The effect of treatment delay on time-to-recovery in the presence of unobserved heterogeneity

A scoping review of studies using observational data to optimise dynamic treatment regimens

BACKGROUND

Dynamic treatment regimens (DTRs) formalise the multi-stage and dynamic decision problems that clinicians often face when treating chronic or progressive medical conditions. Compared to randomised controlled trials, using observational data to optimise DTRs may allow a wider range of treatments to be evaluated at a lower cost. This review aimed to provide an overview of how DTRs are optimised with observational data in practice.

METHODS

Using the PubMed database, a scoping review of studies in which DTRs were optimised using observational data was performed in October 2020. Data extracted from eligible articles included target medical condition, source and type of data, statistical methods, and translational relevance of the included studies.

RESULTS

From 209 PubMed abstracts, 37 full-text articles were identified, and a further 26 were screened from the reference lists, totalling 63 articles for inclusion in a narrative data synthesis. Observational DTR models are a recent development and their application has been concentrated in a few medical areas, primarily HIV/AIDS (27, 43%), followed by cancer (8, 13%), and diabetes (6, 10%). There was substantial variation in the scope, intent, complexity, and quality between the included studies. Statistical methods that were used included inverse-probability weighting (26, 41%), the parametric G-formula (16, 25%), Q-learning (10, 16%), G-estimation (4, 6%), targeted maximum likelihood/minimum loss-based estimation (4, 6%), regret regression (3, 5%), and other less common approaches (10, 16%). Notably, studies that were primarily intended to address real-world clinical questions (18, 29%) tended to use inverse-probability weighting and the parametric G-formula, relatively well-established methods, along with a large amount of data. Studies focused on methodological developments (45, 71%) tended to be more complicated and included a demonstrative real-world application only.

CONCLUSIONS

As chronic and progressive conditions become more common, the need will grow for personalised treatments and methods to estimate the effects of DTRs. Observational DTR studies will be necessary, but so far their use to inform clinical practice has been limited. Focusing on simple DTRs, collecting large and rich clinical datasets, and fostering tight partnerships between content experts and data analysts may result in more clinically relevant observational DTR studies.

A tutorial on frailty models

The hazard function plays a central role in survival analysis. In a homogeneous population, the distribution of the time to event, described by the hazard, is the same for each individual. Heterogeneity in the distributions can be accounted for by including covariates in a model for the hazard, for instance a proportional hazards model. In this model, individuals with the same value of the covariates will have the same distribution. It is natural to think that not all covariates that are thought to influence the distribution of the survival outcome are included in the model. This implies that there is unobserved heterogeneity; individuals with the same value of the covariates may have different distributions. One way of accounting for this unobserved heterogeneity is to include random effects in the model. In the context of hazard models for time to event outcomes, such random effects are called frailties, and the resulting models are called frailty models. In this tutorial, we study frailty models for survival outcomes. We illustrate how frailties induce selection of healthier individuals among survivors, and show how shared frailties can be used to model positively dependent survival outcomes in clustered data. The Laplace transform of the frailty distribution plays a central role in relating the hazards, conditional on the frailty, to hazards and survival functions observed in a population. Available software, mainly in R, will be discussed, and the use of frailty models is illustrated in two different applications, one on center effects and the other on recurrent events.

The effect of treatment delay on time-to-recovery in the presence of unobserved heterogeneity

We study the effect of delaying treatment in the presence of (unobserved) heterogeneity. In a homogeneous population and assuming a proportional treatment effect, a treatment delay period will result in notably lower cumulative recovery percentages. We show in theoretical scenarios using frailty models that if the population is heterogeneous, the effect of a delay period is much smaller. This can be explained by the selection process that is induced by the frailty. Patient groups that start treatment later have already undergone more selection. The marginal hazard ratio for the treatment will act differently in such a more homogeneous patient group. We further discuss modeling approaches for estimating the effect of treatment delay in the presence of heterogeneity, and compare their performance in a simulation study. The conventional Cox model that fails to account for heterogeneity overestimates the effect of treatment delay. Including interaction terms between treatment and starting time of treatment or between treatment and follow up time gave no improvement. Estimating a frailty term can improve the estimation, but is sensitive to misspecification of the frailty distribution. Therefore, multiple frailty distributions should be used and the results should be compared using the Akaike Information Criterion. Non‐parametric estimation of the cumulative recovery percentages can be considered if the dataset contains sufficient long term follow up for each of the delay strategies. The methods are demonstrated on a motivating application evaluating the effect of delaying the start of treatment with assisted reproductive techniques on time‐to‐pregnancy in couples with unexplained subfertility.