A researcher studying a cholesterol drug classifies all participants by their baseline medication status and runs a standard Cox model, even though many participants initiated the drug months into follow-up. What is the most likely consequence?
AThe effect estimate is biased toward the null because unexposed person-time is misclassified as exposed
BThe effect estimate is biased toward the null because exposed person-time is misclassified as unexposed
CThe analysis overcorrects, producing an inflated hazard ratio
DResults are unaffected because Cox models automatically handle time-varying exposure
Participants who later initiate the drug are classified as unexposed for their entire follow-up, including the period after they actually started treatment. This misclassifies exposed person-time as unexposed, diluting the exposure contrast and pushing the hazard ratio toward 1 (null). Standard Cox models do not automatically accommodate time-varying exposure — that requires the counting process (extended Cox) data structure.
Question 2 Multiple Choice
A covariate — illness severity — both predicts who initiates a treatment and is itself affected by prior treatment use, while also predicting the outcome. If you adjust for illness severity using standard Cox regression, what problem arises?
AThe model becomes overidentified and cannot converge
BAdjusting blocks part of the causal effect of treatment on the outcome, biasing the estimate downward
CAdjusting eliminates all confounding and provides an unbiased causal estimate
DThe proportional hazards assumption is violated and must be tested separately
When a covariate is simultaneously a confounder and a mediator — affected by prior exposure and affecting the outcome — it lies partly on the causal path from treatment to outcome. Standard regression adjustment for a mediator blocks the indirect effect, biasing the causal estimate downward. But failing to adjust leaves confounding. Neither standard approach works; this is the motivating problem for marginal structural models with IPTW, which break the feedback loop without conditioning on the mediator directly.
Question 3 True / False
A time-varying confounder that is causally affected by prior exposure can be handled correctly by simply including it as a time-varying covariate in an extended Cox regression model.
TTrue
FFalse
Answer: False
False. When a covariate is both a time-varying confounder and a mediator (affected by prior exposure), conditioning on it in regression — even in an extended Cox model — blocks part of the causal path you are trying to estimate. This creates bias that standard regression cannot correct. The principled solution is marginal structural models with inverse probability of treatment weighting, which create a pseudo-population where treatment at each time point is independent of prior covariate history.
Question 4 True / False
Using baseline exposure classification in a study where many participants change exposure status during follow-up tends to bias the estimated effect toward the null (no effect).
TTrue
FFalse
Answer: True
True. Baseline-only classification misclassifies person-time: participants who later become exposed are treated as unexposed throughout, and participants who stop exposure continue to be classified as exposed. This non-differential misclassification of a binary exposure dilutes the true contrast between exposure groups, attenuating the effect estimate toward null. The correct approach is to restructure data into person-time intervals, each coded with the actual exposure value during that interval.
Question 5 Short Answer
Why can't ordinary regression adjustment solve the problem of a covariate that is simultaneously a time-varying confounder and a mediator? Explain the fundamental dilemma.
Think about your answer, then reveal below.
Model answer: Adjusting for the covariate removes confounding but also blocks the indirect causal path (treatment → covariate → outcome), underestimating the total effect. Not adjusting leaves residual confounding that biases the estimate in the other direction. The dilemma arises because the covariate plays two incompatible roles in the causal structure. Marginal structural models with IPTW resolve this by reweighting observations to create a pseudo-population where prior covariate values no longer predict treatment, eliminating confounding without conditioning on the mediator.
The core problem is that standard regression cannot distinguish 'covariate as confounder' from 'covariate as mediator' when both apply simultaneously. Conditioning always blocks the path. MSMs sidestep this by modeling the probability of observed treatment history given covariate history and using inverse probability weights — rather than directly conditioning on confounders in the outcome model.