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Living forwards or understanding backwards? A comparison of Inverse Probability of Treatment Weighting and G-estimation methods for targeting hypothetical full adherence estimands in longitudinal cohort studies

This paper compares Inverse Probability of Treatment Weighting (IPTW) and G-estimation methods for estimating the causal effect of full medication adherence versus non-adherence on health outcomes in longitudinal observational studies, evaluating their statistical properties through simulations and demonstrating their application using UK Biobank data on statin adherence.

Original authors: Xiaoran Liang, Deniz Türkmen, Jane A H Masoli, Luke C Pilling, Jack Bowden

Published 2026-03-10

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Xiaoran Liang, Deniz Türkmen, Jane A H Masoli, Luke C Pilling, Jack Bowden

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to figure out how much taking your medicine every single day actually improves your health. This is a classic problem in medicine: we know people should take their pills, but in real life, many forget, skip doses, or stop taking them entirely.

The problem is that people who forget their medicine often have other things going on in their lives (like being sicker, having less money, or being more stressed) that also make them less healthy. If you just look at the data, it's hard to tell if they are sick because they didn't take the pill, or if they didn't take the pill because they were already sick.

This paper is about two different ways to solve this puzzle using computer models to separate the "medicine effect" from the "sick-life effect." The authors call these methods IPTW and G-estimation.

Here is the breakdown using simple analogies:

The Core Problem: The "Time-Traveling" Confusion

Imagine you are watching a movie where the hero's health changes every week.

Week 1: The hero takes his medicine.
Week 2: He feels better, so he goes to the gym.
Week 3: Because he went to the gym, he takes his medicine even more regularly.

The problem is: Did he feel better in Week 3 because of the medicine in Week 1, or because of the gym in Week 2? And did the gym happen because of the medicine? It's a tangled web of cause and effect that changes over time.

The Two Methods: "Living Forwards" vs. "Understanding Backwards"

The authors use a famous quote by the philosopher Kierkegaard: "Life must be lived forwards, but understood backwards." They use this to describe their two methods.

1. IPTW (Inverse Probability of Treatment Weighting) = "Living Forwards"

The Analogy: Imagine a crowded room where some people are taking medicine and some aren't. The people taking medicine look different (maybe they are richer or healthier to begin with).

How it works: IPTW acts like a magical scale. It looks at every person in the room and gives them a "weight."
- If a person is very likely to take medicine (because they are rich/healthy) but didn't, the scale makes them count for 10 people.
- If a person is unlikely to take medicine but did, the scale makes them count for 10 people.
The Goal: By the end, the "weighted" room looks like a perfectly balanced experiment where taking the medicine was random. It tries to create a fake "perfect world" where everyone is equal, moving from the start of the study to the end.
The Flaw: If the rules of the room are too strict (e.g., only very healthy people can take the medicine), the scale has to give some people a weight of "1,000,000" to balance the room. This makes the math unstable and prone to crashing.

2. G-estimation = "Understanding Backwards"

The Analogy: Imagine you are watching the movie of the hero's life, but you are watching it in reverse.

How it works: You start at the end (Week 3) and ask, "How much of this health was caused by the medicine taken right now?" You calculate that effect and subtract it from the hero's health record. You call this "blipping down" the outcome.
Then you move to Week 2. You ask, "Now that we've removed the effect of Week 3, how much of the remaining health was caused by Week 2's medicine?" You subtract that too.
The Goal: You keep peeling away the layers of the onion, working backward from the end to the beginning, isolating the specific contribution of the medicine at each step.
The Advantage: It doesn't need to create a giant, unstable scale. It just mathematically removes the "noise" step-by-step. The paper finds this method is usually more stable and accurate, especially when the data is messy.

The "Secret Weapon": Instrumental Variables (IV)

Sometimes, even the best methods fail because there are hidden factors we can't measure (like a secret genetic trait that makes people lazy and sick).

The Analogy: Imagine you want to know if rain makes grass wet, but you suspect the grass is also wet because of a hidden sprinkler.
The Solution: You look for a "Secret Signal" (Instrument) that only causes the rain but has nothing to do with the sprinkler. In this study, they used genetics (DNA) as the signal. Some people have genes that make statin drugs work better, so they naturally take them more. Since your DNA is fixed at birth, it can't be changed by your current sickness.
The Catch: In their real-world test with 13,000 people, the "genetic signal" was very weak. It was like trying to hear a whisper in a hurricane. The method worked in theory, but the results were too fuzzy to be precise.

What Did They Find? (The Real-World Test)

They applied these methods to 13,000 people taking statins (cholesterol medicine) in the UK. They wanted to know: "If everyone took 100% of their pills, how much lower would their cholesterol be compared to taking 0%?"

The Result: Both methods agreed that taking the medicine helps a lot.
- IPTW said: "Full adherence lowers cholesterol by about 15–20%."
- G-estimation said: "Full adherence lowers cholesterol by about 15–20%."
- They matched up well!
The Timing: They found that recent adherence matters most. Taking your pill today has a bigger impact on your cholesterol today than taking it three years ago.
The Winner: While both worked, G-estimation was more reliable. When the data got messy (like when sick people stopped taking pills), IPTW started to wobble and give weird answers, while G-estimation stayed steady.

The Bottom Line

If you are a doctor or a researcher trying to figure out if a drug works in the real world:

IPTW is like trying to balance a scale; it's easy to understand but can tip over if the data is messy.
G-estimation is like peeling an onion backwards; it's a bit more complex to set up, but it's much tougher and gives you a clearer picture of the truth.

The paper suggests that for long-term studies with continuous data (like daily pill counts), G-estimation is the better tool to use, provided you have the right software to run it.

1. Problem Statement

The paper addresses the challenge of estimating the causal effect of time-varying continuous drug adherence on health outcomes in observational longitudinal studies.

The Core Issue: In routine care, patients often do not adhere to medication regimens. Standard regression methods fail in this setting because of time-varying confounding: a patient's health status (confounder) influences future adherence, but is also influenced by past adherence. Adjusting for this intermediate health status blocks part of the causal pathway, while failing to adjust leaves the effect confounded.
The Goal: The authors aim to estimate a hypothetical estimand: the average difference in health outcomes if a specific group of treated individuals had maintained full adherence (100% Medication Possession Ratio, MPR) versus zero adherence (0% MPR) over a sustained period.
Context: The study focuses on continuous exposures (adherence levels), which presents specific statistical challenges (e.g., positivity violations) compared to binary treatments.

2. Methodology

The authors compare three causal inference approaches within a unified longitudinal framework, all targeting the same estimand: $E[Y(1_k) - Y(0_k) | S=1]$ .

A. Inverse Probability of Treatment Weighting (IPTW)

Framework: Uses Marginal Structural Models (MSM).
Mechanism ("Living Forwards"): IPTW re-weights observations sequentially from the start of the study to the end. It constructs weights based on the inverse probability of the observed adherence history given the past.
Implementation: The authors utilize Covariate Balancing Propensity Scores (CBPS) for continuous exposures to estimate weights that balance observed covariates.
Assumptions: Requires Sequential Exchangeability (No Unmeasured Confounding - NUC), Consistency, and Positivity.
Vulnerability: Highly sensitive to "near-positivity violations" (where adherence is highly predictable based on history), leading to unstable, extreme weights and finite-sample bias.

B. G-estimation of Structural Nested Mean Models (SNMM)

Framework: Uses Structural Nested Mean Models (SNMM).
Mechanism ("Understanding Backwards"): G-estimation works backwards from the final outcome to the baseline. It "blips down" the outcome by subtracting the estimated causal effect of adherence at each time step, creating a counterfactual "adherence-free" outcome.
Implementation: The authors propose a Joint Generalized Method of Moments (GMM) approach. Instead of the traditional recursive backward step, they stack moment conditions across all time points to estimate parameters simultaneously. They also implement an efficient two-step GMM using double-residualization (residualizing both the outcome and the exposure).
Assumptions: Requires NUC, Consistency, and Positivity (though less stringent than IPTW in practice).
Advantage: Generally more robust to positivity violations and more statistically efficient than IPTW in continuous exposure settings.

C. Instrumental Variable (IV) G-estimation

Framework: An extension of SNMM using an Instrumental Variable (IV) to relax the NUC assumption.
Mechanism: Uses a genetic variant (Polygenic Score) as an instrument for adherence. It identifies the causal effect even if unmeasured confounders exist, provided the IV assumptions hold.
Implementation: Uses a decay model parameterization ( $\beta_{k(j)} = \beta \alpha^{t_k - t_j}$ ) to reduce the number of parameters, making the model identifiable when the number of time points exceeds the number of moment conditions provided by a single time-fixed instrument.
Assumptions: Requires a valid IV (relevance, exclusion restriction, independence) and the decay model structure.

3. Key Contributions

Unified Framework: The paper demonstrates that IPTW (via MSM) and G-estimation (via SNMM) can be parameterized to target the exact same causal estimand (the contrast between full and zero adherence), allowing for direct comparison.
Continuous Exposure Adaptation: It specifically adapts these methods for continuous adherence measures (MPR), addressing the unique challenges of weight instability in IPTW and model specification in G-estimation for continuous data.
Efficient GMM Implementation: The authors provide a novel joint GMM implementation for G-estimation that estimates all time-specific effects simultaneously, offering better variance estimation and computational symmetry compared to traditional recursive G-estimation.
Practical Resources: The authors release R code for implementing both basic and efficient GMM formulations of longitudinal G-estimation, filling a gap in accessible software for applied researchers.
Empirical Application: They apply these methods to a real-world dataset of 13,000 UK Biobank participants to estimate the effect of statin adherence on LDL-cholesterol control, using a Polygenic Score as a potential IV.

4. Results

Simulation Studies

Performance under NUC: Under the "No Unmeasured Confounding" assumption, G-estimation (both basic and efficient GMM) outperformed IPTW.
- IPTW: Showed significant finite-sample bias and instability when there was strong feedback between exposure and time-varying confounders (leading to near-positivity violations). Standard errors from weighted regression severely underestimated true variability.
- G-estimation: Remained stable and unbiased across all scenarios. The efficient GMM version provided standard errors that closely matched empirical variability, yielding near-nominal confidence interval coverage.
Performance under Unmeasured Confounding: Both IPTW and NUC-based G-estimation became inconsistent (biased) when unmeasured confounding was present.
IV Performance: The IV-based G-estimation remained consistent under valid IV assumptions but suffered from low efficiency (large standard errors) when the instrument was weak. It was highly sensitive to weak instruments and incorrect adjustment for time-varying covariates.

Applied Example (Statin Adherence & LDL-c)

Findings: Both IPTW and G-estimation estimated that full adherence (MPR=100%) versus non-adherence (MPR=0%) resulted in a 15–20% reduction in LDL-cholesterol.
- The effect was time-dependent: adherence closest to the measurement had the largest impact.
- Sensitivity: IPTW results varied significantly depending on the CBPS weighting option ("exact" vs. "over-identified"), whereas G-estimation provided stable estimates.
IV Results: The genetic instrument was extremely weak (partial F-statistics < 1). Consequently, IV estimates were highly imprecise (wide confidence intervals), though the point estimates suggested a larger effect (40–50%) than the NUC-based methods. This highlights the difficulty of applying IV methods to adherence in current observational datasets without massive sample sizes.

5. Significance and Conclusion

Methodological Shift: The paper argues that for longitudinal studies with continuous time-varying exposures (like drug adherence), G-estimation is a superior alternative to IPTW. It offers greater robustness to positivity violations and higher statistical efficiency.
Practical Guidance: The authors recommend using G-estimation (specifically the efficient GMM approach) as the primary method for such analyses, reserving IPTW for cases where software constraints exist or for sensitivity checks.
Future Directions: The study highlights that while IV methods are theoretically powerful for handling unmeasured confounding, current observational datasets often lack the sample size and instrument strength required for precise estimation. The authors suggest that future large-scale biobanks (e.g., Our Future Health) will be necessary to make IV-based longitudinal adherence studies feasible.
Interpretation: The "living forwards" (IPTW) vs. "understanding backwards" (G-estimation) metaphor effectively captures the algorithmic differences, but the paper concludes that both can yield valid causal estimates if assumptions are met, with G-estimation being more robust in the specific context of continuous adherence.