Incremental propensity score effects of buprenorphine retention on opioid-involved overdose events in pregnancy

<span style="font-size: 50px;"> Incremental propensity score effects of buprenorphine retention on opioid-involved overdose events in pregnancy </span> <br>
<span style="font-size: 28px; color: #a8c5d8;">  </span>

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<td style="border: none; border-right: 1px solid #6ca3d9; padding: 2px 5px; background: transparent;"><strong>Ashley I Naimi, PhD</strong></td>
<td style="border: none; padding: 2px 5px; background: transparent;">Dept of Epidemiology</td>
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<td style="border: none; border-right: 1px solid #6ca3d9; padding: 2px 5px; background: transparent;">Professor</td>
<td style="border: none; padding: 2px 5px; background: transparent;">Emory University</td>
</tr>
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<div style="line-height: 1.2;">
<svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M64 112c-8.8 0-16 7.2-16 16v22.1L220.5 291.7c20.7 17 50.4 17 71.1 0L464 150.1V128c0-8.8-7.2-16-16-16H64zM48 212.2V384c0 8.8 7.2 16 16 16H448c8.8 0 16-7.2 16-16V212.2L322 328.8c-38.4 31.5-93.7 31.5-132 0L48 212.2zM0 128C0 92.7 28.7 64 64 64H448c35.3 0 64 28.7 64 64V384c0 35.3-28.7 64-64 64H64c-35.3 0-64-28.7-64-64V128z"/></svg> &nbsp; <a href="mailto:ashley.naimi@emory.edu">ashley.naimi@emory.edu</a> <br>
<svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M352 256c0 22.2-1.2 43.6-3.3 64H163.3c-2.2-20.4-3.3-41.8-3.3-64s1.2-43.6 3.3-64H348.7c2.2 20.4 3.3 41.8 3.3 64zm28.8-64H503.9c5.3 20.5 8.1 41.9 8.1 64s-2.8 43.5-8.1 64H380.8c2.1-20.6 3.2-42 3.2-64s-1.1-43.4-3.2-64zm112.6-32H376.7c-10-63.9-29.8-117.4-55.3-151.6c78.3 20.7 142 77.5 171.9 151.6zm-149.1 0H167.7c6.1-36.4 15.5-68.6 27-94.7c10.5-23.6 22.2-40.7 33.5-51.5C239.4 3.2 248.7 0 256 0s16.6 3.2 27.8 13.8c11.3 10.8 23 27.9 33.5 51.5c11.6 26 20.9 58.2 27 94.7zm-209 0H18.6C48.6 85.9 112.2 29.1 190.6 8.4C165.1 42.6 145.3 96.1 135.3 160zM8.1 192H131.2c-2.1 20.6-3.2 42-3.2 64s1.1 43.4 3.2 64H8.1C2.8 299.5 0 278.1 0 256s2.8-43.5 8.1-64zM194.7 446.6c-11.6-26-20.9-58.2-27-94.6H344.3c-6.1 36.4-15.5 68.6-27 94.6c-10.5 23.6-22.2 40.7-33.5 51.5C272.6 508.8 263.3 512 256 512s-16.6-3.2-27.8-13.8c-11.3-10.8-23-27.9-33.5-51.5zM135.3 352c10 63.9 29.8 117.4 55.3 151.6C112.2 482.9 48.6 426.1 18.6 352H135.3zm358.1 0c-30 74.1-93.6 130.9-171.9 151.6c25.5-34.2 45.2-87.7 55.3-151.6H493.4z"/></svg> &nbsp; <a href="https://ainaimi.github.io/">https://ainaimi.github.io/</a>
</div>

---

# My Research

<div class="jt-cards two large">
  <div class="jt-card">
    <span class="jt-card-title">The problems</span>
    Reproductive, perinatal, and maternal health. <br> Causal inference, Machine Learning, Study Design, Statistical Inference, Reproducibility.
  </div>
  <div class="jt-card">
    <span class="jt-card-title">The questions</span>
    What would happen if something was different? For whom? How do we estimate this <em>credibly</em> from data (when possible)?
  </div>
</div>

<br>

.font130[
Methodological themes: **causal estimands** chosen to fit the question/decision; **doubly robust estimation with machine learning**; **effect heterogeneity**; **reproducible, auditable workflows**.
]

---

---

# EARTH · The question

.jt-bigq[Does the age-related decline in ovarian reserve depend on a woman's exposure to <em>endocrine-disrupting chemicals</em>?]

.pull-left-a-lot[
<dl class="jt-kv compact">
  <dt>Background</dt>
  <dd>Antral follicle count falls with age: mean 16.9 under 35 versus 11.6 at 35 and older among 775 women at the MGH Fertility Center (EARTH Study, 2004–2019).</dd>
  <dt>Question</dt>
  <dd>Do any of 16 chemicals (11 urinary phthalate metabolites, 3 parabens, bisphenol A, hair mercury) change age associated declines in AFC?</dd>
  <dt>Challenge</dt>
  <dd>Sixteen candidate modifiers, skewed concentrations, possible interactions: standard regression / EMM is not built for this.</dd>
</dl>
]

.pull-right-a-little[
<img class="jt-card-img" src="images/earth/main_scatterplot.png" alt="Scatterplot of antral follicle count against age in 775 women, with a smooth curve declining from about 21 follicles in the mid-twenties to about 9 in the early forties." style="width: 78%; display: block; margin: 0 auto;">
<p class="jt-fig-caption">Antral follicle count by age, EARTH Study.</p>
]

<div class="jt-source">Naimi, Kennedy, Yu, Hauser, Mínguez-Alarcón, Gaskins. <em>Environmental Epidemiology</em>, In Press.</div>

---

# EARTH · Method and results

.pull-left-a-little[
<dl class="jt-kv compact">
  <dt>1 · Nuisance models</dt>
  <dd>10-fold cross-validated Super Learner for P(age ≥ 35 | X) and E(AFC | age, X): random forests, penalized regression, boosting, MARS, GLMs with screened interactions.</dd>
  <dt>2 · Pseudo-outcome</dt>
  <dd>The AIPW score, the efficient influence function of the standardized mean difference. Its average: −5.1 follicles (95% CI −6.2, −3.9).</dd>
  <dt>3 · Which chemicals modify?</dt>
  <dd>Best linear projection of the score on the 16 log-concentrations; Wald statistics, conditional and unconditional.</dd>
  <dt>4 · How?</dt>
  <dd>Cross-validated LOESS of the score on the leading modifiers.</dd>
</dl>
]

.pull-right-a-lot[
<img class="jt-card-img" src="images/earth/cate_functions_paper.png" alt="Three panels showing the age–AFC association (difference in antral follicle count, 35 and older versus under 35) across log concentrations of MiBP, MCOP, and MEHP. The dashed line marks the overall association of about minus 5. For MiBP the curve bends down beyond a log concentration near 1.5; for MCOP beyond about 4; for MEHP it declines steadily across the range." style="width: 100%;">
<p class="jt-fig-caption">Age–AFC difference across MiBP, MCOP, and MEHP; dashed line: the overall −5.1. The decline steepens beyond about 4.5 μg/L of MiBP and 50 μg/L of MCOP, and steadily with MEHP. Other chemicals: no modification.</p>
]

<div class="jt-source">Naimi, Kennedy, Yu, Hauser, Mínguez-Alarcón, Gaskins. <em>Environmental Epidemiology</em>, In Press.</div>

---

---

# COESTAR-IVF · The question

.jt-bigq[During ovarian stimulation, does changing <em>today's</em> gonadotropin dose change the outcome? For which patients? Which days are more/less important?]

.pull-left-a-lot[
<dl class="jt-kv compact">
  <dt>The setting</dt>
  <dd>About 435,000 ART cycles a year in the US; roughly half of cycles in women under 35 end in a live birth; a cycle costs $15,000 to $20,000.</dd>
  <dt>The decisions</dt>
  <dd>A starting dose, adjustments at monitoring visits from estradiol and follicle growth, and the day of trigger, guided by heuristics that vary by physician. In the pilot, 34% of cycles change dose mid-cycle and 94% of changes fall on a visit day.</dd>
  <dt>Why it is hard</dt>
  <dd>Each day's dose responds to markers that earlier doses shaped: time-varying confounding by indication. The sequentially randomized trial that would settle it has never been run in IVF.</dd>
</dl>
]

.pull-right-a-little[
<img class="jt-card-img" src="images/coestar/fig2_dose_trajectories.png" alt="Daily gonadotropin dose trajectories across stimulation days 0 to 15 in the pilot cohort, one jittered line per cycle. Lines concentrate on standard dose levels between 150 and 450 IU, with frequent mid-cycle switches between levels." style="width: 92%; display: block; margin: 0 auto;">
<p class="jt-fig-caption">Daily dose trajectories, pilot cohort: 1,485 autologous cycles, 1,142 women, 2024–2025.</p>
]

<div class="jt-source">COESTAR-IVF: Causal Optimization with Emulated Sequential Trials for Assisted Reproduction. R01 research plan, 2026, with A. Gaskins and the Emory Reproductive Center.</div>

---

# COESTAR-IVF · Method and pilot results

.pull-left-a-little[
<dl class="jt-kv compact">
  <dt>Design</dt>
  <dd>Sequential nested target trial emulation: a trial nested at every decision day, from EHR and SART-CORS data on about 4,000 patients (2014–2025).</dd>
  <dt>Estimand</dt>
  <dd>SNMM blip effects: the change in outcome if today's dose were raised 75 IU (or the trigger given today, or a visit deferred), holding history fixed.</dd>
  <dt>Estimation</dt>
  <dd>G-estimation by residual-on-residual regression; Super Learner nuisance models with cross-fitting; sandwich variance clustered on women; g-sensitivity analysis.</dd>
</dl>
]

.pull-right-a-lot[
<div class="jt-stats three">
  <div class="jt-stat"><span class="jt-num">1.1</span><span class="jt-label">more mature oocytes per +75 IU from pooled regression on daily dose (95% CI −1.4 to 1.9)</span></div>
  <div class="jt-stat"><span class="jt-num accent">5.5</span><span class="jt-label">g-estimated blip for +75 IU on day 3 (95% CI 1.2 to 7.7); days 6, 9, and 12 near null and imprecise</span></div>
  <div class="jt-stat"><span class="jt-num">94%</span><span class="jt-label">interval coverage in a simulation calibrated to the cohort, bias −0.002; pooled regression about 10 times too large</span></div>
</div>

<div style="display: flex; align-items: flex-start; gap: 18px; margin-top: 14px;">
<img class="jt-card-img" src="images/coestar/fig4_blip_effects.png" style="flex: 0 0 44%; width: 44%;" alt="Point estimates with 95 percent confidence intervals of the single-day blip effect of a 75 IU dose increase on total oocytes retrieved at stimulation days 3, 6, 9, and 12. Day 3 is about 5.5 with an interval excluding zero; later days are near zero with wide intervals.">
<p class="jt-fig-caption" style="margin-top: 6px; flex: 1;">Single-day blip effects of +75 IU on total oocytes retrieved, by stimulation day (pilot cohort, 1,485 cycles). The start-dose decision matters; later titration shows little effect so far.</p>
</div>

<p class="jt-note jt-mt10">Next: Aim 2, safety-constrained optimal regimens in a physician-in-the-loop tool; Aim 3, blinded shadow validation in 800 cycles.</p>
]

<div class="jt-source">Pilot: 2024–2025 EHR extract, 1,485 autologous cycles, 1,142 women. Full study: primary outcome cumulative live birth; safety outcome OHSS.</div>

---

# Acknowledgements

<dl class="jt-kv">
  <dt>Manuscript</dt>
  <dd>Rogers, Cooper, Kramer, Sullivan, Naimi. <em>Incremental propensity score effect of buprenorphine retention on opioid-involved overdose and acute hospital encounters during pregnancy and postpartum.</em> Under review.</dd>
  <dt>Support</dt>
  <dd>NIH / NIDA training grant 5T32DA050552. Opinions are the authors' own.</dd>
</dl>

---

# Overdose has become a leading cause of maternal death

.pull-left-a-lot[
<img class="jt-card-img" src="images/cseb/maternal_overdose_deaths_bruzelius2022.png" alt="Line chart of US overdose deaths per 100,000 among pregnant and postpartum persons, 2017 to 2020, by drug type: deaths involving fentanyl and other synthetic opioids rise steeply to nearly 10 per 100,000 by 2020; psychostimulants rise as well; heroin, prescription opioids, and benzodiazepines stay near 1 to 2." style="width: 100%;">
<p class="jt-fig-caption">Drug types driving overdose deaths among pregnant and postpartum persons, United States, 2017–2020.</p>
]

.pull-right-a-little[
<dl class="jt-kv">
  <dt>Opioid use disorder at delivery</dt>
  <dd>More than quadrupled between 1999 and 2014: from 1.5 to 6.5 per 1,000 delivery hospitalizations.</dd>
  <dt>Synthetic opioids</dt>
  <dd>A near-exponential rise in fentanyl-involved deaths during pregnancy and postpartum, mirroring the broader epidemic.</dd>
  <dt>The research gap</dt>
  <dd>Most work on opioids in pregnancy studies birth outcomes. Far less asks what happens to the pregnant person.</dd>
</dl>
]

<div class="jt-source">Bruzelius E, Martins SS. <em>JAMA</em> 2022;328(21):2159 (figure). Haight SC et al. <em>MMWR</em> 2018;67(31):845.</div>

---

# Buprenorphine works, if people stay on it

.pull-left[
<dl class="jt-kv">
  <dt>Standard of care</dt>
  <dd>Buprenorphine or methadone is first-line for pregnant people with OUD.</dd>
  <dt>Guidance</dt>
  <dd>ACOG: universal screening and linkage to agonist therapy, rather than medically supervised withdrawal (detox), which carries high relapse rates.</dd>
</dl>
]

.pull-right[
<dl class="jt-kv">
  <dt>Treatment gap</dt>
  <dd>An estimated ~60% of pregnant people with OUD receive no treatment. Among those who do, many are underdosed.</dd>
  <dt>Retention gap</dt>
  <dd>Fear of provider stigma or custody loss, and providers tapering patients off medication, cut treatment short.</dd>
  <dt>What we know about retention</dt>
  <dd>Poor retention &#10140; worse withdrawal, more ED visits.</dd>
</dl>
]

<div class="jt-source">WHO 2020 guidelines; ACOG Committee Opinion 2017; Suarez et al. <em>NEJM</em> 2022; Martin 2015; Schiff 2020; Caritis 2017; Work 2023; Coker 2018; Lo-Ciganic 2019.</div>

---

# The question

.jt-kicker[Among pregnant people who start buprenorphine, how does staying on treatment affect the risk of:]

<div class="jt-cards">
  <div class="jt-card accent">
    <span class="jt-card-title">Opioid-involved overdose</span>
    Fatal or nonfatal; the outcome we most want to prevent.
  </div>
  <div class="jt-card">
    <span class="jt-card-title">Medically supervised withdrawal (detox)</span>
    An acute encounter that signals discontinuation. Detox without ongoing medication lowers tolerance, and relapse afterward is common and dangerous.
  </div>
  <div class="jt-card">
    <span class="jt-card-title">Opioid-related emergency department visits</span>
    Acute care with an OUD diagnosis on record; an opportunity to re-engage, and a cost.
  </div>
</div>

<br>

.font120[
...during pregnancy and the first year after treatment starts, in a large commercially insured population.
]

---

# Who is in the study

<div class="jt-source">Additional eligibility: no methadone in the 6 months before the index fill (to avoid attributing effects to switching); enrollment from 6 months before pregnancy through the pregnancy outcome. Intermediate counts are person-level; the analytic sample is the manuscript's 3,021 pregnancies (Figure 1 reports pregnancy-level counts).</div>

---

# The analysis flow

.jt-kicker.tight[The comparison we set out to make: the longitudinal average treatment effect.]

`$$\psi = E\!\left(Y^{\bar{a}_{52} = 1,\; D_{52} = 1}\right) - E\!\left(Y^{\bar{a}_{52} = 0,\; D_{52} = 1}\right)$$`

.jt-eq-note[
Risk of the outcome by 52 weeks if everyone were retained every week (and stayed enrolled), minus the risk if no one were retained in any week. Identified under consistency, sequential exchangeability given measured history, no interference, and positivity.
]

---

# Positivity, checked: the contrast is not in the data

.pull-left-a-lot[
<img class="jt-card-img" src="images/manuscript/fig4_cumulative_ps_by_week.png" alt="Box plots of the cumulative propensity score by week of follow-up, weeks 0 to 52, separately for people retained (white) and not retained (black) in that week. Values start near 1 in week 1 and collapse toward zero within a few months; by week 36 nearly all values are below 0.05." style="width: 90%;">
]

.pull-right-a-little[
<dl class="jt-kv">
  <dt>Week 1</dt>
  <dd>Cumulative propensity to have been retained so far: about 0.91 on average.</dd>
  <dt>Week 12</dt>
  <dd>About 0.07 (interquartile range below 0.001 to 0.55).</dd>
  <dt>Week 36</dt>
  <dd>Below 0.001.</dd>
</dl>

<div class="jt-takeaway small">"Retained for all 52 weeks" is essentially unobservable for most people. The ATE is not identified here, and it is not a realistic intervention either.</div>
]

<div class="jt-source">Cumulative propensity score by week, from the manuscript (Figure 4). Positivity violations of this kind grow with the number of time points.</div>

---

# The incremental propensity score intervention

.pull-left[
.jt-kicker.tight[Instead of setting treatment, shift each person's weekly odds of retention by a factor δ:]

`$$q_t(\delta) = \frac{\delta\,\pi_t}{\delta\,\pi_t + 1 - \pi_t}, \qquad \delta = \frac{q_t / (1 - q_t)}{\pi_t / (1 - \pi_t)}$$`

<dl class="jt-kv compact">
  <dt>Example</dt>
  <dd>A person with π = 0.35 this week moves to 0.45 under δ = 1.5, and one with π = 0.5 moves to 0.75 under δ = 3.</dd>
  <dt>δ = 1</dt>
  <dd>The observed world: no intervention on retention.</dd>
  <dt>δ &gt; 1 / δ &lt; 1</dt>
  <dd>Retention made more likely / less likely, for everyone, in proportion to where they start.</dd>
</dl>
]

.pull-right[
<img class="jt-card-img" src="images/ips/shift_plot_numom_dark.png" alt="Shifted propensity score against the odds ratio delta on a log scale from 0.2 to 5, one curve for each observed propensity score from near 0 to near 1. Every curve passes through its observed value at delta = 1, marked by a vertical line, rises toward 1 as delta grows and falls toward 0 as delta shrinks; propensities near 0.5 move the most." style="width: 68%; display: block; margin: 0 auto;">
<p class="jt-fig-caption">Each curve is one observed propensity score; follow it left or right to read q(δ). Vertical line: δ = 1. Naimi et al., <em>Epidemiology</em> 2021.</p>
]

<div class="jt-source">Kennedy EH. <em>JASA</em> 2019;114(526):645. With dropout: Kim, Kennedy, Naimi, arXiv 1907.04004. Rudolph et al. <em>Epidemiology</em> 2023;34(1):38.</div>

---

# The estimand: risk under a shifted retention process

`$$\psi_{52}(\delta) = E\!\left[\,Y^{\bar{Q}_{52}(\delta),\; D_{52} = 1}\right]$$`

.jt-eq-note[
The risk of the outcome by 52 weeks if, each week, retention were drawn with the shifted probability q<sub>t</sub>(δ) instead of the observed π<sub>t</sub>, and no one dropped out. Compare across δ, with δ = 1 as the reference; δ ranged from 0.3 to 3.0.
]

.jt-eq-note[
Reading δ = 3 against δ = 1: what if we tripled everyone's weekly odds of staying on treatment?
]

---

# Incremental effects, formally

.jt-kicker.tight[Single time point (Kennedy 2019): the incremental effect is a weighted average of the two conditional risks, with weights set by the shifted propensity.]
<br><br><br>
`$$\varphi(\delta) = \mathbb{E}\left[ \frac{\delta\,\pi(X)\,\mu(X,1) + \{1 - \pi(X)\}\,\mu(X,0)}{\delta\,\pi(X) + \{1 - \pi(X)\}} \right] = \mathbb{E}\big[\mu(X, A^*)\big], \qquad A^* \mid X = x \sim \text{Bernoulli}\{q(x)\}$$`
<br><br><br>

.jt-eq-note[
Each week's treatment is drawn from the shifted propensity q<sub>j</sub>(δ); the covariate process evolves as observed given the past. Because no factor in the product requires π<sub>j</sub> to be bounded away from 0 or 1, positivity is not needed.
]

<div class="jt-source">Kennedy EH. Nonparametric causal effects based on incremental propensity score interventions. <em>JASA</em> 2019;114(526):645–656. Kim K, Kennedy EH, Naimi AI. Incremental intervention effects in studies with many timepoints, repeated outcomes, and dropout. arXiv:1907.04004.</div>

---

# Estimation

<div class="jt-cards jt-mt20">
  <div class="jt-card">
    <span class="jt-card-title">Why doubly robust?:</span>
    The estimator is built from EIF, so it is consistent if either the treatment/dropout models or the outcome models are right, and converges at parametric rates even if machine-learning used.
  </div>
  <div class="jt-card">
    <span class="jt-card-title">Why Super Learner?</span>
    A cross-validated ensemble of GLMs, random forests, and k-nearest neighbors for every nuisance model. Avoids need to assume logistic regression with 52 weeks of history is correctly specified.
  </div>
  <div class="jt-card">
    <span class="jt-card-title">Why sample splitting?</span>
    Fitting the nuisance models and evaluating the estimator on different folds keeps the machine learning from contaminating variance (empirical process conditions).
  </div>
</div>

---

# What the causal interpretation still requires

<div class="jt-assume">
  <div class="jt-a-name">Consistency</div>
  <div class="jt-a-what">A week classified as "retained" corresponds to a well-defined treatment. Fills are not consumption; this is the assumption most at risk.</div>
  <div class="jt-a-name">Exchangeability</div>
  <div class="jt-a-what">Given measured history (baseline and weekly covariates), retention is as good as random each week. Claims lack stigma, provider practice, social support, and race/ethnicity.</div>
  <div class="jt-a-name">No interference</div>
  <div class="jt-a-what">One person's retention does not affect another's outcome.</div>
  <div class="jt-a-name struck">Positivity</div>
  <div class="jt-a-what struck">Every person could be observed under every treatment history. Not needed for incremental effects.</div>
</div>

<div class="jt-takeaway">Changing the estimand removed the need for the failed assumption, but did nothing about the two we cannot check.</div>

---

# Shifting retention upward lowers the risk of detox

.pull-left-a-little[
<img class="jt-card-img" src="images/manuscript/fig5_hi_detox.png" alt="Estimated 52-week incidence of medically supervised withdrawal across delta from 0.3 to 3.0 with a grey 95 percent confidence band. The curve is near 0.11 for delta below 1, crosses the reference at delta = 1 near 0.104, and falls to about 0.05 by delta = 3." style="width: 70%; display: block; margin: 0 auto;">
]

.pull-right-a-lot[
<div class="jt-callouts">
<div class="jt-callout">
<span class="jt-big">10.4%</span>
<span class="jt-small">risk of detox by 52 weeks under the observed retention process (δ = 1), had no one dropped out (95% CI 8.9 to 11.7)</span>
</div>
<div class="jt-callout accent">
<span class="jt-big">4.9%</span>
<span class="jt-small">risk if everyone's weekly odds of retention were tripled (δ = 3) (95% CI 3.6 to 6.2)</span>
</div>
<div class="jt-callout accent">
<span class="jt-big">−5.5 per 100</span>
<span class="jt-small">risk difference, δ = 3 versus δ = 1 (95% CI −6.9 to −3.9): 55 fewer detox encounters per 1,000 pregnancies. At δ = 2: −4.2 (−5.5 to −3.0).</span>
</div>
</div>
]

<div class="jt-source">Manuscript Figure 5 and Table 2 (retention: at least 5 of 7 days covered in the week; N = 3,021). Grey band: pointwise 95% confidence interval. Dashed lines: the observed world (δ = 1). Making retention less likely (δ &lt; 1) produced no meaningful change.</div>

---

# Overdose and ED visits: the same direction

.pull-left-a-lot[
<div style="display: flex; justify-content: center; gap: 16px;">
<img class="jt-card-img" src="images/manuscript/fig5_hi_overdose.png" alt="Estimated 52-week incidence of opioid-involved overdose across delta with a wide grey 95 percent band. The point estimate is about 0.022 at delta = 1 and declines to about 0.015 at delta = 3; the band spans roughly 0.007 to 0.022 at delta = 3." style="width: 46%;">
<img class="jt-card-img" src="images/manuscript/fig5_hi_ed.png" alt="Estimated 52-week incidence of opioid-related emergency department visits across delta with a 95 percent band. Risk is about 0.145 at delta = 1 and declines to about 0.108 at delta = 3." style="width: 46%;">
</div>
]

.pull-right-a-little[
<div class="jt-callouts">
<div class="jt-callout accent">
<span class="jt-big">2.2% → 1.5%</span>
<span class="jt-small">overdose, δ = 1 to δ = 3; risk difference −0.7 per 100 (95% CI −1.5 to 0.03)</span>
</div>
<div class="jt-callout accent">
<span class="jt-big">14.5% → 10.8%</span>
<span class="jt-small">ED visits with an OUD diagnosis, δ = 1 to δ = 3; risk difference −4.0 per 100 (95% CI −6.1 to −2.0)</span>
</div>
</div>

<div class="jt-takeaway small">Both fall as retention becomes more likely. Overdose is rare, so its interval is wide and just includes zero.</div>
]

<div class="jt-source">Manuscript Figure 5 and Table 2 (N = 3,021). Grey bands: pointwise 95% confidence intervals. Dashed lines: the observed world (δ = 1).</div>

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# Summary of results

<table class="jt-table">
  <thead>
    <tr><th>Outcome by 52 weeks</th><th class="num">Observed</th><th class="num">δ = 1</th><th class="num">δ = 2</th><th class="num">δ = 3</th><th class="num" style="white-space: nowrap;">RD, δ = 3 vs 1 (95% CI)</th></tr>
  </thead>
  <tbody>
    <tr><td>Medically supervised withdrawal (detox)</td><td class="num">8.8%</td><td class="num">10.4%</td><td class="num">7.7%</td><td class="num">4.9%</td><td class="num">−5.5 (−6.9, −3.9)</td></tr>
    <tr><td>Opioid-related emergency department encounter</td><td class="num">11.9%</td><td class="num">14.5%</td><td class="num">11.9%</td><td class="num">10.8%</td><td class="num">−4.0 (−6.1, −2.0)</td></tr>
    <tr><td>Opioid-involved overdose</td><td class="num">2.2%</td><td class="num">2.2%</td><td class="num">1.9%</td><td class="num">1.5%</td><td class="num">−0.7 (−1.5, 0.03)</td></tr>
  </tbody>
</table>

<br>

<div class="jt-takeaway">Making retention on buprenorphine more likely, week by week, reduces acute opioid-related care during pregnancy and the postpartum year. The largest and most precise effect is on detox; overdose moves in the same direction with wide uncertainty.</div>

<div class="jt-source">Risks per 100 pregnancies under the shifted retention process with dropout removed (manuscript Table 2; N = 3,021). "Observed" is the crude incidence among all participants. Below δ = 1 no outcome changed meaningfully. Threshold sensitivity analyses (PDC 0.5 to 0.9, CSEB 2025) show the same trajectories.</div>

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# Limitations

<div class="jt-cards two">
  <div class="jt-card accent">
    <span class="jt-card-title">Consistency: fills are not doses</span>
    Proportion of days covered is a billing proxy for medication taken. Dose changes, which matter in pregnancy, are not captured at all.
  </div>
  <div class="jt-card accent">
    <span class="jt-card-title">Exchangeability: context is missing</span>
    No race or ethnicity, stigma, provider practices, incarceration, or social support. The estimator is doubly robust to model misspecification, not to unmeasured confounding.
  </div>
  <div class="jt-card">
    <span class="jt-card-title">Generalizability</span>
    A commercially insured cohort. About a third of pregnant people with OUD; Medicaid populations face different barriers, especially postpartum.
  </div>
  <div class="jt-card">
    <span class="jt-card-title">Design limits</span>
    Left truncation (entry at the first fill in pregnancy, not at treatment start); first event only; no mortality linkage, so fatal overdoses are captured only if they generated a claim.
  </div>
</div>

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