Update 'Concept paper 2022 02 09'

Concept-paper-2022-02-09.md

@@ -9,11 +9,15 @@ I think I can get two, maybe three, papers out of this:
 
 - How can one statistically describe the way drugs pass through the FDA development pipeline?
 - What is the effect of `policy` on phase completion and phase transition?
+    - What is the impact of surragate endpoints on phase transition completion? on phase transition?
 
 # Models
 
 ## Phase completion: Joint Probability Estimation (single paper?)
 
+This is just following in the footsteps of [[AbrantesMetz-Adams-and-Metz]], but with a possibly different probability estimation approach.
+Also, I think I can improve the richness of the terminal states.
+
 Can probably use the data we have. 
 This would include Plan Normalized duration, where we take the planned completion date and 
 estimate the term: (Actual completion date - start date)/(Planned completion date - start date)
@@ -42,8 +46,31 @@ It would also be straightforward to develop simulations from this approach, as t
 
 # Estimation Strategy
 Probably use a non-parametric bayesian approach to estimating the probability densities?
+[AbrantesMetz-Adams-and-Metz] use a hazards model.
+
+## Phase Completion Probabilities:
+
+The goal is to estimate
+
+- P(completing phase 1 & duration phase 1 | Data)
+- P(completing phase 2 & duration phase 2 | Data & transitioned to phase 2 & duration phase 1)
+- P(completing phase 3 & duration phase 3 | Data & transitioned to phase 3 & durations phases 1,2)
+
+I may also include the combined phases
+
+- P(completing combined phase 1-2 & duration phase 1-2 | Data)
+- P(completing combined phase 2-2 & duration phase 2-3 | Data & transitioned to phase 2 & duration phase 1)
+
+## Phase Transition Probabilities:
+
+The goal is to estimate
+
+- P(transitioning to phase 2 | completing phase 1 & duration phase 1 & Data & market data)
+- P(transitioning to combined phases 2-3 | completing phase 1 & duration phase 1 & Data & market data)
+- P(transitioning to phase 3 | completing phase 2 & durations phases 1,2 & Data & market data)
+- P(transitioning to phase 3 | completing combined phase 1-2 & durations phase 1-2 & Data & market data)
 
-## Identification Strategy
+## Identification Strategies
 
 ### Descriptive identification