Improved control for confounding using propensity scores and instrumental variables?

Transcription

1 Improved control for confounding using propensity scores and instrumental variables? Dr. Olaf H.Klungel Dept. of Pharmacoepidemiology & Clinical Pharmacology, Utrecht Institute of Pharmaceutical Sciences 1

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3 Outline Confounding by indication Propensity scores Comparison with logistic regression Measures of balance and model selection Instrumental variables 3

4 Pubmed citations IV PS < Introduction Assessment of treatment effects in Randomized clinical trials 1. Efficacy 2. Safety Observational studies 1. Safety 2. Effectiveness 4

5 Introduction Randomization assures that groups differ only by chance and usually creates comparison groups with similar probability of outcome (prognosis) Problem with observational studies: non-random allocation of treatments resulting in uncontrolled confounding Control for confounding Select appropriate comparison group only treated subjects, compare treatments untreated candidates for treatment instrumental variables Study design convential designs (cohort, case-control) special designs (case-crossover, case-time-control) Data analytical techniques matching, restriction, stratification, multivariate adjustmen multivariate confounder score, propensity scores Klungel OH, et al. J Clin Epidemiol 2004;57:

6 Confounding by indication Observational cohort study in Sweden RR (myocardial infarction)* Untreated normotensive and hypertensive men 1.0 (reference) Treated hypertensive men DBP 90 mmhg 3.8 ( ) Treated hypertensive men DBP>90 mmhg 1.1 ( ) * adjusted for previous MI, CVA, IHD, IC, diabetes, SBP, duration of antihypertensive therapy, hypercholesterolemia, hypertriglyceridaemia, creatinin, obesity, use of cardiac glycosides, smoking. Conclusion: In men treated for hypertension, DBP should not be reduced to lower than 90 mmhg Merlo J, et al. BMJ 1996;313: Confounding by indication Observational cohort study Dutch women. RR (cardiovascular death) Untreated hypertensive women 1.0 (reference) Treated hypertensive women Crude 1.0 ( ) Adjusted for age 0.7 ( ) +BMI, Pulse rate 0.6 ( ) +smoking, lipids 0.6 ( ) +diabetes 0.5 ( ) Hoes A, et al. BMJ 1997;315:

7 Candidates for treatment 7

8 Observational vs RCT Confounding by indication Case-control study among treated hypertensives Antihypertensive Cases Controls RR (Ischemic stroke) Thiazide diuretic (reference) ß-blocker alone ( ) with thiazide ( ) Calcium antagonist alone ( ) with thiazide ( ) ACE inhibitor alone ( ) with thiazide ( ) Klungel OH, et al. Arch Intern Med 2001;161:

9 Therapy, confounding variables, and outcome of therapy. Propensity score Confounder Therapy Intermediate Factor Outcome Propensity scores introduced by Rosenbaum & Rubin the propensity score is the probability of receiving treatment, given a set of observed covariates: e(x i ) = Pr(Z i =1 X i =x i ) balance treatment groups on observed covariates, hence it is called a balancing score subjects having the same propensity score (PS) will tend to have the same distribution of covariates Rosenbaum P, Rubin D. Biometrika 1983;70:

10 Propensity scores PS for every subject, estimate treatment effect by relating outcome to treatment and adjusting for PS by using it as a matching variable stratification variable continuous covariate to estimate the PS a model should be build that contains all important observed confounders creating optimal balance between treatment groups in practice not enough attention for PS model or guided by wrong statistics to compare models or to select covariates Example: Study of effect of statins post-mi Selection of comparison group Only subjects who were eligible for drug treatment of hypercholesterolemia according to NCEP guidelines Drug therapy in subjects with established CHD if LDL cholesterol > 130 mg/dl Klungel OH et al. Ann Pharmacother 2002;36:

11 Baseline characteristics of MI patients Characteristic Untreated Statin Non-statin Number Pretreatment lipid levels Total-c, mg/dl * 268.7* LDL-c, mg/dl * 176.4* Prior to first MI Age, y * 59.5* Men, % 56 66* 60* Current smoking, % Diabetes, % * Congestive heart failure 23 16* 13* Use of lipid-lowering drugs 9 32* 30* Baseline characteristics of MI patients Characteristic Untreated Statin Non-statin During hospitalization and in first 180 days after MI Angina, % Coronary angioplasty, % 20 38* 33* Coronary bypass surgery, % 21 20* 19* Thrombolytic therapy, % * Use of ACE-inhibitors, % 27 35* 26 Use of Betablockers, % 52 72* 63* Use of Aspirin, % 85 95* 88* 11

12 Stratify on propensity score Percentiles PS Untreated Statin Matching on PS Number of matched pairs Nr of digits Total

13 Characteristics after matching on PS Characteristic Untreated Statin Number Pretreatment lipid levels Total-c, mg/dl LDL-c, mg/dl Prior to first MI Age, y Men, % Current smoking, % Diabetes, % Congestive heart failure Use of lipid-lowering drugs Characteristics after matching on PS Characteristic Untreated Statin During hospitalization and in first 180 days after MI Angina, % Coronary angioplasty, % Coronary bypass surgery, % Thrombolytic therapy, % Use of ACE-inhibitors, % Use of Betablockers, % Use of Aspirin, %

14 Effect of statins on risk of death Matched on propensity score N RR [95%CI] RR [95%CI]* RR [95%CI]** Untreated Statin [ ] 0.68 [ ] <=Full PS model Statin [ ]# 0.53 [ ]# <=Reduced PS model Multivariate adjusted (Cox regression) Untreated Statin [ ] 0.56 [ ] 0.64 [ ] * adjusted for age, sex, diabetes, congestive heart failure, glucose, creatinin, ptca. ** adjusted for all factors in propensity score model # propensity score based on age, sex, diabetes, congestive heart failure, glucose, creatinin, ptca 14

15 Methods of analysis and sets of covariates used Baseline covariate distribution 15

16 Distribution of PS Balance on covariates stratified on PS 16

17 8 covariates 12 covariates 17

18 8 covariates + 1 balanced covariate 18

19 PS vs Logreg or Cox PH Treatment effect N studies % PS>LogR/CPH 24 25% PS=LogR/CPH % PS<LogR/CPH % Overall, Mean Diff 5% [95%CI: ] OR>2 or OR<0.5, Mean Diff 19% [95%CI: ] PS vs Logreg 19

20 PS vs Logreg PS vs Logreg 20

21 Non-collapsibility of OR Z=1 Z=0 Marginal X=1 X=0 X=1 X=0 X=1 X=0 Y= Y= ORxy Z=1 Z=0 Z=1 Z=0 Y= Y= ORzy 5.44 ORxz 1 Conclusion More covariates can be included when # events low Not clear which PS method is best, but stratification less sensitive to inclusion of non-confounders. PS closer to marginal treatment effect compared to LogR-CoxPS More attention to check balance 21

22 Measuring balance and model selection in propensity score methods SV Belitser, EP Martens, WR Pestman, RHH Groenwold, A. De Boer, O.H. Klungel* Pharmacoepidemiol Drug Saf 2011, accepted On behalf of IMI PROTECT Work Package 2 ( How to check balance and to select PS model? amount of balance reached on covariates For which covariates or strata can balance be improved to select among a large number of possible models the model that reaches best balance 22

23 Overlapping coefficient -treated -γ (n=50, µ=6, λ=1) -Untreated -N (n=50, µ=7, σ=1.5) - OVL=0.48 Kolmogorov-Smirnov distance 23

24 Levy distance OVL calculated per covariate and stratum -PS analysis -5 covariates -5 strata 24

25 Simulation study N = 2000, 1600, 1200, 800, 400 True OR 2.0, 50%T/50%U, Pevent= covariates 4 related to treatment and outcome 2 related to treatment only 2 related to outcome only 40 PS models Results of simulations KS r=0.89, Median OR=2.00 Levy r=0.89, Median OR=2.00 SD r=0.90, Median OR=1.99 OVL r=-0.42, Median OR=2.10 For N <400 other approaches more predictive, e.g. t-statistic 25

26 Conclusion KS, L and SD are useful in propensity score analysis to report the balance can be used as model selection tools, mainly for larger sample sizes Further testing in simulations with skewed distributions of covariates and binary covariates Balance measures for propensity score methods:a clinical example on the use of beta-agonist use and the risk of myocardial infarction RHH Groenwold, F de Vries, A de Boer, WR Pestman, FH Rutten, AW Hoes, OH Klungel. Submitted 26

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28 Conclusions PS In case of few events more variables in PS compared to multivariable regression PS insensitive to inclusion of nonconfounders In sample sizes>2000 most measures of balance perform well In empirical examples little advantage of PS 28