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Solution to question 6.4

As this is a prospective study it makes sense to claculate the risk ratios. I've expressed all my risk ratios in terms of the most 'risky' categories. If you've done it the other way round it doesn't matter, as long as your interpretation ends up the same.

Social class

The risk of a 'manual' child having caries is: 162÷736 = 0·220

162 out of 736 'manual' children have caries.

The risk of a 'non-manual' child having caries is: 64÷638 = 0·100

64 out of 638 'non-manual' children have caries.

The risk ratio for having caries for 'manual' children compared to 'non-manual' children is 0·220÷0·100= 2·19

'Manual' children have about twice the risk of caries compared to 'non-manual' children

Brushing frequency

The risk of a child brushing less than twice a day having caries is: 114÷591 = 0·193

114 out of 591 children brushing less than twice a day have caries.

The risk of a child brushing at least twice a day having caries is: 112÷783 = 0·143

112 out of 783 children brushing at least twice a day have caries.

The risk ratio for having caries for children brushing less than twice a day compared to children brushing at least twice a day is 0·193÷0·143= 1·35

Children brushing less than twice a day have about one and a third the risk of caries compared to children who brush at least twice a day

Sugary foods

The risk of a child who eats sugary foods 3 or more times a day having caries is: 165÷966 = 0·171

165 out of 966 children eating sugary foods 3 or more times a day have caries.

The risk of a child who eats sugary foods less than 3 times a day having caries is: 61÷408 = 0·150

61 out of 408 children eating sugary foods less than 3 times a day have caries.

The risk ratio for having caries for children eating sugary foods 3 or more times a day compared to children eating sugary foods less than 3 times a day is 0·171÷0·150= 1·14

Children brushing less than twice a day have about 1·14 the risk of caries compared to children who brush at least twice a day

Which risk factor is worse?

The risk ratio for manual compared to non-manual is by far the biggest of the three we have calculated. We may be justified on this evidence in claiming that the social class of a child has a greater impact on the risk of developing caries than either frequency of toothbrushing or frequency of eating sugary foods.

Of course, the three factors we have looked at are unlikely to be totally independent. Fequency of toothbrushing and frequency of eating sugary foods are likely to be influenced by social class and possibly by each other. We would probably do better to analyse these data with more sophisticated modelling techniques that could take these possible interactions into account. That is too advanced for this course!

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