The Kaplan–Meier method for estimating and comparing proportions in a randomized controlled trial with dropouts

ABSTRACT

We propose a method for estimating and comparing proportions of study participants who reached an event of interest during a randomized controlled trial. Standard methods for estimating this proportion include the intent-to-treat method, which counts the number who reached the event of interest divided by the total number of participants, and the completers-only method, which counts the number who reached the event only among those who completed the entire study. When participants drop out of the study early, however, these methods will either be biased or inefficient. We propose to use the Kaplan–Meier method from survival analysis to estimate the proportion of interest in this non-survival setting. We show through extensive simulation studies that the Kaplan–Meier method has less bias and is more efficient than the standard methods. We demonstrate the performance of all methods for estimating proportions in one sample and for comparing proportions across two samples. Finally, we apply the proposed method to a data-set for estimating and comparing proportions of patients who achieved treatment response during a Parkinson's disease trial for the treatment of impulse control disorders.

KEYWORDS:

• Kaplan–Meier
• proportion
• dropout
• clinical trial
• survival

Acknowledgments

We thank Daniel Weintraub, MD, and the naltrexone trial study team for providing the data used for illustration in this study.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Dr. Xie received support from NIH [grant number R01-NS102324], [grant number AG10124], [grant number AG17586], [grant number NS053488] to conduct this research.

Notes on contributors

Jarcy Zee

Dr Jarcy Zee is a research scientist in biostatistics at Arbor Research Collaborative for Health, a non-profit health research organization. Her methodological research interests are in survival analysis and measurement error, and she conducts applied clinical research in kidney disease, organ transplant, mental health, and women's health. Dr Zee is an awardee of the Nephrotic Syndrome Study Network (NEPTUNE) Career Development Fellowship to research statistical methods for analysing glomerular disease morphology data. She is also an awardee of a Chronic Kidney Disease Biomarkers Consortium Pilot and Feasibility programme study to research statistical methods for predicting time-to-event outcomes with time-varying and high-dimensional biomarkers. Dr Zee received her PhD degree in biostatistics from the University of Pennsylvania.

Sharon X. Xie

Dr Sharon X. Xie is a professor of biostatistics at the University of Pennsylvania. She is currently the principal investigator of a National Institute of Health (NIH) funded R01 grant, which aims to develop novel statistical methods for assessing dementia risk in Parkinson's disease and other neurodegenerative diseases. She is also the principal investigator of the biostatistics and data management core for two NIH-funded neurodegenerative disease research centres: the Alzheimer's Disease Core Center and Morris K. Udall Parkinson's Disease Research Center of Excellence. Dr Xie develops new statistical methods for survival analysis, measurement error problems, missing data, longitudinal analysis, and receiver operating characteristic (ROC) analysis. She also investigates various scientific problems in neurodegenerative diseases and other biomedical areas. Dr Xie received her PhD degree in biostatistics from the University of Washington.