ECONOMICS OF INDIVIDUALIZATION IN COMPARATIVE EFFECTIVENESS RESEARCH AND A BASIS FOR A PATIENT-CENTERED HEALTH CARE

. Author manuscript; available in PMC: 2012 May 1.

Published in final edited form as: J Health Econ. 2011 Apr 23;30(3):549–559. doi: 10.1016/j.jhealeco.2011.03.004

Identification Strategy

Normalization

Indentify

\begin{array}{l} Cov (L^{2}, Y_{0}) \propto E (β_{3}^{2} \cdot θ_{1} \cdot exp (α_{30} \cdot θ_{1})) \\ \approx β_{3}^{2} \cdot Var (θ_{1}) \cdot α_{30} \end{array}

(By 2^nd order Taylor series approximation)

β_{3}^{2} = 1

Var(θ₁) · α₃₀

Similarly,

Cov (L^{1}, Y_{0}) \approx β_{3}^{1} \cdot Var (θ_{1}) \cdot α_{30}

β_{3}^{1}

Cov (Y_{1}^{0}, Y_{0} ∣ D = 0) \approx α_{31}^{0} \cdot Var (θ_{1} ∣ D = 0) \cdot α_{30}

2) Var (θ₁| D = 0) = Var(θ₁)

α_{31}^{0}

Cov (L^{1}, Y_{1}^{0}) \approx β_{3}^{1} \cdot Var (θ_{1} ∣ D = 0) \cdot α_{31}^{0}

Var(θ₁), α₃₀

Cov (L^{1}, Y_{1}^{1}) \approx β_{3}^{1} \cdot Var (θ_{1} ∣ D = 1) \cdot α_{31}^{1}

3) Var (θ₁| D = 1) = Var(θ₁)

α_{31}^{1}

Cov (L^{1}, Y_{1}^{2}) \approx β_{3}^{1} \cdot Var (θ_{1}) \cdot α_{31}^{2}

α_{31}^{2}

⁺

Var (θ₁ |D = 2)=Var(θ₁) because of normalizations 2) and 3).