| Literature DB >> 29573044 |
Baptiste Leurent1, Manuel Gomes2, James R Carpenter1,3.
Abstract
Cost-effectiveness analyses (CEA) conducted alongside randomised trials provide key evidence for informing healthcare decision making, but missing data pose substantive challenges. Recently, there have been a number of developments in methods and guidelines addressing missing data in trials. However, it is unclear whether these developments have permeated CEA practice. This paper critically reviews the extent of and methods used to address missing data in recently published trial-based CEA. Issues of the Health Technology Assessment journal from 2013 to 2015 were searched. Fifty-two eligible studies were identified. Missing data were very common; the median proportion of trial participants with complete cost-effectiveness data was 63% (interquartile range: 47%-81%). The most common approach for the primary analysis was to restrict analysis to those with complete data (43%), followed by multiple imputation (30%). Half of the studies conducted some sort of sensitivity analyses, but only 2 (4%) considered possible departures from the missing-at-random assumption. Further improvements are needed to address missing data in cost-effectiveness analyses conducted alongside randomised trials. These should focus on limiting the extent of missing data, choosing an appropriate method for the primary analysis that is valid under contextually plausible assumptions, and conducting sensitivity analyses to departures from the missing-at-random assumption.Entities:
Keywords: cost-effectiveness analysis; missing data; multiple imputation; randomised controlled trials; sensitivity analysis
Mesh:
Year: 2018 PMID: 29573044 PMCID: PMC5947820 DOI: 10.1002/hec.3654
Source DB: PubMed Journal: Health Econ ISSN: 1057-9230 Impact factor: 3.046
Figure 1Studies selection flow diagram. CEA = cost‐effectiveness analyses; HTA = health technology assessment; RCT = randomised controlled trial
Characteristics of included studies (n = 52)
|
| % | |
|---|---|---|
| Median | (IQR) | |
|
| ||
| Publication year | ||
| 2013 | 14 | 27 |
| 2014 | 15 | 29 |
| 2015 | 23 | 44 |
| CEA time frame | ||
| 0–11 months | 22 | 42 |
| 12 months | 19 | 37 |
| ≥24 months | 11 | 21 |
| Follow‐up design | ||
| Continuous (time to event) | 4 | 8 |
| One follow‐up assessment | 11 | 21 |
| Repeated assessments | 37 | 71 |
| Effectiveness measure | ||
| QALY | 42 | 81 |
| Binary | 6 | 12 |
| Clinical scale score | 3 | 6 |
| Time to recovery | 1 | 2 |
|
| ||
| Report exact number of complete cases | 20 | 38 |
| Proportion of complete cases | 0.63 | (0.47–0.81) |
| Proportion complete effectiveness data ( | 0.73 | (0.55–0.86) |
| Proportion complete cost data ( | 0.79 | (0.67–0.92) |
| Differs between costs and effectiveness | ||
| Yes, more cost data missing | 3 | 6 |
| Yes, more effect data missing | 10 | 19 |
| No | 22 | 42 |
| No missing (<5%) | 5 | 10 |
| Unclear | 12 | 23 |
| Differs between arms | ||
| Yes | 10 | 19 |
| No | 32 | 62 |
| No missing (<5%) | 5 | 10 |
| Unclear | 5 | 10 |
Note. IQR = interquartile range; QALY = quality‐adjusted life year.
Proportion of trial participants with complete cost‐effectiveness data. An upper bound was used if exact number not reported.
More than 5% difference in the proportion of participants with complete cost or effectiveness data.
More than 5% difference in the proportion of complete cases between arms.
Figure 2Proportion of trial participants with complete data for the primary cost‐effectiveness analysis. Shown for cost‐effectiveness (n = 52), effectiveness (n = 47, unclear in 5 studies), and cost data (n = 40, unclear in 12 studies)
Methods for handling missing data in primary analysis (n = 47)
| Primary analysis method |
| % |
|---|---|---|
| Complete‐case analysis | 20 | 43 |
| Multiple imputation | 14 | 30 |
| Other—single methods | ||
| Inverse probability weighting | 1 | 2 |
| Bayesian model, missing data as unknown parameter | 1 | 2 |
| Other—ad hoc hybrid methods | 8 | 17 |
| Using a combination of | ||
| Mean imputation | 6 | |
| Regression imputation | 3 | |
| Inverse probability weighting | 2 | |
| Assuming failure when outcome missing | 2 | |
| Multiple imputation | 1 | |
| Last observation carried forward | 1 | |
| Unclear | 3 | 6 |
Ad hoc hybrid method = several approaches to missing data combined, for example, using mean imputation for missing individual resource use items and multiple imputation for fully incomplete observations.
Mean imputation = replacing missing values by the average across other participants.
Regression imputation = replace missing values by predicted value based on observed variables.
Inverse probability weighting = analysing complete data, weighted according to their modelled probability of being observed. These methods are presented in more details in other references (Baio & Leurent, 2016; Faria et al., 2014).
Approaches to missing data, by year, number of follow‐ups, and extent of missing data (n = 47)
| Primary analysis method | Reported a sensitivity analysis | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| CCA | MI | Other | Yes | No | ||||||
|
| % |
| % |
| % |
| % |
| % | |
| Publication year | ||||||||||
| 2013 ( | 6 | 46 | 3 | 23 | 4 | 31 | 5 | 38 | 8 | 62 |
| 2014 ( | 9 | 60 | 1 | 7 | 5 | 33 | 6 | 40 | 9 | 60 |
| 2015 ( | 5 | 26 | 10 | 53 | 4 | 21 | 11 | 58 | 8 | 42 |
| Number of follow‐up assessments | ||||||||||
| 1 ( | 7 | 70 | 1 | 10 | 2 | 20 | 3 | 30 | 7 | 70 |
| ≥2 ( | 13 | 36 | 13 | 36 | 10 | 28 | 18 | 50 | 18 | 50 |
| Proportion of complete cases | ||||||||||
| <50% ( | 4 | 27 | 6 | 40 | 5 | 33 | 8 | 53 | 7 | 47 |
| 50–75% ( | 10 | 56 | 4 | 22 | 4 | 22 | 9 | 50 | 9 | 50 |
| 75%–95% (n = 14) | 6 | 43 | 4 | 29 | 4 | 29 | 5 | 36 | 9 | 64 |
| Information missing | ||||||||||
| Similar ( | 13 | 59 | 6 | 27 | 3 | 14 | 10 | 45 | 12 | 55 |
| More cost missing ( | 1 | 33 | 2 | 67 | 0 | 0 | 2 | 67 | 1 | 33 |
| More effect missing ( | 4 | 40 | 2 | 20 | 4 | 40 | 6 | 60 | 4 | 40 |
Note. % = row percentages. CCA = complete‐case analysis; MI = multiple imputation.
Excluding one study with continuous follow‐up (n = 46).
For the five studies with less than 5% of incomplete cases, four used CCA and one an ad hoc hybrid method for their primary analysis. One of the five studies conducted a sensitivity analysis to missing data.
Excluding 12 studies where this was unclear (n = 35).
Sensitivity analysis, overall, and by primary analysis method (n = 47)
| None | Sensitivity analysis method | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| CCA | MI (MAR) | MNAR | Other | |||||||
|
| % |
| % |
| % |
| % |
| % | |
|
| ||||||||||
| Total ( | 25 | 53 | 11 | 23 | 9 | 19 | 2 | 4 | 5 | 11 |
|
| ||||||||||
| CCA (n = 20) | 10 | 50 | 0 | 0 | 8 | 40 | 0 | 0 | 2 | 10 |
| MI (n = 14) | 5 | 36 | 9 | 64 | 0 | 0 | 2 | 14 | 2 | 14 |
| Other (n = 13) | 10 | 77 | 2 | 15 | 1 | 8 | 0 | 0 | 1 | 8 |
Note. % = row percentages; CCA = complete‐case analysis; MAR = assuming data missing at random; MI = multiple imputation; MNAR = assuming data missing not at random. Total may be more than 100% as some studies conducted more than one sensitivity analysis.
Other methods used for sensitivity analysis include last observation carried forward (n = 1), regression imputation (n = 1), adjusting for baseline predictors of missingness (n = 1), imputing by average of observed values for that patient (n = 1), and an ad hoc hybrid method using multiple and mean imputation (n = 1).
Review of indicators based on recommendations criteria (n = 47)
| Criterion | Met | Not met | Unclear | |||
|---|---|---|---|---|---|---|
|
| % |
| % |
| % | |
|
| ||||||
| A1. Maximise response rate | 35 | 74 | 12 | 26 | 0 | 0 |
| A2. Alternative data sources | 10 | 21 | 37 | 79 | 0 | 0 |
| A3. Monitor completeness | 17 | 36 | 30 | 64 | 0 | 0 |
|
| ||||||
| B1. Assumption for primary analysis | 17 | 36 | 27 | 57 | 3 | 6 |
| B2. Appropriate primary method | 17 | 36 | 27 | 57 | 3 | 6 |
|
| ||||||
| C1. Discuss departures from the primary assumption | 0 | 0 | 47 | 100 | 0 | 0 |
| C2. Consider broad range of assumptions | 2 | 4 | 45 | 96 | 0 | 0 |
| C3. Method valid under these assumptions | 2 | 4 | 45 | 96 | 0 | 0 |
|
| ||||||
| D1. Missing data by endpoint, arm, and time point | 29 | 62 | 18 | 38 | 0 | 0 |
| D2. Discuss reasons for missing data | 16 | 34 | 31 | 66 | 0 | 0 |
| D3. Describe methods used and assumptions | 17 | 36 | 30 | 64 | 0 | 0 |
| D4. Conclusions in light of missing data | 1 | 2 | 46 | 98 | 0 | 0 |
See Figure 3 and Appendix B for definition of each criterion.
Report demonstrates evidence of having followed this recommendation. Not met if the recommendation was not followed or not mentioned. Unclear if some suggestions the criteria may have been met but information not clear enough. See Appendix B for detailed definitions and methodology used.
Figure 3Recommendations for improving handling of missing data in trial‐based cost‐effectiveness analysis. References: 1, Little et al., 2012; 2, Noble et al., 2012; 3, Faria et al., 2014; and 4, Carpenter and Kenward 2007 [Colour figure can be viewed at http://wileyonlinelibrary.com]
| Search | Query | Items found |
|---|---|---|
| 4 | Search (“health Technol assess”[journal]) AND (“2013/01/01”[date ‐ publication] : “2015/12/31”[date ‐ publication]) AND (“randomised”[title] OR “randomised”[title] OR “trial”[title]) AND (“economic”[title/abstract] OR “cost*”[title/abstract]) NOT (“pilot”[title] OR “feasibility”[title]) | 65 |
| 3 | Search (“Health Technol Assess”[Journal]) AND (“2013/01/01”[Date ‐ Publication] : “2015/12/31”[Date ‐ Publication]) AND (“randomised”[title] OR “randomized”[Title] OR “trial”[Title]) AND (“economic”[Title/Abstract] OR “cost*”[Title/Abstract]) | 74 |
| 2 | Search (“Health Technol Assess”[Journal]) AND (“2013/01/01”[Date ‐ Publication] : “2015/12/31”[Date ‐ Publication]) AND (“randomised”[Title] OR “randomized”[Title] OR “trial”[Title]) | 91 |
| 1 | Search (“Health Technol Assess”[Journal]) AND (“2013/01/01”[Date ‐ Publication] : “2015/12/31”[Date ‐ Publication]) | 236 |
| Indicator | Definition | Notes |
|---|---|---|
| Proportion of complete cases | Proportion of randomised participants for whom all data were available for the primary cost‐effectiveness analysis | If the number of complete‐cases was not clearly reported, we estimated an “upper bound,” from information, such as the proportion of participants with complete cost, or effect, data. See definition of primary analysis below. |
| Proportion complete effectiveness data | Proportion of randomised participants for whom all effectiveness data were Available for the primary cost‐effectiveness analysis | Same as above |
| Proportion complete cost data | Proportion of randomised participants for whom all cost data were available for the primary cost‐effectiveness analysis | Same as above |
| Report exact number of complete cases | Whether the number of participants with complete cost and effectiveness data was clearly reported. | |
| More missing costs or effectiveness | Whether the proportion of complete cases differ between cost and effectiveness variable. | Considered “similar” when the proportion of complete cases was within 5% of each other. |
| Primary analysis method | Methods used to address missing data in the primary (base case) cost‐effectiveness analysis | When multiple effectiveness measures, time‐frames, or cost perspectives were reported, without a base‐case clearly defined, we considered the analysis based on quality‐adjusted life years (QALYs) over the longest within‐trial follow‐up period, from the NHS and social services cost perceptive. |
| Conducted a sensitivity analysis to missing data | Report results under more than one approach for addressing missing data |
| Recommendation | Indicator definition | Examples “yes” | Examples “no” | Notes |
|---|---|---|---|---|
| A1. Maximise response rate (consider questionnaire design, mode of administration, reminders, incentives, participants' engagement, etc.) | Mention taking steps to maximise response rate | Reminder, incentives, home/hospital visit, multiple attempts, | Mention response was maximised for clinical outcome but not reported for cost‐effectiveness endpoints | Can be for overall trial data if implicit includes cost or effect data. Except if steps are clearly for non‐CE variables only (e.g., primary outcome only). |
| A2. Consider alternative data sources (e.g., routinely collected data) | Mention that considered missing data issues when choosing appropriate source, OR mention more than one source used for a CE data. | Use of electronic health records or administrative data, e.g., hospital episode statistics were used to supplement trial's data, for example, about hospital admissions post‐randomisation (which might be otherwise missing). | Using routine data as a primary source: e.g., resource use taken primarily from administrative/hospital records. | |
| A3. Monitor cost‐effectiveness data completeness while trial ongoing | Mentioned monitoring data completeness while trial ongoing. | Data managers checked inconsistent and missing data (if not clear “while trial ongoing” but mention monitoring probably fine). Mention taking new steps to reduce MD (e.g., incentive) as realised lots of MD after trial started. | Mention data checks for inconsistencies, but no mention of checking missing data. | Can be for overall trial data. Except if monitoring clearly for non‐CE variables only (e.g., primary outcome only). |
| B1. Formulate realistic and accessible missing data assumption for the primary analysis (typically, but not necessarily, a form of the missing at random assumption) | Primary (base‐case) CEA based on reasonable missing data assumptions. (likely MAR, or alternative if well justified). | – Used MI for primary analysis ‐ well justified and clear alternative | – Hybrid method, except if clearly explain and justify underlying assumptions | |
| B2. Use appropriate method valid under that assumption (typically, but not necessarily, multiple imputation or maximum likelihood) | Use appropriate analysis method. | – MI for primary analysis ‐Bayesian under MAR ‐ well justified and clear alternative | – Use unadjusted CCA when reporting data are MAR. | |
| C1. Discuss with clinicians and investigators to formulate plausible departures from the primary missing data assumption | Conducted MNAR SA + mention elicitation. | Did not conduct MNAR SA | ||
| C2. Consider a broad range of assumptions, including missing not at random mechanisms | Conducted MNAR SA | Did not conduct MNAR SA | ||
| C3. Use appropriate method valid under these assumptions (typically, but not necessarily, pattern‐mixture models or reference‐based approach) | Conducted MNAR SA, and used an appropriate method (PMM, etc.). | Did not conduct MNAR SA | ||
| D1. Report number of participants with cost and outcome data, by arm and time‐point | Report number (or %) of complete or missing data. Split at least by effectiveness vs. cost, time point (when applicable), and arm | Reported missing data by endpoint and arm, but not by time point. | Do not have to be all at the same time (split by endpoint + time + arm), can be three separate table/texts. | |
| D2. Report possible reasons for non‐response, and baseline predictors of missing values | Mention something about main reason for the missing data, OR Explore factors associated with it. | Comment on why missing data (e.g., “because patients were too ill”). Or explore baseline factors associated with missingness | No mention of reasons for MD in the CE section. | Have to be specific to the CE missing data, or clearly mentioning something like “reasons for MD are discussed in clinical analysis section …” |
| D3. Describe methods used, and underlying missing data assumptions | Clearly state the method used to address missing data, AND the underlying assumption. | No report of missing data assumption or method used | ||
| Draw overall conclusion in light of the different results and the plausibility of the respective assumptions | Conduct sensitivity analyses, and interpret results appropriately. | Did MNAR SA and appropriate conclusion. |
– Did not conduct sensitivity analyses |