What was the research about?
Researchers can use data from health registries or electronic health records to compare two or more treatments. Registries store data about patients with a specific health problem. These data include how well those patients respond to treatments and information about patient traits, such as age, weight, or blood pressure. But sometimes data about patient traits are missing.
Missing data about patient traits can lead to incorrect study results, especially when traits change over time. For example, weight can change over time, and the patient may not report their weight at some points along the way. Researchers use statistical methods to fill in these missing data.
In this study, the research team compared a new statistical method to fill in missing data with traditional methods. Traditional methods remove patients with missing data or fill in each missing number with a single estimate. The new method creates multiple possible estimates to fill in each missing number.
What were the results?
The new method worked better than traditional methods. Patients with certain traits were more likely to have missing data. Accounting for such traits in the analysis made the new method work even better.
What did the research team do?
The research team first developed computer software, which created test data that mimicked a study about patients living with HIV. The data included patient traits that change over time and are often missing, such as body mass index, a measure of weight and height. The team used the test data to compare the new method of filling in missing data with traditional methods.
What were the limits of the study?
When the research team compared the methods, they looked at the test data only in certain situations. For example, because patients with certain traits were more likely to have missing data, they compared results with and without those patients. Findings may differ if the team looked at the test data in other situations.
Future research could compare methods for handling missing data in other situations.
How can people use the results?
Researchers can use the new method to get results that are more accurate in studies with missing data.
To evaluate statistical approaches for handling missing data in longitudinal studies of comparative effectiveness research by (1) developing software packages to generate realistically complex data and (2) comparing multiple imputation (MI)-based strategies with commonly used approaches to analyzing data with missing time-varying covariates
|Data Sources and Data Sets||Simulated data that resemble the complexity of an empirical study to identify antiretroviral therapies associated with increased risk of cardiovascular disease among patients with HIV|
|Analytic Approach||Simulations were conducted using software packages developed by the research team to examine the following approaches: MI, complete-case analysis, and 3 single imputation methods including mean imputation, last value carried forward, and imputation using missing indicators|
|Bias, average standard error, coverage probability, relative mean squared error|
In longitudinal observational data sets, missing data can compromise analyses and bias results. They also pose a unique challenge in that longitudinal studies induce a correlated or clustered data structure. Traditional methods for handling missing data include complete-case analysis, which excludes patients with missing data from the analysis, and single imputation methods, which substitute each missing value with a single value. The MI method generates multiple data sets with imputed values and combines analysis results from these data sets.
Few studies have examined how well MI performs compared with traditional methods in longitudinal studies with missing time-varying covariates and a right-censored outcome, where records are correlated within subjects over time. Time-varying covariates are variables that may change over time, such as a patient’s medical regimens. A longitudinal study outcome is right-censored when the outcome event, such as death, does not occur for all individuals within the study period.
The research team developed two software packages in the R software, called SimTimeVar and SimulateCER, to simulate comparative effectiveness studies with time-varying covariates. They used a software package called PermAlgo to simulate the right-censored outcome. In addition, the team generated auxiliary variables that can help impute the missing data in the MI process but are not part of the main analysis. The software packages generated data that mimic an empirical HIV study. Then, based on the simulated data, the team compared the performance of the MI-based methods with traditional methods, including complete-case analysis and single imputation methods. The team examined the methods under different scenarios, including with and without auxiliary variables, with and without missing values for the covariate of interest, and across missing data mechanisms with different complexity levels.
Software development. The software packages successfully created data sets with right-censored outcomes as well as time-varying and static covariates.
Comparison of methods. For time-varying covariates where the covariate of interest has no missing values, MI outperformed complete-case analysis and single imputation methods. By including auxiliary variables, MI methods performed well even in complex missing-at-random and not-missing-at-random conditions.
For time-varying covariates where the covariate of interest has missing values, the last-value-carried-forward method outperformed other methods if the outcome did not have a strong increasing or decreasing pattern over time. As the missing data mechanism became more complex, the bias increased across all methods. In general, MI outperformed other methods, especially if it included an auxiliary variable strongly related to the missing data mechanism.
The research team used simulated data sets to explore a variety of realistic scenarios. However, results may not generalize to scenarios not examined in this study. The team did not evaluate MI methods that accounted for clustered data structures because of computational limitations.
Conclusions and Relevance
The MI method was advantageous under most scenarios and could enable more robust and valid results in analyses of longitudinal studies with missing time-varying covariates. Including auxiliary variables, especially those related to the missing data mechanism, could greatly improve the performance of MI.
Future Research Needs
Future research could evaluate the MI method under other simulation scenarios. Additional research could also develop software to implement MI methods that account for clustered data structures in complex comparative effectiveness studies.
Final Research Report
View this project's final research report.
Related Journal Citations
Peer review of PCORI-funded research helps make sure the report presents complete, balanced, and useful information about the research. It also assesses how the project addressed PCORI’s Methodology Standards. During peer review, experts read a draft report of the research and provide comments about the report. These experts may include a scientist focused on the research topic, a specialist in research methods, a patient or caregiver, and a healthcare professional. These reviewers cannot have conflicts of interest with the study.
The peer reviewers point out where the draft report may need revision. For example, they may suggest ways to improve descriptions of the conduct of the study or to clarify the connection between results and conclusions. Sometimes, awardees revise their draft reports twice or more to address all of the reviewers’ comments.
Peer reviewers commented, and the researchers made changes or provided responses. The comments and responses included the following:
- Reviewers requested additional information about the missingness models, simulations, and model assumptions. The reviewers noted that it was hard to keep track of the specifics of each simulation study and the results obtained. The researchers added an appendix including a table that summarizes the three main simulation studies, their assumptions, the methods evaluated, and the findings.
- Reviewers asked for additional details about the scenarios used to test the model simulations, to help readers better understand the limitations to the generalizability of these models. The researchers responded by adding discussion of the proportion of missing records and the missing data mechanism. However, they disagreed with the reviewers’ contention that the discrepancies between simulated and observed data limited the generalizability of their findings regarding performance of missing data methods.
- Reviewers noted that the simulations of time-dependent categorical variables did not appear to perform well and asked for additional discussion of the impact of this poor performance on conclusions that could be made from these simulations. The researchers acknowledged that the performance of the simulation tool was not optimal in generating covariates but did not consider this an important issue because the simulation of survival times was excellent. They also noted excellent recovery of true parameter estimates of the relationship between the time-dependent covariates and outcome, which are critical to gauging how well missing data methods handle time-varying covariates.
Conflict of Interest Disclosures
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