Table 3.

Effects of β-carotene alone (BC), α-tocopherol alone (AT) and α-tocopherol and β-carotene combined (AT + BC) on mortality by vitamin C intake, and by fruit and vegetable intake in heavy smokers who started smoking late in their life (Alpha-Tocopherol Beta-Carotene Study 1985–1993)^*

Subgroup	Placebo	BC	AT	AT + BC	Test of interaction: P
Group C: vitamin C ≥ 90 mg/d and fruit and vegetables ≥275 g/d
RR	1·0	6·1	2·8	2·5	0·030
95 % CI	Reference	1·4, 27	0·57, 14	0·48, 13
Deaths	2	13	6	5
Participants	69	81	78	73
Person-years	429	469	468	443
Rate	4·7	27·7	12·8	11·6
Group B: vitamin C ≥ 90 mg/d and fruit and vegetables <275 g/d
RR	1·0	0·45	0·85	0·98	0·08
95 % CI	Reference	0·19, 1·02	0·44, 1·7	0·51, 1·9
Deaths	19	8	16	17
Participants	171	157	168	157
Person-years	1010	945	995	915
Rate	18·8	8·5	16·1	18·6
Group A: vitamin C < 90 mg/d
RR	1·0	2·26	1·50	1·63	0·06
95 % CI	Reference	1·27, 4·00	0·82, 2·70	0·90, 3·00
Deaths	17	35	29	30
Participants	223	214	261	251
Person-years	1341	1228	1532	1463
Rate	12·7	28·5	18·9	20·5
Test of difference (2 df) over the subgroups A to C; P		0·0004	0·3	0·4

RR, risk ratio.

^*This subgroup analysis is restricted to the heavy smokers (≥21/d) who started smoking late in life (≥21 years), i.e. the lower right-hand corner in Table 1. In all, 145 participants with missing dietary data were excluded from this analysis, which left 1903 participants. A conservative approach to analyse this Table is to first assume that each subgroup A to C has a uniform mortality rate over all the trial arms. Thereafter each of the three treatment groups BC, AT and AT + BC in each of the three subgroups A to C are allowed their own treatment effect, leading to a total of 3 × 3 = 9 effect estimates. When the nine treatment effects were allowed for the Cox model, it was improved (χ² (9 df) = 22·0; P = 0·009), compared with the model that assumes no effects of BC or vitamin E or their combination. Thereafter, the heterogeneity within the treatment arms was further examined. Adding a uniform BC effect gave RR 1·56 (95 % CI 1·03, 2·36), a uniform vitamin E (AT) effect gave RR 1·25 (95 % CI 0·82, 1·90), and a uniform AT + BC effect gave RR 1·37 (95 % CI 0·90, 2·08). When individual BC effects shown in this Table were allowed for the three subgroups A to C in the BC arm, the Cox regression model was improved (χ² (2 df) = 15·7; P = 0·0004). When individual AT effects were allowed for the three subgroups of the AT arm, the model was improved (χ² (2 df) = 2·8; P = 0·3), and individual AT + BC effects to the AT + BC arm improved the model (χ² (2 df) = 1·8; P = 0·4). The interaction between BC and vitamin E in subgroups A to C in this Table was calculated by first including the BC and vitamin E effects into the model, and thereafter adding the interaction terms. The fit of the Cox model increased (χ² (3 df) = 11·1; P = 0·011). There are no substantial baseline differences between the four arms in subgroups A, B or C (Supplementary Table S1 of Supplementary material).