Social influence on 5-year survival in a longitudinal chemotherapy ward co-presence network

Chemotherapy is often administered in openly designed hospital wards, where the possibility of patient–patient social influence on health exists. Previous research found that social relationships influence cancer patient’s health; however, we have yet to understand social influence among patients receiving chemotherapy in the hospital. We investigate the influence of co-presence in a chemotherapy ward. We use data on 4,691 cancer patients undergoing chemotherapy in Oxfordshire, United Kingdom who average 59.8 years of age, and 44% are Male. We construct a network of patients where edges exist when patients are co-present in the ward, weighted by both patients’ time in the ward. Social influence is based on total weighted co-presence with focal patients’ immediate neighbors, considering neighbors’ 5-year mortality. Generalized estimating equations evaluated the effect of neighbors’ 5-year mortality on focal patient’s 5-year mortality. Each 1,000-unit increase in weighted co-presence with a patient who dies within 5 years increases a patient’s mortality odds by 42% (β = 0.357, CI:0.204,0.510). Each 1,000-unit increase in co-presence with a patient surviving 5 years reduces a patient’s odds of dying by 30% (β = −0.344, CI:−0.538,0.149). Our results suggest that social influence occurs in chemotherapy wards, and thus may need to be considered in chemotherapy delivery.

a patient scheduled to receive treatment on a Monday included the previous Friday and the 24 following Tuesday. Based on these assumptions, we determine how often each patient would 25 have overlapped with others conditional on when chemotherapy began. We observe with whom 26 overlap and for how long they overlap based on a random sample from the risk set, assuming the 27 periodicity of chemotherapy holds. By repeating this procedure 1000 times for each patient, we 28 create a patient-specific empirical distribution of overlap times, and draw a cutoff at the 99 th 29 percentile of this distribution, forming an edge between the focal actor and the other patient. 30 Formally, this can be written as: Where H(i) is the set of hours spent in the ward by patient i and Q99 is the 99 th percentile of that 33 patient's co-presence times with other patients based on the empirical distribution. For a visual 34 explanation of this method, see Figure S2. 35 Thus, an edge in this co-presence network is drawn between two patients when the 36 amount of time spent co-present in the ward is greater than the time at least one of the patients in 37 question spends with 99% of the risk set of patients randomly sampled. We will refer to the 38 edges in this network as an indicator of patients who are "consistently co-present". Unlike the patients are connected when at least one of them was consistently co-present with the other. The 46 resulting network is shown in Figure S3.

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Although the method to determine this network is stochastic, over 99% of the ties were 48 the same between runs, we create the network one time using 1000 samples of patient schedules.

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Using this network, we construct counts, for each focal patient, of the number of connected or 2-50 path patients who survive 5 years following their chemotherapy and the number of connected or 51 2-path patients who die within 5 years following their chemotherapy at the time the focal patient 52 finishes their chemotherapy. We then fit a GEE with these predictors and the same covariates as 53 in the main model (Table S1, Model A). Due to the dichotomous nature of the network, we also 54 observe a number of isolates (~50% of patient), so we also include an indicator of whether the 55 focal patient was an isolate or not in order to distinguish between those who have small amounts 56 of overlap with many patients vs those who have a lot of overlap with few patients.

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In the consistent co-presence network GEE we fit a term for whether an individual had 58 any significant co-presence (all individuals had at least one weighted edge in the Jaccard index 59 network). The term for whether an individual is an isolate indicates that isolates were more likely 60 to die within five years than those co-present with other patients (0.361 CI:0.195,0.526). Thus, 61 patients benefit from significant co-presence with at least one other patient in the ward, 62 irrespective of alters' outcomes. 63 We observe similar effects as those observed when using Jaccard-weighted person-hours 64 for both a significant positive effect between 5-year mortality and the number of consistently co-65 present patients who died within 5 years following their chemotherapy (0.103 95% CI: 66 0.064,0.142), and a negative significant effect between 5-year mortality and the number of consistently co-present patients who survived for at least 5 years following their chemotherapy (-68 0.117 95% CI: -0.175,-0.059).

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These results indicate that our primary analysis using Jaccard-weighted person-hours is 70 not unduly affected by allowing for co-presence of short periods of time to impact patient health.

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However, the coefficient of the "isolate" variable indicates there may be some sort of threshold 72 effect of consistently spending time with the same person or people. Although the model was 73 stochastic, 99% of individuals stayed the same with respect to "isolate" status across repeated 74 simulations. In all models we include a variable for the total person-hours of co-presence, which 75 is not significant. We separately included a variable for the number of people with whom one 76 was co-present, which was also not significant (we did not include it in the reported models 77 because including both it and the person-hours of overlap caused the model to not converge).

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This indicates that it is likely not diversity of partners with whom one is co-present that impacts patients who are all at least two steps away from one another and should be largely independent.

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These models, run using 1000 samples, give results that are generally in the same direction and 103 approximately the same magnitude as the models with all the data included ( Although our outcome of interest is 5-year survival, our data include precise patient 119 survival times. As such, we also fitted a Cox proportional hazard model to evaluate the 120 robustness of the inferences (Table S1, Model D) (Mills, 2011). This allows assessment of the

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Sensitivity Analysis for Nurses 127 We recognize that nurse heterogeneity could affect the health outcomes of patients and 128 also be correlated to patient-patient co-presence, which could explain our results. We were 129 unable to obtain data on nursing staff, but we present here a sensitivity analysis. First, we create 130 n nurses, ranging from 5 to 95 and randomly assign each a quality of care parameter. This more often than a nurse with a heterogeneity parameter at the 2.5 th percentile. This forced association between nurse parameter and patient outcome is not meant to precisely reflect how 155 nurses are assigned in the ward, but rather to fulfill the necessary condition that nurse assignment 156 is correlated with outcome to induce confounding. Each combination of number of nurses and 157 assortativity probability was run 100 times, and the proportion of significant (p<0.05) direct 158 effects were recorded ( Figure S3).

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Overall, we see that the significance of the main findings is relatively robust to the 160 number of nurses. We observe that the fraction of significance falls below 50% when the

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That being said, we find that the effects of co-presence with patients surviving 5 years are 170 less robust, as in our survival analysis. This may in part be due to the prevailing outcome of 5-

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year mortality and so less variability in co-presence times with surviving patients. It may also 172 reflect real uncertainty in the result that we cannot eliminate with the present data. Additionally, 173 this analysis assumes that, conditional on mortality status and co-presence, nurses are assigned 174 randomly. However, patients' admission consultants are not related to covariates such as age or 175 gender. We therefore believe that this assumption of random assignment reflects reality, 176 particularly given the fact that nurses do not specialize beyond general chemotherapy.
Ties concurrent with pre-existing social ties 178 Given that our study population is drawn from a relatively small catchment area, it is 179 possible that our belief that patients in the chemotherapy ward do not know one another prior to 180 initiating chemotherapy is incorrect. However, we believe ties of this sort are very unlikely, as    Table S1. Results of sensitivity analyses. The first 3 models are GEEs constructed in the same way as the primary analysis but with specific changes. A) Uses the consistent co-presence metric which is dichotomous, and also includes an indicator variable of whether an individual is an isolate or not. B) Treats cancer severity as a categorical variable. C) Is based on a sample of patients who were not co-present with one another to remove correlation between variables. Results are based on 100 trials of sampling a subset of patients in this way. D) Instead of a dichotomous 5-year survival outcome, we treat survival time as the outcome of interest, using a Cox proportional hazards model.