Missingness Methods in trial-based CEA

Introduction

We performed a systematic literature review that assesses the quality of the information reported and type of methods used to handle missing outcome data in trial-based economic evaluations. The purpose of this review is to critically appraise the current literature in within-trial CEAs with respect to the quality of the information reported and the methods used to deal with missingness for both effectiveness and costs. The review complements previous work, covering 2003-2009 (88 articles) with a new systematic review, covering 2009-2015 (81 articles) and focuses on two~perspectives.

First, we provide guidelines on how the information about missingness and related methods should be presented to improve the reporting and handling of missing data. We propose to address this issue by means of a quality evaluation scheme, providing a structured approach that can be used to guide the collection of information, formulation of the assumptions, choice of methods, and considerations of possible limitations for the given missingness problem. Second, we review the description of the missing data, the statistical methods used to deal with them and the quality of the judgement underpinning the choice of these methods.

Quality Evaluation Scheme

In order to judge whether missing data in CEAs have been adequately handled, we assembled guidelines from previous review articles on how information relating to the missing data should be reported. In particular, we defined three broad components of the analysis that are related to the description of the missingness problem (Description), details of the methods used to address it (Methods) and a discussion on the uncertainty in the conclusions resulting from the missingness (Limitations). For each component, information that is considered to be vital for transparency is listed under key considerations, while other details that could usefully be provided as supplementary material are suggested under optimal considerations.

Using the list of key considerations, we determine whether null (all key considerations absent), partial (one or more key considerations absent) or full (all key considerations present) information has been provided for each component. The set of key considerations is defined to ensure a full assessment of the impact that missingness may have on the final conclusions of the analysis with respect to all three components. However, providing a certain level of information on one component (e.g.~full information on Description) typically has a different impact on the results with respect to providing the same level of information on another component (e.g.~full information on Limitations). Based on this, we suggest computing a numerical score that weights each component by the impact that it may have on the final results to summarise the overall information provided on missingness.

Different score values are calculated based on whether full, partial or null information content is provided in each component and by weighting the three components in a ratio of 3:2:1 (Description: Method: Limitations). This weighting scheme has been chosen according to the impact that each component is likely to have on the final conclusions based on assumptions that we deemed to be~reasonable. Specifically, the Limitations component typically has the least importance among the three because of its limited impact on the conclusions. In the same way, the Description component has potentially a higher impact on the results than the Method component as it generally drives the choice for the initial assumptions about the missingness.

Finally, the relevance of the scores in terms of decision analysis is mainly associated with a qualitative assessment of the articles. Therefore, we suggest converting the scores into ordered grades (A-E) to evaluate the studies based on the overall information reported on the handling of the missing data. Studies that are graded in the top categories should be associated with a higher degree of confidence in their results, whereas more caution should be given in the consideration of results coming from studies that are graded in the bottom categories. When qualitatively assessing the articles, the different grading assigned to each of them could be an indication of a lack in the robustness of the conclusions provided due to missingness uncertainty. With respect to the quality assessment of the studies, the aggregation of the quality scores on the components of the analysis (Description, Method and Limitations) into ordered grades could lead to some loss of information compared with the direct use of the quality scores on each component. However, merging the scores into a fewer number of categories ensures a relatively easy comparison of the quality of the information provided across the three analysis components and provides a useful indication about the different degree of confidence to assign to the results obtained by each study.

The Figure below shows a visual representation of the grade (and score) assignment in the quality evaluation scheme. Although the importance between the different components is subjective, the chosen structure represents a reasonable and relatively straightforward assessment scheme.

Quality Evaluation Scheme

The articles reviewed for the two periods are presented and compared by type of analysis performed. First, the base-case methods are considered, i.e.~those used in the main analysis. Second, any alternative methods in these analyses are discussed; when present, these assess the robustness of the results obtained in the main analysis against departures from the initial assumptions on missingness.

Summary of the findings

Our review is based on a sample of recently published studies and should therefore provide a picture of current missing data handling in within-trial CEAs. However, the quality assessment of the articles is based on the information reported in the articles. It is possible that authors had assessed the robustness of their conclusions to the missing data using alternative approaches that were not reported in the published version because of space limitations in journals. In these cases, it is important that on-line appendices and supplementary material are used to report these~alternatives. In our literature review, information about missing data information and methods was available from $4$ and $9$ on-line supplementary materials for the period 2003-2009 and 2009-2015, respectively. Both the larger number of on-line materials and more detailed information reported about missingness handling in the analyses indicate an increased use of this tool in the later period (2009-2015) compared to the first period (2003-2009).

Descriptive Review

Missingness methods by outcome and period

From the comparison of the base-case methods used for the costs and effects between 2009 and 2015, the Figure above shows a marked reduction in the number of methods not clearly described for the effects, compared to those for the costs. A possible reason for this is that, while clinical effectiveness measures are often collected through self-reported questionnaires, which are naturally prone to missingness, cost measures rely more on clinical patient files which may ensure a higher completeness rate. It was not possible to confirm this interpretation in the reviewed studies due to the high proportions of articles not clearly reporting the missing rates in both 2003-2009 and 2009-2015 periods, for effects ($\approx 45%$ and $\approx 38%$) and costs ( $\approx 50%$ and $\approx 62%$). In addition, clinical outcomes are almost invariably the main objective of RCTs and are usually subject to more advanced and standardised analyses. Arguably, costs are often considered as an add-on to the standard trial: for instance, sample size calculations are almost always performed with the effectiveness measure as the only outcome of interest. Consequently, missing data methods are less frequently well thought through for the analysis of the costs. However, this situation is likely to change as cost data from different perspectives (e.g. caregivers, patients, society, etc.) are being increasingly used in trials, leading to the more frequent adoption of self-report cost data which may start to exhibit similar missingness characteristics to effect data.

The review identified only a few articles using more than one alternative method. In addition, these analyses are typically conducted without any clear justification about their underlying missing data assumptions and may therefore not provide a concrete assessment of the impact of missingness uncertainty. This situation indicates a gap in the literature associated with an under-implementation of sensitivity analysis, which may significantly affect the whole decision-making process outcome, under the perspective of a body who is responsible for providing recommendations about the implementation of alternative interventions for health care matters.

Limiting the assessment of missingness assumptions to a single case is unlikely to provide a reliable picture of the underlying mechanism. This, in turn, may have a significant impact on the CEA and mislead its conclusions, suggesting the implementation of non-cost-effective treatments. Robustness analyses assess the sensitivity of the results to alternative missing data methods but do not justify the choice of these methods and their underlying assumptions about missingness which may therefore be inappropriate in the specific context analysed. By contrast, sensitivity analyses, which rely on external information to explore plausible alternative methods and missingness assumptions, represent an important and more appropriate tool to provide realistic assessments of the impact of missing data uncertainty on the final conclusions.

Quality assessment

Generally speaking, most of the reviewed papers achieved an unsatisfactory quality score under the Quality Evaluation Scheme. Indeed, the benchmark area on the top-right corner of the graphs is barely reached by less than $7%$ of the articles, both for cost and effect data.

Overall, the proportions of the studies associated with the lowest category (E) prevails in the majority of the years, with a similar pattern over time between missing costs and effects. All the articles that are associated with the top category (A) belong to the period 2013-2015, with the highest proportions of articles falling in this category being observed in 2015 for both outcomes. The opportunity of reaching such a target might be precluded by the choice of the method adopted, which may not be able to support less restrictive assumptions about missingness, even when this would be desirable. As a result, when simple methods cannot be fully justified it is necessary to replace them with more flexible ones that can relax assumptions and incorporate more alternatives. In settings such as those involving MNAR, sensitivity analysis might represent the only possible approach to account for the uncertainty due to the missingness in a principled way. However, due to the lack of studies either performing a sensitivity analysis or providing high quality scores on the assumptions, missingness is not adequately addressed in most studies. This could have the serious consequence of imposing too restrictive assumptions about missingness and affect the outcome of decision making.

Conclusions

Our review shows, over time, a significant change from more to less restrictive methods in terms of the assumptions on the missingness mechanism. This is an encouraging movement towards a more suitable and careful missing data analysis. The results from the disaggregated analysis by year of publication in the later period (2009-2015) indicates the rise of a better and more transparent approach to handle missingness in the latest years of the review, especially in 2015. In particular, compared to the previous years, the articles reviewed from 2015 are associated with a higher proportion of MI methods used in the base-case analysis, a substantial increase in the number of robustness methods implemented, and a better quality score assignment.

Nevertheless, improvements are still needed as, overall, only a small number of articles provide transparent information about the missing data and almost no study performs a sensitivity~analysis. These failings are probably due to the fact that the implications of using methods that do not handle missingness in a principled way are not well-known among practitioners. In addition, the choice of the missing data methods may also be guided by their ease of implementation in standard software packages rather than methodological reasons. This is a potentially serious issue for bodies such as the NICE who use these evaluations in their decision making, thus possibly leading to incorrect policy decisions about the cost-effectiveness of new treatment options.

The Quality Evaluation Scheme represents a valuable tool to improve missing data handling. By carefully thinking about each component in the analysis we are forced to explicitly consider all the assumptions we make about missingness and assess the impact of their variation on final conclusions. The main advantage is a more comparable formalisation of the uncertainty as well as a better indication of possible issues in assessing the cost-effectiveness of new treatments.

Assistant Professor in Statistics

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