Using R and OpenBUGS for Evaluating the Causal Effect of Dynamic Treatment Regimes

Transcription

1 Using R and OpenBUGS for Evaluating the Causal Effect of Dynamic Treatment Regimes Daniel Scharfstein and Chenguang Wang June 9, 2010 C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 1/42

2 Outline 1 Acute Lung Injury and ARMA Trial 2 Bayesian Causal Inference 3 R and BUGS 4 Application Results of the ARMA Trial 5 Concluding Remarks C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 2/42

3 Acute Lung Injury (ALI) C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 3/42

4 Acute Lung Injury (ALI) ALI is a condition characterized by acute onset of Shortness of breath Rapid breathing rate Low oxygen levels Abnormal chest x-ray C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 3/42

5 Acute Lung Injury (ALI) ALI is a condition characterized by acute onset of Shortness of breath Rapid breathing rate Low oxygen levels Abnormal chest x-ray Adult respiratory distress syndrome (ARDS) is a subset of ALI with more severe hypoxemia. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 3/42

6 Acute Lung Injury (ALI) ALI is a condition characterized by acute onset of Shortness of breath Rapid breathing rate Low oxygen levels Abnormal chest x-ray Adult respiratory distress syndrome (ARDS) is a subset of ALI with more severe hypoxemia. ALI can be a direct injury to the lung (e.g. pneumonia) or indirect lung injury (e.g. pancreatitis). C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 3/42

7 Acute Lung Injury (ALI) ALI is a condition characterized by acute onset of Shortness of breath Rapid breathing rate Low oxygen levels Abnormal chest x-ray Adult respiratory distress syndrome (ARDS) is a subset of ALI with more severe hypoxemia. ALI can be a direct injury to the lung (e.g. pneumonia) or indirect lung injury (e.g. pancreatitis). Several (meta-analysis) studies have found that mortality rate for ALI patients is about 40%. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 3/42

8 Acute Lung Injury (ALI) ALI is a condition characterized by acute onset of Shortness of breath Rapid breathing rate Low oxygen levels Abnormal chest x-ray Adult respiratory distress syndrome (ARDS) is a subset of ALI with more severe hypoxemia. ALI can be a direct injury to the lung (e.g. pneumonia) or indirect lung injury (e.g. pancreatitis). Several (meta-analysis) studies have found that mortality rate for ALI patients is about 40%. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 3/42

9 Mechanical Ventilation for ALI C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 4/42

10 Mechanical Ventilation for ALI ALI patients often require mechanical ventilation in an intensive care unit (ICU) to help them breathe. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 4/42

11 Mechanical Ventilation for ALI ALI patients often require mechanical ventilation in an intensive care unit (ICU) to help them breathe. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 4/42

12 Mechanical Ventilation - Key Terminology C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 5/42

13 Mechanical Ventilation - Key Terminology C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 5/42

14 Mechanical Ventilation - Key Terminology Positive end-expiratory pressure (PEEP): the alveolar pressure at the beginning of the breath C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 5/42

15 Mechanical Ventilation - Key Terminology Positive end-expiratory pressure (PEEP): the alveolar pressure at the beginning of the breath Plateau pressure (PP): pressure experienced by lung at end of each breath C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 5/42

16 Mechanical Ventilation - Key Terminology Positive end-expiratory pressure (PEEP): the alveolar pressure at the beginning of the breath Plateau pressure (PP): pressure experienced by lung at end of each breath Tidal volume (VT): Size of breath given to patient from ventilator (set by doctor) C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 5/42

17 Mechanical Ventilation - Key Terminology Positive end-expiratory pressure (PEEP): the alveolar pressure at the beginning of the breath Plateau pressure (PP): pressure experienced by lung at end of each breath Tidal volume (VT): Size of breath given to patient from ventilator (set by doctor) Lung compliance (LC): stiffness of lungs (increases with severity of ALI) VT LC = PP PEEP C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 5/42

18 ARMA Lower Tidal Volume Trial C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 6/42

19 ARMA Lower Tidal Volume Trial The ARMA study was a randomized, controlled multi-center 2 x 2 factorial study conducted by the National Heart, Blood and Lung Institute (NHBLI) ARDS Clinical Network C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 6/42

20 ARMA Lower Tidal Volume Trial The ARMA study was a randomized, controlled multi-center 2 x 2 factorial study conducted by the National Heart, Blood and Lung Institute (NHBLI) ARDS Clinical Network The study consisted of a drug treatment (Ketoconazole vs. placebo) and a ventilation strategy (6ml/kg tidal volume vs. 12ml/kg tidal volume) C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 6/42

21 ARMA Lower Tidal Volume Trial The ARMA study was a randomized, controlled multi-center 2 x 2 factorial study conducted by the National Heart, Blood and Lung Institute (NHBLI) ARDS Clinical Network The study consisted of a drug treatment (Ketoconazole vs. placebo) and a ventilation strategy (6ml/kg tidal volume vs. 12ml/kg tidal volume) A total of 432 patients were randomized to lower tidal volume ventilation arm. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 6/42

22 Lower Tidal Volume Ventilation (LTVV) Set initial tidal volume to 6 ml/kg predicted body weight (PBW) Decrease VT to 5 or 4 ml/kg, if necessary, to get PP < 30 If VT < 6 ml/kg and PP < 25, increase VT 1 ml/kg (not > 6 ml/kg) If VT = 6 ml/kg, PP < 30, and severe dyspnea, increase VT to 7 or 8 ml/kg (if PP remains < 30) If blood very acidotic, OK for VT and PP to be > 6ml/kg and 30, respectively C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 7/42

23 Controversy: Non-adherence C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 8/42

24 Controversy: Non-adherence ARMA ventilation strategy comparison result: 40% vs. 31% in-hospital mortality (p=0.007) C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 8/42

25 Controversy: Non-adherence ARMA ventilation strategy comparison result: 40% vs. 31% in-hospital mortality (p=0.007) Some argued that the LTVV is not optimal because the adherence to the LTVV protocol was not perfect. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 8/42

26 Controversy: Non-adherence ARMA ventilation strategy comparison result: 40% vs. 31% in-hospital mortality (p=0.007) Some argued that the LTVV is not optimal because the adherence to the LTVV protocol was not perfect. Physicians deviated from the LTVV protocol when they thought specific aspects of the protocol were detrimental to their patients. For example, when patients appeared to be very dyspneic (short of breath) while receiving 6 ml/kg PBW, some physicians raised tidal volume above 6 ml/kg PBW in an attempt to alleviate the dyspnea. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 8/42

27 Controversy: Non-adherence ARMA ventilation strategy comparison result: 40% vs. 31% in-hospital mortality (p=0.007) Some argued that the LTVV is not optimal because the adherence to the LTVV protocol was not perfect. Physicians deviated from the LTVV protocol when they thought specific aspects of the protocol were detrimental to their patients. For example, when patients appeared to be very dyspneic (short of breath) while receiving 6 ml/kg PBW, some physicians raised tidal volume above 6 ml/kg PBW in an attempt to alleviate the dyspnea. The deviations from the LTVV protocol may have improved the outcome of some patients. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 8/42

28 Adherence Specification C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 9/42

29 Adherence Specification In the ARMA trial, VT selection procedure was not recorded C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 9/42

30 Adherence Specification In the ARMA trial, VT selection procedure was not recorded A set of specifications were developed, using VT, PP, PH etc., to determine if LTVV was followed C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 9/42

31 Adherence Specification In the ARMA trial, VT selection procedure was not recorded A set of specifications were developed, using VT, PP, PH etc., to determine if LTVV was followed Plateau pressure > 30 tidal volume 4.5 or ph < 7.2 Tidal volume 3 tidal volume 8.5 ph < 7.2 and set respiratory rate < tidal volume 8.5 (ph < 7.2 and set respiratory rate 35) or (plateau pressure 30 and severe dyspnea) tidal volume 6.5 Plateau pressure 30 or ph < < tidal volume < Plateau pressure tidal volume 4.5 Plateau pressure 25 C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 9/42

32 Adherence Specification In the ARMA trial, VT selection procedure was not recorded A set of specifications were developed, using VT, PP, PH etc., to determine if LTVV was followed Plateau pressure > 30 tidal volume 4.5 or ph < 7.2 Tidal volume 3 tidal volume 8.5 ph < 7.2 and set respiratory rate < tidal volume 8.5 (ph < 7.2 and set respiratory rate 35) or (plateau pressure 30 and severe dyspnea) tidal volume 6.5 Plateau pressure 30 or ph < < tidal volume < Plateau pressure tidal volume 4.5 Plateau pressure 25 Adherence: (1 or 2) AND (3 or 4 or 5 or 6 or 7) C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 9/42

33 Adherence Specification In the ARMA trial, VT selection procedure was not recorded A set of specifications were developed, using VT, PP, PH etc., to determine if LTVV was followed Plateau pressure > 30 tidal volume 4.5 or ph < 7.2 Tidal volume 3 tidal volume 8.5 ph < 7.2 and set respiratory rate < tidal volume 8.5 (ph < 7.2 and set respiratory rate 35) or (plateau pressure 30 and severe dyspnea) tidal volume 6.5 Plateau pressure 30 or ph < < tidal volume < Plateau pressure tidal volume 4.5 Plateau pressure 25 Adherence: (1 or 2) AND (3 or 4 or 5 or 6 or 7) Over 28% observed ventilation days deviated from the LTVV. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 9/42

34 Goal We seek to draw inference about the distribution of survival that would have resulted had all patients in the LTVV arm of the ARDSNet study strictly adhered to the LTVV protocol. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 10/42

35 Statistical Challenges C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 11/42

36 Statistical Challenges Time-Dependent Dynamic Treatment Regime C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 11/42

37 Statistical Challenges Time-Dependent Dynamic Treatment Regime In a non-dynamic (static) treatment regime the treatment level and type are specified before treatment is started and not changed with a patient s response C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 11/42

38 Statistical Challenges Time-Dependent Dynamic Treatment Regime In a non-dynamic (static) treatment regime the treatment level and type are specified before treatment is started and not changed with a patient s response LTVV is individually tailored treatment: the treatment is provided to patients only when it is needed and the level of treatment is adjusted based on time-dependent measurements of the patient s need for treatment C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 11/42

39 Statistical Challenges Time-Dependent Dynamic Treatment Regime In a non-dynamic (static) treatment regime the treatment level and type are specified before treatment is started and not changed with a patient s response LTVV is individually tailored treatment: the treatment is provided to patients only when it is needed and the level of treatment is adjusted based on time-dependent measurements of the patient s need for treatment The challenge is to isolate the effect of LTVV from the confounding effect of the time-dependent confounders C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 11/42

40 Statistical Challenges Time-Dependent Dynamic Treatment Regime In a non-dynamic (static) treatment regime the treatment level and type are specified before treatment is started and not changed with a patient s response LTVV is individually tailored treatment: the treatment is provided to patients only when it is needed and the level of treatment is adjusted based on time-dependent measurements of the patient s need for treatment The challenge is to isolate the effect of LTVV from the confounding effect of the time-dependent confounders G-computation C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 11/42

41 Statistical Challenges Time-Dependent Dynamic Treatment Regime In a non-dynamic (static) treatment regime the treatment level and type are specified before treatment is started and not changed with a patient s response LTVV is individually tailored treatment: the treatment is provided to patients only when it is needed and the level of treatment is adjusted based on time-dependent measurements of the patient s need for treatment The challenge is to isolate the effect of LTVV from the confounding effect of the time-dependent confounders G-computation Missing Data C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 11/42

42 Statistical Challenges Time-Dependent Dynamic Treatment Regime In a non-dynamic (static) treatment regime the treatment level and type are specified before treatment is started and not changed with a patient s response LTVV is individually tailored treatment: the treatment is provided to patients only when it is needed and the level of treatment is adjusted based on time-dependent measurements of the patient s need for treatment The challenge is to isolate the effect of LTVV from the confounding effect of the time-dependent confounders G-computation Missing Data Missing of ventilator parameters was non-negligible(e.g. PP 11.6%, arterial ph 28.7%) C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 11/42

43 Statistical Challenges Time-Dependent Dynamic Treatment Regime In a non-dynamic (static) treatment regime the treatment level and type are specified before treatment is started and not changed with a patient s response LTVV is individually tailored treatment: the treatment is provided to patients only when it is needed and the level of treatment is adjusted based on time-dependent measurements of the patient s need for treatment The challenge is to isolate the effect of LTVV from the confounding effect of the time-dependent confounders G-computation Missing Data Missing of ventilator parameters was non-negligible(e.g. PP 11.6%, arterial ph 28.7%) Fully parametric model assuming missing at random C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 11/42

44 Outline 1 Acute Lung Injury and ARMA Trial 2 Bayesian Causal Inference 3 R and BUGS 4 Application Results of the ARMA Trial 5 Concluding Remarks C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 12/42

45 Data Structure For an individual patient, the observed data is as follows: Var Definition and Description Day 1... Day 28 S t Survival HSP t Hospitalization ICU t ICU indicator VNT t Ventilator indicator LC t * Lung compliance PE t Positive end-expiratory pressure PH t ph PD t PP t PEEP t SO t Oxygen saturation SR t Respiratory set rate DS t Severe dyspnea OF t * Organ failure AP Baseline Apache score * OF is observed at baseline. LC = VT/PD C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 13/42

46 Notation C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 14/42

47 Notation Let L t = {S t,hsp t ICU t,vnt t,lc t,pe t,ph t,pd t,so t,sr t,ds t,of t } be the scheduled observed data on day t (t = 0,...,28) C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 14/42

48 Notation Let L t = {S t,hsp t ICU t,vnt t,lc t,pe t,ph t,pd t,so t,sr t,ds t,of t } be the scheduled observed data on day t (t = 0,...,28) Let L t = {L 0,L 1,...,L t } C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 14/42

49 Notation Let L t = {S t,hsp t ICU t,vnt t,lc t,pe t,ph t,pd t,so t,sr t,ds t,of t } be the scheduled observed data on day t (t = 0,...,28) Let L t = {L 0,L 1,...,L t } Let R t = I(VNT t = 1) be the at-risk indicator on day t C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 14/42

50 Notation Let L t = {S t,hsp t ICU t,vnt t,lc t,pe t,ph t,pd t,so t,sr t,ds t,of t } be the scheduled observed data on day t (t = 0,...,28) Let L t = {L 0,L 1,...,L t } Let R t = I(VNT t = 1) be the at-risk indicator on day t Let H t = {HSP t,icu t,vnt t,lc t } and U t = {PE t,ph t,pd t,so t,sr t,ds t,of t } C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 14/42

51 Notation Let L t = {S t,hsp t ICU t,vnt t,lc t,pe t,ph t,pd t,so t,sr t,ds t,of t } be the scheduled observed data on day t (t = 0,...,28) Let L t = {L 0,L 1,...,L t } Let R t = I(VNT t = 1) be the at-risk indicator on day t Let H t = {HSP t,icu t,vnt t,lc t } and U t = {PE t,ph t,pd t,so t,sr t,ds t,of t } Let A t = I((VT t,pp t,ph t,sr t,ds t ) S) where S is the set of combinations defined in the adherence table C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 14/42

52 Notation Let L t = {S t,hsp t ICU t,vnt t,lc t,pe t,ph t,pd t,so t,sr t,ds t,of t } be the scheduled observed data on day t (t = 0,...,28) Let L t = {L 0,L 1,...,L t } Let R t = I(VNT t = 1) be the at-risk indicator on day t Let H t = {HSP t,icu t,vnt t,lc t } and U t = {PE t,ph t,pd t,so t,sr t,ds t,of t } Let A t = I((VT t,pp t,ph t,sr t,ds t ) S) where S is the set of combinations defined in the adherence table Let A t = 1 if S t = 0 or R t = 0 C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 14/42

53 Notation Let L t = {S t,hsp t ICU t,vnt t,lc t,pe t,ph t,pd t,so t,sr t,ds t,of t } be the scheduled observed data on day t (t = 0,...,28) Let L t = {L 0,L 1,...,L t } Let R t = I(VNT t = 1) be the at-risk indicator on day t Let H t = {HSP t,icu t,vnt t,lc t } and U t = {PE t,ph t,pd t,so t,sr t,ds t,of t } Let A t = I((VT t,pp t,ph t,sr t,ds t ) S) where S is the set of combinations defined in the adherence table Let A t = 1 if S t = 0 or R t = 0 Let S t be the counterfactual survival. That is, the survival that would have been observed had a patient been treated according to the LTVV protocol C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 14/42

54 Notation Let L t = {S t,hsp t ICU t,vnt t,lc t,pe t,ph t,pd t,so t,sr t,ds t,of t } be the scheduled observed data on day t (t = 0,...,28) Let L t = {L 0,L 1,...,L t } Let R t = I(VNT t = 1) be the at-risk indicator on day t Let H t = {HSP t,icu t,vnt t,lc t } and U t = {PE t,ph t,pd t,so t,sr t,ds t,of t } Let A t = I((VT t,pp t,ph t,sr t,ds t ) S) where S is the set of combinations defined in the adherence table Let A t = 1 if S t = 0 or R t = 0 Let S t be the counterfactual survival. That is, the survival that would have been observed had a patient been treated according to the LTVV protocol re: The goal is to estimate P(S t = 1) for all t C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 14/42

55 Assumption I C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 15/42

56 Assumption I Stochastic Consistency: P[S t = 1 S t 1 = 1,Āt 1 = 1, H t 1 = h t 1,Ūt 1 = ū t 1 ] = P[S t = 1 S t 1 = 1,Āt 1 = 1, H t 1 = h t 1,Ūt 1 = ū t 1 ] This assumption implies that the potential survival outcome under the LTVV protocol is uniquely determined. That is, if the physician followed the protocol, the treatment for an individual is unique and therefore her potential survival outcome is unique. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 15/42

57 Assumption II Evaluable Outcome P[A t = 1 S t = 1,Āt 1 = 1, H t = h t,ūt 1 = ū t 1 ] > 0 This assumes that when a group of patients have been treated with the LTVV protocol until day t, at least some of them will continue to be treated with adherence to the protocol on day t+1. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 16/42

58 Assumption III Sequential Randomization A t (S k : k = 2,...,28) Ā t 1,S t = 1,R t = 1, H t,ūt 1 This assumption will hold if H t and Ūt 1 includes all risk factors, other than treatment history, used by the physician to determine the patient s ventilator settings on day t. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 17/42

59 G-computation C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 18/42

60 G-computation Given the distribution of L 28 and the three assumptions above, the potential survivor function at day m (m 28) is identified via the following G-computation formula: C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 18/42

61 G-computation Given the distribution of L 28 and the three assumptions above, the potential survivor function at day m (m 28) is identified via the following G-computation formula: P[S m = 1] = P[Sm = 1 S 1 = 1, H 1 = h 1,U 0 = u 0 ]df(h 1 S 1 = 1,U 0 = u 0,H 0 = h 0 ) h 0 u 0 h 1 P[S 1 = 1 U 0 = u 0,H 0 = h 0 ]df(u 0 H 0 = h 0 )df(h 0 ) = P[Sm = 1 S 1 = 1,A 1 = 1, H 1 = h 1,U 0 = u 0 ] h 0 u 0 h 1 }{{} sequential randomization df(h 1 S 1 = 1,U 0 = u 0,H 0 = h 0 ) P[S 1 = 1 U 0 = u 0,H 0 = h 0 ]df(u 0 H 0 = h 0 )df(h 0 ) C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 18/42

62 G-computation = P[Sm = 1 S 2 = 1,A 1 = 1, H 2 = h 2,Ū1 = ū 1 ] h 0 u 0 h 1 u 1 h 2 df(h 2 S 2 = 1,A 1 = 1, H 1 = h 1,Ū1 = ū 1 ) P[S 2 = 1 S 1 = 1,A 1 = 1, H 1 = h 1,Ū1 = ū 1 ] df(u 1 S 1 = 1,A 1 = 1, H 1 = h 1,U 0 = u 0 ) df(h 1 S 1 = 1,U 0 = u 0,H 0 = h 0 ) P[S 1 = 1 U 0 = u 0,H 0 = h 0 ]df(u 0 H 0 = h 0 )df(h 0 ) = P[Sm = 1 S 2 = 1,Ā2 = 1, H 2 = h 2,Ū1 = ū 1 ]... h 0 u 0 h 1 u 1 h 2 }{{} sequential randomization C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 19/42

63 G-computation. =... P[Sm = 1 S m 1 = 1,Ām 1 = 1, H m 1 = h m 1,Ūm 1 = ū m 1 ] h 0 u 0 h 1 u 1 h m 1 u m 1 m 1 t=1 { P[S t = 1 S t 1 = 1,Āt 1 = 1, H t 1 = h t 1,Ūt 1 = ū t 1 ] df(h t S t = 1,Āt 1 = 1, H t 1 = h t 1,Ūt 1 = ū t 1 ) } df(u t S t = 1,Āt = 1, H t = h t,ūt 1 = ū t 1 ) df(u 0 H 0 = h 0 )df(h 0 ) =... P[S m = 1 S m 1 = 1,Ām 1 = 1, H m 1 = h m 1,Ūm 1 = ū m 1 ] h 0 u 0 h 1 u 1 h m 1 u m 1 }{{} stochastic consistency... C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 20/42

64 Modeling of L 28 The likelihood of L 28 is as follows: Lik = df(h 0 )df(u 0 H 0 ) 28 t=1 { df(u t H t,ūt 1,S t = 1) df(h t H t 1,Ūt 1,S t = 1)} St df(st S t 1 = 1, H t 1,Ūt 1) S t 1. Additional Markovian Assumption Lik = df(h 0 )df(u 0 H 0 ) 28 t=1 { df(u t H t,u t 1,H 0,S t = 1) df(h t H t 1,U t 1,H 0,S t = 1)} StdF(St S t 1 = 1,H t 1,U t 1,H 0 ) S t 1. That is,a patient s status on day t only depends on his most recent history and the baseline H 0. C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 21/42

65 Models of S t df(s t S t 1 = 1,H t 1,U t 1,H 0 ) = df(s t S t 1 = 1,R t 1 = 1,G t 1,U t 1,H 0 ) Rt 1 df(s t S t 1 = 1,HSP t 1 = 1,ICU t 1 = 0,OF t 1,H 0 ) (1 Rt 1)(1 ICUt 1) ICUt 1(1 V NTt 1) df(s t S t 1 = 1,HSP t 1 = 1,ICU t 1 = 1,VNT t 1 = 0,OF t 1,H 0 ) for t = 1,...,28 C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 22/42

66 Models of H t df(h t S t = 1,H t 1,U t 1,H 0 ) = df(hsp t S t = 1,HSP t 1 = 1,ICU t 1 = 0,OF t 1,H 0 ) HSPt 1(1 ICUt 1) df(icu t S t = 1,HSP t = 1,VNT t 1 = 0,OF t 1,H 0 ) HSPt(1 VNTt 1) df(vnt t S t = 1,HSP t = 1,ICU t = 1,R t 1 = 1,G t 1,U t 1,H 0 ) HSPtICUtRt 1 df(vnt t S t = 1,HSP t = 1,ICU t = 1,R t 1 = 0,OF t 1,H 0 ) HSPtICUt(1 Rt 1) df(lc t S t = 1,R t = 1,R t 1 = 1,G t 1,U t 1,H 0 ) RtRt 1 df(lc t S t = 1,R t = 1,R t 1 = 0,OF t 1,H 0 ) Rt(1 Rt 1) df(pe t S t = 1,R t = 1,R t 1 = 1,LC t,pe t 1,PD t 1,DS t 1,OF t 1,H 0 ) RtRt 1 df(pe t S t = 1,R t = 1,R t 1 = 0,LC t,of t 1,H 0 ) Rt(1 Rt 1) for t = 1,...,28 C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 23/42

67 Models of U t df(ut St = 1,Ht,Ut 1,H0) = df(pht St = 1,Rt = 1,Rt 1 = 1,LCt,PHt 1,DSt 1,OFt 1,H0) RtRt 1 df(pht St = 1,Rt = 1,Rt 1 = 0,LCt,OFt 1,H0) Rt(1 Rt 1) df(pdt St = 1,Rt = 1,Rt 1 = 1,LCt,PEt,PDt 1,H0) RtRt 1 df(pdt St = 1,Rt = 1,Rt 1 = 0,LCt,PEt,OFt 1,H0) Rt(1 Rt 1) df(sot St = 1,Rt = 1,Rt 1 = 1,LCt,PEt,PHt,PDt,SOt 1,H0) RtRt 1 df(sot St = 1,Rt = 1,Rt 1 = 0,LCt,PEt,PHt,PDt,OFt 1,H0) Rt(1 Rt 1) df(srt St = 1,Rt = 1,Rt 1 = 1,LCt,PEt,PHt,SRt 1,DSt 1,OFt 1,H0) RtRt 1 df(srt St = 1,Rt = 1,Rt 1 = 0,LCt,PEt,PHt,OFt 1,H0) Rt(1 Rt 1) df(dst St = 1,Rt = 1,Rt 1 = 1,LCt,PEt,PHt,SOt,SRt,DSt 1,OFt 1,H0) RtRt 1 df(dst St = 1,Rt = 1,Rt 1 = 0,LCt,PEt,PHt,,SOt,SRt,OFt 1,H0) Rt(1 Rt 1) df(oft St = 1,Rt = 1,LCt,PEt,PHt,SOt,SRt,DSt,OFt 1,H0) Rt df(oft St = 1,Rt = 0,Rt 1 = 1,LCt 1,PEt 1,PHt 1,SOt 1,SRt 1,DSt 1,OFt 1,H0) (1 Rt)Rt 1 df(oft St = 1,HSPt = 1,VNTt = 0,Rt 1 = 0,ICUt 1 = 1,OFt 1,H0) HSPt(1 VNTt)(1 V NTt 1)ICUt 1 df(oft St = 1,HSPt = 1,VNTt = 0,HSPt 1 = 1,ICUt 1 = 0,OFt 1,H0) HSPt(1 VNTt)HSPt 1(1 ICUt 1) for t = 1,...,28 C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 24/42

68 Monte Carlo Integration Algorithm C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 25/42

69 Monte Carlo Integration Algorithm (a) Set t = 0; sample AP, OF 0 ; set p 0 = 1 C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 25/42

70 Monte Carlo Integration Algorithm (a) Set t = 0; sample AP, OF 0 ; set p 0 = 1 (b) Set t = t+1; set p t = p t 1 P[S t = 1 S t 1 = 1,H t 1,U t 1,H 0 ]. If t = 28, stop C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 25/42

71 Monte Carlo Integration Algorithm (a) Set t = 0; sample AP, OF 0 ; set p 0 = 1 (b) Set t = t+1; set p t = p t 1 P[S t = 1 S t 1 = 1,H t 1,U t 1,H 0 ]. If t = 28, stop (c) Sample HSP t, ICU t, VNT t, LC t C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 25/42

72 Monte Carlo Integration Algorithm (a) Set t = 0; sample AP, OF 0 ; set p 0 = 1 (b) Set t = t+1; set p t = p t 1 P[S t = 1 S t 1 = 1,H t 1,U t 1,H 0 ]. If t = 28, stop (c) Sample HSP t, ICU t, VNT t, LC t (d) Sample PE t, PH t, PD t, SO t, DS t C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 25/42

73 Monte Carlo Integration Algorithm (a) Set t = 0; sample AP, OF 0 ; set p 0 = 1 (b) Set t = t+1; set p t = p t 1 P[S t = 1 S t 1 = 1,H t 1,U t 1,H 0 ]. If t = 28, stop (c) Sample HSP t, ICU t, VNT t, LC t (d) Sample PE t, PH t, PD t, SO t, DS t (e) Set A t = I((VT t,sr t,ph t,pp t,ds t ) S). If A t = 0, go to (d) C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 25/42

74 Monte Carlo Integration Algorithm (a) Set t = 0; sample AP, OF 0 ; set p 0 = 1 (b) Set t = t+1; set p t = p t 1 P[S t = 1 S t 1 = 1,H t 1,U t 1,H 0 ]. If t = 28, stop (c) Sample HSP t, ICU t, VNT t, LC t (d) Sample PE t, PH t, PD t, SO t, DS t (e) Set A t = I((VT t,sr t,ph t,pp t,ds t ) S). If A t = 0, go to (d) (f) Sample OF t ; go to (b) C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 25/42

75 Outline 1 Acute Lung Injury and ARMA Trial 2 Bayesian Causal Inference 3 R and BUGS 4 Application Results of the ARMA Trial 5 Concluding Remarks C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 26/42

76 Flowchart Observed Data Data Manipulation in R R Calls BUGS BUGS Script Processed Data Initial Values Priors BUGS Model BUGS MCMC Sampling Posterior Samples N R Parallel G-computation Jobs N 4 R Summarization Results C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 27/42

77 The BUGS Project C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 28/42

78 The BUGS Project There are several versions of BUGS, which can be confusing C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 28/42

79 The BUGS Project There are several versions of BUGS, which can be confusing WinBUGS C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 28/42

80 The BUGS Project There are several versions of BUGS, which can be confusing WinBUGS Latest version C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 28/42

81 The BUGS Project There are several versions of BUGS, which can be confusing WinBUGS Latest version Stand-alone and considered stable C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 28/42

82 The BUGS Project There are several versions of BUGS, which can be confusing WinBUGS Latest version Stand-alone and considered stable Can be extended. Add-ons: GeoBUGS, PKBUGS C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 28/42

83 The BUGS Project There are several versions of BUGS, which can be confusing WinBUGS Latest version Stand-alone and considered stable Can be extended. Add-ons: GeoBUGS, PKBUGS Can be installed in Linux via wine and virtual screen server (e.g. Xvfb) C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 28/42

84 The BUGS Project There are several versions of BUGS, which can be confusing WinBUGS Latest version Stand-alone and considered stable Can be extended. Add-ons: GeoBUGS, PKBUGS Can be installed in Linux via wine and virtual screen server (e.g. Xvfb) OpenBUGS C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 28/42

85 The BUGS Project There are several versions of BUGS, which can be confusing WinBUGS Latest version Stand-alone and considered stable Can be extended. Add-ons: GeoBUGS, PKBUGS Can be installed in Linux via wine and virtual screen server (e.g. Xvfb) OpenBUGS Latest version C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 28/42

86 The BUGS Project There are several versions of BUGS, which can be confusing WinBUGS Latest version Stand-alone and considered stable Can be extended. Add-ons: GeoBUGS, PKBUGS Can be installed in Linux via wine and virtual screen server (e.g. Xvfb) OpenBUGS Latest version LinBUGS is the Linux based OpenBUGS C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 28/42

87 The BUGS Project There are several versions of BUGS, which can be confusing WinBUGS Latest version Stand-alone and considered stable Can be extended. Add-ons: GeoBUGS, PKBUGS Can be installed in Linux via wine and virtual screen server (e.g. Xvfb) OpenBUGS Latest version LinBUGS is the Linux based OpenBUGS JAGS C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 28/42

88 The BUGS Project There are several versions of BUGS, which can be confusing WinBUGS Latest version Stand-alone and considered stable Can be extended. Add-ons: GeoBUGS, PKBUGS Can be installed in Linux via wine and virtual screen server (e.g. Xvfb) OpenBUGS Latest version LinBUGS is the Linux based OpenBUGS JAGS Just Another Gibbs Sampler, not part of the BUGS project C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 28/42

89 BUGS Script Example script.txt: modelcheck("model.txt") modeldata("data.txt") modelcompile() modelinits("inits.txt") modelupdate(10000) summaryset("a") samplesset("a") modelupdate(10000) summarystats("*") samplesstats("*") samplescoda("*","output") modelquit() C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 29/42

90 BUGS Model Example model.txt: model { for( i in 1 : N ) { mu[i] <- a+b*age[i] price[i] ~ dnorm(mu[i], tau) } tau ~ dgamma(0.001, 0.001) sigma <- 1 / sqrt(tau) a ~ dnorm(0, 1.0E-12) b ~ dnorm(0, 1.0E-12) } C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 30/42

91 BUGS Data Example init.txt: list(a=0, b=0, tau=1) Example data.txt: list(n=9, age = c(13, 14, 14,12, 9, 15, 10, 14, 9), price = c(295, 230, 390, 280, 500, 299, 390, 299, 450)) C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 31/42

92 R Talks to BUGS C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 32/42

93 R Talks to BUGS R2WinBUGS, rbugs C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 32/42

94 R Talks to BUGS R2WinBUGS, rbugs Prepare files needed for running BUGS in batch-mode C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 32/42

95 R Talks to BUGS R2WinBUGS, rbugs Prepare files needed for running BUGS in batch-mode Running BUGS from R C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 32/42

96 R Talks to BUGS R2WinBUGS, rbugs Prepare files needed for running BUGS in batch-mode Running BUGS from R Save posterior samples for easy access in R C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 32/42

97 R Talks to BUGS R2WinBUGS, rbugs Prepare files needed for running BUGS in batch-mode Running BUGS from R Save posterior samples for easy access in R BRugs C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 32/42

98 R Talks to BUGS R2WinBUGS, rbugs Prepare files needed for running BUGS in batch-mode Running BUGS from R Save posterior samples for easy access in R BRugs Part of the OpenBUGS project C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 32/42

99 R Talks to BUGS R2WinBUGS, rbugs Prepare files needed for running BUGS in batch-mode Running BUGS from R Save posterior samples for easy access in R BRugs Part of the OpenBUGS project Instead of generating script file, capable of working interactively with BUGS C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 32/42

100 R Talks to BUGS R2WinBUGS, rbugs Prepare files needed for running BUGS in batch-mode Running BUGS from R Save posterior samples for easy access in R BRugs Part of the OpenBUGS project Instead of generating script file, capable of working interactively with BUGS Not for Linux. A new version may be out in one month or two to support Linux C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 32/42

101 Parallel Computing C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 33/42

102 Parallel Computing High-performance computing (HPC) uses supercomputers and computer clusters to solve advanced computation problems C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 33/42

103 Parallel Computing High-performance computing (HPC) uses supercomputers and computer clusters to solve advanced computation problems Parallel computing can be employed in HPC C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 33/42

104 Parallel Computing High-performance computing (HPC) uses supercomputers and computer clusters to solve advanced computation problems Parallel computing can be employed in HPC Embarrassingly parallel is one parallel computing case where no dependency exists between the parallel tasks C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 33/42

105 Parallel Computing High-performance computing (HPC) uses supercomputers and computer clusters to solve advanced computation problems Parallel computing can be employed in HPC Embarrassingly parallel is one parallel computing case where no dependency exists between the parallel tasks R Parallel Computing Frameworks C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 33/42

106 Parallel Computing High-performance computing (HPC) uses supercomputers and computer clusters to solve advanced computation problems Parallel computing can be employed in HPC Embarrassingly parallel is one parallel computing case where no dependency exists between the parallel tasks R Parallel Computing Frameworks Simple Network of Workstations (SNOW) C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 33/42

107 Parallel Computing High-performance computing (HPC) uses supercomputers and computer clusters to solve advanced computation problems Parallel computing can be employed in HPC Embarrassingly parallel is one parallel computing case where no dependency exists between the parallel tasks R Parallel Computing Frameworks Simple Network of Workstations (SNOW) Simple Parallel R INTerface (SPRINT) C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 33/42

108 Parallel Computing High-performance computing (HPC) uses supercomputers and computer clusters to solve advanced computation problems Parallel computing can be employed in HPC Embarrassingly parallel is one parallel computing case where no dependency exists between the parallel tasks R Parallel Computing Frameworks Simple Network of Workstations (SNOW) Simple Parallel R INTerface (SPRINT) Rmpi C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 33/42

109 Example using Sun Grid Engine Shell Script qsub -N bugs qsub -N gcomp qsub -N rsum bugs.sh -hold_jid bugs -t gcomp.sh -hold_jid gcomp rsum.sh gcomp.sh R --vanilla --args $SGE_TASK_ID < GCOMP.R C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 34/42

110 Outline 1 Acute Lung Injury and ARMA Trial 2 Bayesian Causal Inference 3 R and BUGS 4 Application Results of the ARMA Trial 5 Concluding Remarks C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 35/42

111 Survival Rates Empirical (gray), posterior mean observed (dashed)) and potential (black) survival curves. Shaded area denote 95% posterior credible band for the potential survival curve: Survival Rate Observed Survival (Empirical) Observed Survival (Model Based) Potential Survival (Model Based) Days C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 36/42

112 Survival Rates Difference Posterior mean difference between observed and potential survival curves, with 95% posterior credible band: Difference Days C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 37/42

113 Outline 1 Acute Lung Injury and ARMA Trial 2 Bayesian Causal Inference 3 R and BUGS 4 Application Results of the ARMA Trial 5 Concluding Remarks C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 38/42

114 Summary C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 39/42

115 Summary We used the G-computation formula to estimate the potential survival distribution under the dynamic LTVV treatment regime for patients with acute lung injury C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 39/42

116 Summary We used the G-computation formula to estimate the potential survival distribution under the dynamic LTVV treatment regime for patients with acute lung injury Our results demonstrate that strict adherence to the LTVV algorithm does not lead to increased mortality C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 39/42

117 Summary We used the G-computation formula to estimate the potential survival distribution under the dynamic LTVV treatment regime for patients with acute lung injury Our results demonstrate that strict adherence to the LTVV algorithm does not lead to increased mortality The current methodology relies on untestable assumption that all the time-dependent confounders have been measured, i.e. no unmeasured confounding. Sensitivity of the conclusion to deviations from this assumption should be explored C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 39/42

118 Summary We used the G-computation formula to estimate the potential survival distribution under the dynamic LTVV treatment regime for patients with acute lung injury Our results demonstrate that strict adherence to the LTVV algorithm does not lead to increased mortality The current methodology relies on untestable assumption that all the time-dependent confounders have been measured, i.e. no unmeasured confounding. Sensitivity of the conclusion to deviations from this assumption should be explored We illustrated the utility of R and OpenBUGS for the Bayesian implementation of the proposed methodology C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 39/42

119 Summary We used the G-computation formula to estimate the potential survival distribution under the dynamic LTVV treatment regime for patients with acute lung injury Our results demonstrate that strict adherence to the LTVV algorithm does not lead to increased mortality The current methodology relies on untestable assumption that all the time-dependent confounders have been measured, i.e. no unmeasured confounding. Sensitivity of the conclusion to deviations from this assumption should be explored We illustrated the utility of R and OpenBUGS for the Bayesian implementation of the proposed methodology With the dissemination and popularization of High Performance Computing, parallel computation will become mainstream for all scientific researchers including statisticians C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 39/42

120 THE END C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 40/42

121 BLANK C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 41/42

122 Tips for R Installation C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 42/42

123 Tips for R Installation R version has been released on 05/31/2010 C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 42/42

124 Tips for R Installation R version has been released on 05/31/2010 Use./configure -prefix= to specify the destination folder for installation C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 42/42

125 Tips for R Installation R version has been released on 05/31/2010 Use./configure -prefix= to specify the destination folder for installation Use export R_LIBS= to set up the local R package library path C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 42/42

126 Tips for R Installation R version has been released on 05/31/2010 Use./configure -prefix= to specify the destination folder for installation Use export R_LIBS= to set up the local R package library path To install R2WinBUGS in the latest version R, packages lattice and coda need to be installed separately C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 42/42

127 Tips for R Installation R version has been released on 05/31/2010 Use./configure -prefix= to specify the destination folder for installation Use export R_LIBS= to set up the local R package library path To install R2WinBUGS in the latest version R, packages lattice and coda need to be installed separately Set export BUGS= for rbugs C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 42/42

128 Tips for R Installation R version has been released on 05/31/2010 Use./configure -prefix= to specify the destination folder for installation Use export R_LIBS= to set up the local R package library path To install R2WinBUGS in the latest version R, packages lattice and coda need to be installed separately Set export BUGS= for rbugs Extensions C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 42/42

129 Tips for R Installation R version has been released on 05/31/2010 Use./configure -prefix= to specify the destination folder for installation Use export R_LIBS= to set up the local R package library path To install R2WinBUGS in the latest version R, packages lattice and coda need to be installed separately Set export BUGS= for rbugs Extensions Use Rprof and summaryrprof to find the computation bottleneck C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 42/42

130 Tips for R Installation R version has been released on 05/31/2010 Use./configure -prefix= to specify the destination folder for installation Use export R_LIBS= to set up the local R package library path To install R2WinBUGS in the latest version R, packages lattice and coda need to be installed separately Set export BUGS= for rbugs Extensions Use Rprof and summaryrprof to find the computation bottleneck Use C or Fortran extensions to expedite the computation C. Wang, D.O. Scharfstein, M.J. Daniels Evaluate the Causal Effect of DTR 42/42