A Transformation Perspective on Survival Analysis (Tutorial)

It is well known that many prominent models in survival analysis can be understood as transformation models. Cox' proportional hazards model is maybe the most prominent case, but also other models, such as the Weibull or the reverse time proportional hazards model, belong to this class.

Survival analysts have always been forced to work with models for conditional distributions (usually looking at conditional survivor functions) because a simple mean regression is neither interesting nor appropriate for describing the impact of patient characteristics on some time-to-event outcome.  Thus, the field has much to offer in the recent development of distributional regression models, ie models for a conditional distribution and not just a conditional mean.  For this discussion to be fruitful in practice, however, one has to address some old-fashioned habits, such as application of the partial likelihood for semiparametric inference in Cox models.

We will discuss connections between many well-known and some less well-known and even some novel members in the family of transformation models.  Once we understood the conceptual simplicity of this model family, we'll introduce a generic estimation approach based on simple maximum likelihood estimators for fully parameterised  transformation models.  These estimators are also the key ingredient to machine-learning-flavoured approaches, such as transformation trees, transformation forests, and transformation boosting machines.

ctm.R-forge.R-project.org

Subtleties in the interpretation of hazard ratios

The hazard ratio is one of the most commonly reported measures of treatment effect in randomised trials, yet the source of much misinterpretation. This point was made clear by Hernán (2010) in a commentary, which emphasised that the hazard ratio contrasts populations of treated and untreated individuals who survived a given period of time, populations that will typically fail to be comparable - even in a randomised trial - as a result of different pressures or intensities acting on both populations. The commentary has been very influential, but also a source of surprise and confusion. In this talk, I aim to provide more insight into the subtle interpretation of hazard ratios and differences, by investigating in particular what can be learned about a treatment effect from the hazard ratio becoming 1 after a certain period of time. We further define a hazard ratio that has a causal interpretation and study its relationship to the Cox hazard ratio. I will first give a brief introduction to causal inference.

 

Real world evidence supporting clinical development in Oncology – Using multistate models to analyze treatment sequences in electronic health records

Modern drug development is often associated with the term personalized medicine, tailoring disease treatment to smaller patient groups. In Oncology, patients received many lines of therapy, and the effect of the complete sequence of treatments on the outcomes is of interest. This differs from the individual effect of therapy A or therapy B on the outcome.

A clinical trial would include patients newly diagnosis with malignancies, and randomized them to first line (1L) with therapy A until progression then second-line (2L) with therapy B, or to 1L therapy B until progression then therapy A. Then it would estimate the time from 1L initiation to death for both treatment strategy A then B, or B then A. The analysis could be carried via a conventional Cox Proportional Hazard model.

Nowadays, real‐world data (RWD) such as electronic health records in Oncology have also the potential to fill gaps in knowledge about the performance of approved treatments used in routine care settings (Lasiter 2022). When emulating the targeted clinical trial in RWD (Hernán 2022), patients that have already been treated with A, B, and likely further therapies thereafter or in addition, pose an additional challenge. To account for the dynamic nature of the treatment change from one line to the next lines, multistate model might be useful to model such time-to-event data (Andersen 1993). Although these models are not new, applying them to RWD raises some specific methodological challenges.

Within the context of an Oncology non-interventional study, we will present, the methodological challenges related to both the treatment sequencing and the real-world data, and how to account for them in time-to-event analyses.

References:

Andersen PK, Borgan O, Gill RD, Keiding N. Statistical models based on counting processes. Springer Series in Statistics. 1993.

Hernán MA, Wang W, Leaf DE. Target Trial Emulation: A Framework for Causal Inference From Observational Data. JAMA. 2022;328(24):2446–2447.

Lasiter L, Tymejczyk O, Garrett-Mayer E, Baxi S, Belli AJ, Boyd M, Christian JB, Cohen AB, Espirito JL, Hansen E, Sweetnam C, Robert NJ, Small M, Stewart MD, Izano MA, Wagner J, Natanzon Y, Rivera DR, Allen J. Real-world Overall Survival Using Oncology Electronic Health Record Data: Friends of Cancer Research Pilot. Clin Pharmacol Ther. 2022 Feb;111(2):444-454

 

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