2025_May_23_khandle

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# Estimands for longitudinal continous outcomes in the presence of death and dropout

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

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???

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# Types of research questions

- **Descriptive:**

+ What is the lifetime risk of dementia for women and men born in 1940 in Los Angeles
  
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- **Predictive:**

+ Is subjective cognitive impairment at age 60 a good diagnostic predictor of cognitive impairment at age 70?
  
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- **Causal (etiologic, interventional)**

+ What is the effect of persistent daily interpersonal racial discrimination in midlife in dementia risk over 10 years of follow-up?
  
  + What is the effect of Lecanemab in amyloid deposition over 18 months of treatment?

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# Estimands

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<br><br>

**Definition**: The specific quantity you want to estimate, that answers your research question.

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# Estimands have 5 elements

**1. Target population**

**2. Exposure, treatment, comparison groups**

**3. Outcome (endpoint)**: within a time frame

**4. Summary measure:** A population-level measure of frequency that is _interpretable_
  + `\(Pr(Y_t=1|A=1) - Pr(Y_t=1|A=0)\)`
  + `\(E(Y_t|A=1) - E(Y_t|A=0)\)`

**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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# Ideal study

- Target and study population clearly specified

- Defined observation period at risk

→ e.g., lifetime, 10-year, 2-weeks

- Complete follow-up over the observation period

- Starting point (baseline) is the same for all participants

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## Censoring

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- By design, we want to prevent participant's dropout

- But in real-world data, people are loss to follow-up and drop out during the study period

- *A censoring event* makes the event of interest _unknown_ at all future time points

- Censoring is the *key* feature of time-to-event analysis

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- *Time of end of study* is often defined as *administrative censoring* but I will refrain from using this jargon for now

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## Implications of censoring

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- Statistical literature

- Censoring events are independent of the event of interest
  
  - Censoring events are uninformative
  
- Causal literature

- Counterfactual scenario where censoring events were eliminated
  
  - `\(Pr[Y_{k+1}] = Pr[Y^{\overline{\text{LTFU}} = 0}_{k+1}]\)`
  
  -  `\(Pr[Y^{a = 1, \overline{\text{LTFU}} = 0}_{k+1}]\)` - `\(Pr[Y^{a = 0, \overline{\text{LTFU}} = 0}_{k+1}]\)`

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# Intercurrent event of death

- Let's say we are interested in measuring the outcome **Y** at 1 year of follow-up

- A participant dies at 6 months of follow-up

- If Y is binary, e.g. **dementia diagnosis**, then the probability of **Y** at 1 year is **0** 
  
    → Death is a _competing event_
  
  - If Y is continuous, such as **cognitive function**, then the expected value of **Y** at 1 year is **undefined (maybe not of substantive interest)**

→ Death is a _truncation event_

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# Death and dropout in KHANDLE and STAR?

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<img src=./figs/isolation_km.jpg width="70%"/>
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## How comparable are two groups if they have differential death and dropout?

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<img src=./figs/isolation_box_plot.jpg width="60%"/>
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#### Mean trajectories of functional impairment among those who remain in the study

`\(E(Y_t|SI=1, Death_t = 0) - E(Y_t|SI=0, Death_t = 0)\)`

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<img src=./figs/isolation_while_alive.jpg width="50%"/>
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#### Mean trajectories of functional impairment if we could have eliminated death

`\(E[Y_t^{\overline{\text{Death}} = 0}|SI=1] - E[Y_t^{\overline{\text{Death}} = 0}|SI=0]\)`

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<img src=./figs/isolation_eliminating_death.jpg width="50%"/>
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## Mean differences in functional impairment by social isolation status

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<img src=./figs/isolation_differences.jpg width="70%"/>
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## What about causal effects?

- Contrast of (counterfactual) outcome distributions in the **same individuals** but under **different treatments**.

- The only explanation for a difference is the intervention, not comparing different individuals (including over time)

- Therefore, the **as observed** estimand is not causal

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## Drop by my SER poster on Thursday 12th of June to chat more about this topic!
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<img src=./figs/ser_poster.jpg width="100%"/>
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