Fig 1.
Graphic illustrations of model assumptions.
(a) Assumptions on transitions of patients’ infection and treatment status. (b) Appropriate antibiotics could help reduce the patient’s bacteria population, hence alleviating the infection. But if the patient contracts another bacterial strain resistant to the current antibiotic, a strain switch becomes possible due to selective pressure. On the other hand, strain switch is not possible for patients under inappropriate antibiotics. (c) Case 1 represents an ideally successful treatment where a successful 4-day definitive therapy follows a successful 3-day empiric therapy. Case 2 illustrates an inappropriate 3-day empiric therapy followed with a 7-day correction of definitive therapy. Case 3 refers to a possible occurrence of strain switch during a successful empiric therapy. The unknown strain switch would result in an ineffective definitive therapy for three days, followed by a 7-day correction. Case 4 corresponds to a possible strain switch during the definitive therapy. This unknown strain switch would lead to an ineffective definitive therapy for three days followed by a 7-day correction therapy. (d) Pathogens lying inside each circle are susceptible to the corresponding antibiotic, whereas those outside the circle are resistant to the antibiotic. An infection of any non-PA species can be treated by the correspondingly de-escalated non-PA antibiotics and by the three PA-targeted antibiotics because of their relatively broad spectrum. Bacteria develop resistance against each antibiotic in specific ways. Thus the CIP-resistant strain is susceptible to TZP and vice versa. We assume that the last-resort drugs can ultimately treat the dual-resistant strain.
Fig 2.
Baseline hazard rate functions.
Both functions are parameterized from real data collected in [35]. (a) Hazard rate of discharge., (b) Hazard rate of death.
Table 1.
Model parameters with baseline values.
In Experiment 1, all parameters are fixed at the baseline values. In Experiment 2, each parameter is sampled from a truncated normal distribution with μ being its baseline value and σ = 0.1μ.
Fig 3.
Transmission probability calibration.
The number in each cell represents the fraction of all three outcomes (i.e. prevalence of resistance to CIP and TZP, and PA colonization) falling in the credible ranges over 1,000 experiments. We pick the transmission probability pairs marked in red borders for further simulations. p represents the probability of PA transmission from HCWs to patients upon each contact. q represents the probability of PA transmission from patients to HCWs during each visit.
Fig 4.
Infection prevalence under high transmission mode (p = q = 0.3).
Each trajectory in the background light color tracks the average daily number of super-infected patients in a 64-bed ICU. The solid curves represent the mean value of daily super-infections for the de-escalation and control groups over 1000 simulations.
Fig 5.
Effect size of outcome measurements under high transmission mode (p = q = 0.3).
Each color bar represents the Cohen’s D value of the corresponding outcome measurement between de-escalation and control groups measured at the end of each study period. Simulations are performed for each group for 1000 times with all parameter values fixed as in Table 1. The height of each bar represents the effect size between the distributions of de-escalation and control groups. Large effect size indicates high possibility for one to detect the projected difference in reality. Practically, effect size of 0.2, 0.5, 0.8, and 1.4 respectively correspond to 58%, 69%, 79%, and 92% probability of observing the control group under- or out- perform the mean of experimental group as projected. All measurements shown in (b) represent the trade-offs of de-escalation. All measurements except Deaths shown in (a) refer to the benefits. The use of TZP is a clear benefit of de-escalation with a significant Cohen’s D value, so we omit this benefit in the figure.
Fig 6.
Sample size estimation for RCTs with 16-bed ICUs under various transmission modes.
Each curve represents the number of balanced arm pairs needed to detect an expected difference between de-escalation and continuation groups in the corresponding measurement regarding the length of the study period (assuming 80% power, 5% type I error rate). Panels with white background refer to benefits of de-escalation, and those with gray background refer to trade-offs. High transmission mode refers to p = q = 0.3, low transmission mode refers to p = q = 0.15, and asymmetric transmission mode refers to q = 0.5, p = 0.05.
Fig 7.
Sample size estimation for RCTs under high transmission mode.
Each curve represents the number of balanced arm pairs needed to detect an expected difference between de-escalation and control groups in the corresponding measurement regarding the length of the study period (assuming 80% power, 5% type I error rate). Panels with white background refer to benefits of de-escalation, and those with gray background refer to trade-offs. Each curve type represents an RCT consisting of 16-bed, 32-bed, or 64-bed ICUs, where a 4:1 patient-HCW ratio is always maintained.
Table 2.
Table of measurements: Expectations and required study arms.
Required arms are obtained by taking the least possible sample size for each measurement at a four-year study period among 16-bed, 32-bed, and 64-bed ICUs.