Course 3 · Week 3 — Survival II, causal inference, HTE

Cheatsheet — biostats_courses

Author

R. Heller

Time-varying covariates / landmarking

  • Counting-process data: split follow-up into intervals.
  • Landmark analysis: define a landmark time \(t^*\), condition on surviving to \(t^*\), classify by status at \(t^*\).
library(survival)
coxph(Surv(tstart, tstop, event) ~ x, data = long)
  • Immortal-time bias: exposed group can only be exposed if they live long enough to be exposed → spurious survival benefit.

Competing risks

library(tidycmprsk); library(ggsurvfit)
cif <- cuminc(Surv(time, event_f) ~ x, data = df)
ggsurvfit::ggcuminc(cif, outcome = "event1")

# Fine-Gray subdistribution hazard for event1
crr(Surv(time, event_f) ~ x, data = df, failcode = "event1")
  • Cause-specific HR answers “given you are event-free, what is the hazard for event k?”
  • Subdistribution HR answers “what is the hazard for event k in the whole cohort, treating competing events as obstacles?”

DAGs

library(dagitty); library(ggdag)
dag <- dagitty("dag { X -> Y ; C -> X ; C -> Y }")
adjustmentSets(dag, exposure = "X", outcome = "Y")
impliedConditionalIndependencies(dag)
  • Adjust for confounders, not colliders.
  • Adjusting for a mediator estimates the direct effect only.

Propensity scores / IPTW

library(MatchIt); library(cobalt)
m <- matchit(treat ~ x1 + x2, data = df, method = "nearest")
love.plot(m)   # check balance: SMD < 0.1 is the goal
fit <- lm(y ~ treat, data = match.data(m))

IPTW: weight by \(1/\hat{e}_i\) for treated, \(1/(1-\hat{e}_i)\) for untreated. Stabilised weights stay closer to 1; trim extremes to avoid outliers.

G-methods, IV, DiD, RDD

Method Identifying assumption
G-formula / IPTW positivity + no unmeasured confounding
Instrumental variables exclusion restriction + relevance
Difference-in-differences parallel trends
Regression discontinuity continuity at the cutoff

Heterogeneous treatment effects

  • Causal forest (grf::causal_forest) or meta-learners (S-, T-, X-).
  • Report conditional ATEs with adjusted intervals; avoid spurious subgroup p-values.

Decision rule for Week 3

  • Treatment assigned over time → time-varying Cox.
  • Multiple competing events → cumulative incidence, Fine-Gray.
  • Observational causal question → DAG first, choose identification strategy second.
  • Want the whole distribution of treatment effect? → causal forest.

Common pitfalls

  • Adjusting for a post-treatment variable (induces collider bias).
  • Quoting HR from a Cox model that violates PH.
  • Matching but never checking balance.
  • Calling IV estimates “generalisable” when they are local to compliers.

Further reading

  • Hernán & Robins, Causal Inference: What If.
  • Therneau & Grambsch, Modeling Survival Data.