted in the same month and discharged in the same month.

7. 7. a _i + 1 = d _i = a _j = d _j − 1, i.e. both i's and j's visits spanned two distinct months, and j was admitted in the same month that i was discharged.

8. 8. a _i = d _i − 1 = a _j + 1 = d _j, i.e. both i's and j's visits spanned two distinct months, and i was admitted in the same month that j was discharged.

Graphically, these scenarios can be viewed as shown in Figure A2.

Fig. A2.

A depiction of the eight possible scenarios for how two inpatient visits could intersect in time at a given hospital.

Let N _k denote the number of days in the k ^th earliest month of the set {a _i, d _i, a _j, d _j} according to the calendar year; e.g. if i was admitted in March and discharged in April, j was admitted in February and discharged in March, then N ₁ = 28, N ₂ = 31 and N ₃ = 30. Let ℓ_i denote the length of stay of the i ^th inpatient visit. Then assuming that any day in a month is just as likely to be the admission date as any other day in the same month, the probability that two visits i and j were coincident can be computed in the following way:

• • Scenario 1: ${{\mathop \sum \nolimits_{s = 1}^{N_1-\;\ell _j + 1} [ {\min ( {s + \ell_j-1, \;\;N_1-\ell_i + 1} ) -\max ( {1, \;s-\;\ell_i + 1} ) + 1} ] } \over {( {N_1-\ell_i + 1} ) ( {N_1-\;\ell_j + 1} ) }}$

• • Scenario 2: ${{\mathop \sum \nolimits_{s = N_1 + 1}^{\min ( {N_1 + N_2-\ell_j, \;N_1 + \ell_i-1} ) } [ {N_1-\max ( {N_1-\;\ell_i + 2, \;s-\;\ell_i + 1} ) + 1} ] } \over {( {\ell_i-1} ) ( {N_2-\;\ell_j + 1} ) }}$

• • Scenario 3: ${{\mathop \sum \nolimits_{s = N_1-\;\ell _i + 2}^{N_1} [ {N_1-\;\ell_j + 2-\max ( {1, \;s-\;\ell_j + 1} ) } ] } \over {( {\ell_i-1} ) ( {N_1-\;\ell_j + 1} ) }}$

• • Scenario 4: Similar to Scenario 2.

• • Scenario 5: Similar to Scenario 3.

• • Scenario 6: Always equal to 1.

• • Scenario 7: If N ₁ + N ₂ − ℓ_j + 2 ≤ N ₁ +  ℓ_i − 1, then ${{\mathop \sum \nolimits_{s = N_1 + N_2-\ell _j + 2}^{N_1 + \ell _i-1} [ {N_1-( {s-\ell_i} ) } ] \;} \over {( {\ell_i-1} ) ( {\ell_j-1} ) }}$, else 0.

• • Scenario 8: Similar to Scenario 7.

Using these rules, we constructed a network for all HCFO-CDIs as determined by the decision tree in Figure A1. Controls matched to our cases which were taken from the pool of potential controls identified by the decision tree were also included in the graph. However, visits corresponding to controls were assigned zero out-degree, i.e. no edges emanated from any control as they had no CDI diagnosis. All visits belonging to the other five classifications shown in Figure A1 were included in the network. Community-acquired infections were assigned zero in-degree, as they acquired CDI outside of the hospital. Readmissions had an in-degree of 1, with this single unit of in-degree attributed to the prior CDI visit corresponding to their readmission visit. For community-onset healthcare-associated infections, we computed their in-degree using all visits preceding the index visit which took place entirely (i.e. both admission and discharge) within the prior 4 weeks; for simplicity, we assumed independence between the prior visits in this computation. These previous visits were not used when computing their out-degree.

The computation of in-degree and out-degree was most involved for transfer patients. These patients' consecutive visits were viewed as a single visit involving two facilities; however, we separately computed the in-degree and out-degree for the two visits, respecting the facilities involved for each visit. Each transfer patient was assigned to one of six possible cases based on CDI diagnoses and indication of CDI being present on admission (POA) (either through a specific present on admission tag associated with the CDI diagnosis or by the CDI being a primary diagnosis). These cases, detailed in Table A1, dictated how we computed the in-degrees and out-degrees for the two visits comprising the transfer. For example, the first row of the table represents the case where a transfer patient had no CDI diagnosis in his/her first visit and then had CDI diagnosed as present on admission in his/her second visit. Such a patient only had the potential for non-zero in-degree in his/her first visit, and only had the potential for non-zero out-degree in his/her second visit.

Table A1.

The six possible cases for transfer patients along with the visits that their in-degrees and out-degrees could be non-zero for