Figure 1.
PRISMA flow diagram of identification of randomized clinical trials for inclusion.
Figure 2.
Trial sequential analysis of 6 trials assessing beta-carotene in a dose at or below 9.6 mg daily versus placebo.
The diversity-adjusted required information size (DARIS = 267,631 participants) was based on a proportion of deaths of 10% in the placebo group; a relative risk reduction of 5% in the beta-carotene group; an alpha of 5%; a beta of 20%; and a diversity of 59%. The blue line represents the cumulative Z-score of the meta-analysis. The green lines represent the conventional statistical boundaries. The red lines represent the truncated trial sequential monitoring boundaries.
Figure 3.
Trial sequential analysis of 20 trials assessing beta-carotene in a dose above 9.6 mg daily versus placebo.
The diversity-adjusted required information size (DARIS = 190,906 participants) was based on a proportion of deaths of 10% in the placebo group; a relative risk reduction of 5% in the beta-carotene group; an alpha of 5%; a beta of 20%; and a diversity of 42%. The blue line represents the cumulative Z-score of the meta-analysis. The green lines represent the conventional statistical boundaries. The red inward sloping lines represent the trial sequential monitoring boundaries. The red outward sloping lines represents the area of futility.
Figure 4.
Trial sequential analysis of 8 trials assessing vitamin A in a dose at or below RDA (≤ 800 µg) daily versus placebo.
The diversity-adjusted required information size (DARIS = 48,417 participants) was based on a proportion of deaths of 10% in the placebo group; a relative risk reduction of 15% in the vitamin A group; an alpha of 5%; a beta of 20%; and a diversity of 76%. The blue line represents the cumulative Z-score of the meta-analysis. The green lines represent the conventional statistical boundaries. The red lines represent the truncated trial sequential monitoring boundaries. Had we used a relative risk reduction of 5% as planned, the DARIS would have been 456,748 participants and the program could not have drawn the trial sequential analysis due to the fact that the number of randomized patients out of the DARIS is too small. This is why, we post hoc decided to construct the trial sequential analysis with a larger relative risk reduction.
Figure 5.
Trial sequential analysis of 4 trials assessing vitamin A in a dose above the RDA (> 800 µg) daily versus placebo.
The diversity-adjusted required information size (DARIS = 415,996 participants) was based on a proportion of deaths of 10% in the placebo group; a relative risk reduction of 5% in the vitamin A group; an alpha of 5%; a beta of 20%; and a diversity of 73%. The blue line represents the cumulative Z-score of the meta-analysis. The green lines represent the conventional statistical boundaries. The red lines represent the truncated trial sequential monitoring boundaries.
Figure 6.
Trial sequential analysis of 2 trials assessing vitamin E in a dose at or below RDA (≤ 15 mg) daily versus placebo.
The diversity-adjusted required information size (DARIS = 12,563 participants) was based on a proportion of deaths of 10% in the placebo group; a relative risk reduction of 15% in the vitamin E group; an alpha of 5%; a beta of 20%; and a diversity of 7%. The blue line represents the cumulative Z-score of the meta-analysis. The green lines represent the conventional statistical boundaries. The red lines represent the truncated trial sequential monitoring boundaries. Had we used a relative risk reduction of 5% as planned, the DARIS would have been 119,364 participants and the program could not have drawn the trial sequential analysis due to the fact that the number of randomized patients out of the DARIS is too small. This is why, we post hoc decided to construct the trial sequential analysis with a larger relative risk reduction.
Figure 7.
Trial sequential analysis of 44 trials assessing vitamin E in a dose above the RDA (> 15 mg) daily versus placebo.
The diversity-adjusted required information size (DARIS = 110,505 participants) was based on a proportion of deaths of 10% in the placebo group; a relative risk reduction of 5% in the vitamin E group; an alpha of 5%; a beta of 20%; and a diversity of 0%. The blue line represents the cumulative Z-score of the meta-analysis. The green lines represent the conventional statistical boundaries. The red inward sloping lines represent the trial sequential monitoring boundaries. The red outward sloping lines represent the area of futility.