Journal of the American Geriatrics Society·Thompson et al.·Meta-Analysis
We appreciate the opportunity to respond to the thoughtful points raised by Professors Al Hamad and Sathian in their letter entitled, “Limitations in the additive risk model linking visual impairment and poor mobility to mortality.” As we explained in our brief report [1], the proportional hazards model which tested for interaction did not detect a significant synergistic interaction on the log hazards scale between initial overall visual impairment and impaired mobility (assessed utilizing the short physical performance battery [SPPB]) for the outcome of mortality (aHR 1.47, 95% CI [1.29, 1.67] in those with SPPB ≥ 9; aHR 1.47, 95% CI [1.00, 2.17] in those with SPPB < 9; p = 0.98). Thus, the factors in this particular model remained additive on the log hazards scale, though were not synergistic (i.e., did not have an effect more than expected by summing their individual effects). Although Al Hamad and Sathian reference another study by Xu et al. (2025) which applied mediation analysis to examine the association between self-reported visual difficulty at baseline (no visual difficulty vs. visual difficulty) and self-reported recurrent falls in the last year on mortality in the National Health and Aging Trends Study [2], we do not agree that this means our findings are contradictory with theirs, as a performance-based measure such as low SPPB score is not the same term as self-reported recurrent falls. Self-reported visual difficulty also has been shown to be poorly predictive of performance-based visual impairment using eye charts and should not be used to substitute for an objective measure [3]. Thus, we had different measurements, objective versus subjective, and were not examining the same factors related to physical function. Moreover, we tested for interaction. We intentionally did not test for mediation because vision was only evaluated at a single time point in the Health, Aging and Body Composition (Health ABC) study, so it was our view that the use of structural equations models would have been suboptimal. There are also a myriad of criticisms in the literature about the assumptions that must be met to assume causality when applying mediation analysis in any observational, longitudinal study—for example, no unmeasured confounding—which would be difficult to verify [4]. An initial step in a potential mediation analysis would be to explore the total effect of the exposure (initial vision) on mortality without considering possible mediators; these are the results we have presented. We went one step further to investigate if this relationship was modified by an initial performance-based measure of physical function. For example, re-expressing the HRs associated with the antagonistic interaction with stereoacuity (Table S5 [1]), we find the sub-additive interaction in that model indicates that the relationship between poor vision and mortality may be present only in those who have better mobility at baseline (aHR 1.35, 95% CI [1.18, 1.54] in those with SPPB ≥ 9; aHR 0.91, 95% CI [0.66, 1.24] in those with SPPB < 9; p = 0.02). There can be any number of intermediate factors that may further mediate this relationship, including changes in vision, treatment for visual impairment, changes in mobility, falls, and so forth. To fully understand the relationship between vision and mortality, it is our view that a more in-depth analysis would require the availability of considerable additional longitudinal data, consideration of initial effect modifiers, and moving beyond a single mediator model. Our observations utilizing the Health ABC study data are associations warranting further exploration, and are not intended as proof of causality. The antagonistic interaction between stereoacuity and poor mobility was not expected. Although we posit some explanations, whether this observation is reproducible in other appropriate datasets should be explored. In general, longitudinal measurements in large, diverse cohorts would be helpful in elucidating the complex relationship of changing vision and changing mobility over time with mortality and other outcomes. We agree that more severe visual impairment can be associated with greater risk of mortality, as has also been observed in the meta-analysis by Ehrlich et al. (2021) [5]. In the Health ABC study, we similarly observed, in comparison to those with visual acuity of 20/40 or better, that older adults with visual acuity worse than 20/60 had a higher adjusted hazard ratio for mortality (aHR 1.60, 95% CI [1.34, 1.90]) than those with visual acuity worse than 20/40 up to 20/60 (aHR 1.23, 95% CI [1.08, 1.39] see Table S6a [1]). As explained in the methods, Cox proportional hazards models were used to generate the hazards ratios in our study. Such models assume proportional hazards through time, but do not assume a constant hazard across time. While our Cox models explicitly model the hazard function over time, it is unclear to us what the authors mean by “time dimension…does not occur in the study design and analysis of the present study.” If this is referencing the lack of multiple measures of vision over time, we agree that this is a limitation of this study as well as prior studies. This underscores the need for longitudinal studies with repeated measures of vision. Our analysis was not designed to test for the effect of any vision or mobility intervention on mortality risk. Future studies should consider whether such interventions could be beneficial and the target population. Currently the literature is quite mixed on the impact of vision correction on falls, for example [6-12], and the effect may differ depending on the specific intervention or characteristics of the cohort including their co-morbid mobility status. As we noted, “whether interventions that address both poor vision and poor mobility can help improve survival should be studied in future work.” We agree that the Health ABC study by design intentionally enrolled individuals who were functionally healthier at baseline. However, we used data that started in the third year of the study, which is when vision was measured. In general, the cohort was not meant to be representative of the entire population. Rather, the study provides a unique opportunity to identify older adults who were initially quite functional and examined the role of initial vision on the hazard ratios for mortality. In the future, being able to identify older adults who are otherwise quite functional but may have subtle risk factors for adverse outcomes, such as mild visual impairment or mobility dysfunction, will be important when designing upstream interventions that can make a meaningful impact on their risk of disability and death. A.C.T. prepared the original draft of the letter. J.R., M.E.M., and S.B.K. reviewed and edited the letter. All authors approved the final version of the letter. The authors have nothing to report. The authors have nothing to report. The authors declare no conflicts of interest. Data sharing is not applicable as no new data was generated; the article describes existing research.