| Literature DB >> 30513709 |
Song-Yi Park1, Minji Kang2,3, Lynne R Wilkens4, Yurii B Shvetsov5, Brook E Harmon6, Nitin Shivappa7, Michael D Wirth8, James R Hébert9, Christopher A Haiman10, Loïc Le Marchand11, Carol J Boushey12.
Abstract
Diet quality based on inflammatory potential, assessed by the Dietary Inflammatory Index (DII®), has been related to mortality, but studies from racially/ethnically diverse populations are scarce. Using data from the Multiethnic Cohort Study in Hawaii and California, we investigated the association of the DII with all-cause, cardiovascular disease (CVD) and cancer mortality, both overall and by race/ethnicity. The analysis included 150,405 African Americans, Native Hawaiians, Japanese Americans, Latinos, and Whites aged 45⁻75 years, with 47,436 deaths during an average follow-up of 18.2 ± 4.9 years. In multivariable-adjusted Cox models, the hazard ratios (95% confidence intervals) for the highest vs. lowest quintile of the DII in men and women were 1.15 (1.09⁻1.21) and 1.22 (1.14⁻1.28) for all-cause, 1.13 (1.03⁻1.23) and 1.29 (1.17⁻1.42) for CVD, and 1.10 (1.00⁻1.21) and 1.13 (1.02⁻1.26) for cancer mortality. In men, an increased risk of all-cause mortality with higher DII scores was found in all racial/ethnic groups except for Native Hawaiians (P for heterogeneity < 0.001). Similarly, in women, an increased risk of CVD mortality was found in the four racial/ethnic groups, but not in Native Hawaiians. These findings support the association of a pro-inflammatory diet with a higher risk of mortality and suggest the association may vary by race/ethnicity.Entities:
Keywords: cancer; cardiovascular diseases; cohort; diet; dietary inflammatory index; mortality; multiethnic population
Mesh:
Year: 2018 PMID: 30513709 PMCID: PMC6315679 DOI: 10.3390/nu10121844
Source DB: PubMed Journal: Nutrients ISSN: 2072-6643 Impact factor: 5.717
Baseline characteristics of participants (n = 150,405) in the Multiethnic Cohort by quintiles of Dietary Inflammatory Index (DII) scores.
| Characteristics | Quintile 1 | Quintile 2 | Quintile 3 | Quintile 4 | Quintile 5 |
|---|---|---|---|---|---|
|
| |||||
| DII score, median (IQR) 1 | −4.43 (0.63) | −3.38 (0.51) | −2.28 (0.60) | −0.90 (0.79) | 1.09 (1.36) |
| Age at cohort entry, years, median (IQR) | 62.0 (14.0) | 61.0 (14.0) | 60.0 (14.0) | 59.0 (15.0) | 56.0 (14.0) |
| Race/ethnicity, | |||||
| African American | 1044 (12.1) | 1289 (12.4) | 1653 (12.7) | 1945 (12.2) | 2517 (13.0) |
| Native Hawaiian | 494 (5.7) | 548 (5.3) | 746 (5.7) | 1137 (7.1) | 1938 (10.0) |
| Japanese American | 2795 (32.5) | 2760 (26.5) | 3510 (27.0) | 4808 (30.1) | 6873 (35.5) |
| Latino | 1824 (21.2) | 2792 (26.8) | 3734 (28.7) | 4405 (27.6) | 3635 (18.8) |
| White | 2438 (28.4) | 3010 (28.9) | 3368 (25.9) | 3665 (23.0) | 4423 (22.8) |
| Body mass index 2, kg/m2, median (IQR) | 25.6 (4.4) | 25.9 (4.5) | 26.1 (4.7) | 26.3 (4.7) | 26.2 (5.2) |
| Physical activity 2,3, h/day, median (IQR) | 1.07 (1.46) | 0.93 (1.32) | 0.82 (1.32) | 0.82 (1.21) | 0.82 (1.21) |
| History of diabetes, | 1333 (15.5) | 1272 (12.2) | 1585 (12.2) | 1646 (10.3) | 1386 (7.1) |
| Smoking status, | |||||
| Never | 3337 (38.8) | 3925 (37.7) | 4507 (34.6) | 4959 (31.1) | 4918 (25.4) |
| Former | 4552 (53.0) | 5323 (51.2) | 6583 (50.6) | 7862 (49.3) | 8633 (44.5) |
| Current | 706 (8.2) | 1151 (11.1) | 1921 (14.8) | 3139 (19.7) | 5835 (30.1) |
| Education 2, | |||||
| ≤12 years | 3104 (36.1) | 3861 (37.1) | 5192 (39.9) | 6602 (41.4) | 7956 (41.0) |
| 13–15 years | 2413 (28.1) | 2862 (27.5) | 3594 (27.6) | 4681 (29.3) | 6276 (32.4) |
| ≥16 years | 3078 (35.8) | 3676 (35.3) | 4225 (32.5) | 4677 (29.3) | 5154 (26.6) |
| Married 2, | 6622 (77.0) | 8111 (78.0) | 10,154 (78.0) | 12,370 (77.5) | 14,387 (74.2) |
| Energy intake, kcal/day, median (IQR) | 2094 (1195) | 2139 (1237) | 2186 (1288) | 2231 (1293) | 2340 (1380) |
| Alcohol intake 4, g/day, median (IQR) | 9.1 (19.0) | 8.2 (19.1) | 9.5 (21.3) | 11.7 (27.6) | 16.4 (39.6) |
|
| |||||
| DII score, median (IQR) | −4.48 (0.66) | −3.42 (0.51) | −2.34 (0.60) | −0.97 (0.79) | 0.92 (1.32) |
| Age at cohort entry, years, median (IQR) | 62.0 (14.0) | 60.0 (14.0) | 59.0 (15.0) | 56.0 (14.0) | 54.0 (14.0) |
| Race/ethnicity, | |||||
| African American | 3613 (17.4) | 3392 (17.8) | 3044 (18.1) | 2705 (18.6) | 2446 (20.6) |
| Native Hawaiian | 1328 (6.4) | 1135 (6.0) | 1069 (6.4) | 1226 (8.4) | 1397 (11.7) |
| Japanese American | 7062 (34.0) | 5181 (27.2) | 4689 (27.9) | 4016 (27.7) | 3256 (27.4) |
| Latino | 3779 (18.2) | 4303 (22.6) | 3943 (23.4) | 3285 (22.6) | 2025 (17.0) |
| White | 4978 (24.0) | 5041 (26.5) | 4081 (24.3) | 3292 (22.7) | 2768 (23.3) |
| Body mass index 2, kg/m2, median (IQR) | 24.8 (6.3) | 25.1 (6.2) | 25.4 (6.7) | 25.8 (7.0) | 26.0 (7.6) |
| Physical activity 2,3, h/day, median (IQR) | 0.71 (1.07) | 0.71 (1.07) | 0.71 (0.86) | 0.71 (0.86) | 0.71 (0.86) |
| History of diabetes, | 2358 (11.4) | 1806 (9.5) | 1480 (8.8) | 1230 (8.5) | 827 (7.0) |
| Smoking status, | |||||
| Never | 13,115 (63.2) | 11,646 (61.1) | 9843 (58.5) | 7979 (54.9) | 5674 (47.7) |
| Former | 5886 (28.4) | 5473 (28.7) | 4697 (27.9) | 3930 (27.1) | 2917 (24.5) |
| Current | 1759 (8.5) | 1933 (10.1) | 2286 (13.6) | 2615 (18.0) | 3301 (27.8) |
| Education 2, | |||||
| ≤12 years | 8834 (42.6) | 8247 (43.3) | 7733 (46.0) | 6736 (46.4) | 5637 (47.4) |
| 13–15 years | 6056 (29.2) | 5674 (29.8) | 4924 (29.3) | 4493 (30.9) | 3777 (31.8) |
| ≥16 years | 5870 (28.3) | 5131 (26.9) | 4169 (24.8) | 3295 (22.7) | 2478 (20.8) |
| Married 2, | 12,577 (60.6) | 11,585 (60.8) | 10,214 (60.7) | 8820 (60.7) | 6985 (58.7) |
| MHT 2,5 ever use, | 13,849 (66.7) | 12,973 (68.1) | 11,753 (69.9) | 10,464 (72.0) | 8977 (75.5) |
| Energy intake, kcal/day, median (IQR) | 1745 (991) | 1753 (1023) | 1760 (1039) | 1772 (1086) | 1869 (1183) |
| Alcohol intake 4, g/day, median (IQR) | 3.5 (10.6) | 3.0 (9.0) | 3.1 (10.1) | 3.8 (12.3) | 4.5 (19.9) |
1 IQR, interquartile range. 2 Missing values were imputed using multiple imputation. 3 Moderate-to-vigorous physical activity. 4 Among drinkers. 5 MHT, menopausal hormone therapy.
Median and interquartile range (IQR) of Dietary Inflammatory Index (DII) scores by sex and race/ethnicity in the Multiethnic Cohort.
| Race/Ethnicity | Men | Women | ||
|---|---|---|---|---|
|
| Median (IQR) |
| Median (IQR) | |
| African American | 8448 | −1.49 (3.34) | 15,200 | −2.67 (2.89) |
| Native Hawaiian | 4863 | −0.74 (3.52) | 6155 | −2.21 (3.43) |
| Japanese American | 20,746 | −1.24 (3.51) | 24,204 | −2.92 (2.83) |
| Latino | 16,390 | −1.72 (2.80) | 17,335 | −2.73 (2.50) |
| White | 16,904 | −1.81 (3.31) | 20,160 | −2.87 (2.64) |
| Total | 67,351 | −1.51 (3.30) | 83,054 | −2.78 (2.77) |
Hazard ratios (HR) (95% confidence intervals (CI)) for all-causes, cardiovascular disease (CVD), and cancer mortality according to quintiles of Dietary Inflammatory Index scores in the Multiethnic Cohort, 1993–2014.
| Men ( | Women ( | ||||||
|---|---|---|---|---|---|---|---|
| Deaths | HR (95% CI) 1 | HR (95% CI) 2 | Deaths | HR (95% CI) 1 | HR (95% CI) 2 | ||
|
| |||||||
| Quintile 1 | 3308 | 1.00 | 1.00 | 6181 | 1.00 | 1.00 | |
| Quintile 2 | 3832 | 1.02 (0.97–1.07) | 1.03 (0.98–1.09) | 5399 | 1.03 (1.00–1.07) | 1.04 (0.99–1.09) | |
| Quintile 3 | 4797 | 1.09 (1.04–1.14) | 1.03 (0.98–1.09) | 4578 | 1.10 (1.06–1.14) | 1.06 (1.01–1.12) | |
| Quintile 4 | 5632 | 1.16 (1.11–1.21) | 1.07 (1.01–1.12) | 3764 | 1.20 (1.15–1.25) | 1.12 (1.06–1.18) | |
| Quintile 5 | 6822 | 1.42 (1.36–1.48) | 1.15 (1.09–1.21) | 3123 | 1.45 (1.39–1.51) | 1.21 (1.14–1.28) | |
| <0.001 | <0.001 | <0.001 | <0.001 | 0.83 | |||
| Continuous | 1.07 (1.06–1.08) | 1.03 (1.02–1.04) | 1.07 (1.06–1.07) | 1.03 (1.02–1.04) | |||
|
| |||||||
| Quintile 1 | 1176 | 1.00 | 1.00 | 2116 | 1.00 | 1.00 | |
| Quintile 2 | 1342 | 1.01 (0.93–1.09) | 1.04 (0.95–1.14) | 1834 | 1.04 (0.97–1.10) | 1.06 (0.98–1.15) | |
| Quintile 3 | 1721 | 1.10 (1.02–1.18) | 1.04 (0.95–1.13) | 1609 | 1.16 (1.09–1.24) | 1.12 (1.04–1.22) | |
| Quintile 4 | 1961 | 1.15 (1.07–1.23) | 1.09 (1.00–1.19) | 1245 | 1.22 (1.13–1.31) | 1.11 (1.02–1.22) | |
| Quintile 5 | 2201 | 1.31 (1.22–1.40) | 1.13 (1.03–1.23) | 1007 | 1.47 (1.36–1.58) | 1.29 (1.17–1.42) | |
| <0.001 | 0.003 | <0.001 | <0.001 | 0.78 | |||
| Continuous | 1.05 (1.04–1.07) | 1.03 (1.01–1.04) | 1.07 (1.05–1.08) | 1.04 (1.03–1.06) | |||
|
| |||||||
| Quintile 1 | 906 | 1.00 | 1.00 | 1658 | 1.00 | 1.00 | |
| Quintile 2 | 1098 | 1.05 (0.97–1.15) | 1.02 (0.92–1.13) | 1481 | 1.02 (0.95–1.09) | 1.02 (0.94–1.12) | |
| Quintile 3 | 1390 | 1.12 (1.03–1.22) | 1.01 (0.92–1.12) | 1263 | 1.05 (0.98–1.13) | 1.01 (0.92–1.10) | |
| Quintile 4 | 1690 | 1.22 (1.12–1.32) | 1.01 (0.92–1.11) | 1134 | 1.20 (1.11–1.29) | 1.06 (0.97–1.17) | |
| Quintile 5 | 2273 | 1.58 (1.46–1.70) | 1.10 (1.00–1.21) | 1005 | 1.45 (1.34–1.57) | 1.13 (1.02–1.26) | |
| <0.001 | 0.03 | <0.001 | 0.02 | 0.92 | |||
| Continuous | 1.09 (1.08–1.10) | 1.02 (1.01–1.04) | 1.07 (1.05–1.08) | 1.02 (1.00–1.04) | |||
1 Adjusted for age at cohort entry and race/ethnicity. 2 Adjusted for age at cohort entry, race/ethnicity, body mass index, history of diabetes, education, marital status, physical activity, alcohol intake, energy intake, and menopausal hormone therapy use (for women only) in the smoking model including smoking status, average number of cigarettes, squared average number of cigarettes, number of years smoked (time-dependent), number of years since quitting (time-dependent), and interactions between ethnicity and smoking status, average number of cigarettes, squared average number of cigarettes and number of years smoked. 3 Based on the multivariable-adjusted models. 4 Tests for linearity.
Hazard ratios (HR) (95% confidence intervals (CI)) for all-causes, cardiovascular disease (CVD), and cancer mortality according to quintiles of Dietary Inflammatory Index scores by race/ethnicity among men in the Multiethnic Cohort, 1993–2014.
| African American | Native Hawaiian | Japanese American | Latino | White | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Deaths | HR (95% CI) 1 | Deaths | HR (95% CI) 1 | Deaths | HR (95% CI) 1 | Deaths | HR (95% CI) 1 | Deaths | HR (95% CI) 1 | ||
|
| |||||||||||
| Quintile 1 | 548 | 1.00 | 213 | 1.00 | 1139 | 1.00 | 624 | 1.00 | 784 | 1.00 | |
| Quintile 2 | 677 | 1.15 (0.99–1.33) | 219 | 0.89 (0.67–1.18) | 1075 | 1.01 (0.92–1.11) | 942 | 1.10 (0.98–1.23) | 919 | 0.98 (0.88–1.10) | |
| Quintile 3 | 822 | 1.07 (0.93–1.23) | 292 | 0.91 (0.70–1.19) | 1318 | 0.98 (0.89–1.07) | 1257 | 1.11 (0.99–1.24) | 1108 | 1.07 (0.96–1.19) | |
| Quintile 4 | 969 | 1.12 (0.98–1.28) | 397 | 0.81 (0.63–1.04) | 1546 | 0.99 (0.91–1.08) | 1498 | 1.18 (1.05–1.31) | 1222 | 1.11 (1.00–1.24) | |
| Quintile 5 | 1290 | 1.13 (0.99–1.30) | 653 | 0.85 (0.67–1.07) | 1987 | 1.06 (0.97–1.16) | 1243 | 1.32 (1.18–1.48) | 1649 | 1.24 (1.11–1.38) | |
| 0.20 | 0.20 | 0.15 | <0.001 | <0.001 | <0.001 | ||||||
| Continuous | 1.02 (1.00–1.04) | 0.98 (0.94–1.01) | 1.01 (1.00–1.02) | 1.05 (1.03–1.07) | 1.05 (1.03–1.06) | ||||||
|
| |||||||||||
| Quintile 1 | 229 | 1.00 | 77 | 1.00 | 369 | 1.00 | 239 | 1.00 | 262 | 1.00 | |
| Quintile 2 | 247 | 1.03 (0.82–1.30) | 78 | 0.96 (0.60–1.55) | 362 | 1.03 (0.88–1.21) | 354 | 1.03 (0.85–1.25) | 301 | 1.09 (0.90–1.33) | |
| Quintile 3 | 311 | 0.90 (0.72–1.12) | 112 | 0.96 (0.62–1.50) | 436 | 1.00 (0.86–1.17) | 466 | 1.07 (0.89–1.28) | 396 | 1.17 (0.97–1.41) | |
| Quintile 4 | 367 | 0.98 (0.79–1.22) | 146 | 0.88 (0.58–1.34) | 498 | 1.03 (0.88–1.20) | 544 | 1.15 (0.96–1.37) | 406 | 1.27 (1.05–1.53) | |
| Quintile 5 | 465 | 0.97 (0.78–1.21) | 240 | 0.96 (0.64–1.42) | 619 | 1.16 (1.00–1.35) | 377 | 1.08 (0.89–1.31) | 500 | 1.32 (1.09–1.59) | |
| 0.82 | 0.84 | 0.05 | 0.26 | 0.002 | 0.24 | ||||||
| Continuous | 1.01 (0.97–1.04) | 1.01 (0.95–1.06) | 1.03 (1.00–1.05) | 1.02 (0.99–1.05) | 1.05 (1.02–1.08) | ||||||
|
| |||||||||||
| Quintile 1 | 142 | 1.00 | 56 | 1.00 | 294 | 1.00 | 173 | 1.00 | 241 | 1.00 | |
| Quintile 2 | 201 | 1.22 (0.94–1.60) | 62 | 0.94 (0.56–1.58) | 307 | 1.04 (0.87–1.23) | 248 | 1.02 (0.82–1.27) | 280 | 0.93 (0.77–1.13) | |
| Quintile 3 | 250 | 1.19 (0.92–1.53) | 94 | 1.17 (0.72–1.93) | 377 | 0.97 (0.82–1.15) | 349 | 1.05 (0.85–1.29) | 320 | 0.95 (0.79–1.15) | |
| Quintile 4 | 298 | 1.26 (0.98–1.62) | 112 | 0.88 (0.55–1.41) | 466 | 0.93 (0.79–1.09) | 427 | 1.07 (0.88–1.32) | 387 | 0.99 (0.82–1.20) | |
| Quintile 5 | 425 | 1.25 (0.97–1.61) | 214 | 1.08 (0.69–1.66) | 678 | 0.96 (0.82–1.13) | 427 | 1.37 (1.11–1.68) | 529 | 1.06 (0.88–1.28) | |
| 0.18 | 0.73 | 0.36 | <0.001 | 0.24 | 0.02 | ||||||
| Continuous | 1.02 (0.99–1.06) | 1.01 (0.95–1.07) | 1.00 (0.97–1.02) | 1.06 (1.03–1.10) | 1.03 (1.00–1.05) | ||||||
1 Adjusted for age at cohort entry, body mass index, history of diabetes, education, marital status, physical activity, alcohol intake, and energy intake in n the smoking model including smoking status, average number of cigarettes, squared average number of cigarettes, number of years smoked (time-dependent), and number of years since quitting (time-dependent). 2 Tests for linearity.
Hazard ratios (HR) (95% confidence intervals (CI)) for all-causes, cardiovascular disease (CVD), and cancer mortality according to quintiles of Dietary Inflammatory Index scores by race/ethnicity among women in the Multiethnic Cohort, 1993–2014.
| African American | Native Hawaiian | Japanese American | Latino | White | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Deaths | HR (95% CI) 1 | Deaths | HR (95% CI) 1 | Deaths | HR (95% CI) 1 | Deaths | HR (95% CI) 1 | Deaths | HR (95% CI) 1 | ||
|
| |||||||||||
| Quintile 1 | 1494 | 1.00 | 430 | 1.00 | 1934 | 1.00 | 966 | 1.00 | 1357 | 1.00 | |
| Quintile 2 | 1381 | 1.04 (0.95–1.15) | 325 | 1.16 (0.93–1.47) | 1359 | 1.07 (0.99–1.15) | 1030 | 0.95 (0.85–1.06) | 1304 | 1.05 (0.96–1.16) | |
| Quintile 3 | 1189 | 1.08 (0.98–1.19) | 289 | 1.02 (0.80–1.29) | 1078 | 1.03 (0.95–1.12) | 945 | 1.05 (0.94–1.18) | 1077 | 1.11 (1.00–1.23) | |
| Quintile 4 | 1030 | 1.23 (1.10–1.36) | 313 | 1.09 (0.86–1.38) | 767 | 1.07 (0.97–1.17) | 774 | 1.10 (0.98–1.24) | 880 | 1.09 (0.97–1.22) | |
| Quintile 5 | 893 | 1.25 (1.12–1.40) | 324 | 1.16 (0.92–1.48) | 565 | 1.13 (1.01–1.27) | 485 | 1.17 (1.02–1.34) | 856 | 1.30 (1.16–1.47) | |
| <0.001 | 0.32 | 0.04 | 0.003 | <0.001 | 0.24 | ||||||
| Continuous | 1.04 (1.02–1.06) | 1.01 (0.98–1.05) | 1.02 (1.00–1.04) | 1.04 (1.02–1.06) | 1.04 (1.02–1.06) | ||||||
|
| |||||||||||
| Quintile 1 | 600 | 1.00 | 142 | 1.00 | 610 | 1.00 | 362 | 1.00 | 402 | 1.00 | |
| Quintile 2 | 540 | 1.06 (0.92–1.23) | 108 | 1.11 (0.75–1.64) | 454 | 1.12 (0.98–1.28) | 360 | 0.91 (0.76–1.09) | 372 | 1.12 (0.93–1.35) | |
| Quintile 3 | 505 | 1.17 (1.00–1.37) | 102 | 0.98 (0.65–1.48) | 352 | 1.08 (0.93–1.26) | 307 | 0.95 (0.79–1.15) | 343 | 1.35 (1.11–1.64) | |
| Quintile 4 | 418 | 1.27 (1.08–1.50) | 94 | 0.71 (0.46–1.08) | 250 | 1.16 (0.98–1.37) | 225 | 0.87 (0.70–1.06) | 258 | 1.21 (0.97–1.50) | |
| Quintile 5 | 331 | 1.39 (1.16–1.66) | 95 | 0.86 (0.56–1.34) | 169 | 1.14 (0.93–1.39) | 162 | 1.17 (0.93–1.48) | 250 | 1.60 (1.27–2.01) | |
| <0.001 | 0.18 | 0.10 | 0.50 | <0.001 | 0.006 | ||||||
| Continuous | 1.06 (1.03–1.09) | 0.95 (0.88–1.01) | 1.02 (0.99–1.05) | 1.03 (0.99–1.07) | 1.07 (1.03–1.11) | ||||||
|
| |||||||||||
| Quintile 1 | 413 | 1.00 | 117 | 1.00 | 491 | 1.00 | 261 | 1.00 | 376 | 1.00 | |
| Quintile 2 | 372 | 0.99 (0.83–1.18) | 93 | 1.20 (0.79–1.82) | 349 | 1.04 (0.89–1.21) | 275 | 0.91 (0.74–1.11) | 392 | 1.11 (0.93–1.32) | |
| Quintile 3 | 304 | 1.00 (0.83–1.21) | 78 | 0.93 (0.60–1.42) | 294 | 0.98 (0.83–1.15) | 277 | 1.01 (0.82–1.24) | 310 | 1.07 (0.89–1.29) | |
| Quintile 4 | 306 | 1.10 (0.90–1.34) | 104 | 1.38 (0.91–2.11) | 230 | 0.96 (0.80–1.15) | 244 | 1.15 (0.93–1.42) | 250 | 0.99 (0.81–1.21) | |
| Quintile 5 | 271 | 1.06 (0.86–1.30) | 114 | 1.47 (0.97–2.23) | 188 | 1.05 (0.85–1.28) | 148 | 1.04 (0.81–1.33) | 284 | 1.30 (1.05–1.60) | |
| 0.40 | 0.05 | 0.98 | 0.20 | 0.09 | 0.44 | ||||||
| Continuous | 1.01 (0.98–1.04) | 1.06 (1.00–1.13) | 1.00 (0.97–1.03) | 1.02 (0.98–1.06) | 1.03 (1.00–1.06) | ||||||
1 Adjusted for age at cohort entry, BMI, history of diabetes, education, marital status, physical activity, alcohol intake, energy intake, and menopausal hormone therapy use. In the smoking model including smoking status, average number of cigarettes, squared average number of cigarettes, number of years smoked (time-dependent), and number of years since quitting (time-dependent). 2 Tests for linearity.