Sensitivity Analysis for Trials with Irregular and Informative Assessment Times: Marginal Mean Models and Sensitivity Parameter Selection

Introduction to the show: ident: Statistics. The day in statistics: methods, theory and the inference under them.

Tom: I'm Tom.

Jane: And I'm Jane, here with Lu, Meng and our in-house large language model, Lalam.

Tom: We're looking at the paper: "Sensitivity Analysis for Trials with Irregular and Informative Assessment Times".

Jane: Here's the gist of the paper. In randomized trials, outcome assessment times often vary across participants and may depend on the underlying outcome process, so outcomes observed near a target time need not represent the target population.

Tom: Whether assessment is informative cannot be determined from the observed data alone.

Jane: The paper extends the sensitivity analysis framework of Smith et al.

Tom: (2024), which is anchored in an explainable assessment assumption and was restricted to continuous outcomes through an identity-link marginal mean model, to a broader class of link functions that accommodates binary and count outcomes.

Title and authors: Jane: It’s about how we can handle situations where people in a trial are assessed at different times, and those assessment times might be informative. It extends some earlier work that focused on continuous outcomes to handle things like binary or count data too.

Tom: So, so it deals with the messiness of assessment timing and making sure our results aren't just capturing timing differences instead of actual treatment effects.

Lu: Exactly, and the authors are extending a framework from Smith et al. two thousand twenty-four that was originally for continuous outcomes using an identity-link marginal mean model to a broader class of link functions that handles binary and count data too <ref:2610.25454#pg1>.

Meng: So they're trying to make the sensitivity analysis robust enough to be used on real-world trial data, not just smooth mathematical models.

Lalam: And they develop this influence function based augmented inverse intensity weighted estimator which is root-n consistent under standard regularity conditions, which is pretty solid for estimation.

The paper's summary: Jane: So what does the paper actually propose? It sets up some assumptions, like the tilting assumption and the generalized marginal mean assumption, to define how we model these irregular assessment times.

Tom: It assumes that for every time t where we see an assessment happening, the distribution of outcomes changes in a specific way relative to the underlying population distribution at that time.

Lu: Specifically, they use a single-index model for the outcome process and an Andersen-Gill model stratified by assessment number to model how often we see someone assessed.

Meng: That sounds like a lot of modeling layered on top of each other, trying to separate the effect of the treatment from the effect of when you got your blood drawn.

Lalam: They then develop these influence functions for the parameter beta and their weighted estimators, which are derived by estimating conditional mean outcomes and computing estimated inverse intensity weights.

The paper's improvements: Tom: So what’s the real improvement here? It’s not just a new estimator; it’s this data driven procedure for selecting the sensitivity parameter.

Jane: They define a true range for the sensitivity parameter alpha, from alpha l to alpha u, by looking at when expected outcomes are above and below some target mean outcome.

Lu: And they use optimization problems and bias corrected via multiplier bootstrap procedures to estimate those bounds, which accounts for uncertainty in selecting that parameter range itself.

Meng: That’s smart because it means we don't just pick a sensitivity number blindly; we find the plausible range based on what the data suggests about the target mean outcome.

Lalam: Then they build a ninety-five percent confidence set for that entire range using either a basic bootstrap or a Wald CI based on those bias corrected point estimates and variance estimators.

Conclusion: Tom: So to wrap up, this paper addresses the core problem of how to analyze trials when assessment times are irregular and informative, and it does so by generalizing the framework to handle binary and count outcomes too.

Jane: It provides a data driven way to select a plausible range for that sensitivity parameter alpha, giving us confidence sets for that range based on the target mean outcome bounds.

Lu: The simulation studies show that even when we violate the explainable assessment assumption, the augmented inverse intensity weighted estimator still performs well and shows smaller bias than original estimators as sample size increases.

Meng: It's good to know it works better under realistic, informative scenarios for our deployment concerns because it suggests the confidence intervals are more reliable than basic bootstrap ones in some cases.

Lalam: Overall, the results for both outcomes indicate that when alpha l and alpha u are similar with a difference no more than zero point eight, there is insufficient evidence to conclude a treatment effect at either follow-up time. When alpha l is greater than alpha u plus zero point eight, the analyses frequently provide evidence that the home visits intervention improves the population mean asthma control outcome relative to portal training alone at both six and twelve months.

Tom: That’s a really concrete finding, linking the sensitivity parameter directly to whether we see a treatment effect or not based on those bounds.

Jane: It shows that when we allow for different informativeness mechanisms between arms, statistically significant treatment effects can emerge under some plausible sensitivity parameter values.

Lu: It broadens the scope substantially by accommodating continuous, binary, and count outcomes through appropriate link functions.

Meng: For us in production, it means we have a principled way to quantify the uncertainty when clinical experts give us ranges for outcome means.