Our analysis indicates that, in most cases, interventions or other factors that influence rodent longevity induce effects consistent with PH models. Truncating the study length to 2 years did not significantly affect the estimated effect; only the variance of this estimate and hence its statistical significance were influenced, a result of reduced sample size and power. This implies that the Cox PH regression model (13
) is sufficient for detecting differences in longevity, even when studies are cut short. We propose that increasing the number of rodents in the study by a factor derived from , by a factor near 5 on average (mean) but in half the cases by a factor of no more than 3.4 (median), can offer power equivalent to a full-length study. In situations where time is critical and the impact of discovery is large, the additional cost burden of a shorter experiment may be justified. It may also be worth commenting on whether diet, strain, environment, cohort, etc. might have the most impact on achieving similarity of results in truncated versus full longevity studies, particularly given that each of these factors can affect both the overall life-span trends and specific mortality trajectories at earlier timepoints. Of course, the truncated approach will not provide full information on diseases of aging compared with a full longevity/disease experiment.
The current results suggest empirical adherence of mouse and rat longevity studies to PH, implying similar effects on mortality rate across the full life span. Thus, although the risk of death (hazard rate) may certainly accelerate with advanced age, it appears that differences in acceleration between groups commonly occur by a proportional factor. This further suggests that cases where early, mean, and median life span are extended, extensions in so-called maximal life span would also be the expected norm. However, exceptions to this general rule may be possible, in principle and observation. It is commonly observed and cited that in addition to mean and median life span, maximal life span is extended in response to calorie restriction, setting it apart from interventions that may increase mean or median life span independent of maximum life span (14
). It is theoretically possible that an intervention that extends both mean and median life span has no benefit on maximal life span or that maximal life span may be increased independent of mean or median benefits. What is less commonly reported is the case where higher early- to mid-life mortality is followed by a subsequent extension of maximal life span. Although such an instance has been reported (4
) and others may exist, it should be noted that the constant effects on longevity would only be expected in response to a single intervention that was maintained for the duration of the longevity study (16
). Therefore, the alteration of a single intervention, as occurred with a methionine restriction protocol that showed increased early-life mortality (using the initial dietary formulation) followed by subsequent extension (as the diet was reformulated at two interim study points), does not contradict the expected proportionality of life span (4
). Whether other studies that show potential differences in either early-life or late-life mortality effects that might contradict the predicted proportionality has not been formally tested. For example, calorie-restricted wild-derived mice were not extended at early- and mid-life but were extended at the 90th percentile (17
); resveratrol was reported to increase the early- and mid-life span of high fat–fed mice, with no benefit on maximal life span (18
Part of the question regarding maximal life-span effects may be related to the lack of proper statistical analyzes of reported maximal longevity results. Clearly, truncating studies at any point prior to the maximal observed life span prevents assessment of any late-life specific effects that might occur. Yet, the limited sample size defining the maximum life span (90th percentile—4 animals of a cohort of 40) results in low-powered comparisons between groups, and it is often unclear whether observed increases in maximum life span are statistically significantly greater rather than simply numerically increased. The application of a standardized method, such as those described in (19
) and (20
) for maximal life-span assessment between studies, would be useful to determine whether longevity studies that have observed early- and mid-life extension consistently occur independent of late-life (maximal) extension. Another point of interest related to the proportionality of survival/mortality is whether the cause of mortality may differ at various points along the survival curve. This is often likely to be the case, at least for comparisons of some groups (eg, sex differences, and if so, then an intervention that affects a specific cause of death that is isolated to late-life in rodents would be unobserved in a truncated study). Of course, our approach assumes that the observed mortality was due to natural causes in shorter lived mice; in practice, the investigator will need to check this assumption by carefully examining the causes of death.
The current results lend support to several practical applications. The first is the potential for statistical analyzes of existing data sets in order to hypothesize about the expected survival impact that may occur in response to a particular diet, compound, or intervention. In particular, we envision the use of toxicology studies of at least 2-year duration where greater than 20% mortality has occurred, potentially advancing aging research without additional study-related costs. Second, although we have specifically evaluated truncated 2-year life-span experiments in order to parallel existing toxicology resources, our results in no way imply that 2-year studies or designs with a fixed stopping point are optimal. Rather than specifying a deterministic study length, an alternative implication from PH would be the potential for applying group sequential or similar clinical trial designs that permit interim analyzes of a life-span experiment (21
). For example, one could envision a life-span study employing planned interim analyzes at 3 to 6-month intervals beginning at 2 years using such approaches as conditional power methodology (22
) or continual monitoring using Bayesian decision-theoretic techniques to evaluate the need to continue the experiment (23
). This methodology may be particularly beneficial, given that recent publications indicate that exploration of factors affecting life span in rodents remains a staple of experimental aging research (24
). Although similar analyzes have been applied to toxicology experiments in clinical drug testing, our analyzes illustrate the potential to apply similar methodologies to a multifactorial endpoint of longevity. However, a meticulous adherence to the planned study design and proper analytic techniques is certainly advised to prevent improper interpretations, such as could occur by simply ending a study when a statistically significant result is obtained.