Stress and sleep cross lagged dynamic panel data with DSEM

Background The onset of the COVID-19 pandemic disrupted and changed sleep as well as elevated stress levels worldwide. Previous research has demonstrated a bidirectional relationship between stress and sleep, in that stress contributes to poorer sleep and poor sleep leads to higher stress. It is hypothesized that perseverative cognition (i.e., worry, racing thoughts) is a key cognitive mechanism in this relationship. In addition, little is known about whether health behaviors such as physical activity could moderate the daily relationships between stress and sleep. The goal of our study was to examine the relationships between stress and sleep during a major global stressor, testing key cognitive and behavioral factors that may influence this relationship. Method 191 adults aged 18 and above were recruited to complete a text-message survey twice per day for 3 distinct weeks spread over a 4-month period. Sleep duration and efficiency during the previous night and evening/overnight perseverative cognition were measured in the morning survey, daily stress levels were measured in the evening survey. Physical activity was measured by the International Physical Activity Questionnaire (IPAQ). Results were analyzed using a DSEM or dynamic structural equations model adjusted for age, gender and race/ethnicity. In traditional SEM analysis, measured variables have an intercept/mean that is a function of an indicator variable a_y. A latent variable/factor of measured variables Y1-4 shares the indicator function a but is allowed to assume its own intercept as a unique function g_F1(a) as well as its own residual D_1. DSEM is a methodological advancement for intensive longitudinal Data, combining three well-established modeling techniques: Time Series Analysis to account for lagged time points within data; Multilevel Modeling for simultaneous analysis of multiple clusters, as well as within and between person effects providing a framework to analyze these quantitative differences and implement proper correlation structures; and Structural Equation modeling for further analysis of these effects through path and factor analysis; together providing a framework through which to analyze cross-lagged variables then standardize and compare them.

1 Sleep, diet, and physical activity during the COVID-19 pandemic -CCTS2915 Written Oral Statistical Report STATISTICIAN: Connor Nicholls, MSTAT Candidate DATASET(S): Redcap Sleep, diet, and physical activity during the COVID-19 pandemic CCTS2915 survey data ABSTRACT: Background The onset of the COVID-19 pandemic disrupted and changed sleep as well as elevated stress levels worldwide. Previous research has demonstrated a bidirectional relationship between stress and sleep, in that stress contributes to poorer sleep and poor sleep leads to higher stress. It is hypothesized that perseverative cognition (i.e., worry, racing thoughts) is a key cognitive mechanism in this relationship. In addition, little is known about whether health behaviors such as physical activity could moderate the daily relationships between stress and sleep. The goal of our study was to examine the relationships between stress and sleep during a major global stressor, testing key cognitive and behavioral factors that may influence this relationship. Method 191 adults aged 18 and above were recruited to complete a text-message survey twice per day for 3 distinct weeks spread over a 4-month period. Sleep duration and efficiency during the previous night and evening/overnight perseverative cognition were measured in the morning survey, daily stress levels were measured in the evening survey. Physical activity was measured by the International Physical Activity Questionnaire (IPAQ). Results were analyzed using a DSEM or dynamic structural equations model adjusted for age, gender and race/ethnicity. In traditional SEM analysis, measured variables have an intercept/mean that is a function of an indicator variable a_y. A latent variable/factor of measured variables Y1-4 shares the indicator function a but is allowed to assume its own intercept as a unique function g_F1(a) as well as its own residual D_1. DSEM is a methodological advancement for intensive longitudinal Data, combining three wellestablished modeling techniques: Time Series Analysis to account for lagged time points within data; Multilevel Modeling for simultaneous analysis of multiple clusters, as well as within and between person effects providing a framework to analyze these quantitative differences and implement proper correlation structures; and Structural Equation modeling for further analysis of these effects through path and factor analysis; together providing a framework through which to analyze cross-lagged variables then standardize and compare them. 2 A two-level DSEM functions by dividing a given dataset into clusters. Variables which have multiple observations x within a given cluster i are decomposed into a within-level variable representing individual observations, and a between-level variable, the mean of the observations x in the cluster. On the within level of the model, within-level variables are modeled using path analysis. For our study we used an autoregressive component with random slope ϕ, lag and error ζ and a cross-lagged y component with random slope β and lag Thus the DSEM would have the within level expression On the between level, we center the latent between level variables, define the random slopes ϕ and β with means γ and error u, which are all correlated as observed by Allison (2015). Thus the DSEM would have the between level expressions Anticipations We anticipated that higher stress ratings during the day would be associated with lesser sleep duration that night. We anticipated higher perseverative cognition would lead to lower sleep duration and either partially or fully mediated this relationship. We anticipated that lesser sleep duration that night would be associated with higher stress ratings the following day. We anticipated participants who are more physically active would have longer sleep duration and efficiency. Such results would demonstrate perseverative cognition is a key mediating factor in the relationships between daily stress and sleep at night. It would also demonstrate that although adults with higher physical activity would have reported better sleep overall, having high habitual physical activity would not necessarily moderate the relationships between stress and sleep. Thus, interventions to reduce perseverative cognition may improve sleep during times of stress, including reducing the sleep-disrupting effects of the COVID-19 pandemic. METHODS Key terminology (Hoyle 2012) - Antipersistance reflexive, back and forth cycling between scores above and beneath subject mean, i.e., resource maintenance 3 - Attraction Dynamic How quickly a score will return to its mean. - Carryover A measure of regulatory weakness, inverse attraction dynamic, measures stay away from the mean for a longer time Sample Study population. 147 of 191 Adults with nonmissing values, participating in a total of 1028 daily Stress and Sleep Surveys. (Week 1) The Reference Group was White Non-Hispanic Males. Operationalization of variables Perseverative Cognition was recorded as the sum of scores on heart racing, jittery, trouble shutting off thoughts, racing thoughts, and pondering events. Each of these 5 terms was recorded by survey on a scale from 0-4, totaling 0-20. Stress was self-reported on a scale of 0-100 on a slider scale. Sleep Length was self-reported in minutes Race was recoded into a 3-level variable: White Non-Hispanic, Non-White Non-Hispanic, Hispanic due to similar effect sizes and small sample size. Age was measured in days since date of birth then converted to years MVPA was recorded as an averaged of MET minutes per week (physical activity via IPAQ: 3.3 METs per minute of walking, 4 per minute of moderate activity, 8 per minute of vigorous activity) scaled down by a factor of 7*24 to equate to average MET minutes per hour, due to variability constraints in MPLUS. Primary Aim 1: Stress and sleep (‘daily’ analyses) We hypothesize that sleep and stress are reciprocally related. In this aim we will evaluate this relationship using structural equations models in the first week of study data. Research hypothesis 1a: Higher stress during the day leads to shorter, less efficient sleep at night, adjusted for age, sex, and race. Research hypothesis 1b: Worse sleep at night leads to higher stress next day, adjusted for age, sex, and race. Research hypothesis 1c: Perseverative cognition (PC) mediates the effect of stress on sleep. Research hypothesis 1d: Average physical activity over the past week moderates the effects of stress on sleep, and sleep on stress. Analytical methods 4 DSEM was conducted in Mplus Version 8.7 (Muthén & Muthén, 2017). The model was run using a Bayes full-information estimator with noninformative priors. The relative output includes a posterior estimate, posterior probability, and credibility interval. We will use a significance factor of 95% of the posterior probability that the estimate is indeed positive/negative. This approach produces results similar to full information maximum likelihood. For Bootstrapping, using seed 3824729, we computed 50,000 Markov chain Monte Carlo iterations, every 10th was recorded for estimation purposes. Dynamic Structural Equation Modeling following the procedures of Asparouhov, Hamaker, and Muthen(2021) as applied by in Armstrong (2019) with extensions outlined in Muthén and Muthén (2017) and Hoyle (2012) The study included 3 nonconsecutive weeks of data. In this project, we applied DSEM to the first week of data, which included 7 consecutive observations per person, similar to the approach of Armstrong (2019). The within-level of the model was constructed by extending the structure in Armstrong (2019) to our parameters, with the inclusion of perseverative cognition. The Betweenlevel of the model was constructed similarly to Armstrong (2019) with the correlation assumption outlined by Allison (2015) and colleagues, as well as added covariates following the procedures in Muthén and Muthén (2017), and non-causal mediation and moderation analysis consistent with the aims of the study, which was introduced using steps outlined in Hoyle (2012). Subject within level variable effects were centered, effects were standardized for comparison of cross-lagged and autoregressive effects. An autoregressive lag-1 (AR1) multilevel DSEM was conducted predicting the outcomes of stress, sleep duration, and perseverative cognition. We were interested in autoregressive and cross-lagged effects in the given model. An autoregressive effect involves one time point in the past predicting current time point (1 lag). For example, if the current night’s sleep is on the 5th day of the week (t; lag 0), the 4th’s nights sleep or previous night’s sleep is 1 lag (t-1, lag 1). We are interested in the capacity for both stress (lag 1) to predict stress (lag 0) and sleep (lag 1) to predict sleep (lag 0). In this study we also are interested in the capacity for stress (lag 1) to predict perseverative cognition and sleep (lag 0), and perseverative cognition and sleep (lag 0) to predict stress (lag 0), these effects are referred to as “cross-lagged”. We were also interested in the effect of between level covariates on these processes. To test moderation, MVPA was used to predict the random slopes of the effects of sleep on stress, stress on sleep, and perseverative cognition on sleep. To test mediation a second model was run with the removal of perseverative cognition. The DSEM Diagram for these relationships are presented in Figure 1. Figure 1 DSEM Diagram 5 *(w) indicates within person estimates, slopes (φ➔) indicate random effects This DSEM can be represented with the following equations 6 RESULTS Data were processed from 147 Daily and Evening Surveys. Missing data (n=44) were primarily due to participants reporting too few days to process (n=24/44). The remaining missing data were from Spanish speaking participants missing MVPA and AGE covariates (n=20/44). Demographic information is presented in Table 1. Table 1. Demographic Information Demographic Mean/% SD Participant Age (years) 41.3 14.8 Participant Gender (male) 46.30% Race/Ethnicity White Non-Hispanic 80.96% Non-White Non-Hispanic 13.60% Hispanic 5.44% MVPA rating (MET/hour) 26.3 27.1 Days of Sleep data 6.6 0.7 Days of Stress data 6.4 1.1 Days of PC (Perseverative Cognition) data 6.6 0.8 Average sleep duration (min) 434 81.5 Average stress rating (0-100) 40.7 29.6 Average PC rating (0-20) 3.1 3.7 The unstandardized effects are presented in Table 2, and standardized effects in Table 3; their paths are represented in Figure 1. For R Squared or the within-person explained variability, the current model explained 28.6% of the within-person variability in daily sleep duration, 16.5% of the within-person variability in daily stress, and 14.5% of the within-person variability in daily perseverative cognition score. Goodness of Fit is not available for DSEM. Evaluating fit for Bayesian models relies on posterior predictive checks which have not yet been developed for DSEM (Hamaker 2021). The inclusion of MVPA led to a significant increase in model fit, 7 Deviance Information Criterion = (26,222.09 with, 26,235.88 without), indicating MVPA was a key explanatory variable. DSEM is Bayesian, and our criterion for significance is whether at least 95% of the posterior distribution lies on one side of zero. MPLUS calculates a one-tailed posterior probability (called a “One-Tailed P-value” by MPLUS in Table 2 below) based on the proportion of the posterior distribution that crosses 0. For a positive estimate, this is the proportion of the posterior distribution beneath 0. This then serves as the probability an estimate is negative. For a negative estimate, this is the proportion of the posterior distribution above 0. This then serves as the probability an estimate is positive. We are interested then in 1-p i.e., for a positive estimate, what is the proportion of the posterior distribution that is positive. Table 2. Unstandardized Effects 8 Unstandardized Effects Autoregressive Effects The autoregressive coefficient for stress was positive and significant (B = 0.192, p<0.001 [95% CI: 0.093, 0.285]), thus indicating no antipersistance, and closer to 0 indicating low carryover. Thus, sedentary time appears to have an attractor dynamic, meaning that after a day of high stress, an individual will quickly return to their mean. The autoregressive coefficient for sleep was positive, but not significant (B = 0.048, p=0.187 [95% CI: -0.055, 0.157]). It should be noted that this is still a strong amount of evidence that this coefficient is usually positive (81.3%) by Bayesian standards. Cross-Lagged Effects Previous day’s sleep had a nonsignificant effect on stress the following day (B = 0.011, p=0.345 [95% CI: -0.046, 0.065]). From a Bayesian perspective, sometimes this coefficient is positive and sometimes its negative. Current day’s stress had a negative but nonsignificant effect on perseverative cognition (B = 0.001, p=0.145 [95% CI: -0.015, 0.004]) It should be noted that this is a strong amount of evidence this coefficient is usually negative (85.5%) by Bayesian standards, however this effect size is clinically unimportant. Current day’s stress had a negative significant effect on that night’s sleep (B = -0.403, p=0.014 [95% CI: -0.753, -0.034]). When comparing across individuals, individuals with higher stress scores participated in less sleep that night. On average, for every 5 stress points individuals would lose 2 minutes of sleep. Current day’s Perseverative cognition had a negative and significant effect on that night’s sleep (B = -8.963, p<0.001 [95% CI: -13.00, -4.96]). When comparing across individuals, individuals with higher perseverative cognition scores participated in less sleep that night. On average, for every 1 perseverative cognition point individuals would lose 9 minutes of sleep. 9 Covariates MVPA had a positive and significant interaction with the effect of stress on sleep (B = 0.008, p = 0.046, [95%CI: -0.00, 0.2]). Here, we rely on the posterior probability, indicating that even though the credibility interval contains 0, 95.4% of the posterior distribution of B is greater than 0. Individuals with a higher average MET minutes per hour experienced a more positive relationship of stress on sleep, therefor dampening the negative effect of stress on sleep. On average, an average of 11.82 MET minutes per hour (as recommended by the CDC) reduced the effect of stress on sleep by 22%. On average, the study average of 26.3 MET minutes per hour led to a 52.2% reduction of the effect of stress on sleep, and 50.4 MET minutes per hour completely counteracted the effect of stress on sleep. Age had a negative and significant effect on mean sleep duration (B = -0.883, p = 0.002, [95%CI: -1.48, -0.295]). Higher aged individuals experienced a decrease in mean sleep duration. On average an increase in 1.13 years of age led to a decrease in 1 minute of sleep per night. Table 3. Standardized Effects Standardized Effects – Relative Strength Autoregressive 10 Standardized within-person autoregression estimates were 0.192 [95% CI: 0.11, 0.27] for stress, and 0.049 [95% CI: -0.04, 0.14] for sleep. These were averaged over all clusters, indicating Stress has more carryover compared to Sleep. Cross-Lagged Effects Standardized within-person cross-lagged coefficients were 0.031 [95% CI: -0.07, 0.120] for the standardized effect of sleep duration on next day stress -0.076 [95% CI: -0.16, 0.007] for the standardized effect of stress on night’s sleep duration -0.254 [95% CI: -0.34, -0.17] for the standardized effect of perseverative cognition on night’s sleep duration. These were averaged over all clusters, indicating in this sample, the average within-person effect of stress on sleep was stronger than the effect of sleep on stress. However, the average within-person effect of perseverative cognition on sleep was much stronger than the effect of stress on sleep. Cross-Comparison Stress Previous Day’s Stress predicted Current Day’s Stress. The effect of Previous Day’s Stress (B=0.192, 95% CI: 0.11, 0.27) was greater than the effect of Sleep on Current Day’s Stress (B=0.031, 95% CI: -0.07, 0.120) Sleep Stress and Perseverative Cognition both predicted current night’s sleep duration. Perseverative cognition served as the best predictor for sleep duration (B=-0.254, 95% CI: -0.34, -0.17), followed by Stress (B= -0.076 95% CI: -0.16, 0.007), and Previous Night’s Sleep Duration (B=0.049, 95% CI: -0.04, 0.14). Mediation: The unstandardized effects of model 2 following the removal of perseverative cognition are presented in Table 4. 11 Table 4. Unstandardized effects without perseverative cognition To illustrate the test for mediation outlined in Hoyle (2012) comparable effects were visualized in Figure 2. Figure 2. Mediation diagram; Model 1 (bottom), Model 2 (top) In model 2, following the removal perseverative cognition, stress had a significant effect on sleep (B = -0.334, p = 0.031, 95%CI: [-0.68, 0.01]). Despite the inclusion of Perseverative cognition in the model 1, stress still had a significant effect on that night’s sleep (B = -0.403, p=0.014 [95% CI: -0.753, -0.034]). 12 Thus, multiple conditions for Mediation were not met: there was a nonsignificant effect of stress on perseverative cognition, and the inclusion of perseverative cognition did not affect the significance or the size of the effect of stress on sleep. This indicates perseverative cognition did not mediate the effect of stress on sleep in our model. DISCUSSION DSEM is still in its early stages and thus incorporation of modern causal methods such as IPW to address confounding and selection bias, with or without mediation and moderation, is a topic of active research. Additionally, from the perspective of modern causal methods, Sleep and Stress as counterfactual interventions are not clearly defined. Thus, the following results were taken to be non-causal. Our results showed that there was a directional predictive relationship of stress on sleep consistent with our research hypothesis 1a; however, we did not observe a directional predictive relationship of sleep on stress. Results indicate that when an individual has a day of higher than usual stress, they experience less sleep than usual the following night. This sleep however had little effect on the following day’s stress. We observed that sleep did not predict stress. However, we did observe a significant effect of previous day’s stress on current day’s stress. Results indicate when an individual had higher than usual stress on a given day, this stress would carry over to the next day, having more of an effect than lower than average sleep did. We observed that Stress and Perseverative Cognition predicted Current Night’s sleep duration. Results indicate that when an individual had a higher than usual Perseverative Cognition or higher than usual Stress, they would experience less than usual sleep that night. The effect of Perseverative Cognition was more so than the effect of Stress on Sleep duration. Both the effect Perseverative Cognition and Stress were more so than the effect of Previous Night’s Sleep duration on Current Night’s Sleep duration. Our results did not show that Perseverative Cognition served as a mediator for stress’s effect on sleep, however, relatively speaking Perseverative Cognition had a distinctly much stronger effect on sleep than stress. Results indicate that when an individual had a higher score of perseverative cognition than usual, they experienced less sleep than usual that night, more so than the effect of stress on that night’s sleep. Our results showed that Average physical activity over the past week moderates the effects of stress on sleep, but not that on the effects of sleep on stress. Results indicate that individuals with 13 higher physical activity scores experience less of a negative effect of stress on sleep. The CDC recommends 500 MET minutes per week in adults, this translates to 2.98 MET minutes per hour. Wanner (2016) compared accelerometry data with the IPAQ and found that there was an overestimation factor of 3.8 in men, and 4.5 in women. Taking this into account we could naively estimate a 5.84 to 6.98 MET minutes per hour, or 981 to 1172 MET minutes per week (4 to 5 hours of moderate activity) as a more appropriate goal for a 52% reduction in the effect of stress on sleep. In addition to our primary aim, we saw low carryover on average when it came to the autoregressive nature of stress and sleep. Stress had a relatively low carryover but more so than sleep which seemed to return to average after one lag. Most of our findings agreed with previous literature; some of our findings did not. Previous literature indicated that sleep had autoregressive behavior. From a Bayesian perspective there was a strong amount of evidence supporting this however, we could not confirm this relationship. Previous literature indicated that poorer sleep duration led to more stress the following day. From our Bayesian perspective, we view the estimate as a distribution not as a singular number, so we found that this effect would have a positive coefficient only slightly more often than it would have a negative coefficient, thus, we can neither confirm or deny this relationship. Previous literature hypothesized high stress was a predicting factor in perseverative cognition. Although we saw a strong amount of evidence that there was a negative effect, it was not enough that we could confidently confirm this relationship. In addition, the effect size was not large enough to be clinically important. Model Considerations and Extensions HLM was considered, however Allison (2015) and colleagues made it clear that putting lagged variables into such a model could result in severe bias. Causal methods such as TMLE were also considered. However, we were concerned that 1) the bidirectional aim of this study was only accomplished by considering multiple exposures and their reciprocal influences simultaneously and 2) from the perspective of modern causal methods, Sleep and Stress as counterfactual ‘interventions’ are not clearly defined. With non-defined interventions to theoretically raise or lower stress, Hernan (2005) outlined that different methods used to change stress levels in a given person might result in different counterfactuals even if they lead to the same stress level. A third issue is that we were interested in the actual betas, and so did not need to re-target inference to a different parameter, such as an odds ratio. Consistent with Allison (2015), DSEM was the best choice not only because it accounted for the lagged correlation Allison warned about, but as it is commonly used in sleep research in this daily diary structure. Armstrong (2019) is the leading application of DSEM in the sleep daily diary interventions approach, and study structure was similar to ours. For this reason, we chose DSEM as our model. 14 Our model extends upon the Armstrong (2019) model in two ways. First, as outlined by the MPLUS User Guide, in the cross lagged panel data model - example 9.37, adjustment variables measured on the participant level can be included in the between level of the DSEM using linear predictive paths on both between-within variables and within-level random slopes. This can be done in parallel with within-level random-slope correlation on the between level to comply with Allison (2015). We used this knowledge to construct a DSEM with all our adjustment variables. Second, following Hoyle (2012), we can use this between level covariate as a naïve moderator on the within-level random slopes, as we did to model the moderation of MVPA on the effect of stress on sleep. We also implemented a third within-level exposure, perseverative cognition, as a potential mediator of stress on sleep. Strengths and Weaknesses The biggest strength of this paper is that the core of this approach is well established. This model closely follows the daily-diary approach of Armstrong (2019) as well as the setup of the within and between level variables and assumptions. This model also has the advantage of being able to take covariates into consideration. The main benefit of using this approach is that we can compare the relative strength of the crosslagged effect of one exposure on the other with the autoregressive strength of an exposure on itself at a different time point. This was one of the initial interests of the study. One weakness of this model is that although it takes advantage of an AR(1) process, for which estimation typically benefits from having at least twenty to thirty time points, the available data only consists of three occasions of seven consecutive days. We ran the model separately for each of the three weeks and found similar results; however, our largest sample was in the first week, thus we used only the first week in the final model. Armstrong (2019) also only had seven consecutive days of data, so we settled on this number. In future research it should be possible to connect these weeks in a second between level in a three-level random model, but we were not able to perform this in this study. Another weakness in our model is the inability to incorporate a modern causal framework, in which causal conclusions could be made. Given the state of the literature and the nature of the variables under investigation, it was simply out of the scope of this study. REFERENCES Hamaker, E. L., Asparouhov, T., & Muthén, B. (2021). Dynamic structural equation modeling as a combination of time series modeling, multilevel modeling, and structural equation modeling. The handbook of structural equation modeling. Armstrong, B., Covington, L. B., Unick, G. J., & Black, M. M. (2019). Featured article: bidirectional effects of sleep and sedentary behavior among toddlers: a dynamic multilevel modeling approach. 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