| Literature DB >> 25734511 |
M A Beydoun1, H A Beydoun2, G A Dore1, M T Fanelli-Kuczmarski3, M K Evans1, A B Zonderman1.
Abstract
Serum cholesterol, both total and lipoprotein fractions, has been associated with mid- and late-life depression. Using longitudinal data on a large and ethnically diverse sample of urban adults, the associations of serum lipid profile measured by high or low total cholesterol (TC; >200 mg dl(-1); <160 mg dl(-1)) and by atherogenic indices, namely high total cholesterol and low-density lipoprotein cholesterol relative to high-density lipoprotein cholesterol, with change in total and domain-specific depressive symptoms over time were examined. Findings were compared by sex. (Hypothesis 1) In addition, baseline depressive symptoms as predictors for longitudinal change in lipid profile trajectory were tested. (Hypothesis 2) Mixed-effects regression analyses stratified by sex was used. Sample sizes of participants (n) and repeated observations (n') were: Hypothesis 1 (Men: n=826 ; n'=1319; Women: n=1099 ; n'=1817); Hypothesis 2 (Men: n=738; n'=1230; Women: n=964; n'=1678). As hypothesized, a higher level of atherogenic indices was linked to faster increase in depressive symptom scores, particularly depressed affect and interpersonal problems, though this relationship was found only among women. Among men a U-shaped relationship between baseline TC and longitudinal increase in somatic complaints and a direct link between low TC and longitudinal putative improvement in positive affect was found. On excluding statin users among women, low TC was associated with slower increase in depressed affect over time, whereas high TC was associated with faster increase in interpersonal problems. In summary, atherogenic indices were directly linked to faster increase in depressive symptoms among women only. More studies are needed to explain these sex-specific associations.Entities:
Mesh:
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Year: 2015 PMID: 25734511 PMCID: PMC4354360 DOI: 10.1038/tp.2015.4
Source DB: PubMed Journal: Transl Psychiatry ISSN: 2158-3188 Impact factor: 6.222
Characteristics of HANDLS study participants by sex and Center for Epidemiologic Studies Depression Scale (CES-D) score (mean across visits)a
| % | P | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| ⩾ | ⩾ | ||||||||
| CES-D, | 8.3±0.2 | 23.0±0.4 | 12.5±0.3 | 8.00±0.17 | 24.1±0.34 | 14.2±0.3 | <0.001 | <0.001 | <0.001 |
| TC, | 182.9±1.9 | 186.0±3.0 | 183.8±1.6 | 190.1±1.5 | 189.6±2.0 | 189.9±1.2 | 0.002 | 0.39 | 0.84 |
| <160 mg dl−1, % | 22.8 | 19.6 | 21.9 | 15.1 | 16.5 | 15.7 | <0.001 | 0.55 | 0.65 |
| >200 mg dl−1, % | 31.2 | 33.8 | 31.9 | 37.3 | 38.7 | 37.9 | |||
| TC:HDL-C, | 4.08±0.06 | 4.17±0.12 | 4.11±0.06 | 3.60±0.04 | 3.76±0.06 | 3.66±0.04 | <0.001 | 0.44 | 0.045 |
| LDL-C:HDL-C, | 2.45±0.05 | 2.44±0.09 | 2.45±0.04 | 2.13±0.04 | 2.24±0.05 | 2.17±0.03 | <0.001 | 0.91 | 0.07 |
| Age (years), | 48.6±0.4 | 48.3±0.6 | 48.5±0.3 | 48.6±0.4 | 48.0±0.4 | 48.4±0.3 | 0.73 | 0.68 | 0.25 |
| African-American, % | 58.4 | 60.8 | 59.1 | 57.3 | 55.0 | 56.4 | 0.23 | 0.52 | 0.44 |
| Marital status, % | |||||||||
| Currently married | 36.3 | 28.8 | 34.1 | 32.1 | 22.6 | 28.5 | 0.017 | 0.05 | 0.002 |
| Missing | 4.1 | 6.7 | 4.8 | 4.4 | 3.8 | 4.2 | |||
| Education, % | 0.26 | <0.001 | <0.001 | ||||||
| <HS | 6.6 | 11.3 | 8.0 | 5.0 | 7.6 | 6.0 | |||
| HS | 55.0 | 67.1 | 58.5 | 53.6 | 66.0 | 58.4 | |||
| >HS | 38.3 | 21.7 | 33.5 | 41.3 | 26.2 | 35.5 | |||
| Missing | 0.0 | 0.0 | 0.0 | 0.0 | 0.2 | 0.1 | |||
| PIR ⩾125%, % | 63.5 | 52.5 | 60.3 | 60.1 | 44.3 | 54.1 | 0.006 | 0.003 | <0.001 |
| Employed, % | <0.001 | <0.001 | <0.001 | ||||||
| Yes | 59.1 | 37.5 | 52.8 | 51.7 | 32.3 | 44.2 | |||
| Missing | 13.3 | 18.3 | 14.8 | 14.5 | 15.6 | 14.9 | |||
| Current smoking status, % | |||||||||
| Currently smoking | 48.2 | 54.2 | 49.9 | 34.7 | 50.5 | 40.8 | <0.001 | 0.28 | <0.001 |
| Missing | 3.2 | 3.3 | 3.3 | 5.6 | 6.4 | 5.9 | |||
| Current use of illicit drugs, % | |||||||||
| Used any type | 57.4 | 57.1 | 57.3 | 30.4 | 41.0 | 34.5 | <0.001 | 0.80 | 0.001 |
| Missing | 6.6 | 7.9 | 7.0 | 9.0 | 6.8 | 8.2 | |||
| Body mass index, kg/m2; | 28.0±0.2 | 27.9±0.4 | 28.0±0.2 | 31.4±0.3 | 31.1±0.4 | 31.3±0.26 | <0.001 | 0.76 | 0.56 |
| Energy, kcal | 2290±44 | 2302±75 | 2364±38 | 1740±29 | 1734±36 | 1738±23 | <0.001 | 0.30 | 0.89 |
| Total carotenoids, mg/1000 kcal | 3847±192 | 3164±236 | 3649±153 | 4371±187 | 3817±226 | 4158±145 | 0.017 | 0.042 | 0.06 |
| Vitamin A, RE per 1000 kcal | 302±19 | 311±36 | 304±17 | 347±17 | 343±36 | 345±17 | 0.10 | 0.82 | 0.90 |
| Vitamin C, mg per 1000 kcal | 38.0±1.6 | 33.9±2.8 | 36.8±1.4 | 42.2±1.5 | 36.5±2.0 | 40.0±1.2 | 0.08 | 0.18 | 0.021 |
| Vitamin E, mg per 1000 kcal | 3.16±0.08 | 2.86±0.10 | 3.1±0.1 | 3.6±0.1 | 3.3±0.1 | 3.5±0.1 | <0.001 | 0.030 | 0.013 |
| Vitamin B-6, mg per 1000 kcal | 0.95±0.02 | 0.88±0.03 | 0.93±0.02 | 0.95±0.02 | 0.86±0.02 | 0.91±0.01 | 0.45 | 0.06 | 0.002 |
| Vitamin B-12, μg per 1000 kcal | 3.08±0.21 | 3.16±0.34 | 3.10±0.18 | 2.97±0.17 | 3.15±0.36 | 3.04±0.17 | 0.79 | 0.84 | 0.62 |
| Folate, μg per 1000 kcal | 181.7±4.2 | 173.4±5.9 | 179.3±3.5 | 193.7±3.9 | 178.3±4.5 | 187.8±3.0 | 0.06 | 0.28 | 0.012 |
| n-3 PUFA:n-6 PUFA ratio | 0.114±0.004 | 0.111±0.003 | 0.113±0.002 | 0.115±0.002 | 0.113±0.002 | 0.114±0.002 | 0.75 | 0.69 | 0.55 |
| Healthy Eating Index-2010 | 42.6±0.4 | 39.7±0.6 | 41.8±0.4 | 45.0±0.5 | 40.9±0.5 | 43.4±0.4 | 0.002 | <0.001 | <0.001 |
Abbreviations: AA, arachidonic acid; ALA, α-linolenic acid; CES-D, Center for Epidemiologic Studies-Depression Scale; DHA, docosahexaenoic acid; DPA, docosapentaenoic acid; EPA, eicosapentaenoic acid; HANDLS, Healthy Aging in Neighborhoods of Diversity Across the Life Span; HDL-C, high-density lipoprotein-cholesterol; HS, high school; LA, linoleic acid; LDL-C, low-density lipoprotein-cholesterol; n-3, omega-3; n-6, omega-6; PIR, poverty income ratio; PUFAs, polyunsaturated fatty acids; TC, total cholesterol.
Values are percent or mean±s.e.m.
P-value was based on independent samples t-test when row variable is continuous and χ2-test when row variable is categorical.
n-3 PUFAs included DHA+EPA+n-3 DPA+ALA. n-6 PUFA included AA+LA.
Analysis of baseline TC (low vs medium; high vs medium) and atherogenic indices (TC:HDL-C; LDL-C:HDL-C) exposures and longitudinal change in CES-D score (sex-stratified), mixed-effects linear regression analysis, HANDLS study, 2004–2013
| γ | P | γ | P | |
|---|---|---|---|---|
| | ||||
| Intercept ( | ||||
| Time ( | +0.83±0.49 | 0.09 | ||
| Agebase | −0.06±0.03 | 0.06 | ||
| Agebase × time | +0.011±0.009 | 0.20 | +0.006±0.009 | 0.50 |
| TClow ( | −0.87±0.67 | 0.19 | −0.38±0.76 | 0.62 |
| −0.81±0.58 | 0.17 | −0.25±0.22 | 0.25 | |
| TChigh ( | −0.03±0.19 | 0.86 | −0.61±0.59 | 0.30 |
| TChigh × time ( | +0.14±0.16 | 0.40 | +0.23±0.17 | 0.17 |
| | ||||
| Level 1 residuals ( | ||||
| Level 2 residuals | ||||
| Intercept ( | ||||
| Linear slope ( | ||||
| | ||||
| Intercept ( | ||||
| Time ( | ||||
| Agebase | ||||
| Agebase × time | +0.012±0.009 | 0.17 | +0.009±0.008 | 0.28 |
| LDL-C:HDL-C ( | −0.29±0.22 | 0.18 | +0.07±0.29 | 0.81 |
| LDL-C:HDL-C × time ( | −0.02±0.07 | 0.73 | ||
| | ||||
| Intercept ( | ||||
| Time ( | ||||
| Agebase | ||||
| Agebase × time | +0.012±0.009 | 0.17 | +0.009±0.008 | 0.30 |
| TC:HDL-C ( | −0.10±0.17 | 0.57 | +0.08±0.23 | 0.73 |
| TC:HDL-C × time ( | +0.01±0.05 | 0.82 | ||
Abbreviations: CES-D, Center for Epidemiologic Studies-Depression Scale; HANDLS, Healthy Aging in Neighborhoods of Diversity Across the Lifespan; HDL-C, high-density lipoprotein-cholesterol; LDL-C, low-density lipoprotein-cholesterol; n-3, omega-3; n-6, omega-6; PUFAs, polyunsaturated fatty acids; TC, total cholesterol.
Models were further adjusted for other covariates (main effects and interaction with time). See Materials and Methods section for more details on covariate coding and model specifications. Time at baseline visit was set to zero. Baseline age was centered at 50 years, total energy intake at 2000 kcal per day, total carotenoid intake at 3 mg per 1000 kcal per d, vitamin C intake at 30 mg per 1000 kcal per day, vitamin A intake at 300 RE per 1000 kcal per day, vitamin E at 3 mg per 1000 kcal per day, vitamin B-6 at 0.8 mg per 1000 kcal per day, vitamin B-12 at 3 μg per 1000 kcal per day, folate at 170 μg per 1000 kcal per day, n-3 PUFA:n-6 PUFA at 0.11. Healthy Eating Index-2010 was centered at 42.
N=number of participants in the analysis; N'=total number of visits included in the analysis. Findings that were significant at a type I error of 0.05 are in bold. γ±s.e.e. refer to the estimated regression coefficients from the mixed-effects regression models with their associated standard error. Random effects are presented only for TC models, but were comparable in the remaining models.
Figure 1(a) Predictive margins of CES-D total score, mixed-effects regression model with TC:HDL-C atherogenic index, controlling for selected covariates, among women. (b) Predictive margins of CES-D total score, mixed-effects regression model with LDL-C:HDL-C atherogenic index, controlling for selected covariates, among women. CES-D, Center for Epidemiologic Studies-Depression; HDL-C, high-density lipoprotein cholesterol; LDL-C, low-density lipoprotein cholesterol; TC, total cholesterol.
Analysis of baseline atherogenic indices and longitudinal change in CES-D component scores among women, mixed-effects linear regression analysis, HANDLS study, 2004–2013a
| γ | P | γ | P | |
|---|---|---|---|---|
| | ||||
| Intercept ( | ||||
| Time ( | ||||
| Agebase | −0.02±0.02 | 0.31 | −0.02±0.02 | 0.31 |
| Agebase × time | +0.004±0.004 | 0.21 | +0.004±0.004 | 0.21 |
| | +0.03±0.15 | 0.83 | +0.02±0.12 | 0.86 |
| | +0.04±0.04 | 0.23 | +0.03±0.03 | 0.30 |
| | ||||
| Level 1 residuals ( | ||||
| Level 2 residuals | ||||
| Intercept ( | ||||
| Linear slope ( | ||||
| | ||||
| Intercept ( | ||||
| Time ( | ||||
| Agebase | −0.02±0.02 | 0.13 | −0.02±0.02 | 0.14 |
| Agebase × time | +0.005±0.004 | 0.14 | +0.005±0.004 | 0.16 |
| | −0.07±0.15 | 0.61 | −0.07±0.12 | 0.53 |
| | ||||
| | ||||
| Level 1 residuals ( | ||||
| Level 2 residuals | ||||
| Intercept ( | ||||
| Linear slope ( | ||||
| | ||||
| Intercept ( | ||||
| Time ( | ||||
| Agebase | ||||
| Agebase × time | −0.000±0.002 | 0.89 | −0.000±0.002 | 0.90 |
| Atherogenic index ( | −0.06±0.09 | 0.53 | +0.13±0.38 | 0.74 |
| −0.04±0.02 | 0.09 | −0.07±0.07 | 0.32 | |
| | ||||
| Level 1 residuals ( | ||||
| Level 2 residuals | ||||
| Intercept ( | ||||
| Linear slope ( | ||||
| | ||||
| Intercept ( | ||||
| Time ( | ||||
| Agebase | −0.01±0.00 | 0.21 | −0.01±0.00 | 0.22 |
| Agebase × time | ||||
| Atherogenic index ( | −0.02±0.05 | 0.75 | −0.02±0.04 | 0.51 |
| Atherogenic index × time ( | ||||
| | ||||
| Level 1 residuals ( | ||||
| Level 2 residuals | ||||
| Intercept ( | ||||
| Linear slope ( | ||||
Abbreviations: CES-D, Center for Epidemiologic Studies-Depression Scale; HANDLS, Healthy Aging in Neighborhoods of Diversity Across the Lifespan; HDL-C, high-density lipoprotein-cholesterol; LDL-C, low-density lipoprotein-cholesterol; n-3, omega-3; n-6, omega-6; PUFAs, polyunsaturated fatty acids; TC, total cholesterol.
Models were further adjusted for other covariates (main effects and interaction with time). aSee Materials and Methods section for more details on covariate coding and model specifications. Time at baseline visit was set to zero. Baseline age was centered at 50 years, total energy intake at 2000 kcal per day, total carotenoid intake at 3 mg per 1000 kcal per day, vitamin C intake at 30 mg per 1000 kcal per day, vitamin A intake at 300 RE per 1000 kcal per day, vitamin E at 3 mg per 1000 kcal per day, vitamin B-6 at 0.8 mg per 1000 kcal per day, vitamin B-12 at 3 μg per 1000 kcal per day, folate at 170 μg per 1000 kcal per day, n-3 PUFA:n-6 PUFA at 0.11. Healthy Eating Index-2010 was centered at 42. N=number of participants in the analysis; N'=total number of visits included in the analysis. Findings that were significant at a type I error of 0.05 are in bold. γ±s.e.e. refer to the estimated regression coefficients from the mixed-effects regression models with their associated standard error. bIn a separate model with interaction of lipid exposures by TIME by sex, including all other terms in the current model, P<0.10 for null hypothesis that this interaction term is=0.
Figure 2(a) Predictive margins of CES-D component 2 score (depressed affect), mixed-effects regression model with TC:HDL-C atherogenic index, controlling for selected covariates, among women. (b) Predictive margins of CES-D component 4 (interpersonal problems), mixed-effects regression model with TC:HDL-C atherogenic index, controlling for selected covariates, among women. (c) Predictive margins of CES-D component 2 score (depressed affect), mixed-effects regression model with LDL-C:HDL-C atherogenic index, controlling for selected covariates, among women. CES-D, Center for Epidemiologic Studies-Depression; HDL-C, high-density lipoprotein cholesterol; LDL-C, low-density lipoprotein cholesterol; TC, total cholesterol.
Analysis of baseline atherogenic indices and longitudinal change in CES-D component scores among men, mixed-effects linear regression analysis, HANDLS study, 2004–2013
| γ | P | γ | P | |
|---|---|---|---|---|
| | ||||
| Intercept ( | ||||
| Time ( | ||||
| Agebase | ||||
| Agebase × time | +0.004±0.004 | 0.34 | +0.004±0.004 | 0.34 |
| Atherogenic index ( | −0.19±0.12 | 0.11 | −0.07±0.10 | 0.47 |
| Atherogenic index ( | −0.03±0.03 | 0.36 | −0.01±0.02 | 0.71 |
| | ||||
| Level 1 residuals ( | ||||
| Level 2 residuals | ||||
| Intercept ( | ||||
| Linear slope ( | ||||
| | ||||
| Intercept ( | ||||
| Time ( | ||||
| Agebase | −0.02±0.02 | 0.35 | −0.02±0.02 | 0.37 |
| Agebase × time | +0.003±0.004 | 0.48 | +0.003±0.004 | 0.48 |
| Atherogenic index ( | −0.21±0.12 | 0.09 | −0.07±0.10 | 0.44 |
| Atherogenic index ( | −0.01±0.03 | 0.67 | −0.01±0.02 | 0.63 |
| | ||||
| Level 1 residuals ( | ||||
| Level 2 residuals | ||||
| Intercept ( | ||||
| Linear slope ( | ||||
| | ||||
| Intercept ( | ||||
| Time ( | ||||
| Agebase | +0.02±0.01 | 0.07 | +0.02±0.01 | 0.07 |
| Agebase × time | −0.004±0.003 | 0.09 | −0.005±0.003 | 0.09 |
| Atherogenic index ( | +0.05±0.07 | 0.53 | +0.03±0.06 | 0.55 |
| Atherogenic index × time ( | −0.02±0.02 | 0.26 | −0.02±0.02 | 0.17 |
| | ||||
| Level 1 residuals ( | ||||
| Level 2 residuals | ||||
| Intercept ( | ||||
| Linear slope ( | ||||
| | ||||
| Intercept ( | ||||
| Time ( | ||||
| Agebase | ||||
| Agebase × time | +0.002±0.002 | 0.17 | +0.002±0.002 | 0.17 |
| Atherogenic index ( | −0.06±0.04 | 0.14 | −0.04±0.03 | 0.27 |
| Atherogenic index × time ( | +0.01±0.01 | 0.58 | +0.00±0.01 | 0.70 |
| | ||||
| Level 1 residuals ( | ||||
| Level 2 residuals | ||||
| Intercept ( | ||||
| Linear slope ( | ||||
Abbreviations: CES-D, Center for Epidemiologic Studies-Depression Scale; HANDLS, Healthy Aging in Neighborhoods of Diversity Across the Lifespan; HDL-C, high-density lipoprotein-cholesterol; LDL-C, low-density lipoprotein-cholesterol; n-3, omega-3; n-6, omega-6; PUFAs, polyunsaturated fatty acids; TC, total cholesterol.
Models were further adjusted for other covariates (main effects and interaction with time). See Materials and Methods section for more details on covariate coding and model specifications. Time at baseline visit was set to zero. Baseline age was centered at 50 years, total energy intake at 2000 kcal per day, total carotenoid intake at 3 mg per 1000 kcal per day, vitamin C intake at 30 mg per 1000 kcal per day, vitamin A intake at 300 RE per 1000 kcal per day, vitamin E at 3 mg per 1000 kcal per day, vitamin B-6 at 0.8 mg per 1000 kcal per day, vitamin B-12 at 3 μg per 1000 kcal per day, folate at 170 μg per 1000 kcal per day, n-3 PUFA:n-6 PUFA at 0.11. Healthy Eating Index-2010 was centered at 42. N=number of participants in the analysis; N'=total number of visits included in the analysis. Findings that were significant at a type I error of 0.05 are in bold. γ±s.e.e. refer to the estimated regression coefficients from the mixed-effects regression models with their associated standard error.
Figure 3(a) Predictive margins of CES-D domain 1 score (somatic complaints), mixed-effects regression model with TC, categorical, controlling for selected covariates, among men. (b) Predictive margins of CES-D domain 3 score (positive affect), mixed-effects regression model with TC, categorical, controlling for selected covariates, among men. CES-D, Center for Epidemiologic Studies-Depression; TC, total cholesterol.
Analysis of baseline CES-D score (X) and longitudinal change in total cholesterol (TC) and atherogenic indices (Y): sex-stratified mixed-effects linear regression analysis, HANDLS study, 2004–2013
| γ | P | γ | P | |
|---|---|---|---|---|
| | ||||
| Intercept ( | ||||
| Time ( | +3.67±2.73 | 0.18 | −1.53±1.82 | 0.40 |
| Agebase | +0.11±0.20 | 0.58 | ||
| Agebase × time | −0.01±0.05 | 0.88 | −0.014±0.031 | 0.65 |
| CES-D ( | −0.17±0.24 | 0.47 | −0.04±0.16 | 0.78 |
| CES-D × time ( | +0.05±0.06 | 0.35 | +0.02±0.03 | 0.49 |
| | ||||
| Level 1 residuals ( | ||||
| Level 2 residuals | ||||
| Intercept ( | ||||
| Linear slope ( | ||||
| | ||||
| Intercept ( | ||||
| Time ( | +0.07±0.06 | 0.22 | ||
| Agebase | −0.01±0.00 | 0.25 | +0.00±0.00 | 0.29 |
| Agebase × time | −0.001±0.001 | 0.49 | −0.000±0.001 | 0.88 |
| CES-D ( | −0.01±0.01 | 0.17 | +0.00±0.00 | 0.31 |
| CES-D × time ( | +0.01±0.00 | 0.48 | +0.00±0.00 | 0.48 |
| | ||||
| Level 1 residuals ( | ||||
| Level 2 residuals | ||||
| Intercept ( | ||||
| Linear slope ( | ||||
| | ||||
| Intercept ( | ||||
| Time ( | +0.13±0.08 | 0.09 | ||
| Agebase | −0.01±0.01 | 0.26 | +0.01±0.00 | 0.23 |
| Agebase × | −0.000±0.001 | 0.84 | −0.001±0.001 | 0.55 |
| CES-D ( | −0.00±0.01 | 0.58 | +0.01±0.00 | 0.25 |
| CES-D × time ( | +0.00±0.00 | 0.41 | +0.00±0.00 | 0.38 |
| | ||||
| Level 1 residuals ( | ||||
| Level 2 residuals | ||||
| Intercept ( | ||||
| Linear slope ( | ||||
Abbreviations: CES-D, Center for Epidemiologic Studies-Depression Scale; HANDLS, Healthy Aging in Neighborhoods of Diversity Across the Lifespan; HDL-C, high-density lipoprotein-cholesterol; LDL-C, low-density lipoprotein-cholesterol; n-3, omega-3; n-6, omega-6; PUFAs, polyunsaturated fatty acids; TC, total cholesterol.
Models were further adjusted for other covariates (main effects and interaction with time). See Materials and Methods section for more details on covariate coding and model specifications. Time at baseline visit was set to zero. Baseline age was centered at 50 years, total energy intake at 2000 kcal per day, total carotenoid intake at 3 mg per 1000 kcal per day, vitamin C intake at 30 mg per 1000 kcal per day, vitamin A intake at 300 RE per 1000 kcal per day, vitamin E at 3 mg per 1000 kcal per day, vitamin B-6 at 0.8 mg per 1000 kcal per day, vitamin B-12 at 3 μg per 1000 kcal per day, folate at 170 μg per 1000 kcal per day, n-3 PUFA:n-6 PUFA at 0.11. Healthy Eating Index-2010 was centered at 42.
N=number of participants in the analysis; N'=total number of visits included in the analysis. Findings that were significant at a type I error of 0.05 are in bold. γ±s.e.e. refer to the estimated regression coefficients from the mixed-effects regression models with their associated standard error.