Falls: In this study, a fall is defined as unintentionally coming to rest on the ground or at some other lower level, not as a result of a major intrinsic event (e.g., stroke or syncope) or overwhelming hazard . Falls will be assessed retrospectively at baseline through 6-month recall to characterize the sample and check for equality of randomization. Falls will be assessed prospectively during the study by monthly reports completed through a web portal or returned by postal and/or electronic mail, methods proven successful in our 2 previous studies and by others, including Dr. Li [3, 4, 22, 58]. In our recently completed observation study of BCS (N=58), we obtained 98% of monthly fall reports over 6 months . If a participant indicates a fall she will then be asked to detail any injury that resulted from each fall. A fall will be considered “injurious” if it results in fractures, head injuries, sprains, bruises, scrapes, or serious joint injuries, or if the participant seeks medical care . Of interest in the study are the number of falls, the number of injurious falls, and medical care resulting from a fall during the intervention period.
Muscle strength. The 1-repetition maximum (1-RM) for leg press will be used to determine changes in lower extremity muscle strength. The 1-RM test is a safe and effective means of evaluating strength, even in geriatric populations that have never lifted weights before [59, 60], in BCS who have strength trained [61–63], and in cancer survivors with lower-extremity lymphedema . We have evaluated maximal strength using the 1-RM technique in 3 studies of BCS (age range: 35–89 yrs) with no adverse events. The 1-RM test will be conducted according to established protocols . We will also consider changes in functional leg strength using the timed chair stand test (see PPB) so that strength changes can also be interpreted in a clinical context .
Postural Stability. Computerized dynamic posturography (CDP; Clinical Research System, Neurocom Intl, Inc.) measures postural stability and is used to identify objective patterns of balance problems consistent with neuropathy, vestibular loss, and CNS disorders that contribute to fall risk . The test protocol used in this study is the sensory organization test (SOT), which systematically removes or alters useful information to the patient’s vision or support surface to create sensory conflict situations. These conditions isolate vestibular control of balance, as well as stress adaptive sensory reweighitng by the central nervous system. Equilibrium scores are determined for each condition based on maximum forward-backward postural sway. The weighted average of the scores of all sensory conditions characterizes the overall level of performance as a composite equilibrium score. Sensory ratios are calculated by comparing individual equilibrium scores in specific conditions to identify impairments of individual sensory systems including the vestibular, somatosensory, and visual systems. Equilibrium scores and sensory ratios range from 0–100, where 100 = perfect stability and 0 = an inability to maintain balance and a fall. In this study, we are interested in the composite equilibrium score and also the somatosensory and vestibular sensory ratios, since the latter may show differential effects of the 2 interventions on physiologic systems affected by cancer chemotherapy that impair stability (i.e., neuropathy and vestibular impairment). Test-retest reliability of composite equilibrium scores ranges from 0.72 - 0.93 .
Physical Functioning will be measured by the Physical Performance Battery (PPB) . The PPB consists of 3 timed performance tests: 5 repeated chair stands, standing balance, and gait speed over 4 meters. We will consider the time scores of the chair stand test and gait speed separately to examine them as clinical measures of strength and postural stability that might mediate fall risk for Aim 2 (see Analysis Plan). Though not a primary aim of our study, the transformed PPB score can be used to evaluate the effect of the intervention on overall physical function, which would be an important additional benefit of the exercise programs. In older adults, low scores on the PPB are significantly associated with subsequent mobility disability, ADL disability, hospitalization, admission to a nursing home, and mortality [68–71]. The PPB is reliable, sensitive to change  and has established norms. Higher scores indicate better physical functioning. Reliability of the PPB is high with intraclass correlation coefficients ranging from 0.88-0.92 for individual tests and the composite score .
Flexibility may improve in the control group, so we will measure flexibility in all groups using the standardized Chair Sit and Reach Test for lower body flexibility and Back Scratch Test for upper body flexibility . These tests are designed for older adults with demonstrated validity and reliability in older adults (test-retest 0.95-0.96) .
Demographic information, including age, education, income, and others will be measured at baseline by a questionnaire developed for this study. In addition, stage of prior cancer diagnosis, type and dates of cancer treatments, additional adjuvant treatments (i.e., hormone manipulation therapy for breast cancer), presence of other chronic conditions, current medications and health habits will be measured. Clinical measures of weight and height will be made. Updated information will be collected at subsequent visits.
Presence of chronic medical conditions that affect physical functioning will be measured by the Functional Comorbidity Index, which is a self- administered 18-item scale and has stronger associations with SF-36 physical function (R =0.29) than other comorbidity indices . Indivdual item responses from this questionnaire will also be used to inform the exercise instructor about medical conditions that might affect participants’ physical ability to exercise.
Fear of falling may impact a participant’s confidence that she can safely engage in a study exercise program. This factor may also change across the intervention. Though this is not a major outcome in this study, it may provide important information about the population and intervention. The Survey of Activities and Fear of Falling in the Elderly (SAFFE)  has 11 items representing activities of daily living associated with fear of falling, mobility, and social activities. The SAFFE score is the average of item responses, with higher scores indicating greater fear of falling and has high internal consistency (intra-class correlation coefficient: 0.91) .
Exercise outside the exercise intervention could affect the fall and function outcomes of the study. The CHAMPS Physical Activity Questionnaire for Older Adults, a valid and reliable instrument , will be used to measure outside physical activity across the course of the study.
Adherence (% of prescribed sessions completed) is tracked from attendance logs recorded by the exercise instructor. Adherence data is used to describe the dose of exercise received by participants. It is expected that women will occasionally miss classes due to travel, illness, or other reasons. However, it is important to count missed classes to get an accurate estimate of received (exercise) dose and to generalize our findings.
Data analysis plan
The univariate distribution of each variable will be examined to check for departure from normality and outliers . For each analysis described below, each subject will be analyzed according to the group to which she was randomly assigned and regardless of missing data (i.e., intention to treat). Medical treatment changes and cancer recurrence during the study will be tracked and used to describe the sample and document why participants may not have completed the study. In the unlikely event of a large subgroup, these data could be used for exploratory sub-group analysis to suggest directions for future research. Age, cancer type (breast or other), and time since cancer treatment completion, will be included as covariates in all analyses.
A negative binomial regression model will be used to test the efficacy of tai chi and strength training (versus stretching control) in reducing the total number of falls per participant that occur during the intervention period (from baseline to 6 months). Negative binomial regression is preferred over Poisson regression for modeling the count data because of the overdispersion that is common with actual research data [40, 77]. Intervention type will be entered into the model as 2 dummy vectors, with the reference group being the control group. Fall rates for participants who drop out of the study will be adjusted by accounting for their exposure time within the study timeframe. A significant incidence rate ratio (IRR) less than 1.0 for the dummy vector representing tai chi and/or strength training would provide support for the hypothesis that the respective intervention reduced the rate of falls compared to the control group (controlling for covariates).
Muscle strength and postural stability will be tested as potential mediators of the relationship between the exercise interventions and falls. We propose that strength and stability will mediate the effect of each intervention on falls because both constructs will be affected by each intervention and are major risk factors for falls. Though we do expect stronger effects of strength training on strength and of tai chi on stability, how each program specifically reduces falls is uncertain, particularly in women treated for cancer. Mediation analyses will be conducted in a structural equation modeling framework (SEM) implemented in Mplus 7.0. A manifest model will be tested with dummy vectors representing tai chi and strength training as exogenous variables, strength and stability (difference score from baseline to 6 months) as endogenous variables (mediators), and number of falls that occurred from baseline to the end of the intervention as an endogenous variable (outcome). The SEM framework allows for the assessment of indirect (mediating) effects with mixed distributional models, in this case Guassian for both mediators and negative binomial for the outcome. Support for mediation will be determined by assessing the magnitude and significance of the indirect effects (standard errors calculated with the multivariate delta method ) from the treatment variables to number of falls through changes in strength and stability. Additional mediation analyses will be conducted replacing composite SOT score as the measure of stability with SOM and VEST scores, and replacing maximal knee extensor force (Nm) and composite SOT with clinical measures of strength (PPB chair stand) and dynamic stability (gait speed).
The persistent effects of the intervention on fall outcomes after formal training stops will be evaluated with a piecewise intent-to-treat negative binomial regression model with the change point occurring at 6 months. Of particular interest is whether the IRRs for the treatment groups differ after the change point. In addition, the moderating effect of participation in an exercise program following the end of the intervention will be examined. Specifically, exercise programs engaged in for least 50% of the follow-up period will be categorized and dummy coded (e.g., infrequent participation versus regular participation). These variables will be entered into a negative binomial regression model along with the product of these dummy vectors and treatment (i.e., interaction effects). Significant interaction effects indicate that continued participation modifies the effect of the intervention on fall rate. With this analytic approach we will be able to determine whether the benefits of the exercise interventions persist with and without continued participation in an exercise program, and whether control participants who begin programs similar to the intervention programs show improvements on the fall rate outcome.