Design, Model and Estimand: What Each Study Design Can Actually Estimate

อ่านฉบับภาษาไทย (Thai version)

Abstract

Study design tells us which information is available, but it does not choose the effect measure alone. Start with the estimand: the quantity that answers the clinical question for a specified population. Then match the sampling scheme and statistical model to that question. An illustrative cohort shows why the same cases can produce different comparisons when the control pool changes. Controls from people without an event identify a risk odds ratio. Controls representing time at risk identify a rate ratio, while baseline controls identify a risk ratio. The arithmetic uses complete population pools to isolate this distinction. Actual sampled controls require an analysis that respects their selection. We also distinguish prevalence from new-event risk and explain how averaging calibrated model predictions produces population risks. Economic models need these absolute probabilities, or a compatible relative effect combined with a local baseline risk. The population, outcome and time horizon must remain aligned throughout.

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State the question before choosing the model

An estimand is the population quantity that answers your clinical question. Specify the population, strategies, outcome, time horizon and summary measure. Also define how treatment changes affect that question. Such changes are intercurrent events when they alter the interpretation or observation of outcomes.

For example, counting outcomes after treatment switching asks what happens after offering each strategy. Asking what would happen without switching targets a different quantity. Removing everyone who switches does not automatically answer either question. Their reasons for switching may also predict the outcome.

Follow-up preserves denominators

A trial assigns treatment; a cohort observes exposure. With complete follow-up, both can estimate risk: the probability of an event by a specified horizon. Dividing group risks gives a risk ratio; subtracting them gives a risk difference. Divide each risk by its complement to obtain odds, then compare those odds for the risk odds ratio.

Event-free person-time is the time people remain observed and at risk. Events divided by person-time give incidence rates. Event times also support hazards, the instantaneous rates among people still event-free, and survival curves. Restricted mean survival time summarizes average event-free time up to a chosen horizon [1].

A randomized assignment supports causal comparisons, but incomplete follow-up can still introduce bias. Observational comparisons also require control of confounding, meaning shared causes of exposure and outcome. These requirements remain even when the estimate is precise. Revisit [[incidence-prevalence-and-the-right-denominator]] for denominators and [[hazard-ratio-proportional-hazards-rmst]] for event timing.

Ask where the controls came from

Case-control sampling selects people using outcome status. Its observed case fraction therefore cannot be read directly as population risk. The controls determine which denominator the exposure comparison represents [2].

End-of-follow-up controls are people without the event. Divide case exposure odds by control exposure odds to obtain the risk odds ratio. This approximates a risk ratio only when the outcome is sufficiently rare in the relevant groups.

A risk set contains people still eligible for the event just before a case occurs. Risk-set controls represent time at risk and may later become cases. Appropriate sampling and analysis estimate a rate or hazard ratio without requiring a rare outcome. The pooled person-time illustration below calculates an incidence rate ratio, rather than fitting a hazard model.

Baseline controls represent the starting population, including people who later become cases. Comparing case exposure odds with baseline exposure odds identifies a risk ratio. This is a case-base analysis. A case-cohort subcohort can instead support weighted survival analysis, so its design label does not fix the measure.

Sampling within a hospital cohort can save assays when exposure measurement is costly. Keep selection probabilities and event times so the analysis can account for sampling. A baseline subcohort can serve several outcomes; nested risk sets preserve comparisons at event times.

# Illustrative cohort. Writes: stdout only; no files.
people <- c(exposed=2000, unexposed=8000)
events <- c(exposed=400, unexposed=800)
risk <- events/people
cat("Exposed people:", people[1], "\n")
cat("Unexposed people:", people[2], "\n")
cat("Exposed events:", events[1], "\n")
cat("Unexposed events:", events[2], "\n")
cat("Exposed risk: ", formatC(100*risk[1], format="f", digits=2), "%\n", sep="")
cat("Unexposed risk: ", formatC(100*risk[2], format="f", digits=2), "%\n", sep="")
cat("Risk ratio:", formatC(risk[1]/risk[2], format="f", digits=3), "\n")
cat("Risk difference (percentage points):", formatC(100*(risk[1]-risk[2]),format="f",digits=2),"\n")

Exposed people: 2000
Unexposed people: 8000
Exposed events: 400
Unexposed events: 800
Exposed risk: 20.00%
Unexposed risk: 10.00%
Risk ratio: 2.000
Risk difference (percentage points): 10.00

Keep time separate from people

People with an event contribute half a year; people without one contribute the whole year. This gives 1800 exposed person-years and 7600 unexposed person-years. The following calculation uses those totals to represent the person-time control pool. They are not counts of sampled controls.

# Illustrative control pools. Writes: stdout only; no files.
people <- c(exposed=2000, unexposed=8000)
events <- c(exposed=400, unexposed=800)
horizon <- 1
noncases <- people-events
years <- (people-events/2)*horizon
case_odds <- events[1]/events[2]
cat("Exposed person-years:", years[1], "\n")
cat("Unexposed person-years:", years[2], "\n")
cat("End pool risk OR:", formatC(case_odds/(noncases[1]/noncases[2]), format="f", digits=3), "\n")
cat("Time pool rate ratio:", formatC(case_odds/(years[1]/years[2]), format="f", digits=3), "\n")
cat("Baseline risk ratio:", formatC(case_odds/(people[1]/people[2]), format="f", digits=3), "\n")

Exposed person-years: 1800
Unexposed person-years: 7600
End pool risk OR: 2.250
Time pool rate ratio: 2.111
Baseline risk ratio: 2.000

A snapshot answers a prevalence question

A cross-sectional study measures disease present at observation. Its prevalence ratio compares the proportions affected, while its prevalence odds ratio compares their odds. Neither directly measures new-event risk over follow-up. Measuring exposure and disease together usually leaves their temporal order unresolved.

Prevalence reflects both new disease and how long people live with it. It can inform current service capacity. Replacing an incidence input with prevalence can therefore distort a prevention model. Choose a model that respects the measured outcome [3].

The model sets a scale; predictions can recover risks

Logistic regression estimates odds ratios; log-binomial regression estimates risk ratios for follow-up outcomes. For cross-sectional outcomes, those same models estimate prevalence odds ratios and prevalence ratios [3,4]. Poisson regression with a person-time offset compares incidence rates; the offset accounts for observed time. A constant Cox hazard ratio requires proportional hazards [1].

Exponentiating an adjusted logistic coefficient gives a conditional odds ratio, comparing people with the same covariates. Marginal standardization instead averages predictions over a chosen population [5]. Predict every person under each strategy while retaining their covariates. Average the probabilities separately, then subtract or divide those averages for the risk difference or risk ratio.

These predictions must represent population probabilities for the relevant outcome and horizon. Ordinary case-control predictions inherit the investigator-selected case fraction. Recovering population risks needs known sampling information or suitable external calibration [4]. Averaging uncorrected predictions cannot supply a missing denominator.

Supply probabilities for the decision population

Economic models need event probabilities and their consequences for each strategy [6]. Use calibrated absolute risks, or combine a relative effect with a compatible local baseline risk. Transportability means the effect remains applicable in the target population. Differences in patient mix or treatment delivery can undermine that assumption.

Match the outcome and horizon before importing an estimate. Carry uncertainty from the actual analysis, including baseline-risk uncertainty. The illustrative pool arithmetic above does not provide confidence intervals for sampled case-control estimates. Continue to [[risk-ratio-odds-ratio-risk-difference-nnt]] for absolute effects and [[chance-bias-and-confounding]] for threats to causal interpretation.

The series, in learning order

1. Health Economics Series Guide: Read the Evidence Before the Costs
2. Incidence, Prevalence and the Right Denominator: The Epidemiology Beneath Cost-of-Illness and Markov Models
3. Design, Model and Estimand: What Each Study Design Can Actually Estimate (this article)
4. Risk Ratio, Odds Ratio, Risk Difference and NNT: One 2×2 Table, Four Answers
5. The Hazard Ratio Is Not a Risk Ratio: Proportional Hazards, Restricted Mean Survival Time and Model Inputs
6. Chance, Bias and Confounding: Why an Association Is Not Yet a Treatment Effect
7. Beyond the Evidence Pyramid: GRADE Certainty and Choosing Effectiveness Inputs for Economic Models
8. From Sensitivity to Cost per Case Detected: Predictive Values, Prevalence and the Economics of Screening
9. Whose Cost, in Which Year? Perspective, Opportunity Cost, Inflation and Discounting
10. QALY, DALY and the Utilities Behind Them: What Is Actually Being Measured
11. ICER, Dominance and the Cost-Effectiveness Plane: Reading the Thai Threshold of 160,000 Baht per QALY
12. Decision Trees, Markov Cohorts and Probabilistic Sensitivity Analysis: How a Model Turns Evidence into a Decision
13. Cost-Effective Is Not Affordable, and Efficient Is Not Fair: Budget Impact and Equity

Related in the wiki: Control Sampling in Stata: Question, Controls and Model Are Three Different Things · Nested Case-Control Studies: Efficient Cohort Sampling for Observational Research