TTE methodology: mapping to reference papers

Overview

This vignette maps the swereg target trial emulation (TTE) implementation to five reference papers. It states which methods swereg implements, which it does not, and the reason for each design choice.

Reference papers

1. Hernán & Robins (2016): “Using big data to emulate a target trial when a randomized trial is not available.” Am J Epidemiol. The theoretical framework. It defines the four emulation failures and their solutions.

2. Hernán et al. (2008): “Observational analyses of the effect of combined estrogen-progestin therapy on coronary heart disease.” Epidemiology. The original “sequence of nested trials” paper. NHS/WHI hormone therapy example.

3. Danaei et al. (2013): “Statins and coronary heart disease events.” Epidemiology. The most detailed methods paper. It covers ITT, per-protocol and as-treated analyses, with SAS code.

4. Caniglia et al. (2023): “Emulating target trials in pregnancy.” Am J Epidemiol. Discusses enrollment period granularity and residual immortal time bias.

5. Cashin et al. (2025): “TARGET Statement.” JAMA. 21-item checklist for transparent reporting of target trial emulations.

Method mapping

Enrollment and trial construction

Method	Paper	swereg implementation
Sequence of nested trials	Hernán 2008, Danaei 2013	TTEEnrollment$new(..., ratio=): Enrollment assesses eligibility and treatment status weekly, then collapses period_width consecutive weeks into one enrollment period. Each enrollment period opens exactly one trial. Initiation in any week of an enrollment period assigns the person to the trial of that period. Time zero is a landmark: the first week after the enrollment period closes. A person enters the trial only if they reach that week under observation and free of every enrollment outcome. See vignette("tte-timing").
Cloning + censoring	Hernán 2016	Not used. Our comparator draw in each enrollment period is an alternative to cloning that is computationally more efficient for large registries. The draw is incidence density sampling, stratified by the period_width-week enrollment period, and it reads no other variable. It forms no matched set.
Grace period	Hernán 2016 (Section 4.4)	Not implemented. A true grace period (initiation allowed within X weeks of assignment without deviation) requires cloning + censoring + weighting. period_width provides slack only for the timing of initiation at enrollment. Treatment that starts in any week of the enrollment period assigns the person to its trial. Follow-up opens at time zero, the first week after the period closes. Deviation thereafter censors at the start of the first discordant week beyond the arm’s tolerance. See vignette("tte-nomenclature").

Weighting methods

Method	Paper	swereg implementation
Baseline IPW (propensity score)	Hernán 2008, Danaei 2013	$s2_ipw(): Logistic regression P(A=1 | L_baseline), stabilized by default. L_baseline is the enrollment-period snapshot .tte_entry__<v>, read at the recruiting week.
Time-varying IPW (as-treated)	Danaei 2013 (Section 4.3)	Not implemented. Requires P(A_t | A_{t-1}, L_t).
IPCW for per-protocol	Danaei 2013 (Section 4.2)	$s4_prepare_for_analysis(estimand = "pp"): censoring at protocol deviation and at loss of observation. ipcw_pp is the product of three factors, each fitted in each arm by default. The loss model fits on the rows without an outcome. The deviation model fits on the rows without an outcome that were not lost. A logistic model for a deviation at time zero fits on every person-trial. The two row-level models are GAM or GLM. Combined weight: analysis_weight_pp = ipw × ipcw_pp.
Baseline IPW for ITT	Hernán & Robins	$s4_prepare_for_analysis(estimand = "itt"): no switch censoring, no IPCW; analysis weight = baseline ipw_trunc.
Weight stabilization	Danaei 2013	IPW: stabilized with marginal treatment probability. IPCW-PP: each row-level numerator is a second model on the same risk set, with the follow-up-time term (tstart) and nothing else. The time-zero numerator is the arm’s proportion that deviates at time zero (see note below).
Weight truncation	Cole & Hernán 2008 (p. 661)	$s3_truncate_weights(): Winsorization at 1st/99th percentiles by default. The untruncated per-protocol result is exported as a sensitivity analysis. Danaei 2013 truncated the stabilised weights at a maximum of 10.

Note on analysis types: swereg supports both per-protocol and intention-to-treat estimands, selected with $s4_prepare_for_analysis(estimand = "pp" | "itt"). Per-protocol censors follow-up at treatment switching and corrects the resulting informative censoring with IPCW (analysis weight analysis_weight_pp[_trunc]). Intention-to-treat keeps follow-up through switching, with no switch censoring and no IPCW, and weights on the baseline IPW alone (ipw_trunc). The production pipeline builds both analysis files per ETT and reports both IRRs and both risk differences side by side. As-treated analysis (time-varying IPW) is not implemented.

Follow-up can end for the seven reasons in the table below. The two estimands handle four of them differently:

• an outcome event and a switch in the same follow-up interval
• a treatment switch
• a deviation at time zero
• a loss of observation

Reason follow-up ends	Per-protocol	Intention-to-treat
Outcome event	ends, counts as event	same
Outcome event AND switch in the same follow-up interval	counts as event only when it falls before the first discordant week beyond tolerance	counts as event
Treatment switch (protocol deviation)	censors, IPCW-corrected	ignored (not censored)
Deviation at time zero	no follow-up; the time-zero factor of the IPCW weights the rest of the arm	ignored (not censored)
Loss of observation (the record ends early, or a week after time zero has no row)	censors, IPCW-corrected; an outcome at or after a missing week never counts	censors, treated as independent; an outcome at or after a missing week never counts
Administrative end (study cutoff)	censors	same
Follow-up horizon	censors	same

Per-protocol weight = ipw × ipcw_pp; intention-to-treat weight = baseline ipw only.

Note on IPCW stabilization: Danaei (2013) describes stabilized IPCW weights with a numerator conditioned on baseline covariates. That requires the same covariates in the outcome model. swereg’s outcome model holds no confounders. Each row-level numerator is therefore a second model, fitted on the same risk set, that carries the follow-up-time term (tstart) only. A numerator covariate must also be in the outcome model (Su et al. 2024, text after eq. 3), and a calendar-period spline is not in the span of the outcome model’s trial and follow-up terms. See vignette("tte-methods") section 1.8.9.

Outcome models

Method	Paper	swereg implementation
Cox proportional hazards	Hernán 2008 (ITT)	Not directly. $survival_curve() provides weighted discrete-time survival curves from the panel (ITT via baseline IPW, or PP via a time-varying weight).
Pooled logistic regression	Danaei 2013, Hernán 2008 (IPW)	$irr(): Weighted Poisson regression with survey::svyglm(family = quasipoisson), computationally equivalent.
Flexible baseline hazard	Danaei 2013 (“month of follow-up and squared terms”)	$irr(): a term in tstart, the time since time zero at the interval start. It is splines::ns(tstart, df = 3) with ≥4 distinct values, factor(tstart) with 2-3, and absent with 1. The term reads tstart and not tstop. On the last row of a person-trial, tstop is the week where follow-up stops, which can fall inside the interval. A tstop term would therefore move the event rows on the time axis.
Trial as covariate	Caniglia 2023, Danaei 2013, Su 2024	The outcome model of $irr(), $irr_by_subgroup() and $effect_modification_test() includes the trial, enrollment_period_id: splines::ns(enrollment_period_id, df = 3) with ≥4 trials, a factor with 2-3, and no term with 1. The loss and deviation denominators instead include period_id, the calendar period of each follow-up interval. It takes the same thresholds, plus a penalised spline for ≥10 under the default GAM. Their numerators include neither. vignette("tte-methods") section 1.8.9 gives the reason for each.
Robust variance	Hernán 2008, Danaei 2013	survey::svydesign(ids = ~person_id_var) provides person-level clustered standard errors.
Heterogeneity test	Hernán 2008, Danaei 2013	$heterogeneity_test(): joint Wald test of the interaction of treatment with splines::ns(enrollment_period_id, df = min(3, n - 1)), where n is the number of trials. The model also holds the tstart term.
Risk difference and number needed to treat	None of the five papers. The NNTB and NNTH labels and the reciprocal interval come from Altman (1998, BMJ). Altman reports an interval that crosses zero as running through infinity; swereg reports no interval there	$risk_difference(): the cause-specific risk difference at each distinct stop time, from weighted discrete-time survival in each arm. Death censors follow-up; there is no competing-risk model. The interval is a percentile bootstrap that resamples persons, with one resample shared by both arms and the weights held fixed. The number needed to treat is -1/rd, labelled NNTB or NNTH by the sign of rd, with an interval only when the risk-difference interval excludes zero. $s3_analyze() runs it for both estimands. See vignette("tte-methods") sections 1.6 (Causal contrasts), 1.8.5 (Absolute scale) and 1.8.6 (Inference).

IRR approximates HR

For rare events (typical in registry-based TTE studies), the incidence rate ratio from Poisson regression approximates the hazard ratio from Cox regression (Thompson 1977). The quasipoisson family in svyglm additionally accounts for overdispersion from survey weights. This approach scales to large registry datasets where survey::svycoxph() would be computationally prohibitive.

TARGET checklist

The TARGET Statement (Cashin et al., JAMA 2025) provides a 21-item reporting checklist. plan$print_target_checklist() maps the 21 TARGET items to the swereg configuration. It shows which items the spec fills in and which need manual reporting.

What is not implemented

Method	Reason
As-treated analysis (time-varying IPW)	Requires a different modeling framework for time-varying treatment weights.
Log-binomial models (risk ratios)	Caniglia (2023) uses these for pregnancy outcomes. Users can fit these externally on $extract() data.
Baseline-conditional IPCW stabilization	Would require the baseline covariates in the outcome model, which has none here. The row-level numerator models carry the follow-up-time term and no confounders.