Advanced studies

TROHOC fallacy (Miettinen)

A case-control study is really a way of sampling from a cohort; with proper sampling (e.g. incidence density) the OR gives valid rate/risk ratios.

Nested case-control study

A case-control study inside an existing cohort; controls (e.g. 1:2) matched to each case from the same cohort.

Nested case-control: strengths

Cheaper/faster than full cohort; exposure measured before disease (less recall bias); less selection bias; good for rare outcomes.

Nested case-control: limitations

Only data/samples already collected; controls only usable for ONE disease; matching is complex; generalizability; time lag.

DDT/DDE example: cohort

100,000 teachers, $100 per assay = $10 million; full-cohort RR = 1.89.

DDT/DDE example: nested case-control

All 2,000 cases + 2 controls each gave OR = (500 x 3,400)/(1,500 x 600) = 1.89: same answer, far cheaper.

Case-cohort study

Nested in a cohort; a RANDOM SUBCOHORT is chosen at baseline and serves as the comparison group for all cases.

Case-cohort: steps

1) Start with a cohort. 2) Select a random subcohort at baseline. 3) Identify all cases during follow-up. 4) Compare exposures between cases and subcohort.

Case-cohort: subcohort member becomes a case

Counted as both a case and part of the subcohort; fine because random sampling is preserved; analysis adjusts (Prentice method, weighted Cox regression).

Case-cohort: strengths

Efficient; same subcohort reusable for many outcomes; less selection bias; time order kept.

Case-cohort: limitations

Complex analysis (weighted Cox, Prentice); overlap of cases and subcohort; misclassification; generalizability.

Nested case-control vs case-cohort: reuse

Nested controls serve ONE disease; the case-cohort subcohort is a baseline random sample reusable for any outcome.

Case-crossover design

For triggers of sudden events; each person is their own control, comparing exposure just before the event to another time.

Case-crossover: hazard window

The period just before the event (e.g. 2 hours before the heart attack).

Case-crossover: referent window

The same clock time on a day WITHOUT the event.

Hazard window too short vs too long

Too short = loses events (less power). Too long = biases toward the null.

Referent window requirements

Far enough from the event to be unaffected by it, and recent enough that the usual exposure rate is comparable.

Bad referent window examples

5 minutes before a crash (phone call can span both); 1 year before (e.g. COVID lockdown changed habits).

Case-crossover measure of association

Matched OR using only discordant pairs (hazard-exposed only / referent-exposed only).

Case-crossover OR: 50 hazard-only, 9 referent-only

50/9 = about 5.6; concordant pairs (4 and 1,165) are ignored.

Case-crossover: strengths

Controls time-invariant confounders (age, sex) even if unmeasured; no separate control group needed.

Case-crossover: limitations

Co-occurring acute exposures; only short-term effects of transient exposures; uses only cases whose exposure varies over time.

Case-crossover examples

Alcohol/exertion and MI; air pollution and stroke; phone use and crashes; new drugs and falls; hospital discharge and opioid overdose.

N-of-1 trial

A randomized, blinded crossover trial with ONE patient who receives active and placebo in random order.

N-of-1: best suited for

Chronic, stable conditions with fast-acting treatments that wash out quickly (chronic pain, ADHD, insomnia).

N-of-1: strengths

Personalized evidence; own control; randomization and blinding possible; patient engagement.

N-of-1: limitations

Not generalizable (one person); needs stable condition; complex; patient burden; carryover (need washout); not for surgery or outcomes like death.

N-of-1 evidence

57 trials completed; 50 gave a clear answer; 15 (39%) changed management.

Which design: big cohort, stored samples, rare outcome, costly assay

Nested case-control.

Which design: same, but several outcomes

Case-cohort.

Which design: sudden event, short-term exposure

Case-crossover.

Which design: does this treatment work for this one patient?

N-of-1 trial.

Long answer checklist: advanced design

Describe design with strengths/weaknesses; justify why it fits the question; say how exposure and outcome are measured; name biases and how to minimize them.