Effects and Estimands

Clinical trial
Observational data

An overview of key terminology

Author

Chi Zhang

Published

September 3, 2023

Effects

\(Y^{a=1}, Y^{a=0}\) are the potential outcomes under treatment 1 and 0. They are random variables. Treatment A has causal effect if \(Y^{a=1} \neq Y^{a=0}\).

For individual \(i\), \(Y_i^{a=1}, Y_i^{a=0}\) are deterministic.

In reality we do not observe both potential outcomes for an individual, since we only have ONE outcome. We observe \(Y\) and \(A\). For a population, average treatment effect (ATE) can be estimate

Estimands

Greifer, N., & Stuart, E. A. (2021). Choosing the estimand when matching or weighting in observational studies. arXiv preprint arXiv:2106.10577.

ATE: average treatment effect in the population

\(E[Y(1) - Y(0)]\)

ATT: average treatment effect among the treated

\(E[Y(1) - Y(0) | Z = 1]\)

ATC: average treatment effect among the controls

\(E[Y(1) - Y(0) | Z = 0]\)

ATM: average treatment effect among the matched

Most of the time we care about ATE and ATT. Pay attention to the matching and weight methods:

  • ATE commonly uses IPW (inverse probability weighting)
  • ATT uses PSM (propensity score matching).

Bias

Data generation Correct causal model Correct causal effect
Collider Y ~ X 1
Confounder Y ~ X; Z 0.5
Mediator Direct effect: Y ~ X; Z. Total effect: Y ~ X Direct: 0; total: 1
M-Bias Y ~ X 1

Selection bias

This bias is the result of selecting a common effect of 2 other variables (collider): a treatment, an outcome.

  • non-response, missing data
  • self-selection, volunteer bias
  • selection affected by treatment before study started

A form of lack of exchangeability between the treated and untreated.

Correct for selection bias: IP weighting

ICE (in clinical trial)

Key question: how to present the data visually?

What are considered as important, what are not?

ITT (intention to treat): include the data after rescue medicine. Includes dropouts

PP (Per-protocol): exclude patients taking rescue medicine, only analyse the complete cases

Trial estimands: trial treatment effect depends on how events occur after treatment initiation.

Treatment effect for a given outcome.

Five core attributes

  • population
  • treatment conditions
  • endpoint
  • summary measure
  • strategies to handle each type of intercurrent event

Intercurrent event

Post-baseline events (post randomisation in RCT) that affects the interpretation of outcome.

Two categories:

  • treatment-modifying events, affects the receipt of assigned treatment. E.g. early discontinuation, use of rescue, wrong dose, wrong type (placebo for example).

  • truncating events, e.g. death, amputation of limb when the limb is relevant for the research question.

Strategies (multiple can be used for different ICE in the same study)

  • treatment policy strategy: treat as it is, ignore ICE
  • composite strategy: modifies the endpoint value, defined by the investigator
  • while-on-treatment (while alive): before intercurrent event data is used.
  • hypothetical strategy
  • principal stratum strategy: redefine the population