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Utility of the Mean Cumulative Function in the Analysis of Fall Events

¹ Department of Health Care and Epidemiology, ² Centre for Clinical Epidemiology and Evaluation, Vancouver Coastal Health Research Institute, ³ Division of Geriatric Medicine, Faculty of Medicine, and ⁴ Department of Family Practice, Faculty of Medicine, University of British Columbia, Vancouver, British Columbia.

Address correspondence to Meghan G. Donaldson, MSc, PhD (C), University of British Columbia, Health Care and Epidemiology, 713-828 West 10th Avenue, Vancouver, BC V5Z 1L8, Canada. E-mail: meghangd{at}interchange.ubc.ca

Background. Falls are the most common cause of injury among elderly people; half of those people fall recurrently. The objective of these simulation studies was to describe the Mean Cumulative Function (MCF) and to evaluate the utility of the MCF in detecting differences between groups experiencing different patterns of event intensities.

Methods. We specified 250 participants per group with a maximum follow-up time of 365 days. A participant could experience 0, 1, 2, 3, or 4 falls. In the baseline experiment, Groups A and B had an average intensity of 60 and 90 days to the first fall event. These event intensities remained constant for events 2–4. Group C represents a short term "strong" initial impact of the intervention modeled for falls 1 and 2, with an average intensity of one fall per 117 days; however, the intervention wanes to "moderate" for falls 3 and 4 with an average intensity of one fall per 90 days. Group D represents a long-term "strong" impact of the intervention modeled by an average intensity of one fall per 117 days for all subsequent events.

Results. The MCF was able to detect differences between groups that had varying intensities of subsequent falls. In Group A, all participants experienced at least one fall, whereas Groups B, C, and D had 4, 9, and 15 participants, respectively, who did not experience any falls. The proportion of participants who had 4 falls declined from 84% to 40% in Groups A and D, respectively. When Group A was compared to Group D, the MCF difference detected the prevention of, on average, one fall per person within 175 days.

Discussion. A novel instrument for this field of clinical research—the MCF—allows investigators to compare the average number of falls per participant when the intervention reduces the intensity of subsequent falls.