Competing events in dementia research

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## Considering questions before methods in dementia research with competing events and causal goals

<br>

.pull.right[

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

]

---
background-image: url(./figs/hill.jpg)
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.footnote[Hill et al. _Ethnicity and disease_. 2015]

---
background-image: url(./figs/press1.PNG)
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.footnote[www.express.co.uk, 2016]

---
background-image: url(./figs/press2.PNG)
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.footnote[Medscape, 2019]

---
background-image: url(./figs/cr_austin.PNG)
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## Cause-specific vs. subdistribution HR

.footnote[Austin et al. _Circulation_.2016]

---
## Systematic review

**Searching criteria**

- Original research published between Jan/2018 to Dec/2019

- Dementia/AD & longitudinal/cohort & hazard/risk

- Alzheimer’s and Dementia, Annals of Neurology, BMJ, Neurology, JAMA, Jama Neurology, Lancet, Lancet Neurology
  
--

**Eligibility criteria**

- Time-to-dementia/AD as primary or co-primary outcome

- With a clear exposure/intervention, and uses methods to handle confounding

- Not a descriptive or predictive aim

---

## Results

Out of **57/209** papers included:

- **56%** report death numbers, **18%** death by exposure level

- **47%** do not include any description about death in the methods section, **26%** consider it a sensitivity example, **14%** only mention it was treated as a censoring event

- **87%** use Cox PH models, **93%** present hazard ratios

- **86%** innacurate interpretations (e.g. "_risks_")

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.center[

![](figs/aje.jpg)

]

---
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![](figs/dag1.jpg)

---
## Total effect

<br>

.center[
.middle[

What is the risk of dementia at 20 years of follow-up had all individuals stopped smoking, compared to had all individuals continued smoking?

`$$Pr[Y_{20}^{a = 1}] - Pr[Y_{20}^{a = 0}]$$`

]]

![](figs/dagte.jpg)

---

## Controlled direct effect

<br>

.center[
.middle[

What is the risk of dementia at 20 years of follow-up had all individuals stopped smoking _and not died_ throughout the study period, compared to had all individuals continued smoking in adulthood _and not died_ throughout the study period?

`$$Pr[Y_{20}^{a = 1, d_{19} = 0}] - Pr[Y_{20}^{a = 0, d_{19} = 0}]$$`

]
]

![](figs/dagde.jpg)

---

## Controlled direct effect

<br>

.center[
.middle[

`$$Pr[Y_{20}^{a = 1, d_{19} = 0}] - Pr[Y_{20}^{a = 0, d_{19} = 0}]$$`

]
]

![](figs/dagde2.jpg)

---

## Identifiability assumptions

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<td headers="<b> Controlled direct effect </b>" class="gt_row gt_left">At each k + 1, conditional on the measured past, death is independent of future counterfactual outcomes had everyone followed A = a and death was eliminated.</td></tr>
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---

## Identifiability assumptions
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<td headers="<b> Controlled direct effect </b>" class="gt_row gt_left">At each k + 1, conditional on the measured past, death is independent of future counterfactual outcomes had everyone followed A = a and death was eliminated.</td></tr>
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---
## Identifiability assumptions

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      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="&lt;b&gt; Controlled direct effect &lt;/b&gt;"><b> Controlled direct effect </b></th>
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<td headers="<b> Controlled direct effect </b>" class="gt_row gt_left">At each k + 1, conditional on the measured past, death is independent of future counterfactual outcomes had everyone followed A = a and death was eliminated.</td></tr>
    <tr><td headers="<b> Assumption </b>" class="gt_row gt_left"><b> Positivity assumption needed for death (competing events)? </b></td>
<td headers="<b> Total Effect </b>" class="gt_row gt_left">Not needed</td>
<td headers="<b> Controlled direct effect </b>" class="gt_row gt_left">For any possibly observed level A = a and covariate history amongst those remaining uncensored (alive) and free of dementia diagnosis through k, some individuals continue to remain alive through _k + 1_.</td></tr>
    <tr><td headers="<b> Assumption </b>" class="gt_row gt_left"><b> Consistency assumption needed for death (competing events) </b></td>
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</div>

---
## Application

- Participants from Rotterdam Study I, recruited between 1990-1993 and with follow-up data

- Current and former smokers

- No prior history of dementia diagnosis

- Complete information at baseline

- Final sample size of 4179 participants

- Mean age at baseline of 62 years

- 368 developed dementia and 1318 died

---
## Analysis plan

- **For confounding:** Inverse probability weighting for treatment (IPTW)

- **Total effect:** Cause-specific cumulative incidence / Aalen-Johansen estimator + IPTW

- **Controlled direct effect:** Kaplan-Meier + Inverse probability censoring weights + IPTW

- Bootstrapping for confidence intervals

Semi-parametric or parametric alternatives are also possible

---
## Results

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</style>
<table class="gt_table" style="table-layout: fixed;; width: 0px" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
  <colgroup>
    <col style="width:400px;"/>
    <col style="width:150px;"/>
    <col style="width:150px;"/>
  </colgroup>
  <thead>
    
    <tr class="gt_col_headings">
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="&lt;b&gt; Causal effect &lt;/b&gt;"><b> Causal effect </b></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="&lt;b&gt; Risk Difference (95%CI) &lt;/b&gt;"><b> Risk Difference (95%CI) </b></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="&lt;b&gt; Risk Ratio (95%CI) &lt;/b&gt;"><b> Risk Ratio (95%CI) </b></th>
    </tr>
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  <tbody class="gt_table_body">
    <tr><td headers="<b> Causal effect </b>" class="gt_row gt_left"><b> Total effect on dementia </b></td>
<td headers="<b> Risk Difference (95%CI) </b>" class="gt_row gt_right">2.1 (-0.1, 4.2)</td>
<td headers="<b> Risk Ratio (95%CI) </b>" class="gt_row gt_right">1.21 (0.99, 1.50)</td></tr>
    <tr><td headers="<b> Causal effect </b>" class="gt_row gt_left"><b> Controlled direct effect on dementia (with IPCW for death) </b></td>
<td headers="<b> Risk Difference (95%CI) </b>" class="gt_row gt_right">-2.6 (-6.1, 0.8)</td>
<td headers="<b> Risk Ratio (95%CI) </b>" class="gt_row gt_right">0.86 (0.72, 1.05)</td></tr>
    <tr><td headers="<b> Causal effect </b>" class="gt_row gt_left"><b> Total effect on mortality </b></td>
<td headers="<b> Risk Difference (95%CI) </b>" class="gt_row gt_right">-17.4 (-20.5, -14.2)</td>
<td headers="<b> Risk Ratio (95%CI) </b>" class="gt_row gt_right">0.68, (0.63, 0.72)</td></tr>
  </tbody>
  
  
</table>
</div>

---

## Results

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---
class: center, middle

![](figs/plot_adjusted.png)

---
## Other possible estimands

- **Survivors average causal effect:** The risk of dementia on a subgroup of individuals who would never experience the competing event.

- **Separable effects:** Effects of modified treatments motivated by
the physical decomposition of the exposure assumed to operate on dementia and death through separate pathways.

- **Composite outcome of dementia and death**

---

## Conclusion

- When competing events are present there is more than one way to consider them as part of the primary research question.

- Let the question guide the most appropiate methods and estimators.

- For various reasons, risks and survival curves should be preferred over hazards.

- Collaborative work between clinical researchers, epidemiologists and statisticians should narrow the gap between methods development and applied research.

---
class: center, middle
# Thank you! Gracias!