| Literature DB >> 25889396 |
Abstract
BACKGROUND: The "gateway hypothesis" usually refers to the possibility that the taking up of habit A, which is considered harmless (or less harmful), may lead to the subsequent taking up of another habit, B, which is considered harmful (or more harmful).Entities:
Mesh:
Year: 2015 PMID: 25889396 PMCID: PMC4369866 DOI: 10.1186/s12954-015-0040-7
Source DB: PubMed Journal: Harm Reduct J ISSN: 1477-7517
Bias in estimating the association between uptake of B and prior use of A
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| Time 0 | 10000 | 0 | 0 | 0 | 0 |
| Start using A |
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| Start using B |
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| Time 1 | 10000 − 250 − 500 = 9250 | 250 | 500 | 0 | 0 |
| Start using A |
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| Start using B |
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| Time 2 | 9250 − 231 − 463 = 8556 | 250 + 231 − 13 = 469 | 500 + 463 − 13 = 950 | 13 | 13 |
| Start using A |
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| Start using B |
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| Time 3 | 8556 − 214 − 428 = 7915 | 469 + 214 − 23 = 659 | 950 + 428 − 24 = 1354 | 13 + 23 = 36 | 13 + 24 = 36 |
| Start using A |
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| Start using B |
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| Time 4 | 7915 − 198 − 396 = 7321 | 659 + 198 − 33 = 824 | 1354 + 396 − 34 = 1716 | 36 + 33 = 69 | 36 + 34 = 70 |
| P1: Proportion who start B among A first users | 69/(824 + 69) | =0.08 | |||
| P2: Proportion who start B among others | (1716 + 70)/(7321 + 1716 + 70) | =0.20 | |||
| P3: Proportion who start B among never A users | 1716/(7321 + 1716) | =0.19 | |||
| OR1 as defined in (using P1 and P2) | (0.08/(1-0.08))/(0.20/(1-0.20)) | =0.34 | |||
| OR2 as defined in (using P1 and P3) | (0.08/(1-0.08))/(0.19/(1-0.19)) | =0.36 | |||
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| Period 1–2 | (13/250)/(463/9250) | =1 | ||
| Period 2–3 | (23/469)/(428/8556) | =1 | |||
| Period 3–4 | (33/659)/(396/7915) | =1 | |||
The example involves four time periods, with starting of A and B assumed to be independent. Rows in normal type style indicate time points, and rows in italicized type style indicate the periods between the time points. In each period, 2.5% of those who have never used A by the previous time point start A, and 5% of those who have never used B by the previous time point start B. The arrows and roman numerals indicate the column to which starters are re-allocated at the next time point. It is assumed that no individual starts both products in a single period. The values are shown rounded to nearest whole numbers but are calculated to full precision (so that there are some apparent discrepancies in the additions).
First example of confounding
| Unadventurous | Risk takers | Overall | |||||||||
| 5000 | 5000 | 10000 | |||||||||
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| (Sum over unadventurous and risk takers) | |||||||||
| ↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ||||||
| A | Not A | A | Not A | A | Not A | ||||||
| 0 | 5000 | 2000 | 3000 | 2000 | 8000 | ||||||
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| (sum) | (sum) | ||||||
| ↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ↙ | ↘ |
| B | Not B | B | Not B | B | Not B | B | Not B | B | Not B | B | Not B |
| 0 | 0 | 0 | 5000 | 800 | 1200 | 1200 | 1800 | 800 | 1200 | 1200 | 6800 |
| OR (within risk takers) = (800/1200)/(1200/1800) =1.00 | OR (overall, unadjusted) = (1000/1200)/(1200/6800) = 3.78 | ||||||||||
It is assumed that there is no use of A or B among the “unadventurous”, and that use of A and B is independent among the ‘risk takers’. The table shows the joint distribution of use of A and B, separately for the “unadventurous” and the “risk takers” and overall, and demonstrates that the unadjusted OR shows a markedly spurious relationship.
Second example of confounding
| Unadventurous | Risk takers | Overall | |||||||||
| 5000 | 5000 | 10000 | |||||||||
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| (Sum over unadventurous and risk takers) | |||||||||
| ↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ||||||
| A | Not A | A | Not A | A | Not A | ||||||
| 0 | 5000 | 2000 | 3000 | 2200 | 8000 | ||||||
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| (sum) | (sum) | ||||||
| ↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ↙ | ↘ |
| B | Not B | B | Not B | B | Not B | B | Not B | B | Not B | B | Not B |
| 0 | 0 | 0 | 5000 | 1000 | 1000 | 900 | 2100 | 1000 | 1000 | 900 | 7100 |
| OR (within risk takers) = (1000/1000)/(900/2100) = 2.33 | OR (overall, unadjusted) = (1000/1000)/(900/7100) = 7.89 | ||||||||||
As in Table 2, it is assumed that there is no use of A or B among the “unadventurous”. Here, however, the use of A and B is assumed to be correlated among the “risk takers”. It is demonstrated that the unadjusted odds ratio is substantially higher than the OR in the “risk takers”.
Third example of confounding
| Unadventurous | Risk takers | Overall | |||||||||
| 5000 | 5000 | 10000 | |||||||||
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| (Sum over unadventurous and risk takers) | |||||||||
| ↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ||||||
| A | Not A | A | Not A | A | Not A | ||||||
| 200 | 4800 | 2000 | 3000 | 2200 | 7800 | ||||||
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| (sum) | (sum) | ||||||
| ↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ↙ | ↘ |
| B | Not B | B | Not B | B | Not B | B | Not B | B | Not B | B | Not B |
| 10 | 190 | 144 | 4656 | 1000 | 1000 | 900 | 2100 | 1010 | 1190 | 1044 | 6756 |
| OR (within unadventurous) = (10/190)/(144/4656) = 1.70 | OR (within risk takers) = (1000/1000)/(900/2100) = 2.33 | OR (overall, unadjusted) = (1010/1196)/(1044/6756) = 5.49 | |||||||||
| OR (overall, adjusted for risk taking) = ((10 × 4656)/5000 + (1000 × 2100)/5000)/((190 × 144)/5000 + (1000 × 900)/5000) = 2.31 | |||||||||||
In this example, unlike in Tables 2 and 3, there is some use of A and B in the “unadventurous”, though much less than in the “risk takers”. It is also assumed that the use of A and B is correlated in both subgroups. It is demonstrated that the unadjusted OR substantially overestimates the adjusted OR.