Louisa H. Smith – Target Trial Emulation in Pregnancy Research

Components	Target trial
Causal question	What is the effect of SARS-CoV-2 mRNA vaccine BNT162b2 on COVID-19?
Eligibility criteria	Inclusion criteria: Healthy women ≥18 years of age who are between 24 0/7 and 34 0/7 weeks’ gestation on the day of planned vaccination, with an uncomplicated, singleton pregnancy. Healthy participants determined by medical history, physical examination, and clinical judgment to be appropriate for inclusion in the study. Documented negative HIV antibody test. Exclusion criteria: Other medical or psychiatric condition including recent (within the past year) or active suicidal ideation/behavior. Previous clinical or microbiological diagnosis of COVID-19. Participants with known or suspected immunodeficiency. Bleeding diathesis or condition associated with prolonged bleeding. Previous vaccination with any COVID-19 vaccine. Current alcohol abuse or illicit drug use. Participants who receive treatment with immunosuppressive therapy.
Treatment strategies	1. Two vaccination doses 2. No SARS-CoV-2 vaccination until the end of pregnancy
Assignment procedures	1:1 randomization into the two treatment arms, stratified by gestational week
Follow-up	Since administering the first dose and up to 1 month post delivery
Outcome	SARS-CoV-2 infection as determined by positive PCR test or clinical COVID-19 diagnosis
Causal contrast	Incidence rate ratios; intention-to-treat (one vaccine dose) and per-protocol (two doses)

Does vaccination timing in pregnancy affect live birth?

Eligibility: Unvaccinated, at/soon after conception

Treatment strategies:

Strategy 0: Never vaccinate during pregnancy
Strategy 1: Vaccinate in trimester 1 only
Strategy 2: Vaccinate in trimester 2 only
Strategy 3: Vaccinate in trimester 3 only

Outcome: Live birth (yes/no)

Pregnancy timeline

Note

We are simplifying things by assuming vaccination happens at the end of a trimester, after any pregnancy losses

Randomized trial data

16 pregnant people randomly assigned to 4 strategies:

Person	Assigned strategy	Loss T1	Vax T1	Loss T2	Vax T2	Preterm	Vax T3	Term birth	Live birth
A	0	0	0	0	0	0	0	1	1
B	0	0	0	0	0	1	-	-	1
C	0	0	0	1	-	-	-	-	0
D	0	1	-	-	-	-	-	-	0
E	1	0	1	0	0	0	0	1	1
F	1	0	1	0	0	1	-	-	1
G	1	0	1	1	-	-	-	-	0
H	1	1	-	-	-	-	-	-	0
I	2	0	0	0	1	0	0	1	1
J	2	0	0	0	1	1	-	-	1
K	2	0	0	1	-	-	-	-	0
L	2	1	-	-	-	-	-	-	0
M	3	0	0	0	0	0	1	1	1
N	3	0	0	0	0	1	-	-	1
O	3	0	0	1	-	-	-	-	0
P	3	1	-	-	-	-	-	-	0

Randomized trial results

By assigned strategy:

Assigned strategy	N	Live births	Probability
0	4	2	0.5
1	4	2	0.5
2	4	2	0.5
3	4	2	0.5

All strategies have 50% live birth rate (we are operating in a situation where the null hypothesis of no effect of vaccination at any time is true)

Moving to observational data

In observational data, we don’t see the assigned strategy.

We only see what actually happened:

When (if) people got vaccinated
When pregnancy losses occurred
Whether there was a live birth and when

Let’s classify people by observed vaccination status and timing…

Observed data

Same 16 people, but now we don’t know their assigned strategy:

Person	Observed treatment	Loss T1	Vax T1	Loss T2	Vax T2	Preterm	Vax T3	Term birth	Live birth
A	0 (Never)	0	0	0	0	0	0	1	1
B	0 (Never)	0	0	0	0	1	-	-	1
C	0 (Never)	0	0	1	-	-	-	-	0
D	0 (Never)	1	-	-	-	-	-	-	0
E	1 (Vax T1)	0	1	0	0	0	0	1	1
F	1 (Vax T1)	0	1	0	0	1	-	-	1
G	1 (Vax T1)	0	1	1	-	-	-	-	0
H	0 (Never)	1	-	-	-	-	-	-	0
I	2 (Vax T2)	0	0	0	1	0	0	1	1
J	2 (Vax T2)	0	0	0	1	1	-	-	1
K	0 (Never)	0	0	1	-	-	-	-	0
L	0 (Never)	1	-	-	-	-	-	-	0
M	3 (Vax T3)	0	0	0	0	0	1	1	1
N	0 (Never)	0	0	0	0	1	-	-	1
O	0 (Never)	0	0	1	-	-	-	-	0
P	0 (Never)	1	-	-	-	-	-	-	0

Naive analysis: by achieved vaccination

Classify by when they actually got vaccinated:

Observed vaccination	N	Live births	Probability
0 (Never)	10	3	0.30
1 (Vax T1)	3	2	0.67
2 (Vax T2)	2	2	1.00
3 (Vax T3)	1	1	1.00

The problem: immortal time bias!

Later vaccination appears highly protective!

But: People who got vaccinated later had to survive to that point

All of the pregnancy losses get assigned to the “Never” or “Vax T1” groups
By the time people are classified as “Vax T2” or “Vax T3”, they have already survived those earlier periods

Think like a randomized trial

In a randomized trial, people are assigned to strategies at time zero – even if they don’t get treatment (by choice, not surviving long enough, etc.), they are analyzed in their assigned group*

Immortal time bias

Generally the not-treated group will underestimate the true risk, and the treated group will overestimate it (the later treated, or longer duration required, the more the bias):

Strategy	True probability	Naive estimate	Bias
0 (Never)	0.50	0.30	↓
1 (Vax T1)	0.50	0.67	↑
2 (Vax T2)	0.50	1.00	↑↑
3 (Vax T3)	0.50	1.00	↑↑

This makes treatment appear to reduce risk when there is actually no effect (or if there were a true effect of treatment, this might mask it)

Emulation via clone-censor-weighting

Pretend you have a randomized trial in which everyone is assigned to all strategies at time zero:

Clone everyone to all compatible strategies
Censor clones when they deviate from assigned strategy
Weight to correct for selection bias from censoring

Step 1: Cloning

For each person, create clones for all treatment strategies

Person	Loss T1	Vax T1	Loss T2	Vax T2	Preterm	Vax T3	Term birth	Live birth
A-0	0	0	0	0	0	0	1	1
B-0	0	0	0	0	1	-	-	1
C-0	0	0	1	-	-	-	-	0
D-0	1	-	-	-	-	-	-	0
E-0	0	1	0	0	0	0	1	1
F-0	0	1	0	0	1	-	-	1
G-0	0	1	1	-	-	-	-	0
H-0	1	-	-	-	-	-	-	0
I-0	0	0	0	1	0	0	1	1
J-0	0	0	0	1	1	-	-	1
K-0	0	0	1	-	-	-	-	0
L-0	1	-	-	-	-	-	-	0
M-0	0	0	0	0	0	1	1	1
N-0	0	0	0	0	1	-	-	1
O-0	0	0	1	-	-	-	-	0
P-0	1	-	-	-	-	-	-	0

Treatment strategy Vax T1

Person	Assigned strategy	Loss T1	Vax T1	Loss T2	Vax T2	Preterm	Vax T3	Term birth	Live birth
A-1	1	0	0	0	0	0	0	1	1
B-1	1	0	0	0	0	1	-	-	1
C-1	1	0	0	1	-	-	-	-	0
D-1	1	1	-	-	-	-	-	-	0
E-1	1	0	1	0	0	0	0	1	1
F-1	1	0	1	0	0	1	-	-	1
G-1	1	0	1	1	-	-	-	-	0
H-1	1	1	-	-	-	-	-	-	0
I-1	1	0	0	0	1	0	0	1	1
J-1	1	0	0	0	1	1	-	-	1
K-1	1	0	0	1	-	-	-	-	0
L-1	1	1	-	-	-	-	-	-	0
M-1	1	0	0	0	0	0	1	1	1
N-1	1	0	0	0	0	1	-	-	1
O-1	1	0	0	1	-	-	-	-	0
P-1	1	1	-	-	-	-	-	-	0

And so on…

Step 2: Censoring

Censor clones when their observed data becomes incompatible with assigned strategy:

Strategy 0 (never): censor if vaccinated in T1, T2, or T3
Strategy 1 (vax T1): censor if not vaccinated in T1
Strategy 2 (vax T2): censor if vaccinated in T1 or not vaccinated in T2
Strategy 3 (vax T3): censor if vaccinated in T1 or T2 or not vaccinated in T3

If there is a pregnancy loss in T1, do not censor afterward–we don’t know whether they would have gotten vaccinated or not (can contribute to multiple strategies)

Censoring

This is why defining the treatment strategies precisely is incredibly important, more so than in a real trial
- In real life, “clinical judgment” may result in someone stopping treatment
- In your emulation, should you censor someone if they stop treatment? Or would they be “allowed” to stop in a real trial?
If everyone ends up censored, you’re trying to study a treatment strategy for which you have no positivity!
- Come up with a new strategy that allows more flexibility!

Practice censoring

Picture

Data

Step 3: Weighting

Selection bias introduced by censoring must be corrected

Use inverse probability weighting:

Weight = 1 / (probability of remaining uncensored)
- This would be conditional on current values of covariates if we had them
Transfers weight from censored to uncensored observations

Calculating probability of remaining uncensored

This varies over time, and can be calculated as the product of interval-specific probabilities:

That is, the probability of still being uncensored at the end of T3 is:

the probability of not being censored in T1

times the probability of not being censored in T2 (given not censored in T1)

times the probability of not being censored in T3 (given not censored in T1 or T2)

Original Data

library(tidyverse)

trial_data <- read_csv("ccw-example-data.csv")
trial_data

# A tibble: 16 × 10
   person assigned loss_t1 vax_t1 loss_t2 vax_t2 preterm vax_t3  term livebirth
   <chr>     <dbl>   <dbl>  <dbl>   <dbl>  <dbl>   <dbl>  <dbl> <dbl>     <dbl>
 1 A             0       0      0       0      0       0      0     1         1
 2 B             0       0      0       0      0       1     NA    NA         1
 3 C             0       0      0       1     NA      NA     NA    NA         0
 4 D             0       1     NA      NA     NA      NA     NA    NA         0
 5 E             1       0      1       0      0       0      0     1         1
 6 F             1       0      1       0      0       1     NA    NA         1
 7 G             1       0      1       1     NA      NA     NA    NA         0
 8 H             1       1     NA      NA     NA      NA     NA    NA         0
 9 I             2       0      0       0      1       0      0     1         1
10 J             2       0      0       0      1       1     NA    NA         1
11 K             2       0      0       1     NA      NA     NA    NA         0
12 L             2       1     NA      NA     NA      NA     NA    NA         0
13 M             3       0      0       0      0       0      1     1         1
14 N             3       0      0       0      0       1     NA    NA         1
15 O             3       0      0       1     NA      NA     NA    NA         0
16 P             3       1     NA      NA     NA      NA     NA    NA         0

Step 1: Cloning

Each person is cloned into 4 copies (one for each vaccination strategy: 0, 1, 2, 3)

cloned_data <- trial_data %>%
  crossing(strategy = 0:3) %>%
  relocate(strategy, .after = person)

cloned_data %>%
  count(strategy)

# A tibble: 4 × 2
  strategy     n
     <int> <int>
1        0    16
2        1    16
3        2    16
4        3    16

16 people × 4 strategies = 64 rows

Step 2: Censoring

censored_data <- cloned_data %>%
  mutate(
    # T1: only at risk if survived T1
    censored_t1 = case_when(
      loss_t1 == 1 ~ NA,  # Already had outcome
      strategy %in% c(0, 2, 3) & vax_t1 == 1 ~ TRUE,  # Deviated by vaccinating
      strategy == 1 & vax_t1 == 0 ~ TRUE,  # Deviated by not vaccinating
      .default = FALSE  # Followed strategy
    ),
    
    # T2: only at risk if uncensored and unvaccinated at T1 and survived T2
    censored_t2 = case_when(
      is.na(censored_t1) | censored_t1 ~ NA,  # Already censored or had outcome at T1
      loss_t2 == 1 ~ NA,  # Had outcome at T2
      vax_t1 == 1 ~ NA,  # Already had vax at T1
      strategy %in% c(0, 3) & vax_t2 == 1 ~ TRUE,  # Deviated by vaccinating
      strategy == 2 & vax_t2 == 0 ~ TRUE,  # Deviated by not vaccinating
      .default = FALSE  # Followed strategy
    ),
    
    # T3: only at risk if uncensored and unvaccinated at T2 and survived T3
    censored_t3 = case_when(
      is.na(censored_t2) | censored_t2 ~ NA,  # Already censored or had outcome at T2
      preterm == 1 ~ NA,  # Had outcome at T3
      vax_t1 == 1 | vax_t2 == 1 ~ NA,  # Already had vax at T1 or T2
      strategy == 0 & vax_t3 == 1 ~ TRUE,  # Deviated by vaccinating
      strategy == 3 & vax_t3 == 0 ~ TRUE,  # Deviated by not vaccinating
      .default = FALSE  # Followed strategy
    ),
    
    # Final censoring: censored if ANY time point is TRUE
    censored = (censored_t1) | (censored_t2) | (censored_t3),
    censored = replace_na(censored, FALSE)
  )

Censoring Summary

Different numbers contribute to each strategy:

censored_data %>%
  group_by(strategy) %>%
  summarise(
    n_total = n(),
    censored_t1 = sum(censored_t1 == TRUE, na.rm = TRUE),
    censored_t2 = sum(censored_t2 == TRUE, na.rm = TRUE),
    censored_t3 = sum(censored_t3 == TRUE, na.rm = TRUE),
    total_censored = sum(censored),
    uncensored = sum(!censored)
  )

# A tibble: 4 × 7
  strategy n_total censored_t1 censored_t2 censored_t3 total_censored uncensored
     <int>   <int>       <int>       <int>       <int>          <int>      <int>
1        0      16           3           2           1              6         10
2        1      16           9           0           0              9          7
3        2      16           3           4           0              7          9
4        3      16           3           2           1              6         10

Step 3a: Calculate Censoring Probabilities

Probability of vaccination can be used to calculate interval-specific censoring probabilities

Set up the data so that people who aren’t eligible to be censored at a given timepoint don’t contribute (have NA for vaccination status and/or subset to those not previously censored or vaccinated
Model the probability of treatment (i.e., a propensity score model!)

Vaccination in T1 = censoring (strategy 0, 2, and 3) or not (strategy 1)

trial_data |>
  filter(!is.na(vax_t1)) |>
  pull(vax_t1, name = person)

A B C E F G I J K M N O 
0 0 0 1 1 1 0 0 0 0 0 0

mod_vax_t1 <- glm(vax_t1 ~ 1, data = trial_data, family = binomial())
p_vax_t1 <- predict(mod_vax_t1, type = "response")[1] # all have same predicted value because no covariates
p_vax_t1

   1 
0.25

Vaccination in T2 = censoring (strategy 0 and 3) or not (2)

(For strategy 1, already censored if not vaccinated in T1 so no one “at risk for” censoring here)

trial_data |>
  filter(vax_t1 == 0, !is.na(vax_t2)) |>
  pull(vax_t2, name = person)

A B I J M N 
0 0 1 1 0 0

mod_vax_t2 <- glm(vax_t2 ~ 1, data = trial_data, family = binomial(),
                  subset = vax_t1 == 0)
p_vax_t2 <- predict(mod_vax_t2, type = "response")[1]
p_vax_t2

        1 
0.3333333

Vaccination in T3 = censoring (strategy 0) or not (3)

(For strategies 1 and 2, already censored if not vaccinated in T1 or T2 so no one “at risk for” censoring here)

trial_data |>
  filter(vax_t1 == 0, vax_t2 == 0, !is.na(vax_t3)) |>
  pull(vax_t3, name = person)

A M 
0 1

mod_vax_t3 <- glm(vax_t3 ~ 1, data = trial_data, family = binomial(), subset = vax_t1 == 0 & vax_t2 == 0)
p_vax_t3 <- predict(mod_vax_t3, type = "response")[1]
p_vax_t3

  1 
0.5

Step 3b: Calculate Weights

Weight = 1 / (cumulative probability of not being censored)

weighted_data <- censored_data %>%
  mutate(
    # Probability of not being censored at each time point
    prob_not_cens_t1 = case_when(
      is.na(censored_t1) ~ 1,  # Not at risk
      strategy == 1 ~ p_vax_t1,  # Strategy 1: needs vax at T1
      strategy %in% c(0, 2, 3) ~ 1 - p_vax_t1,  # No vax at T1
      TRUE ~ 1
    ),
    
    prob_not_cens_t2 = case_when(
      is.na(censored_t2) ~ 1,  # Not at risk
      strategy == 2 ~ p_vax_t2,  # Strategy 2: needs vax at T2
      strategy %in% c(0, 3) ~ 1 - p_vax_t2,  # No vax at T2
      TRUE ~ 1
    ),
    
    prob_not_cens_t3 = case_when(
      is.na(censored_t3) ~ 1,  # Not at risk
      strategy == 3 ~ p_vax_t3,  # Strategy 3: needs vax at T3
      strategy == 0 ~ 1 - p_vax_t3,  # No vax at T3
      TRUE ~ 1
    ),
    
    # Cumulative probability = product
    cum_prob_not_censored = prob_not_cens_t1 * prob_not_cens_t2 * prob_not_cens_t3,
    
    # Weight = inverse probability (only for uncensored)
    weight = if_else(!censored, 1 / cum_prob_not_censored, 0)
  )

Example: Strategy 0 (Never vaccinate)

Uncensored individuals and their weights:

weighted_data %>%
  filter(strategy == 0, !censored) %>%
  select(person, livebirth, weight)

# A tibble: 10 × 3
   person livebirth weight
   <chr>      <dbl>  <dbl>
 1 A              1   4.00
 2 B              1   2.00
 3 C              0   1.33
 4 D              0   1   
 5 H              0   1   
 6 K              0   1.33
 7 L              0   1   
 8 N              1   2.00
 9 O              0   1.33
10 P              0   1

Step 3c: Calculate Weighted Outcomes

weighted_data %>%
  filter(!censored) %>%
  group_by(strategy) %>%
  summarise(
    sum_weights = sum(weight),
    weighted_livebirths = sum(livebirth * weight),
    risk_livebirth = weighted_livebirths / sum_weights
  )

# A tibble: 4 × 4
  strategy sum_weights weighted_livebirths risk_livebirth
     <int>       <dbl>               <dbl>          <dbl>
1        0        16.0                8.00          0.500
2        1        16.0                8.00          0.500
3        2        16.0                8.00          0.500
4        3        16.0                8.00          0.500

Why it works

The three steps:

Cloning eliminates immortal time bias by assigning strategies at time zero
Censoring ensures clones follow their assigned strategy
Weighting corrects for selection bias introduced by censoring

Key assumptions

No unmeasured confounding (of baseline treatment and treatment continuation/discontinuation, i.e., time-varying confounding)
Correct specification of censoring models
- There are many different modeling assumptions we could make, e.g., one model for vaccination with a term for time, or separate models at each time point
Positivity (some probability of continuing the treatment strategy at each time)

When to use clone-censor-weighting

Treatment duration comparisons
Sustained treatment strategies that evolve over time
Variable timing of exposure
Threshold-based or dynamic treatment rules
Any strategy where assignment isn’t identifiable at time zero
Multiple cycles or sequential treatment decisions

Practical considerations

Descriptive analysis of treatment patterns
Check positivity (can strategies actually be followed?)
How will you define confounders (both baseline and time-varying)
Start with simple examples to develop code
Check weight distributions

Extensions and advanced topics

Grace periods for treatment initiation
Nested sequential trials
Joint strategies (treatment + monitoring)

Helpful/interesting papers

Miguel A. Hernán et al. (2008) Cain et al. (2010) Young et al. (2011) Miguel A. Hernán et al. (2016) Miguel A. Hernán and Robins (2016) Labrecque and Swanson (2017) Miguel A. Hernán (2018) Caniglia et al. (2019) Dickerman et al. (2019) Chiu et al. (2020) Maringe et al. (2020) Ben-Michael, Feller, and Stuart (2021) Gaber et al. (2024) Cashin et al. (2025) Fu et al. (2025) Moreno-Betancur, Wijesuriya, and Carlin (2025)

Discussion/Questions

What pregnancy research questions are you working on?
How might you apply target trial thinking?
What challenges do you anticipate?
What tools or resources would be most helpful?

Thank you!

email: l.smith@northeastern.edu

References

Avalos, Lyndsay A., Romain S. Neugebauer, Nerissa Nance, Sylvia E. Badon, T. Craig Cheetham, Thomas R. Easterling, Kristi Reynolds, et al. 2023. “Maternal and Neonatal Outcomes Associated with Treating Hypertension in Pregnancy at Different Thresholds.” Pharmacotherapy: The Journal of Human Pharmacology and Drug Therapy 43 (5): 381–90. https://doi.org/10.1002/phar.2778.

Ben-Michael, Eli, Avi Feller, and Elizabeth A. Stuart. 2021. “A Trial Emulation Approach for Policy Evaluations with Group-Level Longitudinal Data.” Epidemiology 32 (4): 533–40. https://doi.org/10.1097/ede.0000000000001369.

Cain, Lauren E., James M. Robins, Emilie Lanoy, Roger Logan, Dominique Costagliola, and Miguel A. Hernán. 2010. “When to Start Treatment? A Systematic Approach to the Comparison of Dynamic Regimes Using Observational Data.” The International Journal of Biostatistics 6 (2): 1–42. https://doi.org/10.2202/1557-4679.1212.

Caniglia, Ellen C., James M. Robins, Lauren E. Cain, Caroline Sabin, Roger Logan, Sophie Abgrall, Michael J. Mugavero, et al. 2019. “Emulating a Trial of Joint Dynamic Strategies: An Application to Monitoring and Treatment of HIV-positive Individuals.” Statistics in Medicine 38 (13): 2428–46. https://doi.org/10.1002/sim.8120.

Caniglia, Ellen C., Rebecca Zash, Denise L. Jacobson, Modiegi Diseko, Gloria Mayondi, Shahin Lockman, Jennifer Y. Chen, et al. 2018. “Emulating a Target Trial of Antiretroviral Therapy Regimens Started Before Conception and Risk of Adverse Birth Outcomes.” AIDS 32 (1): 113–20. https://doi.org/10.1097/qad.0000000000001673.

Cashin, Aidan G., Harrison J. Hansford, Miguel A. Hernán, Sonja A. Swanson, Hopin Lee, Matthew D. Jones, Issa J. Dahabreh, et al. 2025. “Transparent Reporting of Observational Studies Emulating a Target Trial: The TARGET Statement.” BMJ 390 (September): e087179. https://doi.org/10.1136/bmj-2025-087179.

Chiu, Yu-Han, Krista F. Huybrechts, Elisabetta Patorno, Jennifer J. Yland, Carolyn E. Cesta, Brian T. Bateman, Ellen W. Seely, Miguel A. Hernán, and Sonia Hernández-Díaz. 2024. “Metformin Use in the First Trimester of Pregnancy and Risk for Nonlive Birth and Congenital Malformations: Emulating a Target Trial Using Real-World Data.” Annals of Internal Medicine 177 (7): 862–70. https://doi.org/10.7326/M23-2038.

Chiu, Yu-Han, Mats J. Stensrud, Issa J. Dahabreh, Paolo Rinaudo, Michael P. Diamond, John Hsu, Sonia Hernández-Díaz, and Miguel A. Hernán. 2020. “The Effect of Prenatal Treatments on Offspring Events in the Presence of Competing Events: An Application to a Randomized Trial of Fertility Therapies.” Epidemiology 31 (5): 636. https://doi.org/10.1097/EDE.0000000000001222.

Dickerman, Barbra A., Xabier García-Albéniz, Roger Logan, Spiros Denaxas, and Miguel A. Hernán. 2019. “Avoidable Flaws in Observational Analyses: An Application to Statins and Cancer.” Nature Medicine 25 (10): 1601–6. https://doi.org/10.1038/s41591-019-0597-x.

Fu, Edouard L., Michael Harhay, Sebastian Schneeweiss, Rishi Desai, and Miguel A. Hernán. 2025. “Starting Right: Aligning Eligibility and Treatment Assignment at Time Zero When Emulating a Target Trial.” {{SSRN Scholarly Paper}}. Rochester, NY: Social Science Research Network. https://doi.org/10.2139/ssrn.5177135.

Gaber, Charles E., Kent A. Hanson, Sodam Kim, Jennifer L. Lund, Todd A. Lee, and Eleanor J. Murray. 2024. “The Clone-Censor-Weight Method in Pharmacoepidemiologic Research: Foundations and Methodological Implementation.” Current Epidemiology Reports, February. https://doi.org/10.1007/s40471-024-00346-2.

Hernán, Miguel A. 2018. “How to Estimate the Effect of Treatment Duration on Survival Outcomes Using Observational Data.” BMJ 360 (February): k182. https://doi.org/10.1136/bmj.k182.

Hernán, Miguel A., Alvaro Alonso, Roger Logan, Francine Grodstein, Karin B. Michels, Walter C. Willett, Joann E. Manson, and James M. Robins. 2008. “Observational Studies Analyzed Like Randomized Experiments: An Application to Postmenopausal Hormone Therapy and Coronary Heart Disease.” Epidemiology 19 (6): 766–79. https://doi.org/10.1097/ede.0b013e3181875e61.

Hernán, Miguel A., and James M. Robins. 2016. “Using Big Data to Emulate a Target Trial When a Randomized Trial Is Not Available.” American Journal of Epidemiology 183 (8): 758–64. https://doi.org/10.1093/aje/kwv254.

Hernán, Miguel A., Brian C. Sauer, Sonia Hernández-Díaz, Robert Platt, and Ian Shrier. 2016. “Specifying a Target Trial Prevents Immortal Time Bias and Other Self-Inflicted Injuries in Observational Analyses.” Journal of Clinical Epidemiology 79: 70–75. https://doi.org/10.1016/j.jclinepi.2016.04.014.

Labrecque, Jeremy A., and Sonja A. Swanson. 2017. “Target Trial Emulation: Teaching Epidemiology and Beyond.” European Journal of Epidemiology 32 (6): 473–75. https://doi.org/10.1007/s10654-017-0293-4.

Maringe, Camille, Sara Benitez Majano, Aimilia Exarchakou, Matthew Smith, Bernard Rachet, Aurélien Belot, and Clémence Leyrat. 2020. “Reflection on Modern Methods: Trial Emulation in the Presence of Immortal-Time Bias. Assessing the Benefit of Major Surgery for Elderly Lung Cancer Patients Using Observational Data.” International Journal of Epidemiology 49 (5): 1719–29. https://doi.org/10.1093/ije/dyaa057.

Moreno-Betancur, Margarita, Rushani Wijesuriya, and John B. Carlin. 2025. “The Ideal Trial: Defining Causal Estimands That Balance Relevance and Feasibility in Target Trial Emulations and Actual Randomized Trials.” arXiv. https://doi.org/10.48550/arXiv.2405.10026.

Smith, Louisa H., Camille Y. Dollinger, Tyler J. VanderWeele, Diego F. Wyszynski, and Sonia Hernández-Díaz. 2022. “Timing and Severity of COVID-19 During Pregnancy and Risk of Preterm Birth in the International Registry of Coronavirus Exposure in Pregnancy.” BMC Pregnancy and Childbirth 22 (1): 775. https://doi.org/10.1186/s12884-022-05101-3.

Wong, Carlos K. H., Kristy T. K. Lau, Matthew S. H. Chung, Ivan C. H. Au, Ka Wang Cheung, Eric H. Y. Lau, Yasmin Daoud, Benjamin J. Cowling, and Gabriel M. Leung. 2024. “Nirmatrelvir/Ritonavir Use in Pregnant Women with SARS-CoV-2 Omicron Infection: A Target Trial Emulation.” Nature Medicine 30 (1): 112–16. https://doi.org/10.1038/s41591-023-02674-0.

Young, Jessica G., Lauren E. Cain, James M. Robins, Eilis J. O’Reilly, and Miguel A. Hernán. 2011. “Comparative Effectiveness of Dynamic Treatment Regimes: An Application of the Parametric g-Formula.” Statistics in Biosciences 3 (1): 119–43. https://doi.org/10.1007/s12561-011-9040-7.

Zidan, Mahmoud, Nhung T. H. Trinh, Anteneh Desalegn, Louisa H. Smith, Marleen M. H. J. Van Gelder, Hedvig Nordeng, and Angela Lupattelli. 2025. “BNT162b2 mRNA COVID-19 Vaccine Effectiveness in Pregnancy: Emulating Trial NCT04754594 Using Observational Data from Norwegian Health Registries.” Vaccine in press.

Person	Assigned strategy	Loss T1	Vax T1	Loss T2	Vax T2	Preterm	Vax T3	Term birth	Live birth
A	0	0	0	0	0	0	0	1	1
B	0	0	0	0	0	1	-	-	1
C	0	0	0	1	-	-	-	-	0
D	0	1	-	-	-	-	-	-	0
E	1	0	1	0	0	0	0	1	1
F	1	0	1	0	0	1	-	-	1
G	1	0	1	1	-	-	-	-	0
H	1	1	-	-	-	-	-	-	0
I	2	0	0	0	1	0	0	1	1
J	2	0	0	0	1	1	-	-	1
K	2	0	0	1	-	-	-	-	0
L	2	1	-	-	-	-	-	-	0
M	3	0	0	0	0	0	1	1	1
N	3	0	0	0	0	1	-	-	1
O	3	0	0	1	-	-	-	-	0
P	3	1	-	-	-	-	-	-	0

Person	Loss T1	Vax T1	Loss T2	Vax T2	Preterm	Vax T3	Term birth	Live birth
A-0	0	0	0	0	0	0	1	1
B-0	0	0	0	0	1	-	-	1
C-0	0	0	1	-	-	-	-	0
D-0	1	-	-	-	-	-	-	0
E-0	0	1	0	0	0	0	1	1
F-0	0	1	0	0	1	-	-	1
G-0	0	1	1	-	-	-	-	0
H-0	1	-	-	-	-	-	-	0
I-0	0	0	0	1	0	0	1	1
J-0	0	0	0	1	1	-	-	1
K-0	0	0	1	-	-	-	-	0
L-0	1	-	-	-	-	-	-	0
M-0	0	0	0	0	0	1	1	1
N-0	0	0	0	0	1	-	-	1
O-0	0	0	1	-	-	-	-	0
P-0	1	-	-	-	-	-	-	0

Person	Assigned strategy	Loss T1	Vax T1	Loss T2	Vax T2	Preterm	Vax T3	Term birth	Live birth
A-1	1	0	0	0	0	0	0	1	1
B-1	1	0	0	0	0	1	-	-	1
C-1	1	0	0	1	-	-	-	-	0
D-1	1	1	-	-	-	-	-	-	0
E-1	1	0	1	0	0	0	0	1	1
F-1	1	0	1	0	0	1	-	-	1
G-1	1	0	1	1	-	-	-	-	0
H-1	1	1	-	-	-	-	-	-	0
I-1	1	0	0	0	1	0	0	1	1
J-1	1	0	0	0	1	1	-	-	1
K-1	1	0	0	1	-	-	-	-	0
L-1	1	1	-	-	-	-	-	-	0
M-1	1	0	0	0	0	0	1	1	1
N-1	1	0	0	0	0	1	-	-	1
O-1	1	0	0	1	-	-	-	-	0
P-1	1	1	-	-	-	-	-	-	0

Person	Assigned strategy	Loss T1	Vax T1	Loss T2	Vax T2	Preterm	Vax T3	Term birth	Live birth
A	0	0	0	0	0	0	0	1	1
B	0	0	0	0	0	1	-	-	1
C	0	0	0	1	-	-	-	-	0
D	0	1	-	-	-	-	-	-	0
E	1	0	1	0	0	0	0	1	1
F	1	0	1	0	0	1	-	-	1
G	1	0	1	1	-	-	-	-	0
H	1	1	-	-	-	-	-	-	0
I	2	0	0	0	1	0	0	1	1
J	2	0	0	0	1	1	-	-	1
K	2	0	0	1	-	-	-	-	0
L	2	1	-	-	-	-	-	-	0
M	3	0	0	0	0	0	1	1	1
N	3	0	0	0	0	1	-	-	1
O	3	0	0	1	-	-	-	-	0
P	3	1	-	-	-	-	-	-	0

Person	Loss T1	Vax T1	Loss T2	Vax T2	Preterm	Vax T3	Term birth	Live birth
A-0	0	0	0	0	0	0	1	1
B-0	0	0	0	0	1	-	-	1
C-0	0	0	1	-	-	-	-	0
D-0	1	-	-	-	-	-	-	0
E-0	0	1	0	0	0	0	1	1
F-0	0	1	0	0	1	-	-	1
G-0	0	1	1	-	-	-	-	0
H-0	1	-	-	-	-	-	-	0
I-0	0	0	0	1	0	0	1	1
J-0	0	0	0	1	1	-	-	1
K-0	0	0	1	-	-	-	-	0
L-0	1	-	-	-	-	-	-	0
M-0	0	0	0	0	0	1	1	1
N-0	0	0	0	0	1	-	-	1
O-0	0	0	1	-	-	-	-	0
P-0	1	-	-	-	-	-	-	0

Person	Assigned strategy	Loss T1	Vax T1	Loss T2	Vax T2	Preterm	Vax T3	Term birth	Live birth
A-1	1	0	0	0	0	0	0	1	1
B-1	1	0	0	0	0	1	-	-	1
C-1	1	0	0	1	-	-	-	-	0
D-1	1	1	-	-	-	-	-	-	0
E-1	1	0	1	0	0	0	0	1	1
F-1	1	0	1	0	0	1	-	-	1
G-1	1	0	1	1	-	-	-	-	0
H-1	1	1	-	-	-	-	-	-	0
I-1	1	0	0	0	1	0	0	1	1
J-1	1	0	0	0	1	1	-	-	1
K-1	1	0	0	1	-	-	-	-	0
L-1	1	1	-	-	-	-	-	-	0
M-1	1	0	0	0	0	0	1	1	1
N-1	1	0	0	0	0	1	-	-	1
O-1	1	0	0	1	-	-	-	-	0
P-1	1	1	-	-	-	-	-	-	0

Person	Assigned strategy	Loss T1	Vax T1	Loss T2	Vax T2	Preterm	Vax T3	Term birth	Live birth
A	0	0	0	0	0	0	0	1	1
B	0	0	0	0	0	1	-	-	1
C	0	0	0	1	-	-	-	-	0
D	0	1	-	-	-	-	-	-	0
E	1	0	1	0	0	0	0	1	1
F	1	0	1	0	0	1	-	-	1
G	1	0	1	1	-	-	-	-	0
H	1	1	-	-	-	-	-	-	0
I	2	0	0	0	1	0	0	1	1
J	2	0	0	0	1	1	-	-	1
K	2	0	0	1	-	-	-	-	0
L	2	1	-	-	-	-	-	-	0
M	3	0	0	0	0	0	1	1	1
N	3	0	0	0	0	1	-	-	1
O	3	0	0	1	-	-	-	-	0
P	3	1	-	-	-	-	-	-	0

Person	Loss T1	Vax T1	Loss T2	Vax T2	Preterm	Vax T3	Term birth	Live birth
A-0	0	0	0	0	0	0	1	1
B-0	0	0	0	0	1	-	-	1
C-0	0	0	1	-	-	-	-	0
D-0	1	-	-	-	-	-	-	0
E-0	0	1	0	0	0	0	1	1
F-0	0	1	0	0	1	-	-	1
G-0	0	1	1	-	-	-	-	0
H-0	1	-	-	-	-	-	-	0
I-0	0	0	0	1	0	0	1	1
J-0	0	0	0	1	1	-	-	1
K-0	0	0	1	-	-	-	-	0
L-0	1	-	-	-	-	-	-	0
M-0	0	0	0	0	0	1	1	1
N-0	0	0	0	0	1	-	-	1
O-0	0	0	1	-	-	-	-	0
P-0	1	-	-	-	-	-	-	0

Person	Assigned strategy	Loss T1	Vax T1	Loss T2	Vax T2	Preterm	Vax T3	Term birth	Live birth
A-1	1	0	0	0	0	0	0	1	1
B-1	1	0	0	0	0	1	-	-	1
C-1	1	0	0	1	-	-	-	-	0
D-1	1	1	-	-	-	-	-	-	0
E-1	1	0	1	0	0	0	0	1	1
F-1	1	0	1	0	0	1	-	-	1
G-1	1	0	1	1	-	-	-	-	0
H-1	1	1	-	-	-	-	-	-	0
I-1	1	0	0	0	1	0	0	1	1
J-1	1	0	0	0	1	1	-	-	1
K-1	1	0	0	1	-	-	-	-	0
L-1	1	1	-	-	-	-	-	-	0
M-1	1	0	0	0	0	0	1	1	1
N-1	1	0	0	0	0	1	-	-	1
O-1	1	0	0	1	-	-	-	-	0
P-1	1	1	-	-	-	-	-	-	0