Statistical modeling of causal effects in continuous time

This article studies the estimation of the causal effect of a time-varying treatment on time-to-an-event or on some other continuously distributed outcome. The paper applies to the situation where treatment is repeatedly adapted to time-dependent patient characteristics. The treatment effect cannot be estimated by simply conditioning on these time-dependent patient characteristics, as they may themselves be indications of the treatment effect. This time-dependent confounding is common in observational studies. Robins [(1992) Biometrika 79 321--334, (1998b) Encyclopedia of Biostatistics 6 4372--4389] has proposed the so-called structural nested models to estimate treatment effects in the presence of time-dependent confounding. In this article we provide a conceptual framework and formalization for structural nested models in continuous time. We show that the resulting estimators are consistent and asymptotically normal. Moreover, as conjectured in Robins [(1998b) Encyclopedia of Biostatistics 6 4372--4389], a test for whether treatment affects the outcome of interest can be performed without specifying a model for treatment effect. We illustrate the ideas in this article with an example.Comment: Published in at http://dx.doi.org/10.1214/009053607000000820 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The survival-incorporated median versus the median in the survivors or in the always-survivors: What are we measuring? And why?

Many clinical studies evaluate the benefit of treatment based on both survival and other ordinal/continuous clinical outcomes, such as neurocognitive scores or quality-of-life scores. In these studies, there are situations when the clinical outcomes are truncated by death, where subjects die before their clinical outcome is measured. Treating outcomes as "missing" or "censored" due to death can be misleading for treatment effect evaluation. We show that if we use the median in the survivors or in the always-survivors to summarize clinical outcomes, we may conclude a trade-off exists between the probability of survival and good clinical outcomes, even in settings where both the probability of survival and the probability of any good clinical outcome are better for one treatment. Therefore, we advocate not always treating death as a mechanism through which clinical outcomes are missing, but rather as part of the outcome measure. To account for the survival status, we describe the survival-incorporated median as an alternative summary measure for outcomes in the presence of death. The survival-incorporated median is the threshold such that 50\% of the population is alive with an outcome above that threshold. We use conceptual examples to show that the survival-incorporated median provides a simple and useful summary measure to inform clinical practice

Learn-As-you-GO (LAGO) Trials: Optimizing Treatments and Preventing Trial Failure Through Ongoing Learning

It is well known that changing the intervention package while a trial is ongoing does not lead to valid inference using standard statistical methods. However, it is often necessary to adapt, tailor, or tweak a complex intervention package in public health implementation trials, especially when the intervention package does not have the desired effect. This article presents conditions under which the resulting analyses remain valid even when the intervention package is adapted while a trial is ongoing. Our results on such Learn-As-you-GO (LAGO) studies extend the theory of LAGO for binary outcomes following a logistic regression model (Nevo, Lok and Spiegelman, 2021) to LAGO for continuous outcomes under flexible conditional mean model. We derive point and interval estimators of the intervention effects and ensure the validity of hypothesis tests for an overall intervention effect. We develop a confidence set for the optimal intervention package, which achieves a pre-specified mean outcome while minimizing cost, and confidence bands for the mean outcome under all intervention package compositions. This work will be useful for the design and analysis of large-scale intervention trials where the intervention package is adapted, tailored, or tweaked while the trial is ongoing.Comment: 65 pages, 15 table

CD4 trajectory adjusting for dropout among HIV-positive patients receiving combination antiretroviral therapy in an East African HIV care centre

Objective: Estimates of CD4 response to antiretroviral therapy (ART) obtained by averaging data from patients in care, overestimate population CD4 response and treatment program effectiveness because they do not consider data from patients who are deceased or not in care. We use mathematical methods to assess and adjust for this bias based on patient characteristics. Design: We examined data from 25,261 HIV-positive patients from the East Africa IeDEA Consortium. Methods: We used inverse probability of censoring weighting (IPCW) to represent patients not in care by patients in care with similar characteristics. We address two questions: What would the median CD4 be “had everyone starting ART remained on observation?” and “were everyone starting ART maintained on treatment?” Results: Routine CD4 count estimates were higher than adjusted estimates even under the best-case scenario of maintaining all patients on treatment. Two years after starting ART, differences between estimates diverged from 30 cells/µL, assuming similar mortality and treatment access among dropouts as patients in care, to over 100 cells/µL assuming 20% lower survival and 50% lower treatment access among dropouts. When considering only patients in care, the proportion of patients with CD4 above 350 cells/µL was 50% adjusted to below 30% when accounting for patients not in care. One-year mortality diverged 6–14% from the naïve estimates depending on assumptions about access to care among lost patients. Conclusions: Ignoring mortality and loss to care results in over-estimation of ART response for patients starting treatment and exaggerates the efficacy of treatment programs administering it