Understanding, predicting, and optimizing recovery from a sport-related concussion (SRC) is a prominent research focus in the care of athletes at all levels.1 Clinical recovery from SRC is typically marked by resolution of symptoms, return to baseline on objective testing, and a resumption of normal activities, including school and sport.2 Although the majority of athletes recover within 14 days, several risk factors predispose athletes to prolonged recovery, including demographics (e.g., biological sex);3 health history (e.g., prior concussions,2 psychiatric history);4 and injury-related factors (e.g., severity of acute symptoms).1,2 Although previous literature on SRC recovery has focused primarily on return to play or resolution of symptoms in athletes, a relative dearth of research has focused on the return-to-learn (RTL) process.5,6
Given that most athletes are also students, RTL is an emerging area of focus, with most guidelines suggesting a graduated return to learning activities that begins 24–48 hours postinjury.7–9 However, how a student-athlete completes the RTL process can be variable due to a lack of standardized practices. Moreover, RTL is much less well established compared to the return-to-play process. Cognitive rest is often recommended immediately following concussion, but the nature and duration of cognitive rests continue to evolve.10–13 As symptoms start to improve, student-athletes start attending school as tolerated, often beginning with fewer classes and half days before full days.14,15 School accommodations can vary significantly,16,17 with physicians often recommending more accommodations for students experiencing difficulty with the RTL process.18 Understanding risk factors contributing to prolonged and more challenging RTL can assist in determining proper accommodations for student-athletes early on in concussion recovery. Previous studies have identified the fact that demographic and injury characteristics that predict prolonged RTL are closely aligned with those that predict return to play and symptom resolution.2,19–22 For example, a large epidemiological survey of college athletes noted that female sex was a risk factor for delayed RTL.20 Furthermore, medical history characteristics such as attention deficit hyperactivity disorder (ADHD)/learning disorders (LDs)22 and psychiatric history23 have been shown to prolong RTL in retrospective cohort studies.
Similar to return to play, there has also been a focus on initial symptom burden predicting prolonged RTL. Athletes who reported problems following RTL also reported a greater initial concussion severity.2,19,21 Furthermore, specific symptoms following concussion, such as sleep difficulties and vestibular issues, have been associated with prolonged RTL.19,24 Student-athletes aged 13–19 years who reported cognitive symptoms at their initial concussion clinic visit more frequently noted problems and issues after returning to school during a follow-up interview that occurred an average of 14 months after their injury.19
Given the suggested link between specific cognitive symptoms and subsequent academic and school difficulties, establishing a relationship between cognitive symptom clusters and RTL may be helpful for the refinement of consensus RTL guidelines.25,26 Therefore, the objective of this study was to evaluate the relationship between initial cognitive symptoms and RTL duration. We hypothesized that more severe initial cognitive symptoms may prolong RTL duration.
Methods
Study Design and Patient Selection
A retrospective cohort study was conducted using data from the Vanderbilt Sports Concussion Center (VSCC) registry. Institutional review board approval was obtained and the study was deemed to be exempt, with consent not required. Screening for eligibility of patients diagnosed with a concussion and seen by VSCC providers between November 2017 and October 2020 was conducted (n = 1504). Concussion diagnosis was defined using ICD-9 and ICD-10 concussion codes (850.* and S06.0X**, respectively), in addition to postconcussion syndrome (310.2 and F07.81). Inclusion criteria consisted of acutely concussed athletes aged 12–23 years presenting within 5 days of initial injury to a VSCC provider with subsequently confirmed SRC (n = 653) based on the most recent Concussion in Sport Group guidelines.15 Due to the study’s focus on cognitive symptom clusters and RTL, athletes missing cognitive symptom ratings and RTL data were excluded. Data were stored in a secure REDCap database.27,28
Data Collection and Exposure Variables
Data from the VSCC retrospective concussion registry were used. Data extraction and archiving have been previously described.29 Demographics, medical history, injury characteristics, and postinjury outcomes were extracted. Demographics and pertinent past medical history, including ADHD and LD, were obtained via review of the electronic medical record including self-report intake forms and provider notes. Time to clinic was defined as days from injury to initial presentation at the VSCC. Concussion symptom burden was measured by the Post-Concussion Symptom Scale (PCSS), a widely validated 22-item self-report measure recording symptom severity on a 7-point Likert scale of severity from 0 to 6, administered at the time of initial presentation and at each subsequent encounter (range 0–132).25
Within the PCSS, 4 individual symptom clusters (cognitive, sleep, emotional, somatic) have been defined.26 The cognitive symptom cluster included the following individual symptoms: "feeling slowed down," "feeling mentally ‘foggy,’" "difficulty concentrating," and "difficulty remembering."26,30 Total cognitive symptom cluster score, a continuous variable, was defined as the sum of individual cognitive symptoms (range 0–24).
Primary Independent Variable
The primary independent variable of interest was the Cognitive Symptom Ratio (CSR), defined as total cognitive symptom cluster score divided by total PCSS score from the initial clinic visit; this variable was calculated to assess the effect of cognitive symptoms in the context of total symptoms. CSRs closer to 1.0 suggest that cognitive symptoms are more prevalent in the patient’s overall symptom presentation than other symptom clusters. The CSR was chosen as the primary independent variable of interest over the raw total cognitive symptom cluster score, due to the latter’s extremely strong correlation with total PCSS score (rho = 0.91, p < 0.001).
Outcomes
The primary outcome was time to RTL, defined as the number of days between date of concussion and the date that a patient returned to any school activities. The term "RTL" serves as a proxy for "return to school," with no objective evaluation for patients returning to effective "learning." Nonetheless, it is widely used in concussion literature and is therefore used in this study. RTL was obtained during a clinic visit when the provider gave the patient approval to return to a formal learning environment. It is our institutional practice, adopted by all providers in a uniform fashion, to start with half days at school, and once tolerated, to progress to full days. The RTL time was from time of injury to when half days were started. The single secondary outcome was total length of care, defined as the days between initial visit and last follow-up.
Statistical Analysis
Descriptive statistics were performed on demographics, medical history, injury characteristics, and both the primary (time to RTL) and secondary (length of care) outcomes. Categorical variables were presented as percentage frequencies. A Kolmogorov-Smirnov test was performed to assess the normality of each continuous variable; normally distributed variables included age and initial PCSS score and were presented as the mean ± standard deviation. All other continuous variables were presented as medians with interquartile ranges (IQR), given nonnormal distribution. Correlation between variables was assessed via Spearman’s correlation coefficients.
The primary analysis performed was a multivariable Cox proportional hazards model to assess the effect of CSR (continuous) on the primary outcome of time to RTL. Confounding variables hypothesized to affect time to RTL were chosen a priori based on prior literature and included in the model. These included age (continuous);24 sex (binary);20 race (dichotomized as White and Non-White);31 number of prior concussions (grouped as 0, 1, and ≥ 2 concussions);23 history of ADHD or LD (combined—binary);22 migraine history (binary);32 psychiatric history (binary);4 and time to clinic presentation (continuous).33 The event was defined as RTL. Subsequently, the total initial PCSS score was added to the model to evaluate its role as a mediator.
To maximize the clinical applicability of these findings, we dichotomized the CSR via a median split and compared how high versus low CSR impacted RTL by using Kaplan-Meier survival analyses and log-rank Mantel-Cox test. Additionally, chi-square tests compared the proportion of athletes who achieved RTL at 7 days and 14 days postinjury. Statistical significance was set a priori at p < 0.05. Analyses were performed in SPSS 27 (IBM Corp.).
Results
Demographics and Medical History
Of 653 athletes seen within the study period in the first 5 days after their concussion, those with missing cognitive symptom cluster (n = 277) and RTL (n = 30) data were excluded. The final sample included 346 athletes (Fig. 1). The majority were male (n = 224, 64.7%). The mean age at injury was 16.2 ± 1.9 years. Approximately half of the athletes attended public school (n = 169, 48.8%).
Patient flow diagram. EMR = electronic medical record. Data added to the PRISMA template (from Page MJ, McKenzie JE, Bossuyt PM, Boutron I, Hoffmann TC, Mulrow CD, et al. The PRISMA 2020 statement: an updated guideline for reporting systematic reviews. BMJ. 2021;372:n71) under the terms of the Creative Commons Attribution License. Figure is available in color online only.
Most patients presented with no prior history of concussion (n = 207, 59.8%); of those with a positive concussion history, more patients reported 1 previous lifetime concussion (n = 88, 25.4%) than ≥ 2 prior concussions (n = 51, 14.7%). An ADHD diagnosis was reported in 31 patients (9.0%), whereas 11 patients (3.2%) presented with a history of LD. Family history of migraine (n = 98, 28.3%) was more commonly endorsed than positive personal history of migraine (n = 30, 8.7%). Forty-eight athletes (13.9%) presented with a family history of psychiatric disorder and 37 endorsed a personal psychiatric history (10.7%). Table 1 summarizes the demographics and medical history of the cohort.
Demographics, past medical history, and injury characteristics
| Value | |
|---|---|
| No. of pts | 346 |
| Demographics | |
| Age in yrs, mean (SD) | 16.2 (1.9) |
| Male sex | 224 (64.7%) |
| Race | |
| White | 252 (72.8%) |
| Black/African American | 59 (17.1%) |
| Asian/Asian American | 1 (0.3%) |
| Native American/American Indian | 1 (0.3%) |
| Other/unknown | 33 (9.5%) |
| School type | |
| Private | 89 (25.7%) |
| Public | 169 (48.8%) |
| Unknown | 88 (25.4%) |
| Insurance type | |
| Private | 294 (85.0%) |
| Medicaid | 45 (13.0%) |
| Uninsured/self-pay | 6 (1.7%) |
| Unknown | 1 (0.3%) |
| Medical Hx | |
| Prior concussion | |
| 0 | 207 (59.8%) |
| 1 | 88 (25.4%) |
| ≥2 | 51 (14.7%) |
| ADHD | 31 (9.0%) |
| LD | 11 (3.2%) |
| Positive migraine Hx | 30 (8.7%) |
| Family Hx of migraine | 98 (28.3%) |
| Positive psychiatric Hx | 37 (10.7%) |
| Family Hx of psychiatric disease | 48 (13.9%) |
| Injury characteristics | |
| Amnesia | 81 (23.4%) |
| Loss of consciousness | 49 (14.2%) |
| Time to clinic in days, median (IQR) | 1.0 (0.0–3.0) |
| Initial PCSS score, mean (SD) | 24.9 (21.9) |
| Cognitive Sx cluster, median (IQR) | 4.0 (0.0–9.0) |
| Time to RTL in days, median (IQR) | 4.0 (2.0–7.0) |
| Length of care episode in days, median (IQR) | 14.0 (4.0–29.0) |
Hx = history; pts = patients; Sx = symptom.
Unless otherwise indicated, values are expressed as the number of patients (%).
Symptom Presentation and RTL
The median time to clinic presentation among athletes was 1 day (IQR 0–3 days). On presentation, athletes reported a median initial PCSS score of 21 (IQR 6–37, mean 24.9, SD 21.9). The median cognitive symptom cluster score was 4 (IQR 0–9). Table 2 displays the frequency distribution for the individual cognitive symptoms. Most patients endorsed some degree of "difficulty concentrating" (n = 212, 61.3%) and "feeling slowed down" (n = 191, 55.2%), and almost half reported "feeling mentally ‘foggy’" (n = 164, 47.4%) and "difficulty remembering" (n = 157, 45.4%). The median CSR was 0.18 (IQR 0.00–0.27, mean 0.18, SD 0.14). The total PCSS score and the CSR were significantly correlated (rho = 0.53, p < 0.001). Most athletes initiated the RTL process and returned to school activities within 1 week (median 4.0, IQR 2.0–7.0 days). The median length of care episode in our clinic was 14.0 days (IQR 4.0–29.0 days) (Table 1). Patients reported a median return-to-play duration of 19.5 days (IQR 11.0–34.3 days).
Individual cognitive symptom frequencies
| Sx Severity Score | Feeling Slowed Down | Feeling Mentally "Foggy" | Difficulty Concentrating | Difficulty Remembering |
|---|---|---|---|---|
| 0 | 155 (44.8%) | 182 (52.6%) | 134 (38.7%) | 189 (54.6%) |
| 1 | 54 (15.6%) | 40 (11.6%) | 57 (16.5%) | 52 (15.0%) |
| 2 | 41 (11.8%) | 42 (12.1%) | 43 (12.4%) | 43 (12.4%) |
| 3 | 37 (10.7%) | 38 (11.0%) | 45 (13.0%) | 28 (8.1%) |
| 4 | 34 (9.8%) | 22 (6.4%) | 26 (7.5%) | 14 (4.0%) |
| 5 | 16 (4.6%) | 14 (4.0%) | 26 (7.5%) | 15 (4.3%) |
| 6 | 9 (2.6%) | 8 (2.3%) | 15 (4.3%) | 5 (1.4%) |
Cox Regression Analysis Predicting RTL
In a univariable analysis between the CSR and RTL, an incremental increase of 0.01 in CSR was associated with reduced chance of achieving RTL (HR 0.25, 95% CI 0.11–0.58, p = 0.001). Table 3 summarizes multivariable Cox proportional hazards regression analyses of factors predicting RTL. When adjusted for a priori defined variables that may also be associated with RTL in a multivariable model, higher CSR was associated with prolonged time to RTL (HR 0.30, 95% CI 0.13–0.69, p = 0.004). Female biological sex (HR 0.75, 95% CI 0.60–0.95, p = 0.019) was also significantly associated with prolonged RTL, as was history of ADHD/LD (HR 0.69, 95% CI 0.49–0.98, p = 0.039). Of note, time to clinic presentation was not significantly associated with RTL, nor was race, age, level of education (i.e., middle school age < 14.5 years, high school age 14.5–18 years, collegiate age > 18 years), school type (public vs private), concussion history, or other health history variables (all p > 0.05).
Multivariable Cox proportional hazards regression analyses for variables predicting RTL
| Low CSR | High CSR | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| B | SE | HR | 95% CI | p Value | B | SE | HR | 95% CI | p Value | |||
| Lower | Upper | Lower | Upper | |||||||||
| Primary independent variable of interest | ||||||||||||
| Cognitive to total Sx ratio | −1.219 | 0.429 | 0.295 | 0.128 | 0.685 | 0.004 | −0.394 | 0.437 | 0.674 | 0.286 | 1.588 | 0.367 |
| Covariates | ||||||||||||
| Sex | 0.019 | 0.224 | ||||||||||
| Male (ref) | — | — | — | — | — | — | — | — | — | — | ||
| Female | 0.282 | 0.121 | 0.754 | 0.596 | 0.955 | 0.149 | 0.123 | 0.861 | 0.678 | 1.095 | ||
| Race | 0.915 | 0.553 | ||||||||||
| White (ref) | — | — | — | — | — | — | — | — | — | — | ||
| Non-White | −0.014 | 0.127 | 0.987 | 0.768 | 1.267 | −0.076 | 0.128 | 0.927 | 0.721 | 1.192 | ||
| Age at concussion | 0.046 | 0.030 | 1.047 | 0.987 | 1.110 | 0.127 | 0.030 | 0.031 | 1.031 | 0.970 | 1.095 | 0.328 |
| No. of concussions | ||||||||||||
| 0 (ref) | — | — | — | — | — | — | — | — | — | — | — | — |
| 1 | 0.019 | 0.132 | 1.019 | 0.787 | 1.320 | 0.887 | 0.024 | 0.132 | 1.024 | 0.792 | 1.326 | 0.855 |
| ≥2 | −0.295 | 0.171 | 0.744 | 0.532 | 1.041 | 0.085 | −0.201 | 0.173 | 0.818 | 0.583 | 1.149 | 0.246 |
| ADHD/LD | −0.369 | 0.178 | 0.691 | 0.486 | 0.981 | 0.039 | −0.282 | 0.180 | 0.754 | 0.530 | 1.074 | 0.118 |
| Migraine Hx | −0.085 | 0.198 | 0.753 | 0.520 | 1.092 | 0.667 | −0.093 | 0.200 | 0.911 | 0.615 | 1.349 | 0.641 |
| Psychiatric Hx | −0.283 | 0.189 | 0.753 | 0.520 | 1.092 | 0.135 | −0.275 | 0.191 | 0.760 | 0.522 | 1.105 | 0.150 |
| Time to clinic presentation | −0.018 | 0.032 | 0.982 | 0.922 | 1.045 | 0.127 | −0.029 | 0.032 | 0.972 | 0.913 | 1.034 | 0.366 |
| Initial PCSS score | — | — | — | — | — | — | −0.013 | 0.003 | 0.987 | 0.981 | 0.993 | <0.001 |
SE = standard error.
Boldface type indicates statistical significance.
In the subsequent multivariable model, initial PCSS score was added to assess its role as a mediator of the relationship between CSR and RTL. When initial PCSS score was added to the model, the previously significant association between CSR and RTL was no longer significant (HR 0.67, 95% CI 0.29–1.59, p = 0.367). A higher initial PCSS score was significantly associated with prolonged RTL in this model (HR 0.99, 95% CI 0.98–0.99, p < 0.001). A time-to-RTL survival plot adjusted for all covariates is presented in Fig. 2 upper.
Upper: Multivariable analysis for factors associated with CSR and RTL. Lower: Kaplan-Meier survival analysis for proportion of athletes achieving RTL. The CSR was dichotomized via median split. Figure is available in color online only.
Binary Stratification of CSR
Based on the frequency distribution of the CSR, a median cutoff score of 0.18 was used to dichotomize the sample into low and high ratios (low ≤ 0.18, n = 180, 48.0% vs high > 0.18, n = 166, 52.0%). At 7 days postinjury, a higher proportion of athletes with low CSRs achieved RTL compared to athletes with high CSRs (82.2%, n = 148 vs 69.9%, n = 116; χ2 = 7.28, df 1, p = 0.007). At 2 weeks postinjury, no statistically significant difference was seen between the groups (low 92.2%, n = 166 vs high 87.3%, n = 145; χ2 = 2.26, df 1, p = 0.133). A significant difference was seen in mean time to RTL between the low (5.1 days, 95% CI 4.4–5.9 days) and high (8.2 days, 95% CI 6.5–9.9 days) CSR groups (χ2 = 12.63, df 1, p < 0.001). Figure 2 lower depicts Kaplan-Meier survival analysis stratified by low and high CSRs.
Discussion
This study assessed the relationship between initial cognitive symptoms and RTL duration and revealed a statistically significant relationship between a higher initial cognitive symptom burden (in the form of a ratio to overall symptom burden) and prolonged time to RTL. Correspondingly, 2 athletes with the same overall symptom burden may have different recovery times—and the athletes with a higher CSR may have more difficulty with both returning to school and school activities due to the inherent cognitive nature of the symptoms. Not surprisingly, most patients in our cohort endorsed "difficulty concentrating" and "feeling slowed down," and nearly half reported "feeling mentally ‘foggy’" and "difficulty remembering," at mild or greater severity. Univariable and multivariable Cox proportional hazards regression analyses adjusted for variables hypothesized to be associated with RTL defined a priori demonstrated a statistically significant relationship between higher CSR and longer RTL. In these models, female sex and ADHD/LD were also independent risk factors for prolonged RTL, in line with prior studies examining factors associated with delayed return to school.20,22 When statistically adjusting for initial PCSS score, the association between initial cognitive symptoms and RTL became statistically insignificant. On dichotomization of the sample into low and high CSRs based on frequency distribution, athletes with low CSRs achieved RTL approximately 3 days before their counterparts with high CSRs, a clinically significant difference decreasing the missed academic burden placed on athletes with low CSR on RTL. A higher proportion of athletes with low CSR achieved RTL compared to athletes with high CSR at 7 days, whereas no differences in RTL were observed at 2 weeks postinjury.
Whereas several studies have shown higher acute initial symptom burden following concussion and worse clinical outcome,2,19,33,34 our study is the first to examine the specific effects of the cognitive symptom cluster by using the CSR to assess RTL duration. Preliminary evidence has shown symptom clusters within the PCSS to be predictive of various postconcussion sequelae, including depression and complicated recovery.35,36 Additionally, poor cognitive performance on objective testing immediately following concussion was predictive of worse concussion recovery outcomes.35 The results of our study using the CSR provide a novel and potentially useful method to examine acute postconcussion symptoms. Given the specific cognitive demands needed to reengage in academic activities, we thought that the CSR used in our study might be a unique, additional predictor in addition to overall symptom severity. The CSR variable may help explain why some athletes with low overall symptoms have difficulty with the RTL process. Athletes with low overall symptoms but high CSRs may benefit from additional early academic accommodations and/or RTL assistance than previously thought.
In our initial multivariable Cox proportional hazards regression analysis accounting for several other factors that have been associated with prolonged recovery in prior literature, the CSR was still predictive of longer RTL. This preliminary evidence suggests that CSR may be a valuable and important predictor of prolonged RTL. Furthermore, when dichotomized by low and high CSRs, we found that athletes with low CSRs achieved RTL approximately 3 days before those with high CSRs, which may be of clinical significance. Depending on what is being learned, students may fall behind on important foundational concepts as well as a variety of homework assignments. The effects of concussion in adolescents on long-term school grades and standardized testing is mixed,37 but there is ample evidence suggesting that concussed athletes miss significantly more school time compared to adolescents suffering non–head trauma.37,38 Our results may contribute to further understanding of the postconcussion recovery process and help predict athletes at risk for prolonged RTL and missed school days. Athletes with high CSRs at initial presentation can be targeted for additional academic support prophylactically prior to beginning the RTL process. The use of initial cognitive symptom burden data provides a more granular variable within the PCSS to assess RTL duration, given the proposed associations between cognitive symptoms and difficulties on returning to school in athletes with SRC.19,24
Although the association between the CSR and RTL became nonsignificant when modeled simultaneously with initial total PCSS score, the CSR may still be useful in several populations. Prior literature has suggested that patients with low initial total PCSS scores achieve RTL more rapidly than those with high initial symptom burden.2,19 However, not all patients with low PCSS may return to school quickly and without difficulty. Therefore, the use of the CSR in patients with low total PCSS scores may provide a further level of risk stratification and target athletes who may encounter academic difficulties on RTL. Patients with a relatively high cognitive symptom burden in the context of low overall symptom scores should be followed closely by providers on graduated RTL, with frequent follow-up to assess progression through school activities. In these patients, initial cognitive symptom burden may be more predictive of academic functioning on RTL than total PCSS scores.
Although our study provides a novel way of measuring postconcussion cognitive symptoms and suggests a relationship between initial cognitive symptom burden and RTL, it is not without limitation. First, our interpretation of RTL was based on data extracted from provider notes and limited to those athletes whose RTL process was documented in the electronic medical record. Furthermore, although our institution uses a graduated RTL protocol beginning with half days of school before progressing to full days as tolerated, school accommodations were not taken into account in our analysis. Although RTL may have been achieved by an athlete, testing accommodations, decreased workload, and other modifications to school routines were not taken into account. Additionally, once athletes were documented to begin the RTL process, it was unknown whether they tolerated the graduated resumption of school activities from half days to full days, or whether there were issues with RTL once the process was initiated. In addition, the CSR cutoff score used for dichotomization in our Kaplan-Meier analysis was based on the frequency distribution of our sample; to our knowledge, this score has not been previously used in the literature, and further studies are indicated to validate this methodology. In addition, our cohort was composed of middle school, high school, and collegiate athletes; although there are distinct differences between these learning environments and, consequently, the RTL process, we found no differences in RTL duration when stratifying the cohort by level of education. Finally, the generalizability of our study may be limited due to data being extracted from a single institution’s specialty concussion clinic; further prospective multiinstitutional studies may be important, given that many athletes with SRC do not present to specialty concussion centers and that there may be variability in RTL policies by institution. Finally, although this study focused on the effects of the CSR on RTL, it did not take into account how this symptom cluster may have affected return to play. Future studies evaluating the effects of individual symptom clusters on return to play are indicated.
Conclusions
An acute cognitive symptom burden, measured through the CSR, is a significant predictor for prolonged RTL. This significant association is mediated when adjusting for total PCSS score. The results of our study suggest that an acute ratio of cognitive symptoms can be used to predict and stratify risk in patients at increased risk for prolonged RTL and to provide clinicians and patients with more clarity in predicting patients without high total PCSS scores who may experience difficulties once resuming school activities.
Disclosures
Dr. Yengo-Kahn is a consultant for BlinkTBI. Dr. Terry is a consultant for REACT Neuro, Inc., and he is on the scientific advisory board for HitIQ.
Author Contributions
Conception and design: Terry, Tang, Yengo-Kahn, Zuckerman. Acquisition of data: Tang, Davis, Williams, Grusky, Hajdu, Hou. Analysis and interpretation of data: Terry, Tang, Davis, Williams, Grusky, Hajdu, Hou, Yengo-Kahn. Drafting the article: Terry, Tang, Davis, Williams, Grusky, Hajdu, Hou. Critically revising the article: all authors. Reviewed submitted version of manuscript: all authors. Approved the final version of the manuscript on behalf of all authors: Terry. Statistical analysis: Terry, Tang. Study supervision: Terry, Yengo-Kahn, Zuckerman.
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