a Division of Biostatistics, Department of Community Medicine, University of Connecticut School of Medicine, Farmington, CT 06030-6325, USA.
b Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD, USA.
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Abstract |
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Methods The authors applied different logistic regression models on a case-control study concerning the risk of colorectal adenomas due to meat and its different subsets such as white meat, red meat and well-done red meat.
Results By calculating OR for a fixed amount of intake, the authors suggest a method for partitioning the risk of one dietary item into that associated with increasingly detailed sub-components. A graph is presented for illustrating such partitions in terms of both addition and substitution effects.
Conclusions Odds ratios based on upper versus lower quantiles or percentiles are useful as they compare the risk between the upper and lower ends of the consumption range. A complimentary set of OR are those based on fixed amounts of consumption. These allow for direct comparisons between nested subgroups of dietary components, in order to disentangle the risk linked to specific groups of foods or nutrients.
Keywords Data interpretation, statistical, diet, epidemiological methods, nutrition assessment
Accepted 7 June 2000
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Introduction |
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When dissecting the risk of a dietary group into that which is generated by its various subsets, it is of interest to compare odds ratios (OR). For quantiles, such comparisons are misleading when the typical amounts consumed differ for different subsets. We illustrate this problem using an example of meat consumption, cooking practices and the risk of colorectal adenoma. An alternative approach allowing for direct comparison is to calculate all OR using the same fixed amount of intake, such as 10-g increments. We then demonstrate how to partition the risk associated with total meat consumption to that of its sub-components.
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Materials and Methods |
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After returning home, participants filled in a self-administered food frequency questionnaire concerning their usual diet approximately one year before sigmoidoscopy/colonoscopy. Among other things they provided the frequency and portion size consumed of different types of meat and how well cooked they were. From that we calculated the estimated daily grams of meat consumed for each combination. A typical individual reported both well done and medium/rare consumption, but in varying quantities.
Odds ratios were calculated using logistic regression, with the meat variables being either in their original continuous form or categorized into quintiles. All analyses were adjusted for age, gender, total energy intake, physical activity, pack-years of smoking, non-steroidal anti-inflammatory drug use, and reason for colorectal screening.
Four sequentially nested models were analysed. In Model 1, total meat is the only meat variable included. In Model 2, this variable is divided into red meat (beef, pork and lamb) and white meat (chicken and fish). In Model 3, red meat is split into five types of red meat that are cooked to variable levels (beef steak, hamburgers/cheeseburgers, pork chops/ham steaks, sausage/hot dogs and bacon), referred to as variably cooked red meat. Also in this model are the remaining types of red meat that are either cooked to a standard level or for which it was not known how well they were cooked (liverwurst, liver, luncheon meats, beef stew, pork roast, spaghetti sauce with meat, other ground beef, and lamb) are referred to as other red meat. Finally, in Model 4, the variably cooked red meat is split into whether it was prepared well done or medium/rare. White meat was retained in Models 3 and 4 and other red meat was retained in Model 4, so that total meat consumption was accounted for in all models.
We looked at addition effects, the risk associated with adding the amount of one subgroup (e.g. red meat) while keeping the consumption of other subgroups (e.g. white meat) constant, as well as substitution effects, where the total consumed is held fixed so that adding to the amount consumed of one subgroup (red meat) is offset by subtracting an equal amount consumed of the other subgroups (white meat). The OR of the substitution effect is 1 if there is no difference in the risk associated with red and white meat. By including red and white meat as two separate variables in the regression equation we obtained estimates and confidence interval (CI) for the addition effects. When instead the total meat variable is used, this reflects the addition effect of white meat (red meat is fixed) while the red meat variable provides the estimate and CI for the substitution effect of red versus white meat (total meat is fixed).10
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Results |
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A way to depict the partition of OR for a nested set of variables is through a graph as illustrated in Figure 2. Marked on the left side is the OR of 1.04 associated with a 10-g increase in total daily meat consumption. As we move right in the Figure, this is then partitioned into an OR of 1.11 for red meat and 0.95 for white meat, and so on. As another example, the OR for variably cooked red meat is 1.17, which is partitioned into 1.10 for medium/rare and 1.30 for well done red meat.
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In the example above we used a model where the risk associated with increased consumption changes according to a linear function on the log scale. That fits very well with the data, giving a higher log likelihood value than the categorical models. Adding a quadratic term did not significantly improve the model fit. This may or may not be true for other data set though, and the proposed dissection and comparisons can also be used when the regression equation contains non-linear terms, if these non-linear terms represent the total consumed of the different sub-components.
Using the same data, Table 2 presents the dissection of the OR when a quadratic term is added to the model. The nature of a non-linear term is that the increase in the odds due to a fixed increase in consumption is different depending on the original amount consumed. For example, when fitting a quadratic rather than linear term, the OR for a 10-g increase of total meat are 1.024, 1.025, 1.026, 1.029 and 1.033 for original consumptions of 0, 10, 20, 50 and 100 g, respectively. As before, it is possible to dissect how much of this risk is due to various sub-components. This is done by including in the logistic regression model a linear term for each of the meat subtypes, plus a quadratic term for total meat. For example, with our data the OR of 1.026 associated with an increase of total meat consumption from 20 to 30 g is dissected into OR of 1.113 and 0.956 for red and white meat, respectively.
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Discussion |
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In our example, there are a total of 10 different substitution effects that can be calculated, one in Model 2, three in Model 3 and six in Model 4, as every dietary component can be substituted for every other component in the same model. The OR for each of these substitution effects are easily read using Figure 2, by measuring the distance between the two dietary components that are to be substituted, and comparing that distance with the scale on the y-axis. A table reporting 10 additional and 10 substitution effects would, by contrast, be much harder to comprehend.
When applying and interpreting the proposed type of analysis, some caution is warranted. It is inadvisable to split a variable into two components that are highly correlated with each other. How correlated they can be depends on the size of the data set. The key way to determine whether a dissection is informative is to look at the width of the CI for both the addition and substitution effects. It is also important to note that the proposed method cannot be used to compare OR for exposures that are measured in different units. That is a different type of problem, related to attributable risk.13
Odds ratios based on upper versus lower quartiles or quintiles are useful, as they compare the risk between the upper and lower ends of the consumption range in the population under study. Hence the OR reflect a risk differential that is reasonably achievable through preventive measures. A complimentary set of OR are those based on fixed amounts of consumption. These allow for direct comparisons between nested subgroups of dietary components, in order to disentangle the risk linked to specific groups of foods or nutrients. They may also be applied for other types of exposure that have natural sub-components, such as physical activity, occupational histories, radiation exposure or smoking.
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References |
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