Summary statistics for perceptual discrimination, accuracy (perceptual sensitivity, A), and reaction time variability across all assessments are reported in Table 1.
Longitudinal Training and Maintenance in Retreat 1
We first analyzed longitudinal change across training (pre-, mid-, and postassessment) and years of follow-up (6 month, 1.5 year, 7 year) for retreat 1 training participants. For each measure, we fit an initial model describing change across block, retreat, and YSR (reported in Table 2). For accuracy and RTCV, we then examined interactions between block and training, and block and YSR. Finally, we examined age as a predictor of performance. Figure 1 depicts mean A and RTCV for the retreat 1 training group across RIT blocks at each assessment. Figure 2 depicts observed changes in discrimination, A, and RTCV across YSR for each individual, with the intercept indicating performance at postassessment (YSR = 0) and the trajectory representing performance over YSR.
The inclusion of a random slope for YSR (− 2ΔLL(3) = 21.9, p < .001) significantly improved model fit. There were significant linear, β = 0.545, p < .001, and quadratic, β = − 0.201, p < .001, trajectories across retreat, but no significant linear yearly change over YSR, β = − 0.019, p = .184 (see Fig. 2a). Training participants’ discrimination threshold was estimated to increase (p < .001) by .344° of visual angle from pre- to midassessment. This rate then slowed over time such that participants increased (p < .001) a total of .286° of visual angle from pre- to postassessment. Finally, we included age as a model predictor. Age did not significantly predict discrimination, β = − 0.0013, p = .689, and there were no higher-order interactions of age with training or YSR.
The inclusion of random slopes for block (− 2ΔLL(2) = 20.8, p < .001), training (− 2ΔLL(3) = 34.8, p < .001), YSR (− 2ΔLL(4) = 112.7, p < .001), and quadratic training (− 2ΔLL(5) = 39.4, p < .001) significantly improved model fit. We observed a significant vigilance decrement (i.e., effect of block) with an estimated decline (p < .001) of − .0084 units of A at each RIT block. Random effects confidence intervals (CI) suggested that 95% of participants showed a decrement between − .017 and .0004 units of A for each block. In addition, we observed significant linear, β = 0.126, p < .001, and quadratic, β = − 0.045, p < .001, slopes across training assessments, indicating significant increases in accuracy over retreat. Compared to preassessment, participants increased (p < .001) an estimated total of .081 units of A by midassessment, and an estimated total (p < .001) of .071 units by postassessment.
There were, however, no significant linear changes in A across YSR, β = 0.004, p = .119, 95% CI [− .0012, .0097] (see Fig. 2b). This non-significant change across YSR offers no affirmative statistical evidence in support of maintenance. We therefore further evaluated the estimated change across YSR using TOST equivalence procedures (Lakens 2017). Specifically, we examined the years for which the total accumulated change was significantly smaller than a minimally meaningful effect, defined as half the total increase in accuracy over retreat (ΔL = − 0.035, ΔU = 0.035). The accumulated change across follow-up was practically equivalent to zero from the end of retreat to at least year 4, after which the 90% CI of the remaining years’ estimates overlapped with the upper equivalence bound (see Fig. 3). Maintenance over years 5 to 7 was thus statistically undetermined.
We next examined whether the within-task performance decrement changed across retreat assessments or YSR. There was no significant interaction between block and linear, β = − 0.004, p = .390, or quadratic training, β = 0.002, p = .439, suggesting that the vigilance decrement was unaffected by training in retreat 1. The effect of block, however, was significantly attenuated across YSR, β = 0.0007, p = .037. Finally, we examined the effects of aging on response inhibition accuracy. Age did not significantly predict A, β = − 0.0003, p = .611, and there were no higher-order interactions between age, block, training, and YSR.
Reaction Time Variability
Random slopes for block (− 2ΔLL(2) = 42.9, p < .001), training (− 2ΔLL(3) = 53.4, p < .001), linear YSR (− 2ΔLL(4) = 54.6, p < .001), and quadratic YSR (− 2ΔLL(5) = 64.6, p < .001) all significantly improved model fit. We observed a significant linear effect of block, indicating an average increase (p < .001) of .006 units of RTCV per block. Random effects CI suggested that 95% of participants showed a per-block change in RTCV between − .005 and .017 units. We also observed a significant linear effect of training, β = − 0.013, p = .003, indicating significant reductions in RTCV. Ninety-five percent of individuals had a slope between − 0.044 and .019 units of RTCV across retreat assessments. Finally, we observed significant linear, β = 0.056, p = .006, and quadratic, β = − 0.007, p = .008, slopes across YSR (see Fig. 2c), indicating that participants lost the benefits of training in the years following retreat, but that this rate of loss slowed and then reversed over time. One year after postassessment (YSR = 1), participants were estimated to have increased (p = .005) .048 units of RTCV, whereas 7 years later, the estimated total increase (p = .031) was .031 units.
No significant interaction between block and training, β = 0.0012, p = .202, was observed when included in the model. There were significant interactions between block and both the linear, β = − 0.009, p = .001, and quadratic, β = 0.0012, p = .001, YSR trends, however, indicating that the within-task increase in RTCV was significantly reduced in the years following training. Finally, age did not significantly predict RTCV, β = − 0.0004, p = .556, in retreat 1 participants. There were no higher-order interactions between age, block, training, or YSR.
Significant increases in accuracy were observed across retreat 1 training assessments, which were then definitively maintained for at least 4 years following retreat. Improvements (i.e., reductions) in reaction time variability were also observed across retreat, but were lost over the course of follow-up. Interestingly, within-task decrements in performance accuracy and RTCV were attenuated across years of follow-up, but not during retreat, suggesting possible benefits of long-term continued practice. No significant effects of aging were observed.
Longitudinal Training and Maintenance in Retreat 2
We next examined longitudinal change across blocks, training, and YSR in retreat 2 training participants. Parameter estimates are reported in Table 3, and Fig. 1 depicts mean A and RTCV across blocks at each assessment. In retreat 2, the RIT target was pre-set to each participant’s preassessment discrimination threshold for all remaining assessments, excluding the 7-year follow up assessment, for which target length was re-parameterized (see Table 1).
Model fit was significantly improved by inclusion of a random slope for YSR (− 2ΔLL(3) = 31.8, p < .001) only. We observed a significant linear increase in discrimination across training, β = 0.060, p = .002, and a significant yearly decrease over YSR, β = − 0.027, p = .029 (see Fig. 2d), suggesting training-related improvements in discrimination capacity that were then lost over years of follow-up. There were no significant effects of age on discrimination threshold, β = − 0.004, p = .101.
Inclusion of random slopes for block (− 2ΔLL(2) = 23.9, p < .001), and YSR (− 2ΔLL(4) = 139.5, p < .001), significantly improved model fit; the random effect of training (− 2ΔLL(3) = 5.1, p = 0.139), however, did not improve fit, suggesting minimal influence of individual differences on change in accuracy across training. The fixed effect of block was significant, β = − 0.008, p < .001, indicating an average per-block reduction of − .008 units of A. The random effects CI suggested that 95% of participants had a vigilance decrement between − .016 and − .0005 units of A. In addition, we observed significant linear, β = 0.045, p < .001, and quadratic, β = − 0.012, p = .012, trends across training, such that participants improved in accuracy during retreat, but that the rate of improvement slowed across assessments. Compared to preassessment, participants increased (p < .001) an estimated total of .033 units of A by midassessment, and an estimated total (p < .001) of .043 units by postassessment.
Although no overall significant yearly changes in A were observed following retreat, β = − 0.004, p = .128, 95% CI [− 0.0094, 0.0013] (see Fig. 2e), we observed significant individual differences in rates of yearly change: 95% of individuals demonstrated changes ranging from − 0.028 to .020 units of A per each year of follow-up. To formally evaluate maintenance, TOST equivalence procedures were used to examine the years for which the total accumulated change in accuracy over YSR was significantly smaller than half the total increase accrued over retreat (ΔL = − 0.022, ΔU = 0.022). Accumulated change was equivalent to zero until at least the second year following retreat, after which maintenance was statistically undetermined (see Fig. 3).
We next investigated whether within-task decrements in A changed across retreat assessments or YSR. There was a significant interaction between block and the linear effect of training, β = 0.0022, p = .030, suggesting that the magnitude of the vigilance decrement was attenuated across training. Specifically, the performance decrement over blocks (β = − 0.008) was estimated to diminish by .002 units at each assessment. The interaction between block and the quadratic effect of training was not significant, β = 0.0009, p = .644, and there was no change in the vigilance decrement over YSR, β = − 0.0006, p = .118, 95% CI [− 0.0013, 0.00015]. These patterns suggest that meditation training improved performance and moderated the vigilance decrement, and that these benefits did not change over years of the follow-up.
Finally, we examined age as a predictor of response inhibition accuracy. There was a significant main effect of age on A, β = 0.0007, p = .048. We next explored interactions between age and other model effects. Age was unrelated to block or to the rate of improvement across training, but was a significant moderator of change after retreat, β = − .0004, p = .026. Specifically, older participants declined at a greater rate across years of follow-up than did younger participants. Moreover, although retreat 2 participants retained training improvements across the follow-up on average, yearly losses were estimated to occur specifically in older (i.e., age = 65) participants, β = − 0.009, p = .036. Figure 4a depicts individual subject trajectories of A at each follow-up assessment as a function of age.
Reaction Time Variability
Random effects for the linear slope of training (− 2ΔLL(3) = 55.2, p < .001), and both linear (− 2ΔLL(4) = 78.5, p < .001) and quadratic slopes of YSR (− 2ΔLL(6) = 50.5, p < .001), significantly improved model fit. We observed a significant within-task increase of .004 RTCV units across blocks, β = 0.004, p < .001. There were also significant linear, β = −0.067, p < .001, and quadratic, β = 0.019, p < .001, decreases in RTCV across retreat assessments. The quadratic trend indicates that RTCV was reduced across training, but that the rate of decrease slowed across assessments. At midassessment, participants showed an estimated − .048 (p < .001) unit reduction in RTCV compared to preassessment, while the estimated reduction (p < .001) from pre- to postassessment was − .058 units. Significant linear, β = 0.045, p < .001, and quadratic, β = − 0.006, p < .001, trends in YSR (see Fig. 2f) were also observed. Although participants gradually lost the benefits of training over follow-up, the rate of loss slowed over time: 1 year after postassessment, participants showed an estimated increase (p < .001) of .039 units of RTCV, whereas 7 years later the estimated increase (p = .025) was .044 units.
We observed no significant interactions between block and any other linear or quadratic trajectories, indicating that the per-block increase in RTCV was unaffected by training or YSR. Finally, although there was no significant linear effect of age, β = 0.003, p = .145, we observed a significant quadratic, β = 0.00012, p = .026, effect of age on RTCV. The relationship between RTCV and age was ∪-shaped, such that RTCV was reduced in middle age and increased in older age. Figure 4b depicts individual subject trajectories of RTCV at each follow-up assessment as a function of age.
Training participants demonstrated overall improvements in discrimination and performance accuracy during retreat 2, and significant attenuation of the vigilance decrement. No statistically significant changes in overall accuracy and vigilance were observed over years of follow-up, with equivalence testing suggesting that changes in accuracy were maintained below half the level of total retreat gains for approximately 2 years. However, when pooled across both retreats, total change in accuracy across YSR was closer to zero, such that the weighted estimate (β = 0.0004, 90% CI [− 0.021,0.021]) remained within the equivalence bounds up to 7 years following retreat. Thus, the true degree of maintenance was likely underestimated across individual retreats. As in retreat 1, RTCV was reduced during training in retreat 2, but improvements were then lost following retreat. Age was a significant predictor of RTCV, and interacted with rate of change over YSR such that losses in performance accuracy were estimated to occur specifically in older participants.
Meditation Practice Moderates Age-Related Decline in Performance
In a final set of analyses, we examined whether the observed age-related declines in performance among retreat 2 participants were moderated by meditation practice across the follow-up period. Estimates of continued practice (M = 2834.2 h, range = 406–11,900) and intensive retreat participation (M = 176.7 days on retreat, range = 0–1460) were available for 19 participants. These variables were entered separately into models for A and RTCV across YSR, after removing participants for whom no practice estimates were available. Hours of practice were rescaled to aid interpretation of model parameters (1 unit represents 100 h).
We first included estimates of continued practice (in hours) over follow-up as a predictor of performance accuracy. Parameter estimates from this model are reported in Table 4. We observed a significant interaction between hours and YSR, β = 0.001, p = .029, and a significant three-way interaction between age, hours, and YSR, β = 0.00004, p = .018. Figure 5 depicts model-estimated simple slopes across YSR at low (1250 h), medium (2000 h), and high (2750 h) values of continued practice for middle-aged (45 years) and older individuals (65 years). As can be seen in Fig. 5, older individuals who engaged in a relatively smaller amount of continued practice over YSR were predicted to experience greater losses of training-related benefits in A. Middle-aged individuals did not experience training losses over YSR, irrespective of their continued practice across this interval. For older individuals, however, there was a marginally significant slope across YSR at lower practice estimates (1250 h), β = − 0.052, p = .099, that reached statistical significance at approximately 750 h of estimated practice.
We next examined whether continued practice moderated the effects of aging on RTCV (see Table 5 for parameter estimates). We observed significant linear, β = 0.017, p < .001, and quadratic, β = 0.0004, p < .001, trends across age, a significant effect of total practice hours, β = − 0.008, p < .001, and a significant interaction between hours and the linear, β = − 0.0004, p = .004, and quadratic age parameters, β = − .000007, p = .019, for RTCV. Thus, in contrast to performance accuracy, continued meditation practice appeared to directly moderate age-related declines in reaction time variability. Figure 6 illustrates model-estimated simple slopes for low (1250 h), medium (2000 h), and high (2750 h) values of practice across continuous age. As shown in Fig. 6, individuals who engaged in relatively fewer hours of practice over YSR demonstrated greater age-related impairments in RTCV.
Finally, intensive retreat practice (in days) over the follow-up period was examined as a predictor of A and RTCV. Although there were no significant effects on performance accuracy, more reported days on retreat over follow-up was a marginally significant predictor of lower overall RTCV, β = − .00007, p = .058. There were no significant interactions.