Exploratory Subgroup Analyses in Clinical Research

Name: Exploratory Subgroup Analyses in Clinical Research
Brand: Wiley
Price: 78.99 EUR
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Gerd Rosenkranz(Autor*in)

Wiley (Verlag)

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Erschienen am 27. März 2020

248 Seiten

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Inhalt

Preface xi

Acknowledgments xiii

Acronyms xv

About the Companion Website xix

Introduction xxi

1 Some History of Subgroup Analysis 1

1.1 Introduction 1

1.2 Questionable Subgroup Analyses 5

1.2.1 Star Signs May Matter 5

1.2.2 Unjustified Under-treatment 7

1.2.3 Misinterpretation of Center Effects 8

1.2.4 The End of a Career 10

1.3 Encouraging Subgroup Analyses 12

1.3.1 Higher Efficacy 12

1.3.2 Harm Prevention 13

1.3.3 Avoiding Unnecessary Treatment 16

1.4 Subgroups and Drug Approvals 18

1.4.1 A Convincing Subgroup 18

1.4.2 Inconsistencies Across Regions 19

1.4.3 Detecting Non-responders 22

1.4.4 In Search for Benefit 26

1.5 Concluding Remarks 29

2 Objectives and Current Practice of Subgroup Analyses 31

2.1 Introduction 31

2.2 Objectives of Subgroup Analyses 32

2.3 Definitions Around Subgroups 34

2.4 Confounding 37

2.5 Two Types of Subgroup Analyses 39

2.6 Reporting of Subgroups 43

2.7 Concluding Remarks 45

3 Pitfalls of Subgroup Analyses 47

3.1 Introduction 47

3.2 Extreme Effect Estimates 48

3.3 Selection Bias 51

3.4 Reversal of Effects 53

3.5 Regression to the Mean 57

3.6 Simpson's Paradox 60

3.7 Post-hoc Analyses 63

3.8 Concluding Remarks 65

4 Subgroup Analysis and Modeling 67

4.1 Introduction 67

4.2 Modeling and Prediction 69

4.3 Subgroups and Hierarchical Models 72

4.3.1 Stein's Discovery 72

4.3.2 The Normal-Normal Hierarchical Model 73

4.4 Subgroups and Regression Models 76

4.4.1 Subgroups Defined in Terms of Variables 76

4.4.2 The Predicted Individual Treatment Effect 79

4.4.3 Comparison of the Two Options 83

4.5 Variable Selection in Regression 85

4.5.1 Classical Variable Selection 86

4.5.2 Regularized Estimators 87

4.5.3 Variable Selection and Confounding 88

4.6 Concluding Remarks 89

5 Hierarchical Models in Subgroup Analysis 91

5.1 Introduction 91

5.2 A General Hierarchical Model 94

5.2.1 Robbins' Theorem and Tweedie's Formula 94

5.2.2 Mixture Priors 97

5.2.3 The False Discovery Rate 100

5.3 Parameter Estimation 101

5.3.1 Posterior Means and Variances 101

5.3.2 Estimation Bias 104

5.3.3 Selection Bias 106

5.4 Case Studies 111

5.4.1 The Toxoplasmosis Dataset 111

5.4.2 The BCG Dataset 113

5.4.3 The Prostate Cancer Dataset 119

5.5 Concluding Remarks 124

6 Selection Bias in Regression 129

6.1 Introduction 129

6.2 Correction for Selection Bias 131

6.3 Variance Estimation 136

6.4 A Case Study 139

6.5 Concluding Remarks 144

7 The Predicted Individual Treatment Effect 147

7.1 Introduction 148

7.2 Definition of the PITE 149

7.3 Confidence Intervals of the PITE 150

7.3.1 MLE for the Full Model 151

7.3.2 MLE Under a Reduced Model 151

7.3.3 Scheffé Confidence Bounds 152

7.3.4 LASSO with Post-selection Intervals 152

7.3.5 Randomized LASSO 154

7.3.6 Simulation Study 154

7.3.7 Extension to Other Endpoints 157

7.4 Case Studies 159

7.4.1 An Alzheimer Dataset 160

7.4.2 The Prostate Cancer Study Again 161

7.4.3 Renal Safety of Contrast Media 165

7.5 Concluding Remarks 173

8 Prediction models 175

8.1 Introduction 176

8.2 Prediction Error 177

8.3 Model Selection or Averaging 180

8.4 Prediction Error of the PITE 182

8.5 A Case Study 187

8.6 Concluding Remarks 190

9 Outlook 193

Bibliography 197

Index 217

1
Some History of Subgroup Analysis

The essence of tragedy has been described as the destructive collision of two sets of protagonists, both of whom are correct. The statisticians are right in denouncing subgroups that are formed post hoc from exercises in pure data dredging. The clinicians are also right, however, in insisting that a subgroup is respectable and worthwhile when established a priori from pathophysiological principles. (Feinstein, 1998)

Alvan R Feinstein (1925-2001)

The Problem of Cogent Subgroups: A Clinicostatistical Tragedy.

1.1 Introduction

The history of subgroup analysis is characterized by a strong difference in opinions about its value. One group of scientists has a skeptical attitude towards the topic warning of the risks of subgroup analysis and other attempts to target treatments. For example, Yusuf et al. (1984) stated that ".it would be unfortunate if desire for the perfect (i.e. knowledge of exactly who will benefit from treatment) were to become the enemy of the possible (i.e. knowledge of the direction and approximate size of the effects of treatment of wide categories of patients)." Many clinicians are afraid of applying the overall results of large trials to individual patients without consideration of determinants of individual responses (Rothwell, 2005) while most prominently statisticians have raised concerns (Assmann et al., 2000, Sleight, 2000, Lagakos, 2006, Guillemin, 2007, Lonergan et al., 2017) and requested that:

Investigators should be cautious when undertaking subgroup analyses.
Subgroup findings should be exploratory, and only exceptionally should they affect the conclusions from trials.
Editors and reviewers of journals need to correct any inappropriate, over-enthusiastic uses of subgroup analyses.

The statement "subgroups kill people" was attributed - rightly or wrongly - to statistician Sir Richard Peto in van Gijn and Algra (1994). In fact, Peto commented on subgroup analyses undertaken on the GISSI1 study (GISSI Study Group, 1986): "The GISSI study.is one of the most important randomized trials ever conducted and when it was published provided the best evidence then available that thrombolytic therapy reduced mortality. But the ability of the GISSI report to save lives could be substantially compromised by misinterpretation by clinicians of some of the data-dependent subset analyses that it contained." (Peto, 1990)

A second camp of scientists and pharmaceutical executives is more attracted by the opportunities than by the risks of subgroup analysis driven by the vision of "personalized" medicine. In 1977, Sir Richard Sykes, at the time chief executive officer of Glaxo-Wellcome, later chairman of GlaxoSmith-Kline and rector of Imperial College London, wrote:

"It will soon be possible for patients in clinical trials to undergo genetic tests to identify those individuals who will respond favorably to the drug candidate, based on their genotype, and therefore the underlying mechanism of their disease. This will translate into smaller, more effective clinical trials with corresponding cost savings and ultimately better treatment in general practice. In addition, clinical trials will be capable of screening for genes involved in the absorption, metabolism and clearance of drugs and the genes that are likely to predispose a patient to drug-induced side-effects. In this way, individual patients will be targeted with specific treatment and personalized dosing regimens to maximize efficacy and minimize pharmacokinetic problems and other side-effects." (Sykes, 1977), quoted from Senn (2001). It took another 20+ years until the first targeted medicine in oncology, trastuzumab for HER2 positive breast cancer, was approved by the US Food and Drug Administration (FDA) in 1998.

More and more drugs were approved for targeted patient populations during the following years. A selective list is displayed in Table 1.1. In 2013, the FDA issued a report "Paving the way to personalized medicine" (FDA, 2013) describing how the agency was planning to support the development of new drugs with companion diagnostics to guide their use. In 2017, the agency approved 16 targeted medicines (FDA, 2017).

Table 1.1 Approved targeted therapies

Indication Marker Compound Breast cancer HER2+ trastuzumab pertuzumab HER2-/ER+ everolimus Colorectal cancer KRAS cetuximab panatumumab Cystic fibrosis G551D ivacaftor Melanoma BRAF V600E vemurafenib dabrafenib BRAF V600E or V600K trametinib NSCLC ALK crizotinib

1.2 Questionable Subgroup Analyses

1.2.1 Star Signs May Matter

A trial that Peto mentioned in his critique on the GISSI study to justify his concerns on subgroup analyses was ISIS-22 (ISIS-2 Collaborative Group, 1988). This study enrolled 17 187 patients in 417 hospitals up to 24?h after the onset of suspected myocardial infarction. Patients were randomized to (i) a one hour iv infusion of streptokinase; (ii) one month of 160?mg/day aspirin; (iii) both active treatments; or (iv) neither. In the end, streptokinase reduced five week vascular mortality by as compared to placebo (). Aspirin reduced five week vascular mortality by as compared to placebo (). The combination of both aspirin and streptokinase reduced five week vascular mortality by as compared to placebo ().

The study authors concluded on subgroup analyses: "Even in a trial as large as ISIS-2, reliable identification of subgroups of patients among whom treatment is particularly advantageous (or among whom it is ineffective) is unlikely to be possible. When in a trial with a clearly positive overall result many subgroup analyses are considered, false negative results in some particular subgroups must be expected." They underlined their opinion with "the most entertaining example of an inappropriate subgroup analysis" (Horton, 2000): "For example, subdivision of the patients in ISIS-2 with respect to their astrological birth signs appears to indicate that for patients born under Gemini or Libra there was a slightly adverse effect of aspirin on mortality ( odds increase; NS), while for patients born under all other astrological signs there was a strikingly beneficial effect () odds reduction; )." The results for the aspirin-placebo comparison are shown in Table 1.2

The reason for this odd item appearing in the paper originated in negotiations between authors and editors. The Lancet was keen to include clinically relevant subgroup findings. The authors agreed under the proviso that the journal allowed the star sign groups to appear first to underline for readers the reliance they might put (or not) on the validity of these analyses (Horton, 2000).

Table 1.2 Vascular deaths in the ISIS-2 study

Source: ISIS-2 Collaborative Group (1988)

Aspirin Placebo Star sign deaths (%) deaths (%) Odds ratio Gemini/Libra 1357 150 11.1 1442 147 10.2 1.09 Other 7228 654 9.0 7157 868 12.1 0.72

1.2.2 Unjustified Under-treatment

The artificial subgroup analysis just described has at least one real world counterpart that caused serious under-treatment of a subgroup of patients for at least a decade because of a subgroup analysis: a Canadian Cooperative Study Group trial came to the conclusion that aspirin was effective in preventing stroke and death in men but not in women. The gender by treatment interaction turned out to be significant () and aspirin was effective in preventing stroke and death in men (RR, ) but not in women (1.42, ) (The Canadian Cooperative Study Group, 1978).

As part of a major meta-analysis of studies of high risk subjects in which individual patient data were obtained it was concluded that antiplatelet therapy for high risk patients appeared to reduce the odds of vascular events by a roughly similar proportion regardless of age or gender of the subjects...

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