Simulated Cost-effectiveness and Long-term Clinical Outcomes of Addiction Care and Antibiotic Therapy Strategies for Patients With Injection Drug Use–Associated Infective Endocarditis

Key Points Question What is the most clinically beneficial and cost-effective antibiotic treatment strategy for injection drug use–associated infective endocarditis (IDU-IE)? Findings In this decision analytical modeling study simulating 4 treatment strategies among 5 million individuals with IDU-IE in the US, a validated microsimulation model suggested that outpatient parenteral antimicrobial therapy was the most cost-effective strategy for the treatment of IDU-IE. A partial oral antibiotic treatment strategy was associated with the highest treatment completion rate and was most cost-effective when methicillin-resistant Staphylococcus aureus was not a causative pathogen. Meaning This study found that outpatient parenteral antimicrobial therapy and partial oral antibiotic therapy regimens were likely to be as clinically beneficial as and less costly than 6 weeks of inpatient intravenous antibiotic therapy for the treatment of IDU-IE.


Introduction
The analyses reported in the main manuscript use the Reducing Inf ections Related to Drug Use Cost Ef f ectiveness (REDUCE) Model of acquisition and treatment f or bacterial inf ections and overdose associated with injection drug use. The REDUCE model tracks several clinical outcomes including number of people with inf ective endocarditis (IE) and overdose (OD) (otherwise known as 'sequelae'), number of cases identif ied, number linked to inpatient and outpatient care, number of people initiating therapy, and number achieving cure f rom their sequelae of drug use. The model also tracks sequelaerelated mortality, quality of lif e, undiscounted lif e expectancy, discounted quality-adjusted lif e expectancy (QALE), discounted lif etime medical costs f rom the health system perspective, and non-discounted program costs f rom the payer perspective (f or interventions designed to improve f ollow-up). This technical appendix provides details on key f eatures of the model and modeling approach used f or this analysis. We constructed the model and perf ormed analyses using C++ and R (3.2.2). The model has been previously described in the peer-reviewed literature. 1 The model is available f or review upon discussion with the authors and as resources are available. We did not use every component of the model f or the current analysis. In addition, we provide f igures and several tables detailing input parameter values and additional results cited in the manuscript.

REDUCE model
The REDUCE model is an individual-based, stochastic simulation model of the natural history of injection drug use designed to estimate the outcomes and costs associated with various strategies of prevention, treatment, and improving drug use-related care. The model uses a cycle length of one week.

Overview
The model is designed as a number of modules through which simulated individuals pass. Brief ly, a cohort module helps to "create" the population of interest. Next, individuals created during cohort generation enter the "sequelae of drug use (SDU)" module, which is where they encounter probabilities of f atal or nonf atal overdose, inf ective endocarditis, or skin and sof t tissue inf ections. From the SDU module, individuals enter back into the simulation or link to the "inpatient" module. In the "inpatient" module, individuals are hospitalized f or their SDU. There are a variety of interventions (beyond standard hospital treatment) that individuals may encounter if those services are turned "on" by the user. Following the inpatient module, individuals have a probability of linking to outpatient care in the "outpatient" module. Linkage to outpatient care may vary based on the type of services an individual encountered in the hospital and/or the type of SDU they have (overdose vs inf ection). They may unlink f rom the outpatient module or never enter it (based on probabilities). The "behavioral transitions" module is when individuals have the probability of moving between injection f requency drug use stat es (high f requency, low f requency, or no current drug use), between sterile injection practice states (skin cleaning or no skin cleaning), and sharing/reusing needles. Af ter the "behavioral transitions" module, individuals move to the "mortality, cost, and quality of lif e" module. At this point, the model begins again in cycle n+1.

Cohort initiation
When the model is initiated, a cohort of individuals is generated using 6 parameters: (1) ever injection drug use status (ever/never) (2) age (0-99) (3) sex (M/F) (4) injection f requency (high/low/no current/never) (5) reusing/sharing equipment (yes/no/never). (6) sterile injection practice (cleaning/no cleaning/never) From these parameters, the initializing cohort includes people who have "ever" or "never" injected drugs. Those who are "ever" injectors are stratif ied by injection f requency and injection practices. The model is structured such that f irst the user specif ies the proportion of the population that has ever injected drugs. Following that, there are two methods by which the model can draw age and sex. The f irst is by using age/sex tables and the second is by directly specif ying age and sex distribution parameters. In the latter method of drawing f rom age and sex, the user inputs values directly int o the deterministic parameter f ile. These inputs include proportion male, average male age, standard deviation male age, average f emale age, standard deviation f emale age, and minimum age.
Next, among those who are ever drug users, the probability of injection f requency is drawn f rom an age/sex stratif ied table-high, low, and no current injection drug use. Within the literature, injection f requency is usually reported as summary of behavior within the past month and while f requency may change daily depending on drug availability, we assume that overall f requency is stable over a one-week period. For generating the f requency of injection, all three probabilities f or an age/sex group equals 1 and the model draws f rom this set of probabilities. Finally, all persons who are "ever" drug users, are assigned an initial status of being a skin cleaner and a needle sharer which does not depend on age and gender. While these are the initial attributes, all individuals have the possibility of changing attributes as they move through the model. All never drug users are assigned "never" injection f requency, skin cleaning and needle sharing status.
Assumptions built into the model f or the initial cohort: 1) no one starts on treatment f or opioid use disorder 2) no one starts out with a history of overdose 3) no one starts with a history of inf ection 4) no one begins in care or in the hospital setting.
For the present analysis, we initialized a cohort representing a national sample of people with injection drug use with the characteristics presented in eTable 1. Population characteristics were based on the U.S. Census and the published literature.

Sequelae of drug use
Once the cohort is initialized and each individual has been assigned an initial drug use status, age, sex, and injection f requency and practices, individuals enter the sequelae of drug use (SDU) module. Broadly, the SDU in this model include inf ective endocarditis (IE) and overdose (OD). When they f irst enter, the model checks their ever/never status. If they are "never," then they return to the simulation. Theref ore, only "ever" drug users can progress through this module. The model then checks their injection f requency. If they are "no current," then they return to the simulation. Theref ore, only "low f requency" and "high f requency" injectors progress through this module. Additionally, if the individual is currently in inpatient care, they return to the simulation. If a person is currently on antibiotics, they progress through the SDU module but they cannot acquire a new inf ection (IE). At this point, remaining individuals are subject to probabilities f or acquiring an SDU. On the f irst cycle of this model, no one has a history of SDU, but have the possibility of acquiring one or multiple throug h their lif e. History of SDU is tracked as it has implications f or f uture SDU. One assumption of the model is that SDUs can only be acquired while not "inpatient" or on antibiotics (next module).
Individuals who are eligible f or an SDU, progress through a number of probabilities of acquiring an SDU. All SDUs are stratif ied by injection f requency (high and low) and the inf ectious SDU are also stratif ied by injection practices (skin cleaning, needle sharing). SDU probabilities are not stratif ied by age and s ex. The model is structured such that an individual f irst encounters a combined probability of overdose (f atal + nonf atal), stratif ied by injection f requency. If an individual has a current inf ection their overdose rate is multiplied by the current inf ection multiplier. A proportion of overdoses are f atal and a proportion are nonf atal. One aspect of the model is that at this point, if a person draws a f atal overdose then they are f lagged as "dead, f atal overdose." They continue to proceed through the rest o f the modules but cannot acquire any f urther attributes (e.g., they cannot get another inf ection, be hospitalized, start MOUDs, change their behaviors). These individuals, however, accrue the f ull costs of the cycle (based on background costs, costs of fatal overdose, and costs of any other SDUs that are untreated) and utilities (based on age, sex, and other current health states at the end of the cycle). For those that have a nonf atal overdose or do not have an overdose, they then f ace a combined probabili ty of IE, stratif ied by injection f requency, skin cleaning and needle sharing attributes. The model is structured to account f or a history of SDU (treated in hospital, resolved because it was a nonf atal OD) and f or existing SDUs. An existing SDU is anything that an individual has during the current cycle. From a clinical perspective, this represents an "untreated" inf ection (e.g., someone has not gone to the hospital f or their endocarditis or someone is currently on outpatient antibiotics but not cured) or a current nonf atal overdose. Once treatment is complete or the SDU resolves (as is the case with nonf atal overdose which resolves in 1 cycle), then the person is f lagged with a history of the corresponding SDU.
An existing SDU causes a change in the likelihood of another SDU. In the model, there is a single multiplier f or one or more existing SDUs that is applied to both the probability of OD and the probability of inf ectious SDU. This multiplier exists until the individual is treated f or the SDU. For tho se who have a nonf atal overdose, the existing SDU multiplier will be applied to the probability of inf ection in the same cycle only since an existing nonf atal OD (that does not link to inpatient), only lasts one cycle. Additionally, a history of SDUs changes the probability of future SDUs. Multipliers are only applied to the SDU f or which there is a history (e.g., OD history changes the probability of recurrent OD; any inf ection history changes the probability of future inf ection [any inf ection, not just the one that occurred]). For OD, there are 4 multipliers (e.g., 1 past nonf atal OD, 2-3 past nonf atal OD, 4-7 past nonf atal OD, and 8+ past nonf atal ODs). For history of treated inf ections, there is only one multiplier (1+ past treated inf ections). For instance, in cycle 1, an individual gets IE but does not go to the hospital/receive treatment and does not die in cycle 1. By cycle 2, having IE makes that individual have a greater probability of OD. For this model, individuals will not be able to acquire the same SDU in that next cycle. From the previous example, the individual with IE will only be able to acquire OD, not IE in cycle 2. While that inf ection remains untreated, there is an ef f ect on getting another inf ection/OD. Once that inf ection is treated, then there is a separate ef f ect of this inf ection on f uture inf ections. Theref ore, this module has two multipliers: 1) one that can change the probability of an additional SDU if current SDU is untreated, and 2) one that can change the probability of a recurrent SDU (in the f uture) if the current SDU is f ully treated and they survive it.
If an individual does not acquire an SDU in the current cycle and does not have an untreated SDU f rom a past cycle, they return to the simulation. If they acquire one or more SDUs, or have an untreated SDU f rom a past cycle, then individuals draw linkage probability to inpatient f rom the SDU. Linkage to inpatient depends on the linkage probability of their SDU; if an individual has more than one SDU, their linkage probability is the highest of the linkage probabilities f or the SDUs they have. There remains the possibility that an individual does not link to inpatient. In the case of nonf atal OD, it implies that the OD was not severe enough to require hospitalization (or was treated in the f ield). In the subsequent cycle, there should not be a f lag f or untreated overdose. All nonf atal overdoses are, by def inition, treated so the "existing" state can only last f or the cycle in which the non-f atal overdose occurs. In the case of endocarditis, the untreated f lag should remain on until the person either dies or links to inpatient care and gets cured. This is because endocarditis is generally unif ormly f atal if untreated. Individuals who go to the hospital will be classif ied as "inp atient" starting in the same cycle and will have an "in-hospital mortality." Once they leave the hospital, they are considered as having a history of inf ection. If an individual does not link to inpatient, they are classif ied as having "existing" SDU and have dif f erent risks of death (untreated mortality probabilities f or each SDU). Individuals who come to the SDU module on subsequent cycles with an additional SDU (>1 SDU at a time) will have the probability of hospitalization that is equal to the highest probability of the SDUs.
Attributes that an individual can acquire in this module and are tracked:

Inpatient hospitalization
One assumption of the model is that any individual that has either a) current injection drug use or b) a current, untreated SDU is presumed to have opioid use disorder (OUD). Some sequelae of OUD are inf ectious and some are non-inf ectious (e.g., overdose).
Each individual with 1+ SDU has a probability per cycle of presenting to an inpatient setting f or their care. When individuals enter the inpatient module, the model checks their current SDU status. If they do not have a current untreated SDU or died of f atal overdose in the previous module, or they are on outpatient antibiotics, then they return to the simulation. Theref ore, only those individuals with active SDU can progress through this module.
The path through the inpatient module is conditional on the SDU(s) that an individual has: nonf atal OD, IE, or combination. The hospitalization duration f or overdose is 1 cycle; the hospitalization duration f or IE is drawn stochastically f rom a normal distribution with a user def ined mean and standard deviation; the model allows f or a maximum hospitalization to be set so that at the end of the max amount of time a person will leave the hospital. Each hospitalization is associated with a cost that is accrued in later module. The key f eature of this module is that individuals may encounter a variety of in hospital services. These services are either turned on or of f by the user depending on the analysis. If they are on, then individuals will have a probability of being offered and of accepting those services during their hospitalization. Each service has an ef f ect either within this module or elsewhere in the simulation. Each service is associated with a cost that is applied in a separate module at the end of t he simulation. These interventions are applied only in the last cycle of hospitalization and they will have post -treatment ef f ective cycles drawn f rom a normal distribution. Individuals should be "marked" as using/receiving a service such that the cost can be tabulated in the separate module. Additionally, some of the services have an independent ef f ect on quality of lif e. Similar to cost, this is applied in a separate module at the end of the simulation. Hospitalization is associated with a decreased QoL s o there is a hospitalization QoL weight that can be applied in a separate module at the end of the simulation.
Each individual has a probability of in-hospital mortality that is discussed in detail in the mortality section. It is mentioned here to note that it is an attribute that an individual can acquire. During hospitalization, individuals "carry" a f lag/marker that designates them as hospitalized. While hospitalized, individuals cannot get a new SDU so they will not enter SDU module. They have an "in hospital" mortality that is conditional on the SDU f or which they are hospitalized. For the duration of their hospitalization, their injection f requency is considered to be "no current" regardless of their actual status and they are not exposed to behavior transitions. The exception to this rule is as f ollows: in the last hospitalization cycle, individuals are exposed to behavior transitions based on their pre-hospitalization status. If they have received any intervention that would af f ect their behaviors (MOUD, skin cleaning education or clean needle distribution), the intervention ef f ect will be applied to their actual or pre-hospitalization behaviors and post-treatment ef f ective cycles will be drawn. These behavioral changes are assigned in the last inpatient cycle so that they take ef f ect the f irst cycle out of inpatient. However, cost -lif e-mortality module still consider them as "no current". We assume that 5% of patients leave against medical advice (AMA) per week or as a patient-directed discharge prior to completion of treatment, inf ormed by published studies reporting a high rate of AMA within this patient population. 10,11 When the inpatient hospitalization time has lapsed or patients leave against medical advice, individuals move to the outpatient module. In the outpatient module, they have a probability of then linking to dif f erent types of care.

Outpatient care
There are two dif f erent ways by which an individual can enter the outpatient module. First, an individual can enter via background linkage. This means that those who are not hospitalized but "decide" to seek care can do so by entering this module. Second, an individual can enter via the inpatient module.
For individuals entering from the simulation (background). Each individual encounters the outpatient module. Individuals with a "death" f lag f rom a previous module (f atal overdose) enter the outpatient module and immediately return to the simulation. Individuals who are currently hospitalized immediately return to the simulation. All other "ever" drug user individuals have a probability of linking to outpatient care and progress through the outpatient module, regardless of history of SDU or drug use status. If individuals do not draw "linkage" then they return to the simulation.
For individuals entering from the inpatient module (inpatient linkage). When the inpatient hospitalization time has lapsed, then individuals encounter a linkage p robability to the outpatient module depending on inpatient services they have received.
Outpatient addiction care. Individuals have a probability of linking to outpatient addiction care (either with or without MOUDs). One cannot be simultaneously in outpatient addiction care with MOUDs and without MOUDs (these are separate states). But individuals can be simultaneously in outpatient addiction care (with or without MOUDs) and outpatient antibiotics.
Individuals have a probability of unlinking f rom outpatient addiction care either with or without MOUDs or transitioning between MOUD states. There is a separate probability of linking to outpatient addiction care (with or without MOUDs) f or those coming f rom the inpatient module and those coming f rom the simulation (spontaneous linkage/background linkage). There are dif f erent linkage probabilities f or the f ollowing groups: 1. Individuals who have received inpatient addiction care but did not get MOUD 2. Individuals who have received inpatient addiction care and got MOUD 3. Individuals who did not receive inpatient addiction care but got inpatient MOUD 4. Individuals who did not receive any relevant inpatient services or individuals coming f rom the background (no hospitalization) If an individual is in outpatient addiction care and acquires an inf ection they will automatically be linked to inpatient care in the next cycle. In this case, they will unlink f rom outpatient care and all outpatient related f lags/cycles will be cleared. For the present analysis, we added two outpatient antibiotic strategies which are described in detail below under the sections titled "Outpatient parenteral therapy" and "Partial oral antibiotic therapy".

Behavioral transitions
Following the inpatient and outpatient modules, individuals move to the behavioral transitions module. Individuals may also enter this module "f rom the simulation." The latter rep resents the ability of someone to change their behaviors organically (without interventions). This is the module in which they can move between high f requency, low f requency, and no current use states, move f rom never and ever IDU, move between skin cleaning and not skin cleaning states, and move between sharing needles and not sharing needles states. There is a prior probability of movement between states (status quo) and various "f lags" acquired throughout the model progression that impact certain probabilities. These have been outlined in various other module descriptions but are also be outlined below.

Treatment Effects:
The primary driver of morbidity and mortality in the module is the injection f requency. High f requency individuals are at higher risk than low f requency injectors of sequelae of drug use (SDUs), which include overdose, skin/soft tissue inf ections, and endocarditis in this model. All persons who are "ever" injectors have the possibility of moving to a higher or lower injection f requency st ate (depending on their current state) or staying in their current state per cycle. For instance, a high f requency injector may remain as a high f requency injector or may move to low f requency or no current use states. There are a f ew ways that the injection f requency can be modif ied in the model.

Mechanisms by which transitions between injection frequency states are changed:
1) Hospitalization.

Mortality
There are two places in the model that an individual can die: f atal overdoses in the SDU module and in the mortality module. To review, in the SDU module, an individual draws a combined probability of all types overdose which is stratif ied by injection f requency (high and low f requency). From that combined probability, an individual can draw either a f atal or non-f atal overdose. If an individual draws a f atal overdose, they go through the remainder of the cycle with a "f atal OD" f lag up which does not allow them to get any f urther interventions, collect additional costs, change their behavior status, etc., however, they will accumulate the background cost and utility of that cycle. As such, the background mortali ty in the mortality module should exclude overdose mortality.
The background mortality risk is an age and sex adjusted mortality probability (excluding f atal overdose).
There are a number of occurrences in the model that can impact the weekly risk of mortality. First, individuals who are hospitalized f or an SDU (non-f atal overdose or endocarditis) have an increased risk of death. If the inpatient individual receives an ID consult, their inf ection inpatient mortality rate is augmented by an ID consult mortality multiplier (ID consult will not af f ect overdose mortality). Second, individuals who have an untreated skin and sof t tissue inf ection or untreated inf ective end ocarditis have an increased risk of death. These risks are input as probabilities (and converted to rates by the model) which are then added to the background mortality at the end of each cycle. Once a patient is cured of their inf ection, their SDU f lags are removed and their mortality goes back to background mortality. The mortality risk only applies f or each cycle that they have that risk. For example, a person gets endocarditis and does not present to inpatient care during a cycle. Then they have an "existing endocarditis" f lag that the end of the cycle should prompt the rate of death f or untreated endocarditis to be added to the background mortality. On cycles 2-5 that same individual, however, is hospitalized and being treated f or their endocarditis. For those cycles, they get an "in-hospital f or endocarditis" f lag such that the in-hospital endocarditis mortality rate is added to their background mortality each cycle. On cycle 6, this person leaves the inpatient setting (completes treatment) so all f lags are, theref ore, of f and at the end of that cycle they get only background mortality. We do not include an additional mortality risk f or being an active drug user since most of that risk will be f olded into overdose and other SDUs.
Cause of death as an output: In the model, individuals can die of background causes or as a direct result of their injection drug use. Direct causes of injection drug use include: 1. Overdose (combination of f atal overdose/ hospitalized and nonf atal OD that dies in the hospital ) 2. Endocarditis (combination of hospitalized and non-hospitalized) Aside f rom f atal overdose, all of the other causes of death get added to the background mortality as outlined above. For instance, an individual's weekly probability of death (conditional o n not dying of a f atal overdose) may be pd and they may have endocarditis which increases their risk of death by x. The individual's weekly risk of death is, theref ore, the sum of the rates converted to a probability. However, as an output, we need to be able to determine the attributable cause of death (this person may have died of endocarditis OR background causes). To do this, we use the sum of the rates as the denominator and the individual mortality risk (rates) as the numerator in drawing the cause of death. Important f or consistency, the input parameters are probabilities and theref ore all rates are calculated in the model.

Costs
Costs are accrued f or a variety of reasons. At the end of each cycle, costs associated with certain characteristics are added to the background costs. All costs and lif e expectancy have a discount rate applied at the end of the cycle so that we can derive a discounted cost and a discounted lif e expectancy.

Outpatient parenteral antimicrobial therapy (OPAT)
Outpatient parenteral antimicrobial therapy (OPAT) is widely used to treat inf ections requiring prolonged antibiotic therapy with a proven saf ety record . 12 Several recent studies have provided an evidence regarding saf ety of OPAT f or persons with injection drug use (PWID). [13][14][15] Suzuki et al. perf ormed a systematic literature review to evaluate the saf ety and ef f ectiveness of OPAT among PWID. 13 Six studies were U.S.-based. In general, patients were discharged to home f ollowing hospital admission; however, studies also reported discharge to a medical respite f acility, skilled nursing f acility, residential treatment f acility, and a group home. Outcomes on treatment completion, mortality, and active substance use f ollowing admission were used to parameterize the OPAT treatment module.

Percent uptake
For the main analysis, we assumed that all patients admitted with DUA-IE would be eligible f or OPAT at a one point in their treatment. If the probability of discharge on OPAT by 6 weeks is 99%, the weekly probability of discharge on OPAT is 53.6% (eTable 6). We lowered this percent to 50% within a scenario analysis described within the "Scenario analyses" subsection.

Duration of treatment
Fannuchi et al. conducted a pilot randomized trial comparing usual care (IV antibiotics in the hospital) to receiving combined OPAT and MOUD f or persons with OUD hospitalized with a IDU-associated inf ection. 15 The reported average length of hospital stay was 22.4 (SD=7.1) f or OPAT participants compared to 45.9 (SD=7.8) f or usual care participants. All 10 participants assigned OPAT completed treatment which involved an average of 20.1 (SD=11.1) days of outpatient antibiotics. On average, OPAT involved a 3 week stay within the hospital f ollowed by 3 weeks outpatient antibiotics within the model.

Treatment discontinuation and readmission
Every week f ollowing hospitalization and prior to the completion of the antibiotic regimen (with a mean duration of six weeks), there is a weekly probability of unlinking f rom antibiotics. This represents both treatment f ailure as well as a patient voluntarily d iscontinuing. If the antibiotic regimen is not f ully completed (i.e., patient unlinks f rom antibiotics at f our weeks rather than six), there is a 100% probability of relapse of inf ection and the patient will be re-admitted or die.
To parameterize the probability of unlinking f rom OPAT f ollowing an inpatient stay f or DUA -IE, we used data f rom Fanucchi et al. and a recent study by D'Couto et al. 14 We calculated the mean percentage of treatment completion reported by D'Couto et al. f or participants who were discharged to home on OPAT (81% completed treatment) as well as Fanucchi et al. (100% completed treatment) and weighted by sample size to calculate that 87% of patients initiating OPAT with an of fer of ACS and MOUDs complete treatment. We used the inverse and re-scaled to calculate a weekly probability of discontinuing treatment and readmission (4.54% per week).
For a range around this estimate, we used the systematic review f rom Suzuki et al. which f ound that OPAT completion rates of predetermined duration ranged f rom 64% to 91% in U. S. based studies. 13 We converted these to an inverse probability to represent the probability of discontinuing treatment and then to weekly probabilities (3-14%).

Cost
Costs included within the model include the cost of medication (antibiotics) as well as treatment utilization, including physician visits and typical laboratory testing.

Pharmaceutical costs
To specif y antibiotic regimens and estimate associated costs, we f irst estimated the distribution of organisms leading to DUA-IE. Rodger et al. reported on 202 f irst-episode cases of DUA-IE and f ound that staphylococcus aureus inf ections were the causative organism in 77.2% of cases in PWID (156 of 202), f ollowed by 6.4% (13 of 202) with a polymicrobial inf ection, and 5.4%(11 of 202) caused by enterococci. 16 Hartnett et al. reported that 11% of drug -use associated inf ections (not just but inclusive of DUA-IE) were caused by streptococci. 17 Inf ectious disease physicians on our study team examined the data f rom both studies and estimated that DUA-IE inf ections were due to the f ollowing organisms: 56% Methicillinsensitive Staphylococcus aureus, 21% Methicillin-resistant Staphylococcus aureus, 11% streptococci, 6% enterococci, and 6% other (polymicrobial, culture negative, pseudomonas or acinetobacter, etc.).
Using this distribution of organisms, we then used recommended regimens based on guidelines published by the American Heart Association 18 to assign the most likely IV antibiotic regimen (see eTable 7). We then looked up medication costs using the Federal Supply Schedule (https://www.va.gov/opal/nac/fss/pharmPrices.asp , accessed 2/23/2021). If multiple prices were reported f or the same medication, we averaged the price and used the costs to create a range f or the probabilistic sensitivity analyses. For the estimated cost f or OPAT, we calculated a weighted average daily cost using the f ollowing f ormula:

Treatment costs
Bef ore discharge, patients who go on to receive OPAT have a PICC line placed as well as a chest x-ray which leads to an inpatient cost of $126.46.
Following discharge f rom inpatient care, patients with DUA-IE could receive OPAT at home or in a skilled nursing f acility, rehabilitation center, or another post-acute care f acility. Costs of treatment per day within a post-acute care f acility were estimated using data f rom Boston Medical Center (see eTable 8) and includes nursing visits, laboratory testing, and physician visits.
Treatment costs associated with receiving OPAT at home were derived f rom studies reporting typical treatment services received during OPAT at home. 19,20 We assumed that, on average, home inf usion would lead to the f ollowing treatment costs: physician visit every two weeks, weekly nurse visit, weekly complete blood count (CBC) with dif ferential, weekly liver f unction testing, and weekly blood urea nitrogen and creatinine testing. In addition, we assumed that 10% of patients on OPAT would require a CT angiogram and 5% of patients would req uire an echocardiogram due to suspected septic emboli or other complications based on expert opinion. Costs were calculated in 2020 USD using the Physician Fee Schedule and Laboratory Fee Schedule (both accessed on 4/19/2021). On average, the cost of home inf usion per week was $469.10 ($461.05-479.46), including costs of antibiotics as calculated above. This is in line with the cost estimate included within a report to Congress f rom MedPac on Medicare coverage and payment f or home inf usion therapy which stated an average gross drug cost per user of $1,250 per person (includes bundled payment of drug and equipment but no nursing visits) or $417 per week if assuming OPAT f or three weeks.
To estimate an overall weighted weekly cost of OPAT, we assumed that 50% of patients discharged on OPAT would have home inf usion therapy and 50% would receive OPAT at a post-acute f acility. Data received f rom Boston Medical Center indicated that 50% of patients with DUA-IE were homeless, and theref ore, could not be discharged home. We also assumed that percentage of patients would pref er or require the additional support of a post-acute f acility. We used cost data f rom patients with DUA-IE staying at post-acute f acilities to parameterize the average weekly co st of OPAT at a post-acute f acility. The average weekly cost at a post-acute f acility was $2,569.00 with a minimum weekly cost of $637.00 and maximum weekly cost of $11,613. We then added the cost of antibiotics to calculate the total cost. We assumed that 50% of OPAT recipients were discharged home and 50% went to a post -acute f acility f or care.

Percent uptake
For the main analysis, we assumed that only patients admitted with DUA -IE with non-MRSA organisms would be eligible f or partial oral antibiotics. In a study of 202 f irst-episode DUA-IE, Rodger et al. reported that methicillin-resistant staphylococcus aureus inf ections were the causative organism in 21.3% of cases. 16 Theref ore, we assumed that 79% patients admitted with DUA-IE would be eligible f or PO at a one point in their treatment. If the probability of discharge on PO by 6 weeks is 79%, the weekly probability of discharge on PO is 22.9%. To explore the implications of a lower percentage of MRSA organisms. For these analyses, we ran a scenario analysis where we assumed that all DUA-IE cases were non-MRSA.

Duration and rate of treatment completion
Every week f ollowing hospitalization and prior to the completion of the antibiotic regimen (with a mean duration of six weeks), there is a weekly probability of unlinking f rom antibiotics. This represents both treatment f ailure as well as a patient voluntarily discontinuing. If the antibiotic regimen is not f ully completed (i.e., patient unlinks f rom antibiotics at f our weeks rather than six), there is a 100% prob ability of relapse of inf ection and the patient will be re-admitted or die.
To parameterize the probability of unlinking f rom partial oral therapy f ollowing an inpatient stay f or DUA -IE, we used data f rom Marks et al. who compared outcomes f or 293 PWID hospitalized with invasive inf ections who either completed a f ull course of inpatient IV antibiotics or received oral antibiotics upon patient-directed discharge f ollowing a partial course of IV antibiotics. 21 Within this study, 83 PWID initiated oral antibiotics f ollowing a patient-directed discharge and 8/83 did not complete a f ull course of oral antibiotics. 21 Theref ore, 75/83 or 90.4% successf ully completed a f ull course of PO f ollowing hospitalization. We converted this to an overall rate of f ailure and scaled the probability by the average duration of PO regimen (i.e., 3 weeks) f or 3.3% weekly probability of unlinking f rom PO treatment.

Cost
Costs included within the model include the cost of medication (antibiotics) as well as treatment utilization, including physician visits and typical laboratory testing.

Pharmaceutical costs
To specif y antibiotic regimens and estimate associated costs, we f irst estimated the distribution of organisms leading to DUA-IE (described f ully within the Pharmaceutical costs subsection of the OPAT subsection).
Using this distribution of organisms, we then used recommended regimens reported in Marks et al. and used within the POET trial to assign the most likely oral antibiotic regimen. 21,22 Due to the unlikelihood of an oral antibiotic regimen being prescribed f or a Methicillin-resistant Staphylococcus aureus (MRSA) inf ection because of a lack of evidence base, we assumed that individuals with DUA -IE related to MRSA would not be eligible f or PO and would remain hospitalized f or the duration of their antibiotic treatment. This was varied in sensitivity analyses.
We then used medication costs using the Federal Supply Schedule (https://www.va.gov/opal/nac/fss/pharmPrices.asp , accessed 2/23/2021). If the medication was not included within the FSS, we used the average wholesale price and subtracted by 23% to estimate cost. If multiple prices were reported f or the same medication, we averaged the price and used the costs to create a range f or the probabilistic sensitivity analyses. The weighted weekly cost of outpatient oral antibiotics was $260.71 ($17.29-1,170.03) per week.

Treatment costs
Treatment costs associated with receiving PO at home were derived f rom Marks et al. and consulting with an expert panel. 21 We assumed that, on average, patients on a PO regimen would receive the f ollowing services: a physician visit every two weeks, weekly nurse visit, biweekly complete blood count (CBC) with dif f erential, biweekly liver f unction testing, and biweekly blood urea nitrogen and creatinine testing. In addition, we assumed that 10% of patients on OPAT would require a CT angiogram and 5% of patients would require an echocardiogram due to suspected septic emboli or other complications based on expert opinion. Costs were calculated in 2020 USD using the Physician Fee Schedule and Laboratory Fee Schedule (both accessed on 4/19/2021). On average, the cost of partial oral antibiotics was $380.56 ($137.14-$1,289.88).

Incremental Cost Effectiveness Ratios (ICERs)
Following guidance f rom the Second Panel on Cost-Ef f ectiveness in Health and Medicine, ICERs were calculated as the dif f erence in costs between the intervention and comparator (status quo) scenario divided by the dif f erence in health benef its. 24 Costs and LYs were discounted at a rate of 3% in line with current recommendations.

Model scenarios
We used the REDUCE model to compare the f ollowing treatment strategies f or DUA-IE: 1) 4-6 weeks of inpatient IVA along with opioid detoxification, status quo (SQ); 2) 4-6 weeks of inpatient IVA along with inpatient addiction care services (ACS) which of f ers medications f or opioid use disorder (SQ with ACS); 3) 3 weeks of inpatient IVA with ACS f ollowed by OPAT (OPAT); and 4) 3 weeks of IVA with ACS f ollowed by PO antibiotics (PO). Key input parameters are summarized in eTable 12.
For this analysis, we simulated a cohort over a lif etime in order to estimate long-term outcomes including: mortality and hospitalizations attributable to DUA-IE, the average percent completing treatment f or DUA-IE, lif e-expectancy, average cost per person, and incremental cost -ef f ectiveness ratios (ICERs). We compared costs using a payer system perspective and denominate currency in 2020 US dollars. We discounted all costs and benef its by 3% annually and expressed ICERs as cost per lif e-year gained with a willingness-to-pay threshold of $100,000 per LY (19). Probabilistic sensitivity analyses and a threshold analysis were perf ormed to evaluate major f indings. Additional details and f indings are reported within the accompanying manuscript.

Scenario analyses
Deterministic scenario analyses were perf ormed to evaluate the robustness of the model results to uncertainty in the input parameters. These were run with half a million individuals over a lif etime and compared on key outcomes. We varied the 1) percentage of DUA-IE patients eligible f or PO (tied to non-MRSA percentage); 2) the percentage of patients leaving the hospital with patient -directed discharge or against medical advice (f rom 5% to 2.5% weekly); 3) treatment uptake of OPAT and PO (f rom 99% to 50% f or OPAT and f rom 79% to 50% f or PO); 4) where the rate of overdose within the community and outpatient settings is quadrupled, 5) the uptake of ACS and MOUD while inpatient is increased to 75% f rom and 6) inpatient stay and average cost of medication within the PO scenario. These results are presented within Table 4 in the accompanying manuscript.

Threshold analyses
We conducted threshold analyses to determine what value f or selected parameters (i.e., treatment uptake, treatment completion) changed our major f indings. These were run with half a million individuals over a lif etime and compared on key outcomes. Average discounted costs per person, discounted lif eyears, and ICERs are presented in eTable 13 while Figure 1 within the accompanying manuscript outlines the impact of these values on our major f indings. eFigure 1 and eFigure 2 present the threshold values f or treatment uptake and costs of OPAT and PO.

Probabilistic sensitivity analyses
We ran probabilistic sensitivity analyses (credible intervals presented in Table 3 within the manuscript) where we held the percent of patients leaving against medical advice and treatment uptake constant while varying the uptake of MOUDs and ACS while hospitalized, cost of antibiotics, and the probability of discontinuing antibiotics post-hospitalization. Parameter distributions presented in Table 2 16,17 Recommended regimen (Marks et al. 23