Introduction to the Target Trial Emulation Framework KRSK (@koro485) 1

Randomized Trial and Observational Study • Ideally, we want to conduct an RCT to answer our questions • Not always feasible • Alternatively, use observational data • Results can differ substantially(!) Example: Postmenopausal hormone therapy and heart disease? • Preventive! • e.g., HR = 0.68 • (Grodstein et al. 2006) Observational Study • Harmful! • e.g., HR = 1.24 • (Manson et al. 2003) RCT 2

1. Lack of randomization (i.e., confounding) Sources of Discrepancies 2. Other sources of bias (selection, immortal time, measurement error) 3. Different, and often ambiguous, causal estimand (answering different questions) Target trial emulation 3 Study design, regression, propensity scores

On Confounding Adjustment • ”Adjusting for”, “controlling for”,… • Assumption: 𝒀𝒂∐𝑨|𝑳 A Y L U • Unmeasured confounder(s) U? • Almost always the case in observational epi • Estimates are biased, but perhaps not terribly… • Magnitude of bias by U needs to be strong conditional on L • Rationale behind the E-value analysis References: Ø VanderWeele, Tyler J., and Peng Ding. "Sensitivity analysis in observational research: introducing the E-value." Annals of internal medicine 167.4 (2017): 268-274. 4

1. Temporal ordering (require at least three time points!) 2. Covariate selection 1SFFYQPTVSF XBWF #BTFMJOF XBWF 'PMMPXŠVQ XBWF Covariates Exposure Outcomes References: Ø VanderWeele, T. J. (2019). Principles of confounder selection. European Journal of Epidemiology, 34:211-219. Ø Ideally, choose based on a DAG and backdoor criterion (i.e., use theory) Ø More pragmatic approach: Ø Control for a cause of the exposure, the outcome, or both Ø Key covariates: pre-baseline values of outcomes and exposure Ø Require a large sample size 5 On Confounding Adjustment

1. Lack of randomization (i.e., confounding) Sources of Discrepancies 2. Other sources of bias (selection, immortal time) 3. Different, and often ambiguous, causal estimand (answering different questions) Target trial emulation 6 Too much focus on this!

1. Imagine a protocol of an ideal trial that answers your question 2. Emulate it by using observational data • Only pragmatic trial (no blinding, no placebo) Target Trial Emulation Protocol Component Description Eligibility Who’s in the study? Assignment Randomly. When? Follow-up period From randomization Treatment strategies How do you treat patients? Causal contrast of interest ITT vs Per-protocol? Aligning key time points prevents some form of bias Clarify causal question of interest References: Ø Hernán, Miguel A., and James M. Robins. "Using big data to emulate a target trial when a randomized trial is not available." American journal of epidemiology 183.8 (2016): 758-764. 7

Why Emulate? • Target trial emulation is a framework • Forces you to ponder the key elements of a strong study design • Causal inference is sometimes feasible without emulation But, if we obtain comparable results from RCTs & emulated trials using observational data… • More confidence in the conditional exchangeability assumption (i.e., emulation of randomization) • Can expand the emulated trial to other types of questions that RCTs cannot address: • Rare events, long-term effects, etc 8

Benefit of Emulation 1: Clarifying Causal Estimand 1. Well-defined interventions • Dose? Duration? Initiation? Discontinuation? • Consistency assumption (a component of SUTVA) • 𝐸[𝑌" 𝐴 = 𝑎 = 𝐸[𝑌|𝐴 = 𝑎] 2. Causal contrast • Intention-to-Treat effect or per-protocol effect? 9

Treatment Incidence vs Prevalent Treatment Randomized trial Observational study NOT emulating a target trial Problems? 1. Unclear “effect” estimand • Implicit assumption: Equivalence of initiation/discontinuation 2. Prevalent user bias • Type of selection bias Non-users Control group Treatment group Current users Current non-users 10

Prevalent user bias 1. Consider current exposure (A1 =0 vs A1 =1) 2. Exposure might have started much earlier (e.g, A0 ) 3. A0 might affect probabilities of attrition/censoring C • e.g., Death before the current exposure assessment 4. An unmeasured common cause of C and Y (U) • Comparing A1 status among those who managed to survive up to time 1 and participate in the survey (C=0) induces selection bias A1 Y L A0 C U 11

Treatment Incidence vs Prevalent Treatment Randomized trial Observational study emulating a target trial 1. Analysis is conditional on prior exposure (A0 ) 2. Estimating the effect of treatment initiation Non-users before assignment Control group Treatment group Current users Current non-users Non-users at baseline 12

0 months 6 months 12 months × × Observational Data Taking aspirin Not taking aspirin Event × ID A Y 1 1 1 2 0 1 3 0 0 4 1 0 5 ? 1 × Estimating Effects of Treatment “Duration” Aspirin use of <6 months (A=0) vs ≥6 months (A=1) • Two possible scenarios for ID=5: 1. Assigned to A=0 2. Assigned to A= 1 but died before 6 months References: Ø Hernán, Miguel A. "How to estimate the effect of treatment duration on survival outcomes using observational data." bmj 360 (2018). 13

0 months 6 months 12 months × × Observational Data Taking aspirin Not taking aspirin Event × ID A Y 1 1 1 2 0 1 3 0 0 4 1 0 5 0 1 × Estimating Effects of Treatment “Duration” Incorrect Approach 1: Use observed duration Problems: • Immortal time bias • Those with A=1 by definition survive longer • A=1 seems protective even under the null 14

Estimating Effects of Treatment “Duration” Incorrect Approach 2: Analyze who were alive at 6months Problems: • Selection bias • Conditioning on being alive up to 6 months, post-treatment eligibility criteria • Solution? See the BMJ paper by Hernan (2018) 0 months 6 months 12 months × × Observational Data Taking aspirin Not taking aspirin Event × ID A Y 1 1 1 2 0 1 3 0 0 4 1 0 5 ? 1 × 15

Causal Contrast • RCTs: • Intention-to-treat (ITT) effect • Effect of assignment X • Per-protocol effect • Effect of treatment ̅ 𝐴 • Observational studies: • Intention-to-treat (ITT) effect • Effect of baseline treatment A0 • Per-protocol effect • Effect of treatment ̅ 𝐴 A0 Y X A1 U0 U1 A0 Y A1 L U1 16

Causal Contrast • Baseline exposure analysis • ITT effect • e.g., 𝐸[𝑌#!$% − 𝑌#!$&] • Time-varying exposure analysis • Per-protocol effect • e.g., 𝐸[𝑌#!$%,#"$% − 𝑌#!$&,#"$&] A0 Y A1 L0 L1 • When exposure varies substantially over time, the estimated ITT effect may be small (as in RCT with low adherence) • Example • Social participation and depressive symptoms among older adults 17

● ● Point Exposure Time−varying Exposure 0.80 0.85 0.90 0.95 1.00 Estimated Prevalence Ratio Type of Exposure Joint intervention in social participation in two time points (i.e., per-protocol effect of sustained social participation) Single point intervention, in which people may deviate from the baseline exposure over time (i.e., ITT effect of baseline exposure) Social participation is more beneficial References: Ø Shiba, Koichiro, et al. "Estimating the impact of sustained social participation on depressive symptoms in older adults." Epidemiology 32.6 (2021): 886-895. 18

Three key time points in a target trial • Eligibility (E) • Treatment assignment (A) • “Time-zero” (t0 ) Benefit of Emulation 2: Align key time points E Follow-up A t0 • In an ideal RCT • E before A and t0 • A and t0 coincide • In an observational study • Often misaligned 19

Misalignment 1: Eligibility After Assignment E Follow-up A t0 • Selection bias • Eligibility criteria affected by treatment (assignment) • Example: Assessing individuals whose outcomes were observed Misalignment 2: Time Zero After Assignment E Follow-up A t0 • Selection bias • Conditioning on no loss-to- follow-up until t0 • Example: Prevalent user analysis 20

Misalignment 3: Assignment After Time Zero • Immortal time bias • Treatment assignment is determined sometime after the time zero • Example: Analysis of treatment duration E Follow-up A t0 References: Ø Hernán, Miguel A., et al. "Specifying a target trial prevents immortal time bias and other self-inflicted injuries in observational analyses." Journal of clinical epidemiology 79 (2016): 70-75. Emulating a target trial forces you to think through how to align E, A, and t0 21

1. Lack of randomization (i.e., confounding) Sources of Discrepancies (Revisited) 2. Other sources of bias (selection, immortal time) 3. Different, and often ambiguous, causal estimand (answering different questions) Easy to fix by target trial emulation Hard to fix The low-hanging fruit for causal inference! 22

Successful Cases of Target Trial Emulation 1. Dickerman, B. A., Gerlovin, H., Madenci, A. L., Kurgansky, K. E., Ferolito, B. R., Figueroa Muñiz, M. J., ... & Hernán, M. A. (2022). Comparative effectiveness of BNT162b2 and mRNA-1273 vaccines in US veterans. New England Journal of Medicine, 386(2), 105-115. 1. Emilsson L, García-Albéniz X, Logan RW, Caniglia EC, Kalager M, Hernán MA. Examining Bias in Studies of Statin Treatment and Survival in Patients With Cancer. JAMA Oncol. 2018 Jan 1;4(1):63-70. doi: 10.1001/jamaoncol.2017.2752. Erratum in: JAMA Oncol. 2018 Jan 1;4(1):133. PMID: 28822996; PMCID: PMC5790310. 2. Dickerman, B.A., García-Albéniz, X., Logan, R.W. et al. Avoidable flaws in observational analyses: an application to statins and cancer. Nat Med 25, 1601–1606 (2019). 3. García-Albéniz X, Hsu J, Bretthauer M, Hernán MA. Effectiveness of Screening Colonoscopy to Prevent Colorectal Cancer Among Medicare Beneficiaries Aged 70 to 79 Years: A Prospective Observational Study. Ann Intern Med. 2017 Jan 3;166(1):18-26. 23