The first months of this project have been used to study our models, based on stochastic differential equations, in the light of semi-parametric theory. This means that we think of our models as geometrical objects that allows a differentiable structure. The motivation for this strategy is that it often enables one to identify the theoretical limit to how good one can use the underlying data for estimating a particular parameter. We will apply this to determine if our proposed methods for statistical estimation are optimal or not.
The overall objective of this project is to develop better causal inference methodology for trustworthy evaluation of cancer treatments from registry data in order to support decision makers when forming official clinical guidelines.
Making such decisions based on results from emulated trials will necessarily involve uncertainty. However, in the absence of RCTs, this might be the best source of information that is available. Choosing the right treatment can be a matter of life and death, so it is important to also pay attention to the amount of uncertainty that is involved in these analyses.
We will therefore put much emphasis on developing methods for assessing how trustworthy such analyses will be in various settings. This will both involve robustness towards model misspecification and general tools to evaluate the statistical uncertainty.
Most of the available observational data for evaluating cancer treatments is on a time-to-event form, like the data one usually consider in survival analysis. We claim, with some exceptions, that the survival analysis aspect has not been taken sufficiently into account in causal inference. Methods, designed for other settings, are often applied to survival data in an ad hoc manner that results in less transparent modeling assumptions and more statistical uncertainty than necessary.
We believe, however, that there is much potential in exploiting more of the mathematical machinery related to SDEs that is currently being used in mathematical finance and related fields. Our research plan will if successful provide a streamlined toolbox for using registry data to evaluate effects of cancer treatments based on such techniques.