Integrating relative survival in multi-state models – a non-parametric approach
If you ask a doctor to wish for a superpower, he would probably wish to be able to correctly estimate prognosis of the patient on the onset of a disease and after the treatment is administered, and also probabilities of different events and their real causes, including probability of death, relapse, or remission.
Image credit: CDC/ Judy Schmidt, Public Domain
In the field of medicine, it is often difficult to determine the real causes of patient mortality, because death is not always related to the main illness or similar causes. This question has been discussed in the research paper by Damjan Manevski, Hein Putter, Maja Pohar Perme, Edouard F. Bonneville, Johannes Schetelig, and Liesbeth C. de Wreede titled “Integrating relative survival in multi-state models – a non-parametric approach” that forms the basis of the below text. In this paper, the researchers have proposed a non-parametric model to estimate the mortality of patients and correctly determine contributing effects.
Importance of this research
This research proposes a model with many practical applications in evaluating potential long-term benefits or adverse effects of medications, treatment modes, lifestyle choices, etc., especially for older patients.
How to estimate mortality?
While estimating mortality, death could be caused by a lot of different factors. It could be disease-related or non-disease-related mortality, or it could also be treatment-related. It could also occur due to other causes. Multi-state models in mortality studies provide a framework for simultaneously analyzing competing events and sequences of events and their effect on mortality. They help to study the impact of intermediate events on the prognosis of patients and allow to estimate separate probabilities of death with and without the intermediate event at multiple time horizons.
Analysis Setting
This study was done in patient group after an allogeneic hematopoietic stem cell transplantation (alloHCT).
These patients are at significant risk for two competing failures: relapse of the underlying disease and non-relapse mortality (NRM), which for a large part is due to the transplantation and pre-treatment. The occurence of relapse leads to a very poor prognosis. We investigated the contribution of population mortality to both death after relapse and NRM. This enabled us to estimate the probability of excess NRM, which especially for older patients and for long-term outcomes may provide a better estimate for treatment-related mortality than all NRM.
Image credit: arXiv:2106.12399
The above image from the research paper explains a basic multi-state model where an individual who is relapse-free & alive can move to Non-relapse mortality or can transition to relapse and then succumb to death after relapse.
The proposed extended model of mortality and survival evaluation can be represented as shown in the diagram below.
Image credit: arXiv:2106.12399
Simulations were done in R software using the packages mstate and relsurv using the above model. The packages were also provided along with the research paper by the researchers. The goal is to investigate how the proposed multi-state model with population mortality performs in various simulation scenarios. The researchers studied their bias, standard errors, and coverage probabilities, among multiple related statistical parameters.
Results of Simulations
- Bias: Bias was negligible in all scenarios. It decreased as the sample size increased.
- Standard Errors: Standard errors were smaller for population-related transitions than for their excess counterparts. When the number of population deaths was increased, the Standard Error of these population-related transitions also increased.
- Confidence Intervals: On average, coverage probabilities were more stable and closer to the nominal value for transition probabilities than that for hazards.
Conclusion
In the words of the researchers,
An upgraded non-parametric approach to estimation, where population mortality is taken into account. Precise definitions and suitable estimators are given for both the transition hazards and probabilities. Variance estimating techniques and confidence intervals are introduced and the behaviour of the new method is investigated through simulations. The newly developed methodology is illustrated by the analysis of a cohort of patients followed after an allogeneic hematopoietic stem cell transplantation. The work is also implemented in the R package mstate.
Source: Damjan Manevski, Hein Putter, Maja Pohar Perme, Edouard F. Bonneville, Johannes Schetelig, and Liesbeth C. de Wreede “Integrating relative survival in multi-state models – a non-parametric approach”. Link: https://arxiv.org/pdf/2106.12399.pdf