Subgroup analysis methods for IPD from trials

Ordinary meta-analyses that synthesize aggregated data from several similar studies are a popular form of analyses. The methodology has been used for many years and hence is very well established. Individual patient data (IPD) meta-analyses on the other hand, regarded as the gold standard for meta-analyses, use the original individual patient data from each of the studies, which makes the analyses rather different. IPD meta-analyses have greater power and are particularly more useful compared to individual trials and ordinary meta-analyses methods when patient-level covariates are of interest rather than or in addition to just the mean effects. Though it is the ideal approach for performing meta-analyses, like any method, there are a number of challenges faced mainly to do with the approach being resource intensive (71).

Performing IPD meta-analyses has only recently gained much popularity and therefore its methods are not as well established as ordinary meta-analyses methods.

When performing IPD meta-analyses, in particular subgroup analyses, the existing methodology requires that one takes either a two-step approach or a one-step approach. In the two-step approach, the subgroup analyses are carried out in each individual dataset separately to obtain subgroup effect estimates along with their respective variance estimates. These estimates are then synthesized in a similar

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manner to when performing ordinary meta-analysis using existing techniques. However, a problem with this approach is that often a simple fixed-effect pooling is used that does not incorporate the heterogeneity among the studies (137). This issue is overcome by using a one-step approach, a more flexible approach, which fits a single and simple hierarchical model with the inclusion of an interaction term (similar to the linear/logistic regression models) and also includes random effects to account for the between study heterogeneity.

Despite IPD meta-analyses having greater power when wanting to identify moderators of treatment effect, the current methodology used may not be ideal. The problem is that we only know how to extend the simpler models to the IPD meta-analyses setting. To be more precise, when either a one stage or a two stage approach is used for

subgroup analyses, interaction tests are performed testing one patient characteristic at a time; they do not consider the multiple characteristics of patients. This is the exact same issue highlighted earlier with the methods used in single trials. Therefore, although IPD meta-analyses provide an ideal framework for subgroup analyses, there is a need for methodological development to incorporate multiple patient

characteristics when performing subgroup analyses.

5.5 Discussion

The term subgroup analysis is interpreted differently by different people. The

distinction between prognostic subgroups and differential subgroups was made at the start of this chapter where the latter is of interest in this thesis. Differential subgroup analyses are most commonly performed using a regression based approach with the inclusion of a treatment-covariate interaction to test for treatment effect moderation. This chapter performed a broad literature review to explore the wider literature for other proposed methods of performing subgroup analyses. The review process found a

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number of methods that have been proposed to date for investigating subgroup effects and subgroup identification using individual patient characteristics and also using multiple characteristics as well. Moreover, IPD meta-analysis methods were briefly described since an IPD framework is ideal for performing subgroup analyses. However, it became apparent from this review that there is a need for methodological

development in both the single trial case and IPD meta-analysis case to incorporate multiple patient characteristics when identifying subgroups because in general only the simpler regression type models with a single interaction effect are used.

Having reviewed the literature and identified various methods, it would not be possible to explore and evaluate every single method. Therefore, it is probably worthwhile at this stage to contrast what is written in current proposed guidelines for performing subgroup analyses to the findings from the systematic review of subgroup analyses in the area of low back pain presented in Chapter 4. One of the key recommendations in current proposed guidelines is that a clear distinction be made between pre-specified and post-hoc analyses where the former is for hypothesis testing (confirmatory analyses) and the latter for hypothesis generating (exploratory analyses). A limited number of pre-specified subgroups for investigation must be chosen using either a clear clinical justification or it must be based on findings from previous studies. As highlighted in chapter 3, if clinical justification is used then this could be quite subjective and it may be that important subgroups may go unnoticed. On the other hand if one were to base their choice of subgroups on findings from previous studies, then this may not be very wise if the quality, conduct and reporting of subgroup analyses in that particular field is poor; as was found in the systematic review in Chapter 4. For these reasons, it often makes sense to keep the subgroup analyses entirely exploratory in nature and use a method that investigates the entire covariate space such that no important subgroup effects go unnoticed. Any subgroups that are

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identified from the exploratory analyses can then be tested in a future trial. Tree based methods, as described in this review, are one such method that can accommodate this. Furthermore, recent development of this methodology makes this a promising

approach for subgroup identification in the context of clinical trials. The rest of this thesis will therefore focus on the evaluation, development and application of tree based methodology for identifying subgroups when using individual patient data from

several similar trials.

A key constituent of tree based approaches is the utilization of a technique referred to as recursive partitioning. Therefore the following chapter will introduce the recursive partitioning methodology, followed by a description of the several advanced tree based method variants that have been proposed in the literature to date for performing differential subgroup analyses. A simulation study will be performed thereafter to assess the performance of these variant methods in detecting interactions in a single trial setting and the results presented.

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Chapter 6

Introduction to

Recursive Partitioning

6.1 Introduction

The previous chapter provided a broad review of the available methods for conducting subgroup analysis or subgroup identification in a single trial based setting as well as methods typically used for individual patient data (IPD) subgroup meta-analyses. Of the methods described in the review, it was identified that tree based methods are an attractive possibility for performing subgroup analyses using multiple patient

characteristics. Whilst the application of tree based methodology is evident elsewhere as a valuable tool for identifying subgroups, its use in IPD meta-analyses and clinical trials of musculoskeletal disorders research is un-explored.

Tree based methods are a data driven approach from the field of data mining that use a simple intuitive technique called recursive partitioning. It is important to initially fully understand the underlying recursive partitioning methodology of the tree based methods before looking at advanced variants of this methodology and considering possible extensions to an IPD meta-analyses setting. This chapter will therefore start

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by describing the recursive partitioning methodology along with its relevant steps. Since outcome measures in the area of low back pain research are mainly of the

continuous type, the explanation of the recursive partitioning procedure in this chapter will be for the continuous outcome case (regression trees). It is important to note here that the recursive partitioning methodology described in this chapter will first focus on identifying subgroups of patients that differ in terms of outcome, thereafter recursive partitioning methods to find moderators of treatment effect will be considered. However in traditional subgroup analyses, the aim is to identify subgroups that differ in terms of treatment effect i.e. treatment effect heterogeneity. Therefore the sole purpose of section 6.2 is for the reader to gain a good understanding of the concepts and basic methodology of recursive partitioning for tree based methods. The advanced variants of this methodology that have been proposed in the literature to date to identify treatment effect heterogeneity will be explained thereafter in section 6.3.