Abstract
Purpose
A joint modeling approach is recommended for analysis of longitudinal health-related quality of life (HRQoL) data in the presence of potentially informative dropouts. However, the linear mixed model modeling the longitudinal HRQoL outcome in a joint model often assumes a linear trajectory over time, an oversimplification that can lead to incorrect results. Our aim was to demonstrate that a more flexible model gives more reliable and complete results without complicating their interpretation.
Methods
Five dimensions of HRQoL in patients with esophageal cancer from the randomized clinical trial PRODIGE 5/ACCORD 17 were analyzed. Joint models assuming linear or spline-based HRQoL trajectories were applied and compared in terms of interpretation of results, graphical representation, and goodness of fit.
Results
Spline-based models allowed arm-by-time interaction effects to be highlighted and led to a more precise and consistent representation of the HRQoL over time; this was supported by the martingale residuals and the Akaike information criterion.
Conclusion
Linear relationships between continuous outcomes (such as HRQoL scores) and time are usually the default choice. However, the functional form turns out to be important by affecting both the validity of the model and the statistical significance.
Trial registration
This study is registered with ClinicalTrials.gov, number NCT00861094.
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Data availability
The dataset from the PRODIGE 5/ACCORD 17 clinical trial is not publicly available due to confidentiality requirements. Data are however available from the main coordinator, Pr. Thierry Conroy, upon reasonable request, and with permissions of the study sponsor UNICANCER R&D.
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Acknowledgements
We thank the editor for his thoughtful comments and constructive suggestions.
Funding
This work was supported by the “Ligue nationale contre le cancer” (“Projet de Recherche en Epidémiologie Ligue” 2019) and the “SIRIC Montpellier Cancer” (Grant INCa_Inserm_DGOS_12553).
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UNICANCER R&D, the sponsor of the PRODIGE 5/ACCORD 17 trial (ClinicalTrials.gov Identifier: NCT00861094), provided permission for the data base access.
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Informed consent was obtained from all individual participants included in the study. Patient consent was not required for this study as we performed a secondary analysis on existing data.
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Supplementary Information
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11136_2022_3252_MOESM1_ESM.pdf
Supplementary file1 (PDF 3799 KB) Figure S1 Diagnostic plots for the linear (on the left) and the spline-based (on the right) joint models on global health status. Description is given from top to bottom. For the longitudinal outcome submodel: the observed standardized marginal and subject-specific residuals (black points) with their corresponding multiply imputed residuals (gray points) (for 10 imputations). The solid red line represents a LOESS (locally estimated scatterplot smoothing) fit on the observed marginal/subject-specific residuals and the dashed line a weighted LOESS fit based on all the residuals (i.e., marginal or subject-specific). For the survival submodel; first, the martingale residuals against the subject-specific fitted value for the longitudinal outcome and the fit of the LOESS smoother (gray line); second, the Kaplan-Meier estimates with confidence intervals of the Cox-Snell residuals (black line) and the survival function of the unit exponential distribution (gray line)
11136_2022_3252_MOESM2_ESM.pdf
Supplementary file2 (PDF 3399 KB) Figure S2 Diagnostic plots for the linear (on the left) and the spline-based (on the right) joint models on physical functioning. Description is given from top to bottom. For the longitudinal outcome submodel: the observed standardized marginal and subject-specific residuals (black points) with their corresponding multiply imputed residuals (gray points) (for 10 imputations). The solid red line represents a LOESS (locally estimated scatterplot smoothing) fit on the observed marginal/subject-specific residuals and the dashed line a weighted LOESS fit based on all the residuals (i.e., marginal or subject-specific). For the survival submodel; first, the martingale residuals against the subject-specific fitted value for the longitudinal outcome and the fit of the LOESS smoother (gray line); second, the Kaplan-Meier estimates with confidence intervals of the Cox-Snell residuals (black line) and the survival function of the unit exponential distribution (gray line)
11136_2022_3252_MOESM3_ESM.pdf
Supplementary file3 (PDF 4028 KB) Figure S3 Diagnostic plots for the linear (on the left) and the spline-based (on the right) joint models on fatigue. Description is given from top to bottom. For the longitudinal outcome submodel: the observed standardized marginal and subject-specific residuals (black points) with their corresponding multiply imputed residuals (gray points) (for 10 imputations). The solid red line represents a LOESS (locally estimated scatterplot smoothing) fit on the observed marginal/subject-specific residuals and the dashed line a weighted LOESS fit based on all the residuals (i.e., marginal or subject-specific). For the survival submodel; first, the martingale residuals against the subject-specific fitted value for the longitudinal outcome and the fit of the LOESS smoother (gray line); second, the Kaplan-Meier estimates with confidence intervals of the Cox-Snell residuals (black line) and the survival function of the unit exponential distribution (gray line)
11136_2022_3252_MOESM4_ESM.pdf
Supplementary file4 (PDF 3380 KB) Figure S4 Diagnostic plots for the linear (on the left) and the spline-based (on the right) joint models on pain. Description is given from top to bottom. For the longitudinal outcome submodel: the observed standardized marginal and subject-specific residuals (black points) with their corresponding multiply imputed residuals (gray points) (for 10 imputations). The solid red line represents a LOESS (locally estimated scatterplot smoothing) fit on the observed marginal/subject-specific residuals and the dashed line a weighted LOESS fit based on all the residuals (i.e., marginal or subject-specific). For the survival submodel; first, the martingale residuals against the subject-specific fitted value for the longitudinal outcome and the fit of the LOESS smoother (gray line); second, the Kaplan-Meier estimates with confidence intervals of the Cox-Snell residuals (black line) and the survival function of the unit exponential distribution (gray line)
11136_2022_3252_MOESM5_ESM.pdf
Supplementary file5 (PDF 2639 KB) Figure S5 Diagnostic plots for the linear (on the left) and the spline-based (on the right) joint models on dysphagia. Description is given from top to bottom. For the longitudinal outcome submodel: the observed standardized marginal and subject-specific residuals (black points) with their corresponding multiply imputed residuals (gray points) (for 10 imputations). The solid red line represents a LOESS (locally estimated scatterplot smoothing) fit on the observed marginal/subject-specific residuals and the dashed line a weighted LOESS fit based on all the residuals (i.e., marginal or subject-specific). For the survival submodel; first, the martingale residuals against the subject-specific fitted value for the longitudinal outcome and the fit of the LOESS smoother (gray line); second, the Kaplan-Meier estimates with confidence intervals of the Cox-Snell residuals (black line) and the survival function of the unit exponential distribution (gray line)
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Winter, A., Cuer, B., Conroy, T. et al. Flexible modeling of longitudinal health-related quality of life data accounting for informative dropout in a cancer clinical trial. Qual Life Res 32, 669–679 (2023). https://doi.org/10.1007/s11136-022-03252-6
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DOI: https://doi.org/10.1007/s11136-022-03252-6