Looking at competing risks through a different lens

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## Looking at competing events through a different lens in dementia research

.right[L. Paloma-Rojas Saunero.

**Epidemiology Department**

**Causal Inference, Neuro-Epi Group**]

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Hello
My name is Paloma Rojas-Saunero, I am a PhD candidate at Erasmus MC and today I will present my work called: Looking at competing events through a different lens.

---

### Introduction

Whenever we study **time-to-dementia**, **death** challenges the research question and the analytical methods.

--
<br>

.center[<img src=./images/survival_plot.png width="100%"/>]

???
For example:
if we have data on a cohort
at baseline everyone was alive
but by the first year 2 individuals, presented in red, have died.
By the next time point, this subjects are eliminated from the dataset, and they can't longer develop dementia at year 2, year 3, year 4.
As more subjects die over time, less subjects can be at risk of developing dementia.

As subjects die over time, less subjects can be at risk of developing dementia (**_death is a competing event_**).

We can't consider that the ones who died are similar to the one's who stay in the cohort.

---

### Aims

1. Demonstrate how  two questions that consider death differently can lead to different results, using educational attainment, sex and APOE-ε4 as examples

???
For this reason I would like to 
first...
second...

2. Describe common practices in the analysis and interpretation of time-to-dementia through a systematic review

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### Application to the Rotterdam Study

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To answer our first aim, we worked with the Rotterdam Study Cohort and included participants from the first wave of inclusion between 1990-1993 and followed at different time points

- Participants from Rotterdam Study I, recruited between 1990-1993 and followed during 1993-1995, 1997-1999 and 2002-2005

- No prior history of dementia diagnosis

- Complete information at baseline

- Final sample size of **5370** participants
  
- Mean age at baseline of 66 years

- **783** individuals were lost to follow-up, **749** developed dementia and **1726** died

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### Measurements

- _**Lower educational attainment**_ (primary education, lower or intermediate general education or lower vocational education) vs. _**Higher educational attainment**_ (intermediate vocational education or higher general education and higher vocational education or university)

- _**Women**_ vs _**men**_ (based on self-reported questionnaire)

- _**APOE-ε4 carrier**_ (at least one ε4 allele) vs _**APOE-ε4 non-carriers**_

- Outcome and Follow-up

+ **Dementia diagnosis**, **Death**, **Lost to follow-up**

+ Follow-up: 20 years since individual baseline

???
We measured and compared...

---

### Methods

.footnote[Young J. et al. Stat Med. 2020]

???
Let's review the different questions that can ask
The first is the "...." and the methods that can answer this question are
This question does not require any assumption on the competing event of death
However, the interpretation can be tricky since part of the effect we see in dementia may be throug...
For example, when we study the risk of smoking and dementia and we see a protective effect, it might be because smoking increases the risk of cancer.

---

### Methods

<table class="table table-hover table-responsive" style="font-size: 20px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;color: #011A5E !important;"> Question </th>
   <th style="text-align:left;color: #011A5E !important;"> Methods </th>
   <th style="text-align:left;color: #011A5E !important;"> Key Assumptions on competing event </th>
   <th style="text-align:left;color: #011A5E !important;"> Interpretation </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: #011A5E !important;background-color: white !important;"> The risk of dementia regardless of death </td>
   <td style="text-align:left;background-color: white !important;"> Cause-specific cumulative incidence* or Fine and Gray subdistribution hazard </td>
   <td style="text-align:left;background-color: white !important;"> N/A </td>
   <td style="text-align:left;background-color: white !important;"> Part of the primary effect is through the effect between the exposure and death. Analogous to a total effect. </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #011A5E !important;background-color: white !important;"> The risk of dementia with elimination of death </td>
   <td style="text-align:left;background-color: white !important;"> Kaplan Meier estimate or Cause-specific hazard model </td>
   <td style="text-align:left;background-color: white !important;"> Death is uninformative, given available data* </td>
   <td style="text-align:left;background-color: white !important;"> The effect between exposure and dementia if we could prevent death. Analogous to a controlled direct effect. </td>
  </tr>
</tbody>
</table>

.footnote[Young J. et al. Stat Med. 2020]

* This question requires that we **censor** people that die, but this is not equivalent to **ignoring**

???
The second question we can ask is ....
whenever we use KM or the cause-specific hazard model we are answering this question
but this requires the strong assumption that, given the data death is uninformative. However, the challenge is that this q. is interpreted as.... which means, within a hypothetical scenario were we prevent death from happening.

In addition, to answer this question we need to censor...so lets see how we would do this

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### The risk of dementia regardless of death

`\(Pr[Dem^{a, ltfu = 0} = 1]\)`

- `\(L0\)`: baseline confounders

- `\(CE_k\)`: competing event death

- `\(Dem\)`: dementia diagnosis

- `\(L_k\)`: confounders

- `\(Ltfu_{k+1}\)`: Loss to follow-up

---

### The risk of dementia eliminating death

`\(Pr[Dem^{a, ltfu = 0, ce = 0} = 1]\)`

- `\(L0\)`: baseline confounders

- `\(CE_k\)`: competing event death

- `\(Dem\)`: dementia diagnosis

- `\(L_k\)`: confounders

- `\(Ltfu_{k+1}\)`: Loss to follow-up

---

### Additional alternative research questions

- The combined risk of dementia or death

- The risk of dementia if the exposure can be decomposed in different pathways (separable effects)*

.footnote[*Stensrud M.J. et al. JASA. 2020]

- The risk of dementia on a subgroup of individuals who would never experience the competing event (survivor average causal effect)

---

### Statistical analysis

We used inverse probability weighting (IPW) of marginal structural models

Generalizable to time-dependent confounding and selection bias

- Weights for **lost to follow-up** at each time point:
<br><br>
`\(W^{LTFU} = 1/Pr[LTFU = 0| L, A]\)`

- Weights for the **death** at each time point:
<br><br>
`\(W^{Death} = 1/Pr[Death = 0| L, A]\)`

**Regardless of death**: `\(W^{LTFU}\)`

**Eliminating death**: `\(W^{LTFU} * W^{Death}\)`

---

### Statistical analysis

Weights using the following covariates:

- **Baseline**: age, sex, APOE-ε4, education, history of heart disease

- **Time-updated**: systolic blood pressure, BMI, smoking habit, development of diabetes, heart disease, stroke, cancer

Standardized cumulative incidence curves

We present comparable estimands (risk difference, risk ratio)

95%CI were calculated through bootstrap

???
The advantage of this method is that we can also draw...
and it gives...
Now, let's see how the 2 questions can lead to different results

---
### Higher vs. lower educational attainment

<table class="table table-hover table-responsive" style="font-size: 18px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;background-color: white !important;"> Question </th>
   <th style="text-align:left;background-color: white !important;"> Risk Difference % (CI95%) </th>
   <th style="text-align:left;background-color: white !important;"> Risk Ratio (CI95%) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;background-color: white !important;"> Risk of dementia regardless of death </td>
   <td style="text-align:left;background-color: white !important;"> -6 (-7, -4) </td>
   <td style="text-align:left;background-color: white !important;"> 0.67 (0.6, 0.74) </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;"> Risk of dementia if we eliminate death </td>
   <td style="text-align:left;background-color: white !important;"> -7 (-9, - 5) </td>
   <td style="text-align:left;background-color: white !important;"> 0.72 (0.64, 0.77) </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;"> Death </td>
   <td style="text-align:left;background-color: white !important;"> -4 (-6, -2) </td>
   <td style="text-align:left;background-color: white !important;"> 0.92 (0.88, 0.96) </td>
  </tr>
</tbody>
</table>

???
when we compare higher vs. lower educational attainment we observe that 
individuals with lower education had a higher risk of dementia compared to the higher education group. But risks are similar whether we estimated the risk of dementia with or without elimination of death. Regarding death, the trends are similar and only looks higher by the end of follow up for the lower education group

---
### Women vs. men

<table class="table table-hover table-responsive" style="font-size: 18px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;background-color: white !important;"> Question </th>
   <th style="text-align:left;background-color: white !important;"> Risk Difference % (CI95%) </th>
   <th style="text-align:left;background-color: white !important;"> Risk Ratio (CI95%) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;background-color: white !important;"> Risk of dementia regardless of death </td>
   <td style="text-align:left;background-color: white !important;"> 1 (0, 3) </td>
   <td style="text-align:left;background-color: white !important;"> 1.08 (0.98, 1.22) </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;"> Risk of dementia if we  eliminate death </td>
   <td style="text-align:left;background-color: white !important;"> 3 (1, 6) </td>
   <td style="text-align:left;background-color: white !important;"> 1.17 (1.07, 1.32) </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;"> Death </td>
   <td style="text-align:left;background-color: white !important;"> -14 (-16, -12) </td>
   <td style="text-align:left;background-color: white !important;"> 0.74 (0.7, 0.77) </td>
  </tr>
</tbody>
</table>

???
When we compare women vs. men, Women had an increased risk of dementia compared to men only when we estimate the risk in the hypotethical case we could prevent of death during follow up, men have a higher risk of death over the entire follow up.

---

### APOE-ε4 carriers vs. non-carriers

<table class="table table-hover table-responsive" style="font-size: 18px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;background-color: white !important;"> Question </th>
   <th style="text-align:left;background-color: white !important;"> Risk Difference % (CI95%) </th>
   <th style="text-align:left;background-color: white !important;"> Risk Ratio (CI95%) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;background-color: white !important;"> Risk of dementia regardless of death </td>
   <td style="text-align:left;background-color: white !important;"> 11 (9, 12) </td>
   <td style="text-align:left;background-color: white !important;"> 1.9 (1.71, 2.1) </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;"> Risk of dementia if we eliminate death </td>
   <td style="text-align:left;background-color: white !important;"> 15 (13, 18) </td>
   <td style="text-align:left;background-color: white !important;"> 1.88 (1.74, 2.11) </td>
  </tr>
  <tr>
   <td style="text-align:left;background-color: white !important;"> Death </td>
   <td style="text-align:left;background-color: white !important;"> 1 (-1, 3) </td>
   <td style="text-align:left;background-color: white !important;"> 1.02 (0.97, 1.08) </td>
  </tr>
</tbody>
</table>
???
Apoe4 carriers had an increased risk of dementia compared to the non-carriers, though the difference would be even larger if we could prevent death over time, and the risk of death is similar to both groups over the study period

---

### Systematic review

.pull-left[

**Searching criteria**

- Jan/2018 to Dec/2019

- Dementia/AD & longitudinal/cohort & hazard/risk 
<br>
- Alzheimer’s and Dementia
- Annals of Neurology
- BMJ
- Neurology
- JAMA, Jama Neurology
- Lancet, Lancet Neurology
  
]

.pull-right[

**Eligibility criteria**

- Includes time-to-dementia/AD as primary or co-primary outcome

- **210** selected

- **78** included

]

???
To meet our second aim, we did a systematic review selecting

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### Results: Systematic Review

Out of 78 papers:

- **53%** report death numbers, **12%** death by exposure level

???
53 report how many died over time, only 12 present how many died at each exposure level

- **27%** described death as competing event in the methods section

- **88%** present hazard ratios, **85%** use Cox PH models

- Only one paper that used cause-specific hazard model mentioned the assumption of uninformative censoring

- No paper interpreted the risk of dementia if death could be prevented

- **32%** discuss mortality in the discussion

---

### Take-home messages

- When we study time-to-dementia, death needs to be considered as part of the question.

- Pick your question wisely. If your results can impact clinical or public health decisions, stick to this world*.

.footnote[*Andersen PK & Keiding N. Stat Med. 2012]

- Evaluate assumptions and interpret results carefully

- In any case, explore the relation between your exposure and death

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

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### Acknowledgments

- Sonja A. Swanson

- M. Arfan Ikram

- Jessica G. Young

- Vanessa Didelez

- Mats J. Stensrud

- Causal inference team EMC

- Neuro epi team EMC

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# Thank you!!!

###Keep in touch!
<i class="fas  fa-paper-plane " style="color:#011A5E;"></i></i>&nbsp;l.rojassaunero@erasmusmc.nl</a><br>

<i class="fab  fa-twitter " style="color:#011A5E;"></i> <a href="http://twitter.com/palolili23"> </i>&nbsp; @palolili23</a><br>

<i class="fab  fa-github " style="color:#011A5E;"></i> <a href="http://twitter.com/palolili23"> </i>&nbsp; @palolili23</a><br>

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I look forward to discuss in more detail about the questions and methods of this study over chat or you can contact me by email or twitter. The code for this project is at my github repo