In medical research, the Kaplan–Meier (KM) estimator has long been a fundamental tool for estimating survival functions from time-to-event data. It has proven invaluable, particularly in clinical trials and epidemiological studies, where it allows researchers to assess the impact of various interventions on patient outcomes. However, the utility of KM estimation is inherently limited by certain conditions, primarily its dependence on binary event data and its inability to capture the nuanced trajectory of ordinal outcomes. These limitations have spurred the development of a novel statistical approach known as Weighted Trajectory Analysis (WTA). WTA, as introduced by Dr. Utkarsh Chauhan, Dr. Kaiqiong Zhao, Dr. John Walker, and Professor John R. Mackey from the University of Alberta in a recent publication in the BioMedInformatics Journal, seeks to address the shortcomings of KM estimation. It does so by offering a method that combines the simplicity and practicality of KM estimation with the capability to evaluate ordinal variables and bidirectional outcomes. In this editorial, we delve into the intricacies of WTA, its methodology, theoretical underpinnings, and practical applications.
Before delving into the specifics of WTA, it is crucial to understand the limitations of the conventional KM estimator. KM estimation is well-suited for binary event data, where the event of interest is dichotomous, such as life or death. However, when dealing with ordinal outcomes, such as toxicity grades or disease severity stages, KM estimation faces several challenges. First, KM estimation necessitates that the event of interest be binary in nature or coded into binary form (0 for non-occurrence, 1 for occurrence). This poses a significant challenge when dealing with ordinal outcomes, as it often requires the arbitrary definition of a threshold to classify events, leading to information loss and potential inaccuracies. Secondly, KM estimation inherently assumes that event occurrence results in a drop in the KM curve. This simplifies the analysis but fails to account for conditions that can both improve and worsen over time, such as patient responses to treatments that initially alleviate symptoms but later prove ineffective. Thirdly, Once a patient experiences the event of interest, they are typically excluded from further analysis. This exclusion may not be suitable for studying conditions with fluctuating severity.
The authors developed the WTA to overcome these limitations and provide a more comprehensive analytical framework for clinical research. WTA redefines events in terms of changes in ordinal scores rather than relying on binary coding. This allows for the analysis of variables with multiple severity levels without the need for arbitrary thresholding. Unlike KM estimation, WTA can capture the nuanced trajectory of conditions that can both improve and worsen over time, making it well-suited for assessing the effects of interventions that may have variable impacts during treatment. WTA permits the continued analysis of participants even after changes in the variable of interest, which is crucial for understanding the long-term effects of interventions.
To determine statistical significance in WTA, the researchers developed “weighted” logrank test. This test accounts for the novel features of WTA and ensures robust hypothesis testing. The methodology of WTA builds upon the principles of Kaplan–Meier analysis but introduces several innovative modifications. It supports the analysis of ordinal variables by redefining events based on changes in disease scores, thus eliminating the need for binary coding. Instead of plotting probabilities, WTA presents trajectory plots that track health status for different treatment arms over time. To ensure statistical validity, WTA employs a modified version of Peto et al.’s logrank test, which may be conservative in smaller trials but approaches a more conventional significance level as trial size increases. This computational approach is resource-intensive but maintains precision and accuracy regardless of trial size.
The authors demonstrated the WTA’s practicality and effectiveness through two randomized clinical trial simulation studies. The first study focused on chemotherapy toxicity, an example where ordinal outcomes ranged from one to five (shifted to zero to four). WTA consistently exhibited greater sensitivity and power compared to KM estimation, often requiring fewer patients to achieve similar statistical power. The second study delved into schizophrenia disease course, a more complex scenario with ordinal outcomes ranging from zero to six. Again, WTA showcased superior sensitivity and power, outperforming the Generalized Estimating Equations (GEE) method. Furthermore, they applied WTA to real-world clinical trial data with promising results. In one application, it assessed time-dependent toxicity grades in melanoma patients undergoing different immunotherapy regimens, revealing a more nuanced understanding of treatment-related toxicities. In another application, WTA re-evaluated a phase III registration trial for an anti-angiogenic drug in metastatic breast cancer, providing a comprehensive view of patient outcomes.
Weighted Trajectory Analysis offers numerous advantages, including its ability to capture detailed trajectory outcomes, increased power, and the mapping of exacerbation and improvement in ordinal outcomes. These strengths are built upon the foundations of Kaplan–Meier analysis, including the ability to censor patients and compare treatment arms using a simple hypothesis test. Importantly, WTA-dependent trial design can substantially reduce sample size requirements, making phase III clinical trials more practical and cost-effective.
However, it is essential to acknowledge the limitations of WTA. Notably, it does not facilitate Cox regression analysis or generate hazard ratios. WTA is a novel method and lacks an established clinical or regulatory track record, necessitating further evaluation and validation. Additionally, WTA relies on the assumption of non-informative censoring, prompting the exploration of alternative censoring approaches, such as inverse-probability-of-censoring weighting (IPCW). Finally, WTA’s use of direct numerical weights assumes that the change between adjacent ordinal severities is equally important, which may not always hold true. Future research will explore nonlinear scoring systems and alternative statistical methods to address these issues.
In conclusion, Weighted Trajectory Analysis represents a significant advancement in the field of clinical research and statistical analysis. Its ability to handle ordinal outcomes, track trajectories, and provide continued analysis of participants makes it a powerful tool for assessing the effects of interventions. While it is not without limitations, the promise it holds for reducing the cost, duration, and risk of type II errors in phase III clinical trials cannot be understated. As WTA continues to evolve and gain traction, it may well become a standard tool in the arsenal of biostatisticians and researchers seeking a more comprehensive understanding of complex clinical datasets.
Utkarsh Chauhan, Kaiqiong Zhao, John Walker, John R. Mackey. Weighted Trajectory Analysis and Application to Clinical Outcome Assessment. BioMedInformatics, 2023; 3 (4): 829 DOI: 10.3390/biomedinformatics3040052