2025_June_melodem

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# .yellow[Causal estimands for memory trajectories in the presence of truncation by death]

.center[

L. Paloma Rojas-Saunero MD, PhD
<br>
Postdoctoral scholar
<br>
Department of Epidemiology, UCLA

]

???
“In aging research, especially when studying outcomes like memory decline, death is not just a nuisance—it's a fundamental part of the data-generating process. If we ignore it, we risk answering the wrong question. This talk is about how we define causal questions—or estimands—in the presence of death, and why getting those questions right is essential for interpreting results that inform science, care, and policy.”

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# Estimand

.center[<img src=./figs/estimands_meme_horizontal.jpg width="120%"/>]

.center[.bigger[Specific quantity that we want to estimate that answers our research question (_parameter of interest_).]]

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# Causal estimands have 5 elements

1. Target population

2. Exposure/Treatment arms

3. Outcome: within a time frame

4. Summary measure: A population-level measure of frequency that is _interpretable_ (e.g. mean difference, risk difference, risk ratio)

**5. Intercurrent events:** Events that will prevent us from observing the exposure or outcome (e.g. adverse reactions, death, loss to follow-up)

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# Intercurrent event of death

- We are interested in an an outcome at 1 year of follow-up, and participant dies at 6 months of follow-up

- If outcome is **dementia** (binary), the probability of dementia at 1 year is **0** 
  
    → Death is a **competing event** _(Rojas-Saunero et al, AJE, 2023)_

- If outcome is **memory** (continuous), then the expected value of **memory** at 1 year is **undefined**

→ Death is a _truncation event_
    
--

- Two randomized groups are not comparable **on their outcome distribution** in the presence of intercurrent events

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# What is the effect of APOE-ε4 on memory trajectories over 16 years of follow-up on US older adults?

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# Notation

- `\(A\)` = APOE-ε4 carriership (carrier/non carrier)

- `\(Y_{t,....t+k}\)` = Memory over time

- `\(D_{t,....t+k}\)` = Indicator of death over time

- `\(Z\)` = time-fixed common causes of death and memory function (e.g. education)

- `\(Z_t\)` = time-varying common causes of death and memory function (e.g. cardiovascular)

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# Counterfactual Notation

- `\(E(Y^{a=1}_{t+k})\)` = Mean memory score had everyone was an APOE-ε4 carrier

- `\(E(Y^{a=0}_{t+k})\)` = Mean memory score had everyone was an APOE-ε4 non-carrier

- `\(E(Y^{a=1}_{t+k})\)` - `\(E(Y^{a=0}_{t+k})\)` = Mean differences in memory function

.center[.bigger[**But this estimand is incomplete as we have not incorporated death as part of the estimand**]]

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# Controlled direct effect (CDE)

.pull-left[

Effect of `\(A\)` on `\(Y_{t+k}\)`, eliminating `\(\overline{D_k}\)`

`\(E(Y^{a=1, \overline{d} = 0}_{t+k}) - E(Y^{a=0, \overline{d} = 0}_{t+k})\)`

<img src=./figs/cde.png />
]

.footnote[
_Weuve et al. Epidemiology, 2012_
]

--
.pull-right[

**Key assumptions for death:**
- We assume death is independent of future memory function had everyone followed 𝐴=𝑎, conditional on measured past and had death been eliminated.

- No unmeasured common causes of death and memory function

]

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# Conditional separable effect (CSE)

All effect of `\(A\)` on `\(Y_{t+k}\)`, outside of `\(\overline{D_k}\)`

.center[
<img src=./figs/cse.png width="40%"/>

]

.footnote[
_Stensrud et al. JASA, 2023_

]

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# Conditional separable effect (CSE)

**Key assumptions for death:** 
- `\(A_Y\)` increases amyloid and tau production & `\(A_D\)` targets lipid metabolism and endothelial function

- No causal paths from `\(A_Y\)` to `\(D_{t+k}\)`

- No unmeasured common causes of death and memory function

- `\(E(Y^{a_Y=1, a_D = 0}_{t+k}|D^{a_Y=1, a_D = 0}_{t+k} = 0) - E(Y^{a_Y=0, a_D = 0}_{t+k}|D^{a_Y=0, a_D = 0}_{t+k} = 0)\)`

.footnote[
_Stensrud et al. JASA, 2023_

]

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# Application

- **Data:** Health and Retirement Study

- **Population:** Participants with genetic data collected between 2006-2012 (N = 15896), 58% women, mean baseline age 64 (SD: 11)

- **Exposure:** APOE-ε4 genotype (26% carriers/ 74% non-carriers)

- **Outcome:** Memory scores from 2006 to 2022

- **Covariates:** age at APOE-ε4 measurement, sex/gender, education; _time-varying_: self-reported health status, BMI, diagnosis of: hypertension, diabetes, cancer, lung disease, heart disease and stroke

- **Intercurrent events**: 30% died and 19% were lost to follow-up by end of study

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# Statistical analysis

We derived marginal mean differences in memory scores at every study wave contrasting APOE-ε4 carriers versus non-carriers. 95%CI from bootstrapping

- **CDE:** Following Weuve et al (2012), we used a GEE model + IPCW with a working exchangeable correlation matrix

- **CSE:** Following Stensrud et al (2023), we used an outcome regression estimator

- **As observed:** `\(E(Y|A=1, D_{t+k} = 0) - E(Y|A=0, D_{t+k} = 0)\)`,
not causal, estimated for comparison. GEE with independent correlation matrix

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## .center[Marginal mean differences in memory scores comparing APOE-ε4 carriers and non-carriers]

.center[
<img src=./figs/results.png width="60%"/>
]

???
APOE-ε4 carriers scored lower on memory function compared to non-carriers, and this difference grew larger over time

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# Take aways

- Different estimands lead to different magnitudes of the estimates

- What estimand should we choose? No right or wrong answer, it’s a trade-off between assumptions, interpretation, and computational feasibility

- What about mix and joint models? We need to map these estimators to estimands first

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# Thank you, Gracias!

.pull-left[

**Mayeda Research Group**

**Collaborators:**

- Yixuan (Juliet) Zhou 
- Yingyan Wu
- Lan Wen
- Onyiebuchi A. Arah
- Joan A. Casey
- Elizabeth Rose Mayeda

**NIA R01AG074359**
]

.pull-right[

]

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# Other estimands

- Survival Average Causal Effect

`\(E[Y_t^{a=1}|D_t^{a=1} = D_t^{a=0} = 0] - E[Y_t^{a=0}|D_t^{a=1} = D_t^{a=0} = 0]\)`

- Composite Outcome

`\(E[Y_{t}^{a = 1}  \text{ or } {Y|D}_{t}^{a = 1} = x] - E[Y_{t}^{a = 0} \text{ or } {Y|D}_{t}^{a = 0} = x]\)`, where `\(x\)` is a value for memory function after death

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## Controlled direct effect controversies

Thernau, Survival R Package documentation, 2023

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<img src=./figs/chaix2012.png width="80%"/>

Chaix et al, Epidemiology, 2012

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<img src=./figs/andersen.png width="70%"/>

Andersen & Keiding, Statistics in Medicine, 2012

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## History of competing events analysis

.footnote[During the 18th century smallpox epidemic, smallpox inoculation was a controversial therapy]

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## History of competing events analysis

- Bernoulli wanted to estimate how smallpox inoculation could improve life expectancy (LE)

- He compared a hypothetical scenario of universal inoculation (eliminating smallpox deaths) to observed LE, concluding innoculation would increase LE

- D’Alembert criticized Bernoulli’s approach before the Académie des Sciences, arguing it introduced subjective biases into mathematical probability, shaped by moral and political views.

- Counterfactual scenarios, such as preventing tuberculosis or cancer deaths, became increasingly popular

.footnote[Colombo & Diamanti, Lettera Matematica, 2015]

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## CSE estimation