In the final dataset of 23 studies included in the data analysis, the participants had an average age of 24.8 years, ranging from 7.3 to 78.0. The average female representation among participants was 49.5%. The average sample size for each study was 31.7 participants, ranging from 10 to 151. Each study contributed four effect sizes for each coupling measure on average. The included studies consist of 17 overnight and 6 nap studies, in which a total of 19 tasks for declarative memory and 6 tasks for procedural memory were measured. In addition, we assessed the risk of bias for each study before conducting data analysis (see Figure 3).

We first assessed the association between the preferred phase of SO-SP coupling and memory retention following sleep. 23 studies (k = 90) were included in the Bayesian hierarchical model. We transformed the circular-linear correlation to standardized coefficients (see Methods: Standardized circular-linear correlation coefficient). Forest and regression plots for overall and moderation models are reported in Figure 4. In addition, the results of hypothesis tests for the overall and moderator models are reported in Table 1 using the Bayes factor and posterior probability. Consistent with the funnel plot (Appendix 4—figure 1A), neither Egger’s regression (p = 0.59) nor rank correlation test (p = 0.52) found the existence of publication bias.

By aggregating individual-level data across studies, we found that phase of SO-fast SP coupling has a significant quadratic association with memory retention in frontal regions (see Figure 5A), r=0.26\begin{document}$r=0.26$\end{document}, rz=0.20\begin{document}$r_{z}=0.20$\end{document}, p<0.01\begin{document}$p \lt 0.01$\end{document}. However, this association is not significant in either central (r=0.11\begin{document}$r=0.11$\end{document}, rz=0.05\begin{document}$r_{z}=0.05$\end{document}, p=0.22\begin{document}$p=0.22$\end{document}) or posterior regions (r=0.08\begin{document}$r=0.08$\end{document}, rz=0.01\begin{document}$r_{z}=0.01$\end{document}, p=0.47\begin{document}$p=0.47$\end{document}).

Another important finding is a considerable shift of the preferred coupling phase from frontal to posterior regions, similar to Kurz et al., 2021. After taking into account the repeated measurement, the frontal area has a preferred phase around 0.13 rad [0.00, 0.27], which is the closest to the peak of SO (0 rad). The coupling consistently happened earlier when moving towards further dorsally, reflected by the phase in central (−0.27 rad [−0.37, −0.18]) and posterior area (−0.41 rad [−0.54,−0.27]).

Extremely strong evidence supports a considerable difference of the preferred coupling phase between frontal and central areas, Δ=−0.40\begin{document}$\Delta=-0.40$\end{document} rad, BF10=+∞\begin{document}$BF_{10}=+\infty$\end{document}, probability = 1.00; between frontal and posterior areas, Δ=−0.54\begin{document}$\Delta=-0.54$\end{document} rad, BF10=+∞\begin{document}$BF_{10}=+\infty$\end{document} (An ‘infinite’ BF₁₀ value indicates that all posterior samples are overwhelmingly compatible with H₁, given the data and priors. It reflects a reporting convention where BF₁₀ becomes unbounded as the likelihood under H₀ approaches zero.), probability = 1.00; and between central and posterior areas, Δ=−0.14\begin{document}$\Delta=-0.14$\end{document} rad, BF10=34.4\begin{document}$BF_{10}=34.4$\end{document}, probability = 0.97. Differences can be observed from the shift of the posterior distribution in Figure 5B and the location of data clusters in Figure 5C. Moreover, the consistency of coupling phase across subjects also decreases from frontal (z=0.69\begin{document}$z=0.69$\end{document}, p<0.05\begin{document}$p \lt 0.05$\end{document}, Rayleigh test) to posterior areas (z=0.59\begin{document}$z=0.59$\end{document}, p<0.05\begin{document}$p \lt 0.05$\end{document}, Rayleigh test). The differences in coupling phase can explain part of the discrepancy of the timing of coupling occurrence among previous studies (Bastian et al., 2022; Hahn et al., 2020; Muehlroth et al., 2019; Joechner et al., 2023).

In summary, we observed that SO-fast SP coupling in the frontal region occurred at the latest phase observed across all regions, characterized by the highest precision and strength of phase-locking. We also found the strongest phase-memory association in frontal regions following a typical quadratic relationship.

We next assessed the association between the amplitude/power of SP and memory retention during the learning night. 18 original studies (k=78)\begin{document}$(k=78)$\end{document} were included in the Bayesian hierarchical model. The mean amplitude of fast SPs (in μV) is 33.99 [26.44,41.55], while the mean amplitude of slow SPs is 39.41 [33.61, 45.22]. Forest and regression plots for the overall and moderation models are reported in Figure 6. In addition, the results of hypothesis tests for the overall and moderator models are reported in Table 2. The publication bias of the amplitude-memory association studies is unclear but potentially provides evidence of asymmetry. Egger’s regression test (p=0.02)\begin{document}$(p=0.02)$\end{document} indicated potential publication bias, whereas the rank correlation test (p=0.11)\begin{document}$(p=0.11)$\end{document} and funnel plot (Appendix 4—figure 1C) did not suggest significant bias.

Next, we measured the association between coupling strength and memory retention. 21 original studies (k=86)\begin{document}$(k=86)$\end{document} were included in the Bayesian hierarchical model. The mean SO-fast SP coupling strength measured by mean vector length is 0.33 [0.27, 0.39], while the mean SO-slow SP coupling strength is 0.23 [0.19, 0.27]. Forest and regression plots for the overall and moderation models are reported in Figure 7. In addition, the results of hypothesis tests for the overall and moderation models are reported in Table 3. Neither Egger’s regression (p=0.53)\begin{document}$(p=0.53)$\end{document} nor rank correlation test (p=0.67)\begin{document}$(p=0.67)$\end{document} showed evidence of potential publication biases.

The last part of our analysis focused on the association between the percentage of SPs coupled with SOs and memory consolidation. 11 studies (k=43)\begin{document}$(k=43)$\end{document} were included in the Bayesian hierarchical model. The mean SO-fast SP coupling percentage (%) is 21.17 [15.95, 26.39], while the SO-slow SP coupling percentage (%) is 24.07 [17.59, 30.56]. Forest and regression plots for the overall and moderator models are reported in Figure 8. In addition, the results of hypothesis tests for the overall and moderator models are reported in Table 4. Consistent with the funnel plot (Appendix 4—figure 1E), both Egger’s regression (p=0.78)\begin{document}$(p=0.78)$\end{document} and rank correlation test (p=0.87)\begin{document}$(p=0.87)$\end{document} showed no publication bias.

In previous meta-analyses focusing on spindle events, the amplitude and power of SPs have been considered the most predictive measures for memory consolidation (Kumral et al., 2023) and cognitive abilities (Ujma, 2021). However, our findings indicate that the SP amplitude-memory association is subject to high variability. Only the association between fast SP amplitude and hippocampal-dependent memory consolidation is supported by strong evidence. In contrast, the precision and strength of coupling between the fast SP peak amplitude and the up-state peak of SOs are more crucial indicators for predicting memory retention performance. Our result confirmed the importance of cross-frequency coupling in the hierarchical temporal nesting within the hippocampus-thalamus-cortex information transmission loop, proposed in the active system consolidation theory (Klinzing et al., 2019; Staresina et al., 2015; Born and Wilhelm, 2012; Klinzing et al., 2016). Together with other studies included in the review (Hahn et al., 2020; Helfrich et al., 2018; Niknazar et al., 2015; Muehlroth et al., 2019; Mölle and Born, 2011b), our results suggest a crucial role of coupling but did not support the role of spindle events alone in memory consolidation.

Moreover, we found that the phase and strength of coupling between fast SPs and SOs retain strong predictive ability for memory retention performance in most sub-groups of the moderator analysis. This result confirms the robustness of the connection between coupled SO-fast SP phase and memory consolidation as a general physiological mechanism. Similar results were not observed with slow SPs. Since we did not find publication bias in both analyses regarding coupling phase and strength, it reduces the likelihood of overestimating true effect sizes. Given we have identified predictive powers for memory retention in both coupling phase and strength, and Weiner et al., 2024 reported a synergistic interaction between phase and strength, future studies are necessary to further investigate the relationship between these phase-amplitude level measures.

Most of the studies included in the meta-analysis supported the significance of the association between the coupling phase and memory consolidation. However, conflicting conclusions have been reported regarding the direction of the phase. In terms of the preferred coupling phase, we find two predominant views, with a subset of studies reporting that coupling events are concentrated before the up-state peak (−π/2\begin{document}$-\pi/2$\end{document} to 0) of SOs (Cox et al., 2018; Kurz et al., 2021; Niknazar et al., 2015; Perrault et al., 2019; Ladenbauer et al., 2021; Schreiner et al., 2021). Other authors found that the preferred phase is when fast SPs are precisely coupled with the up-state peak (0) (Hahn et al., 2020; Halonen et al., 2021; Helfrich et al., 2018; Mikutta et al., 2019; Mylonas et al., 2020; Mylonas et al., 2022). In either case, however, most of the studies agreed that coupling occurring closer to the up-state peak of SOs could predict better memory retention performance.

In addition to differences in signal processing approaches and age leading to discrepancies in phases reported, we believe that another reason is different PSG electrodes and SP frequencies filtered to detect coupling events. Research found that fast SPs occur more frequently in centroparietal regions, while slow SPs are predominantly in frontal regions (Mölle et al., 2011a; Anderer et al., 2001; De Gennaro and Ferrara, 2003; Urakami, 2008). This evidence led some research to apply this conclusion to coupling studies and detecting fast SPs only from centro-parietal electrodes or slow SPs only from frontal electrodes (Bastian et al., 2022; Niknazar et al., 2015; Perrault et al., 2019; Schreiner et al., 2021). However, we suspect that this approach restricts researchers from considering the origin and spread of oscillations. The prefrontal cortex has been proposed to be responsible for the generation of posterior-propagating global SOs (Staresina et al., 2015; Massimini et al., 2004; Marshall et al., 2006; Achermann and Borbély, 1997), while global SPs, the majority of SP events, propagate in a rotating direction following gradients (Dickey et al., 2021; Muller et al., 2016; O’Reilly and Nielsen, 2014). The significance of this dynamic interaction of oscillations for spatiotemporal coordination remains poorly understood.

SO-SP coupling can be widely detected across the frontoparietal cortex (Fernandez and Lüthi, 2020), and the interaction between centroparietal-dominated fast SPs and frontal-dominated SOs, along with their propagations, is proposed to be crucial for long-range transmission of memory-related information from thalamus to neocortex (Maingret et al., 2016; Marshall et al., 2006; Helfrich et al., 2019; Hahn et al., 2020; Baena et al., 2023). Our spatiotemporal analysis provides extremely strong evidence that the post-peak SO-fast SP coupling phase recorded from frontal regions occurs significantly closer to the up-state peak of SOs and considerably later than the pre-peak phase in centro-parietal regions, which supports phase shifts across electrodes found in previous studies (Cox et al., 2018; Denis et al., 2022; Denis et al., 2021), emphasizing the importance of coupling precision but not intensity. Moderator models of all four coupling measures consistently indicate that coupling detected from frontal regions has the largest association with memory consolidation. Moreover, a significant quadratic phase-memory relationship is only observed in frontal regions. In addition, the frontal region has the strongest and most active SOs as its origin site (Massimini et al., 2004; Kurth et al., 2017; Malerba et al., 2019; Niethard et al., 2018), which may contribute to the role of frontal coupling. To the best of our knowledge, our study is the first to provide consistent evidence supporting that successful memory consolidation is modulated by spatiotemporal specificity, emphasizing the precise coupling of frontal fast SPs targeting the up-state peak of SOs.

The predictive ability of coupling for memory consolidation has been studied across various types of memory, including emotional, spatial, verbal, and motor tasks. Surprisingly, our results indicate that the coupling phase has a widespread predictive role for both declarative and procedural memory. In contrast, evidence only supports a correlation between coupling strength and hippocampus-dependent memory. In addition, Hahn et al., 2022 and Hahn et al., 2020 provided a region-specific view, claiming significant associations of SO-SP coupling with declarative and procedural memory exist in the frontal lobe and motor cortex, respectively. Therefore, it is worthwhile for future research to study both shared mechanisms and region specificity of coupling across different memory types, including those traditionally considered non-hippocampus-dependent. However, we must exercise caution that the number of effect sizes extracted for emotional and spatial tasks is limited, making it susceptible to the influence of any single study.

One disadvantage in our analysis of age as a moderator is the limited number of studies on children and older adults. The linear meta-regression as a function of age did not capture the moderating pattern of development but only reflected aging through the decreasing trend of the coupling-memory association. For older adults, the meta-regression showed that all four measures approached null hypothesis levels of non-significance, indicating a diminishing effect in predicting memory consolidation through coupling phase or strength with aging. These results support previous studies on memory consolidation impairment in older adults (Helfrich et al., 2018; Muehlroth et al., 2019). While our results did not directly reflect the influence of development on the coupling-memory association, evidence from past research suggested that the strength of SO-SP coupling in frontal lobes increases with developmental age, indicating the development of long-term memory networks (Hahn et al., 2020). We suggest future studies to further compare SO-SP coupling across different age groups, contrasting the regional distribution of coupling changes during development and aging.

However, evidence did not support the moderation role of stage conditions, including sleep stages and bouts, in the coupling-memory association, which is somewhat surprising. SOs are predominant in SWS (Dang-Vu et al., 2008), while sleep SPs are the primary oscillation feature in N2 (De Gennaro and Ferrara, 2003). Our included studies showed that the co-occurrence rate of SO-SP coupling is higher during SWS compared to N2. One possible explanation, as suggested by our meta-analysis results, is that the precision and strength of coupling is more predictive of memory consolidation than the coupling percentage. Thus, considering the contribution of different stages to memory consolidation through co-occurrence rates may not be meaningful. Regarding sleep bouts (naps versus overnight sleep), no differences were found in any coupling measures between overnight sleep and naps, consistent with the results of a meta-analysis focusing on spindle-memory association (Kumral et al., 2023; Schmid et al., 2020). It implies the potential benefits of napping in memory consolidation and the clearance of hippocampal traces for storing new knowledge during the daytime.

One of the crucial factors limiting further interpretation of our results is the variation in statistical methods across studies, including differences in the definition of behavioral and physiological measures, the event detection and analysis methods employed, and limitations in estimating nonlinear relationships. Firstly, we agree with (McConnell et al., 2021) that there has been confusion in previous studies, where the term “slow spindle” is inconsistently used to refer to either frontal SPs (∼10–14 Hz) or low-frequency slow SPs (∼7–11 Hz). Compounding this issue, individual differences in spindle frequency are often overlooked, leading to challenges in reliably distinguishing between slow and fast spindles. Our result reveals that frontal fast SPs (∼10–14 Hz) occurring near the up-state peak of frontal-predominant global SOs with lower frequency than the centro-parietal fast SPs (∼14–17 Hz), which becomes predominant with development (Hahn et al., 2019; Shinomiya et al., 1999; McConnell et al., 2022; McConnell et al., 2021). Some studies have also reported difficulty in separating these two types of spindles (Hahn et al., 2020). In contrast, slow SP occurs before the trough of the SO down-state. Our findings support a detailed categorization of SP types proposed in previous studies (McConnell et al., 2021; Bernardi et al., 2018; McConnell et al., 2022; Siclari et al., 2014), involving separate measures between pre-peak early-fast SPs, post-peak (or peak) late-fast SPs (see Figure 5C), and pre-trough slow SPs (see Appendix 6—figure 1C). Alternatively, an effective approach could involve extracting signals from electrodes across different cortical areas for each type of SP for comparison. In addition, the current definition of moderators is also quite vague and conflicted. Some studies conducted analyses across mixed conditions, including using a global frequency range (e.g., 10–16 Hz) for SP detection, as well as reporting only one shared effect size for all conditions.

Moreover, we observed significant between-study differences in the measures for memory retention performance. Specifically, multiple retention measures already exist when solely considering verbal tasks for measuring declarative memory, including (1) the value difference in the number of correctly recalled words (Post-sleep – Pre-sleep number of correct words) (Weiner et al., 2024; Niknazar et al., 2015; Perrault et al., 2019); (2) the value difference in the percentage of correctly recalled words (Post-sleep – Pre-sleep % of correct words) (Hahn et al., 2020; Zhang et al., 2020; Ladenbauer et al., 2021); and (3) the ratio difference in the percentage of correctly recalled words (Post-sleep / Pre-sleep % of correct words) (Denis et al., 2021; Mikutta et al., 2019; Schreiner et al., 2021). Similar situations exist in measures for other memory retention tasks. When we tested the sleep-memory association using these three formulas separately, we found that in some extreme cases, different measures could even alter the direction of the association. Thus, we strongly suggest the consistency in memory retention measures in future studies (Németh et al., 2024).

In addition, misinterpretation of phase-memory associations in some studies poses a threat to the validity of results. Most studies use circular-linear correlation to measure this association, but we observed a prevalence of exaggeration when explaining the effect size. Circular-linear correlations lack directionality (Mardia, 1976), making it challenging to precisely estimate the improvement or decay of memory consolidation at specific SO phases. It is likely to be influenced by fluctuations in memory scores in any segment of SO phases, so associating it with hypotheses targeting specific phases might lead to incorrect conclusions. An effective solution is to visualize the regression and superimpose quadratic fit lines to assess whether it follows a typical quadratic relationship around the global maximum or minimum. In addition, through simulation studies (see Appendix 5), we observed that circular-linear correlation coefficients exhibit weak robustness and severe deviation from normal distribution for small to medium sample sizes (n<100\begin{document}$n \lt 100$\end{document}), commonly encountered limitations in PSG studies.

To suppress the bias introduced by non-linear relationships, we believe there are two available solutions: (1) Hahn et al., 2020 calculated the absolute distance of the preferred phase of each participant from the upstate peak (0), while Kurz et al., 2023 and Weiner et al., 2024 applied this method to transform the phase-memory association into a linear relationship for subsequent testing. Our results provided solid support for using SO up-state peaks as the center of transformation. (2) We developed a method to standardize the circular-linear correlation coefficient by transforming the sampling distribution of correlation to be normally distributed and centered at 0 under null, which takes into account the sample size to eliminate the overestimation of effect sizes and becomes comparable with Pearson’s correlation to enhance the comparability across studies (see Methods: Standardized circular-linear correlation coefficient).

In reporting results, despite the tendency to introduce multiple comparison issues due to the presence of multiple time points and electrodes during PSG recording (Yang et al., 2018), less than half of the included studies conducted corrections for multiple comparisons. We suggest that researchers adopt a combination of cluster-based permutation, hierarchical models, surrogate testing (Cox and Fell, 2020), and ROI to address the complexity of data structures across temporal, spectral, and spatial domains, and report both corrected and uncorrected results. Furthermore, we found that the majority of studies tend to selectively report results for significant electrodes, memory types, or coupling measures. These practices increase the likelihood of false positives and the overestimation of effect size (Ioannidis et al., 2014). We advocate for the standardization in reporting (1) all three coupling metrics, including coupling phase, strength, and prevalence, (2) their interactions with each other, and (3) their associations with memory performance. Each metric captures a distinct property of the coupling process and may interact with one another (Weiner et al., 2024), so it is necessary to provide a more comprehensive understanding of the coupling mechanism. We suggest that researchers should at least report exact values of effect sizes (e.g. correlation coefficients, standardized mean differences, or odds ratios), sample sizes, test statistics, p-values, and standard errors or confidence intervals for both significant and insignificant results to allow effective comparisons between studies. While only 2 out of the 23 studies included in our analysis disclosed all processed data and analysis code in their publication, we appreciate the responses of almost all authors who provided valid data or clarifications upon email requests that helped us mitigate heterogeneity and publication bias in subsequent analyses.

The between-study discrepancy in measuring cross-frequency coupling presents a potential challenge to the comprehensive inclusion of studies. Due to methodological disparities and the limited prevalence of PETH studies, our current analysis only included studies using the preferred phase to measure the precision of coupling. Additionally, due to the expectation of high heterogeneity, we excluded gray literature without peer review and memory measures with low comparability to other studies, such as the targeted memory reactivation (Hu et al., 2020). While the inclusion of a restricted number of published studies may introduce a potential publication bias, we effectively addressed this concern through data requests, focal and sensitivity analysis, and meta-regression, finally constraining the overall risk of bias of most studies to a small to moderate level.

One of the advantages of our study is attributable to a substantial number of effect sizes and sample sizes. However, only a few studies reached a sample size of 30–50. In addition, our analysis focused on studies with healthy populations. Future research should consider adopting more homogeneous analysis methods and openly sharing processed sleep and memory data, thereby aggregating sufficiently large and representative sample sizes in larger-scale studies. Moreover, our findings of no differences in the coupling-memory association between naps and overnight sleep suggest that nap paradigms may be efficient and thereby allow for a larger number of subjects.

Besides our suggestion for the classification of memory types and SP frequency, our results offer insights into studying causal sequences through more precise detection and stimulation of neural oscillations and offer insights for enhancing consolidation under aging or pathological conditions. We believe tracing dynamic distributions of SO-SP coupling and considering memory type and age-related regional changes would be intriguing and might be crucial for the understanding of the selective mediation of the spike-timing-dependent synaptic plasticity. High-density PSG has been instrumental in enhancing spatial sampling density for localizing SOs, subcortical areas, and even analyzing intra- and inter-regional PAC (Massimini et al., 2004; Krishnaswamy et al., 2017; Gong et al., 2021; Riedner et al., 2007; Roehri et al., 2022; Routier et al., 2017; Seeber et al., 2019; Siebenhühner et al., 2016). Moreover, integrating techniques with higher spatial resolutions, such as MRI and iEEG, will enhance the interpretative capacity of PSG results.

Finally, efforts must be made in future sleep research towards open science. To the best of our knowledge, as the first meta-analysis conducted on cross-frequency couplings, we have made our analysis code and data publicly available. Our posterior parameters predicted for each coupling measure can serve as priors in future meta-analyses, allowing for the integration of new data to update the model. We recommend that future sleep research should complete pre-registration on platforms such as OSF and clearly delineate pre-registered analyses from exploratory analyses in their reports to enhance methodological consistency and reproducibility. We also encourage original studies to share individual-level data and code. These efforts will contribute to enhancing reproducibility and comprehensive inclusion of results in future meta-analyses.

This meta-analysis revealed the crucial role of the precise and strong SO-fast SP cross-frequency coupling in promoting memory consolidation with data demonstrating sufficient statistical power for the first time. By aggregating effect sizes of associations between four commonly used coupling measures and memory retention performance, we observed very strong evidence that the precision and strength of coupling can both predict enhanced memory retention scores across almost all conditions as a general physiological mechanism, while fast SP amplitudes detected in the frontal lobe also showed associations with memory consolidation. Although the effect sizes of the main models are relatively small, our moderator analyses demonstrated the dynamic nature of coupling-memory relationships. Stronger associations were observed in subgroups including young adults, frontal regions, fast spindles, and declarative memory, all of which have historically demonstrated relationships with better memory performance. Therefore, our results provide important information regarding complex memory consolidation mechanisms.

This evidence provides insights for future research on how the contribution of coupling to memory consolidation is modulated by behavioral and physiological factors, as well as meaningful information for the simultaneous implementation of MRI and electrical stimulation in the SO-SP coupling analysis. We believe that SO-SP coupling can offer more precise predictions for memory consolidation within the context of spatiotemporal specificity. This meta-analysis emphasizes the need for standardization and replication studies and points to those measures to focus on for future research in the field.

The retrieval and screening of relevant studies were conducted in accordance with the 2020 PRISMA statement (Page et al., 2021). The PRISMA checklist is reported in Supplementary file 1. A comprehensive literature search was performed in three databases based on the retrieval qualities evaluation (Gusenbauer and Haddaway, 2020; Martín-Martín et al., 2021): PubMed, Web of Science, and PsycINFO, covering the period up to July 1, 2023. Only studies that have undergone peer review and have been published were included in the meta-analysis. Boolean operators were utilized to combine the following search terms, (sleep OR nap) AND (slow oscillat* OR slow wave OR sleep oscillat* OR slow-wave OR SO) AND (spindle OR sigma OR SP) AND (coupl* OR pair* OR lock* OR coordinat* OR interact* OR synchro*) AND (motor learning OR memory OR cogniti*). After filtering the papers based on inclusion criteria, a citation search was conducted and all papers identified from article citations underwent manual screening.

We applied the following criteria (Meline, 2006) to identify articles eligible for the meta-analysis as of July 1, 2023. Studies were included if the study (1) had memory encoding task before and recall measures after a sleep interval; (2) was published in English; (3) measured at least one of the standard SO-SP coupling measures (coupling phase, strength, percentage, and or SP amplitude) by phase-amplitude coupling (PAC) or comparable methods; (4) assessed the correlation between memory retention and SO-SP coupling during N2 and or SWS stage(s); (5) was published as an original research paper in a peer-reviewed journal. Studies were excluded if they (1) only measured SO-SP coupling influenced by the impact of medication or interventions (e.g. brain stimulation method) with no control condition; (2) only included non-human subjects, patient groups, or clinical groups (no control healthy group); (3) were a group under the wake condition. If a study included both groups that met the inclusion and exclusion criteria and those that did not, only data from the group(s) that met the criteria (e.g. control condition, control group) were included in the following analysis.

For the study selection, data retrieved from the three databases listed above were imported into EndNote 21 for automatic and manual duplication removal. The screening process is reported in Figure 9. After preliminary screening for titles, abstracts, and article types, 105 original research papers were screened by independent full-text review. Reviewers discussed all papers with discrepancies regarding their inclusion and ultimately achieved consistency. Finally, we included 23 eligible studies in the meta-analysis, comprising a total of 297 effect sizes from four types of coupling measurements with 730 samples.

In the studies included in the meta-analysis, relevant effect sizes and specified study characteristics were extracted by two reviewers independently in accordance with PRISMA guidelines (Page et al., 2021) to minimize the bias introduced by subjective judgments. The consistency of data extraction between reviewers is 99.6%, and all discrepancies were resolved through discussion. Four specific measures of SO-SP coupling (Figure 1) were examined for their association with memory retention performance: (1) preferred coupling phase; (2) SP peak-to-trough amplitude; (3) coupling strength; and (4) coupling percentage. After extracting effect sizes, phase-radian alignment was corrected (Figure 1C). Extracted study characteristics included: (1) sample size, age, gender distribution; (2) pre-specified moderators (see Methodological characteristics and moderators for more details); (3) publication details. A summary of the main information for each study is outlined in Appendix 2—table 2. The detailed data for each effect size can be found in Source data 1 (study-level), source data of Figures 4, 6—8 (effect size-level), and the publicly available repository, https://osf.io/9mh5d/. The overall quality of studies is assessed in accordance with the Robins-I (Jüni, 2016; Sterne et al., 2016) and NIH criteria (National Heart, Lung, and Blood Institute, 2019), with adjustments (detailed in Appendix 1—table 1) made to accommodate the specific attributes of the study.

Due to the relatively large heterogeneity and discrepancies in methodology and results reported between studies, as well as the non-parametric nature of the direction in circular-linear correlations, we improved comparability and credibility across studies by requesting both unreported effect sizes and processed individual-level memory and physiological data to reduce the publication bias. If a study measured relevant sleep and memory features but either (1) did not report any extractable or convertible effect sizes; (2) reported imprecise p-values due to insignificance; (3) reported only one effect size for cross-group data; (4) reported effect sizes that were not comparable to other studies, coupled with the absence of data in supplementary material, we requested missing data or processed individual data from corresponding authors via email. 21 out of 23 authors responded positively and provided the requested data. Studies without a response after two months or declined our requests were excluded or partially excluded from the meta-analysis for the part where insufficient information was provided for calculating effect sizes. For studies reporting correlations only through scatterplots, linear correlations were estimated using software from the ShinyDigitise package (Pick et al., 2019; Ivimey‐Cook et al., 2023) in R, while circular-linear correlations were first assessed by extracting estimated individual data from the plots by the online software WebPlotDigitizer (Rohatgi, 2014), followed by the circular-linear correlation analysis in R. Additionally, key missing study characteristic data was requested via email at the same time to broaden the scope of moderator analysis.

To standardize effect sizes for comparability across studies, we chose to standardize the bounded circular-linear correlation coefficient (Mardia, 1976; Fisher, 1995) to unbounded rz\begin{document}$r_{z}$\end{document} to examine the association between coupling phase (in radians) and memory consolidation. We used the Pearson product-moment correlation coefficient r (Lipsey and Wilson, 2001) (hereinafter referred to as Pearson’s r) and transformed Fisher’s z to report the linear relationships between SP amplitude (in μV), coupling strength (mean vector length or modulation index), coupling percentage (%), with memory consolidation separately. All transformable effect size measures including t-statistic, p-value, β statistic, and η2\begin{document}$\eta^{2}$\end{document}, were extracted and converted to Pearson’s r. In cases where effect measures were reported as non-parametric correlation including Spearman’s rho (ρ\begin{document}$\rho$\end{document}, i.e. rs\begin{document}$r_{s}$\end{document}) and no author response could reanalyze for parametric correlation, we used it as an imperfect estimation of Pearson’s r (Myers and Sirois, 2014) and excluded from sensitivity analyses.

In previous studies, researchers have applied different experimental designs to investigate coupling and summarized divergent conclusions regarding each coupling parameter. To develop a more systematic understanding of the heterogeneity of approaches, six moderators were selected in the moderator analysis. Appendix 2—table 2 provides a complete list of moderators in each study, and categories that define moderators are listed below, the range represents the number of effect sizes included in the analysis across four types of coupling measures:

We chose to fit overall and subgroup (moderator) models using Bayesian hierarchical random-effects and mixed-effects models, respectively, due to the common occurrence of multiple effect sizes for the same set of participants reported within the same study, violating the assumption of independence of effect sizes, as well as the limited and unequal group size and potential high heterogeneity. In comparison to frequentist models, Bayesian models incorporate prior probabilities for each parameter by considering likelihood information (i.e. the effect sizes we extracted) to establish a model for predicting the posterior probability distribution of parameters, which provides transparent inferences with lower risks of false positives. In the posterior distribution, confidence intervals (CIs) reported by frequentist methods are replaced by credible intervals (CrI), which can be interpreted as ‘there is a 95% probability that the parameter lies within the interval’, thereby providing a more precise prediction of true probabilities. Additionally, Bayesian methods could more effectively build models that account for multiple sources of heterogeneity and allow the analysis of the impact of moderator variables representing different measures and participant groups on the pooled effect size (Sutton and Abrams, 2001). As Kruschke and Liddell, 2018 described, the shrinkage property of Bayesian models helps prevent false alarms by pulling extreme values toward the group mean, which is especially valuable when accounting for potentially outlying estimates. This explains the observed differences between model distributions and the raw effect sizes in our forest plots. All statistical analyses for Bayesian models were conducted in R using the brms package (Bürkner, 2017) along with supporting packages bayesplot (Gabry et al., 2019), metaviz (Wagner et al., 2018), and customized codes for visualization. Contrary to the misconception that Bayesian models are overly complex or opaque, they are increasingly valued for their accuracy and transparent inferences (Kruschke and Liddell, 2018). We also recognize that some researchers may prefer frequentist approaches. To support transparency and comparability, we also provided the traditional meta-analytic results in Supplementary file 5, which demonstrate consistency with our Bayesian findings.

For each overall and subgroup model (Appendix 2—table 1), we applied the Markov chain Monte Carlo (MCMC) method, a general family of algorithms used to approximate complex probability distributions, with the no-U-turn Hamiltonian Monte Carlo (HMC) sampler, the default algorithm in Stan, to set up four chains, with each chain undergoing 12,000 iterations (including 2000 warm-ups), the minimum requirement for calculating accurate Bayes Factors (BF; Kass and Raftery, 1995), which reflects how much more likely the data are under one hypothesis. The target average acceptance probability was set to 0.99 with the maximum tree depth to 15 to ensure robustness in the posterior distribution.

Convergence of the MCMC was checked following the suggestion of WAMBS-Checklist (Depaoli and van de Schoot, 2017) through 1. graphical posterior predictive checks to evaluate how well the model-predicted data replicated the observed data; 2. trace plots; and 3. the Gelman-Rubin diagnostic to assess convergence of the Markov chains. Ideally, the posterior distribution should overlap with the distribution of the test data generated, the trace plot distribution should resemble a uniformly undulating wave with high overlap between chains, and the Potential Scale Reduction Factor (Rˆ) should be less than 1.1. Autocorrelation plots were used to ensure low temporal dependency between successive samples. Examples of diagnostic plots were reported in Supplementary file 2. Any non-convergence at the aforementioned stages led to reconfiguration of chains and iterations for analysis. Estimation of each intercept, moderator, and heterogeneity in the posterior distribution was extracted, and the estimation of mean, distribution, and 95% credible interval of each effect size and the pooled effect size were reported in forest plots.