Propensity score methods in observational studies [Elektronische Ressource] : estimating the marginal odds ratio / vorgelegt von Susanne Stampf

hPropensity score methods inobservational studies - estimating themarginal odds ratioDissertation zur Erlangung des Doktorgradesder Mathematischen Fakulta¨tder Albert-Ludwigs-Universita¨t Freiburg im Breisgauvorgelegt vonSusanne StampfAugust 2010Dekan: Prof. Dr. Kay Ko¨nigsmann1. Referent: Prof. Dr. Martin SchumacherInstitut fu¨r Medizinische Biometrieund Medizinische InformatikAlbert-Ludwigs-Universita¨t Freiburg im BreisgauStefan-Meier-Str. 2679104 Freiburg2. Referent: Prof. Claudia Czado, Ph.D.Technische Universita¨t Mu¨nchenZentrum MathematikLehrstuhl fu¨r Mathematische StatistikParkring 13 (Zimmer 2.01.17)85748 GarchingDatum der Promotion: 30.11.2010iiiDankeGeho¨rt es doch zum guten Ton,dass man sagt Dank’ an dieser Stelle,ganz aufrichtig und nicht schnelle,denn Undank ist der Welten Lohn!Dank gebu¨hrt zuerst den Eltern,sie waren da, wenn ich sie brauchte,¨so dass manch‘ Arger schnell verrauchte.Ich danke hier, ich danke gern!Meiner Schwester sei nun gedankt,sie versuchte stets, mich zu erheitern,und zu bewahren vor dem Scheitern.Dank dir hab ich viel Kraft getankt!Auch den Großeltern sei Dank gesagt,denn sie mich jederzeit moralisch unterstu¨tztenund waren somit große Stu¨tzendenn Motivation war oft gefragt!Nun dank’ ich Freunden und Kollegen,welch’ stets zu helfen wussten,egal ob’s wollten oder mussten,sie ließen mich niemals stehen im Regen!
Publié le : vendredi 1 janvier 2010
Lecture(s) : 31
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Source : D-NB.INFO/1009504126/34
Nombre de pages : 166
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h
Propensity score methods in
observational studies - estimating the
marginal odds ratio
Dissertation zur Erlangung des Doktorgrades
der Mathematischen Fakulta¨t
der Albert-Ludwigs-Universita¨t Freiburg im Breisgau
vorgelegt von
Susanne Stampf
August 2010Dekan: Prof. Dr. Kay Ko¨nigsmann
1. Referent: Prof. Dr. Martin Schumacher
Institut fu¨r Medizinische Biometrie
und Medizinische Informatik
Albert-Ludwigs-Universita¨t Freiburg im Breisgau
Stefan-Meier-Str. 26
79104 Freiburg
2. Referent: Prof. Claudia Czado, Ph.D.
Technische Universita¨t Mu¨nchen
Zentrum Mathematik
Lehrstuhl fu¨r Mathematische Statistik
Parkring 13 (Zimmer 2.01.17)
85748 Garching
Datum der Promotion: 30.11.2010iii
Danke
Geho¨rt es doch zum guten Ton,
dass man sagt Dank’ an dieser Stelle,
ganz aufrichtig und nicht schnelle,
denn Undank ist der Welten Lohn!
Dank gebu¨hrt zuerst den Eltern,
sie waren da, wenn ich sie brauchte,
¨so dass manch‘ Arger schnell verrauchte.
Ich danke hier, ich danke gern!
Meiner Schwester sei nun gedankt,
sie versuchte stets, mich zu erheitern,
und zu bewahren vor dem Scheitern.
Dank dir hab ich viel Kraft getankt!
Auch den Großeltern sei Dank gesagt,
denn sie mich jederzeit moralisch unterstu¨tzten
und waren somit große Stu¨tzen
denn Motivation war oft gefragt!
Nun dank’ ich Freunden und Kollegen,
welch’ stets zu helfen wussten,
egal ob’s wollten oder mussten,
sie ließen mich niemals stehen im Regen!
Dem Chef gedankt sei nun von Herzen,
ein Chef, der stets zugegen war
und immer wußte, was geschah,
und wenn nicht, wir konnten dru¨ber scherzen!
Mit diesen Versen mo¨chte ich mich bei allen bedanken, die Anteil an der Entstehung und
Fertigstellung dieser Arbeit haben. Auch wenn es nicht immer so froh und heiter in den ver-
gangenen vier Jahren zugegangen ist, so hab ich doch viel gelernt, nicht nur fu¨r das wissen-
schaftliche Arbeiten, sondern insbesondere fu¨r das Leben.
Susanne StampfSummary
In the last three decades, the methodology of the propensity score has attracted increasing
attention for estimating treatment effects in observational studies. Propensity score methods
are designed to estimate causal marginal effects in contrast to regression techniques offering
the estimation of associational, conditional effects. The propensity score is defined as the pro-
bability of the assignment to a certain treatment given covariates and it can be used to mimic
data situations as in randomized experiments which in turn permits to estimate marginal treat-
ment effects without further covariate adjustments. In studies with binary outcome, the effect
is often described as an odds ratio and the marginal odds ratio is defined as the change
in odds of outcome if everybody versus nobody were treated. To estimate it, the popular
Mantel-Haenszel estimator has been used for stratified data, although it was shown that it is
an inappropriate estimator for the marginal odds ratio. We study recently proposed alterna-
tive estimators for the marginal odds ratio, one stratified for the propensity score, the other
derived from logistic regression. Additionally, we adapt the methodology of the logistic re-
gression based estimator to covariate adjustment by the propensity score. We also derive
corresponding variance estimators applying the Delta-method and parametric bootstrapping.
The applicability of the proposed estimators and their variance estimators will be illustrated
in two data examples. The first example deals with respiratory tract infections in children in
Germany. The aim is to detect the impact of exposure to a certain virus type on the severity
of respiratory tract infections. Heart diseases are of interest in the second data example,
investigating the short-term outcome after coronary bifurcation lesions. The effect of stent
types used in percutaneous catheter intervention to treat bifurcation lesions on the need for
target re-vascularization or the occurrence of death or an myocardial infarction is to ascertain.
Furthermore, simulation studies are carried out to investigate relative bias and coverage pro-
babilities of the marginal odds ratio estimators and the performance of the corresponding
variance estimators. Whenever outcome rates or regression based approaches are used,
reasonable performance of the marginal odds ratio estimators can be shown. The variance
estimators also perform well if specific assumptions are fulfilled. In contrast, the stratified
Mantel-Haenszel estimator is substantially biased in some situations due to problems of non-
collapsibility and thus is generally inappropriate for a reliable estimation of the marginal odds
ratio.
vContents
Summary v
1 Introduction 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Overview and history of the propensity score 5
2.1 Causation vs. association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 The role of observational studies . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 History of the propensity score . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 The propensity score in general . . . . . . . . . . . . . . . . . . . . . . 9
2.3.2 The estimation of the propensity score . . . . . . . . . . . . . . . . . . . 10
2.3.3 The propensity score challenges the odds ratio . . . . . . . . . . . . . . 12
3 The propensity score and related methods 15
3.1 The propensity score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Stratification by the propensity score . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 Matching by the propensity score . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.4 Inverse probability weighting by the propensity score . . . . . . . . . . . . . . . 23
3.5 Covariate adjustment by the propensity score . . . . . . . . . . . . . . . . . . . 25
4 A new approach for estimating the marginal odds ratio 29
4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 Estimators for the marginal odds ratio . . . . . . . . . . . . . . . . . . . . . . . 32
4.2.1 Stratification by the propensity score . . . . . . . . . . . . . . . . . . . . 33
4.2.2 Logistic regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.3 Covariate adjustment by the propensity score . . . . . . . . . . . . . . . 35
4.2.4 Inverse probability weighting by the propensity score . . . . . . . . . . . 36
4.3 Variance estimators for marginal odds ratio estimators . . . . . . . . . . . . . . 36
viiviii CONTENTS
4.3.1 Stratification by the propensity score . . . . . . . . . . . . . . . . . . . . 39
4.3.2 Logistic regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3.3 Covariate adjustment by the propensity score . . . . . . . . . . . . . . . 42
4.4 Estimators for the covariance between marginal outcome probabilities . . . . . . 43
4.4.1 Empirical covariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.4.2 Bootstrap resampling for covariance estimation . . . . . . . . . . . . . . 44
5 Simulation studies investigating properties of marginal odds ratio estimators 49
5.1 Simulation design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.1.1 Generating process for covariates and treatment . . . . . . . . . . . . . 50
5.1.2 Generating process for outcome . . . . . . . . . . . . . . . . . . . . . . 51
5.1.3 Generation of data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 Analysis concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.1 Regression based analysis . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.2 Propensity score analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.3 Simulation scheme for covariance estimation . . . . . . . . . . . . . . . 54
5.2.4 Summary of analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3.1 Results regarding mean estimates and relative bias . . . . . . . . . . . . 57
5.3.2 Results regarding mean variance estimates and coverage probability . . 66
6 Application to real data examples 81
6.1 Lower respiratory tract infections in infants and children in Germany (PRI.De) . . 81
6.2 Bifurcations Bad Krozingen (BBK) registry: Analysis of short-term outcome
after coronary bifurcation lesions . . . . . . . . . . . . . . . . . . . . . . . . . . 86
7 Discussion 97
A Glossary 103
B Supplemental material regarding the simulation study 107
B.1 Pre-defined parameters in simulation settings . . . . . . . . . . . . . . . . . . . 107
B.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
C Check of balance for covariates in data examples 141
C.1 Lower respiratory tract infections in infants and children in Germany (PRI.De) . . 141
C.2 Bifurcations Bad Krozingen (BBK) registry: Analysis of short-term outcome
after coronary bifurcation lesions . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Bibliography 147Chapter 1
Introduction
1.1 Introduction
‘Propensity scores: help or hype’ is the title of a critical work of Winkelmayer and Kurth (2004)
concerning the application of propensity score methods to a pharmacoepidemiological study.
It reflects the controversial role of the propensity score in the analysis of data from obser-
vational studies, which has been lively discussed to this day. It is a discussion whether the
application of propensity score methods is necessary to analyze observational data precisely
or whether it is rather a temporary fashion used as a supplemental analytical tool which entails
sometimes more confusion about its correct application and parameter interpretation than it
does support the data analysis estimating causal effects.
Randomized controlled trials (RCTs) are the gold standard for the conduction of clinical trials.
1They permit to estimate causal treatment effects as unadjusted differences or ratios since,
in expectation, patients‘ baseline characteristics (covariates) are comparable between treat-
ment groups. Due to ethical, financial, social or temporal hindrances, RCTs are not always
feasible and preferable, respectively, such that observational studies are sometimes the sole
source to reveal the impact of a certain treatment on the outcome of interest. In observa-
tional studies, differences in patients‘ covariates between treatment groups are hard to avoid
since the assignment of treatment is not random as in RCTs, but it depends on patients‘
covariates. Therefore, simple differences and ratios are not appropriate to estimate causal
treatment effects accurately due to systematic differences in measured covariates for reasons
other than effects caused by the treatment (Rosenbaum 2005). The non-consideration of
differences in covariates affecting the outcome can lead to biased estimates and therefore
sometimes to extensive consequences.
The methodology of the propensity score was introduced by Rosenbaum and Rubin (1983)
and it offers an opportunity to deal with imbalances of measured covariates, that is to say con-
1Treatment effects can also be results of a certain exposure. For brevity, we will only refer to ‘treatment’ in the
following.
12 1. Introduction
founding. The propensity score is defined as the conditional probability to receive a certain
treatment given patients‘ covariates (Rosenbaum and Rubin 1983) and its correct applica-
tion needs some assumptions to be satisfied. For the major audience, the theory behind
propensity score approaches seems to be puzzling, but their application has been, how-
ever, frequently increasing in the last decades in diverse research fields including epidemio-
logy, health care research and services, social science and economics (Shah et al. 2005;
Stu¨rmer et al. 2006). Figure 1.1 illustrates the at first rather moderate acceptance of this
new method. This changed suddenly at the beginning of this millennium such that propensity
score methods nowadays seem to be a fashionable tool for the analysis of observational data.
Reasons for this abrupt increase are unclear, but frequently cited papers (Rubin 1997; Joffe
and Rosenbaum 1999) and tutorials (D’Agostino 1998) have maybe influenced it.
Figure 1.1: The distribution of publications referring to propensity score methods
2listed by their publication year
700
Total amount of 3711 publications
from 1983 to July 2010
600
500
400
300
200
100
Publication year
Several approaches exist that make use of the propensity score, but they are not popular to
the same degree. Both matching and stratification by the propensity score are apparently easy
to understand and hence seem to be user-friendly. However, stratification by the propensity
score is clearly less used than matching by the propensity score which was suggested as the
most efficient propensity score method (D’Agostino 1998). The method of inverse probability
weighting by the propensity score is rarely used probably due to the more complex theory
behind its application. A fourth approach is the method of covariate adjustment by the pro-
pensity score (referred to as covariance adjustment by Rosenbaum and Rubin (1983)) where
the propensity score serves as the sole covariate in an appropriate outcome model in addition
to the treatment variable.
2This publication list, made on the 4th in August 2010, consists of 3711 publications and it is the result of
a literature search in the ‘Web of Science’ database looking for the phrases ‘propensity score’ and ‘propensity
scores’, respectively, in the title or the abstract of the publication.
<1990
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
< July 2010
Number of publications

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