Two Periods With two periods and strict exogeneity △yt=yay1=8+(x2-X1)β+u Consider a treatment" that takes place between time 1 and time 2 for some of the individuals Ay=δ。+(△x》β+8T+u T=the treatment dummy This is a classical regression model. If there are no regressors, A1=△y| treatment-△ y control difference in differences" estimator Average change in yi for the treated
Two Periods With two periods and strict exogeneity, This is a classical regression model. If there are no regressors, it i2 i,1 0 i2 i1 i i 0 i i i y = y -y = + ( - ) + u Consider a "treatment" that takes place between time 1 and time 2 for some of the individuals y = + ( ) + T + u T = the "treatment dummy" i x x β x β 1 0 i ˆ y | treatment - y | control = "difference in differences" estimator. ˆ Average change in y for the "treated" = =
Application of a Two Period Model a Hemoglobin and Quality of Life in Cancer Patients with anemia Finkelstein(MID), Berndt(MId), Greene(NYU), Cremieux(Univ of Quebec 口1998 a With Ortho Biotech -seeking to change labeling of already approved drug erythropoetin r-HuEPo
Application of a Two Period Model “Hemoglobin and Quality of Life in Cancer Patients with Anemia,” Finkelstein (MIT), Berndt (MIT), Greene (NYU), Cremieux (Univ. of Quebec) 1998 With Ortho Biotech – seeking to change labeling of already approved drug ‘erythropoetin.’ r-HuEPO
QoL Stud Quality of life study 1,..1200+ clinically anemic cancer patients undergoing chemotherapy treated with transfusions and or r-HuEPO t=0 at baseline, 1 at exit. interperiod survey by some patients was not used) a it self administered quality of life survey, scale =0,.,100 D X= hemoglobin level other covariates Treatment effects model(hemoglobin level) Background- r-HuEPO treatment to affect Hg level a Important statistical issues Unobservable individual effects The placebo effect Attrition sample selection FDA mistrust of "community based"-not clinical trial based statistical evidence a objective- when to administer treatment for maximum marginal benefit
QOL Study Quality of life study ◼ i = 1,… 1200+ clinically anemic cancer patients undergoing chemotherapy, treated with transfusions and/or r-HuEPO ◼ t = 0 at baseline, 1 at exit. (interperiod survey by some patients was not used) yit = self administered quality of life survey, scale = 0,…,100 xit = hemoglobin level, other covariates ◼ Treatment effects model (hemoglobin level) ◼ Background – r-HuEPO treatment to affect Hg level Important statistical issues ◼ Unobservable individual effects ◼ The placebo effect ◼ Attrition – sample selection ◼ FDA mistrust of “community based” – not clinical trial based statistical evidence Objective – when to administer treatment for maximum marginal benefit
Regression-Treatment Effects Model QOL=a,+"other covariates βHb+βHb+阝}b+…BHb5 t C+E Hb hemoglobin level, grams/deciliter, range 3+ to 15 Hb it= 1 s Bit <7.5)(Base case; B,=0) Hb8=1(7.5≤Hbt<8.5) Hb=1(145sHbt≤15)
Regression-Treatment Effects Model it t 7 8 9 15 7 it 8 it 9 it 15 it i it it 7 it it QOL + "other covariates" + Hb + Hb + Hb + ... Hb + c + ε Hb hemoglobin level, grams/deciliter, range 3+ to 15 Hb 1(3 Hb < 7.5) (Base = = = 7 8 it it 15 it it case; = 0) Hb 1(7.5 Hb < 8.5) Hb 1(14.5 Hb 15) = =
Effects and covariates o Individual effects that would impact a self reported Qol Depression, comorbidity factors (smoking) ,recent financial setback recent loss of spouse etc 口 Covariates Change in tumor status Measured progressivity of disease Change in number of transfusions Presence of pain and nausea Change in number of chemotherapy cycles Change in radiotherapy types Elapsed days since chemotherapy treatment Amount of time between baseline and exit
Effects and Covariates Individual effects that would impact a self reported QOL: Depression, comorbidity factors (smoking), recent financial setback, recent loss of spouse, etc. Covariates ◼ Change in tumor status ◼ Measured progressivity of disease ◼ Change in number of transfusions ◼ Presence of pain and nausea ◼ Change in number of chemotherapy cycles ◼ Change in radiotherapy types ◼ Elapsed days since chemotherapy treatment ◼ Amount of time between baseline and exit