One-way sensitivity analysis

Holding all other parameter values fixed, I systematically increased and decreased each parameter value by 30% and recorded the impact on model outcome variables: unique BUP recipients, opioid overdose deaths, and diverted buprenorphine. I report the percentage difference of the means of 30 replications of these outcome variables from baseline level means and present results as tornado diagrams on each

outcome variable to highlight the sensitivity of model outcomes to changes in particular parameters (Eschenbach, 1992). If confidence intervals on the mean for outcome levels of tested parameters overlapped with the baseline mean, the difference in the mean is not detectable due to random variation in the model. These parameters are in not included in the diagrams.

The number of buprenorphine recipients was sensitive to three treatment seeking parameters, and three provider specific parameters, as shown in Table 3-10.

The number of buprenorphine recipients was sensitive to the incidence of treatment seeking—the percentage of people with OUD who would seek treatment in the model year starting the year uninterested in treatment, and the initial percentage of people with OUD who start the year in treatment or seeking treatment, but only when these parameters were reduced. Increasing these parameter values did not significantly increase the number of buprenorphine recipients at year end. The relative percentage of people with OUD who start the model year in or seeking treatment who

Table 3-10: Tornado diagram of sensitivity analysis on the number of unique buprenorphine recipients. In general, an increase (or decrease) in the parameter value resulted in an increase (or decrease) in the number of buprenorphine recipients, with the exception of the number of OTPs (*), for which a 30% increase in the number of OTPs resulted in a 5% decrease in unique recipients of BUP

+/-30% change in paramter value

incidence of treatment seeking -10%

initial % people with OUD in/seeking tx -8%

% providers = specialist high-cap -6%

initial % seeking vs in tx -5% 4%

number of OTPs * -5%

% providers accept private insurance -4%

Unique BUP recipients: percentage difference from baseline

.

are assigned into treatment increases buprenorphine recipients when increased, and decreases it when decreased.

Decreasing the percentage of providers who are addiction medicine specialists with high waivers and replacing those providers with an equal number of non-specialists who have low waivers resulted in a 6% decrease in buprenorphine recipients. Even though the percentage of specialist providers was only reduced from 12% to 9% of all providers, providers of this type were initialized with preferences for the highest number of patients (often over 100) and were replaced by providers with the lowest preference levels (around 10).

Increasing the number of OTPs in the model decreased the number of buprenorphine recipients significantly, but did not affect the number of people who received any OAT. Conversely, decreasing the number of OTPs by 30% did result in a 7%

decrease in OAT treatment overall, while having no detectable effect on the number of people receiving buprenorphine. This suggests that increasing OTPs results in a

treatment substitution effect in the model.

The amount of diversion in the model was sensitive to three types of parameters (see Table 3-11): diversion-specific parameters, poverty and affordability parameters, treatment seeking parameters, and two parameters that didn’t fall into those

categories: number OTPs, and % patients with 16 mg BUP daily dose.

Table 3-11: Tornado diagram of sensitivity analysis on the amount of buprenorphine diverted to non-patients. An increase (or decrease) in the parameter value resulted in an increase (or decrease) in the amount of diversion, with the exception of parameters marked with an (*).

Not surprisingly, increasing the percentage of patients who divert medication for various reasons resulted in large increases in diversion. This is due to model logic that does not require that an increase in one reason for diversion be offset by a decrease in another reason. A person may divert medication both because she can’t afford

treatment and because she wants money. Increasing the weeks a person is willing to wait to begin treatment before relapsing increases diversion because of the way the demand for diverted buprenorphine is coded. People who are waiting for treatment will ask friends in treatment to divert, and will stop asking for diverted medication when they stop self-treatment and treatment seeking and resume regular opioid use. So in the model, relatively quick abandonment of treatment seeking results in less diversion demand.

Incidence of treatment seeking increases demand for diverted buprenorphine as people self-treat with diverted buprenorphine while waiting for formal treatment spots to open. Decreasing incidence of treatment seeking also likely reduces the supply of diverted buprenorphine since it also decreases the unique number of buprenorphine recipients.

Changes to poverty parameters affect diversion because most of the reasons for diversion are due to poverty. People with incomes below two times the poverty level might divert because they can’t afford treatment or need money. In the model, people whose incomes are above those levels will not divert due to affordability or money issues. The cost of treatment and medication did affect diversion because they impact affordability logic. A patient who pays less for treatment is less likely to find treatment unaffordable, and hedge the cost of treatment by selling medication.

Changes in the number of OTPs affects diversion from the supply side, by changing the relative proportion of people receiving methadone versus BUP for OAT.

Finally, the amount of diverted buprenorphine decreases when the percentage of people who require 16 mg per day of buprenorphine increases because of how required dosages are set. Increasing the number of people who require 16 mg doses squeezes down on the number of people getting 32 mg per day, followed by 24 mg per day, while decreasing the number of people who need 16 mg per day increases the number of people who need 8 mg per day. When diverting medication in the model,

people give up a fraction of what they receive. So if most people get less medication, less is diverted per diversion occasion.

The number of opioid overdose deaths was only affected by changes in the crude mortality rate for people not in treatment, and the change was approximately 1:1. A 30% increase in the mortality rate resulted in 27% more overdose deaths overall, and a 30% decrease resulted in a 28% decrease. That no other parameter impacted opioid overdoses is likely due to the fact in the model, the vast majority of people with OUD are not in treatment.