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The alternative hypothesis, as shown above, capture all possible situations other than equality of all means specified in the null hypothesis.

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The correlation between maternal age and prevalence of Down syndrome is much stronger than the correlation with birth order, and a woman having her 5th child is clearly older than when she gave more to her children. Learning Objectives After completing this module, the student will be able to: Explain the three key properties of a confounder Define and identify confounding Identify three ways to control confounding in the de phase of a study, and identify the strengths and weaknesses of each approach Describe ways to control for confounding in the analysis phase now a study Explain and calculate crude and stratum-specific measures of association Compare crude and adjusted measures of association to identify whether confounding is present and characterize the direction Thai massage sex Leeuwarden magnitude of confounding Describe residual confounding and identify possible sources Define and provide an example of effect modification What is Confounding?

A confounder cannot be an intermediary step in the causal pathway from the exposure of interest to the outcome of interest. In "Epidemiology - An Introduction" Ken Rothman says the following about this complexity: "The research process of learning about and controlling sex confounding can be thought of as a walk through a maze toward a central goal.

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Is the effect of maternal age confounded by birth order? These authors investigated the association between birth order and the risk of Down syndrome.

For example, subjects who are physically active may drink more fluids e. For example, in the hypothetical cohort study testing the association between exercise and heart disease, age is a confounder because it is a risk factor for heart disease.

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Obviously, women giving birth to their fifth child are on average, older than women giving birth to their first. Effect modification is distinct from confounding; it occurs when the magnitude of the effect of the primary exposure on an outcome i.

For example, socioeconomic status may be a confounder in this example because lower socioeconomic status is a marker for a complex set of poorly understood factors that seem to carry a higher risk of heart disease. In analysis of variance we are testing for a difference in means H0: means are all equal versus H1: means are not all equal by evaluating variability in the data.

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This shows an even more striking relationship between maternal age at birth and the child's risk of being born with Down syndrome. In other words, birth order of children is mixed up with maternal age when is born. However, consider also that the order in which a women's children are born is also linked to her age at the time bbs her bw birth. If the null hypothesis is false, then the F statistic will be large.

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While it is Old naughty finder Illinois easy to see the extension, the F statistic shown above is a generalization of the test statistic used for testing the equality of exactly two means. The decision rule again depends on the level of ificance and the degrees dex freedom.

like this also invite us to think about the mechanisms by which this occurred. Refining Our Understanding of Confounding Rothman and others use a study by Stark and Mantel to illustrate the key features of confounding.

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On the other hand, if one now examines changes in prevalence within each of the birth order groups by looking from front to back within a given birth order, there is npw a marked increase in prevalence as maternal age increases within all five levels of birth order. As the layers of confounding are left behind, we gradually approach a deeper causal understanding of the underlying biology.

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In the diagram below, the primary goal is to ascertain the strength of association between physical inactivity and heart disease. On now Sex Dating Vandling hand, xex who go to a gym regularly active may be more likely to be males and perhaps more likely to have a family history of heart disease, i. If those people who exercised regularly were more likely to take Noo, and aspirin reduces the risk of heart disease, then aspirin sex would be a confounding factor that would tend to exaggerate the benefit of exercise.

The rejection region for the F test is always in the upper right-hand tail of the distribution as shown more. Why might birth order cause a greater risk of Down syndrome?

The numerator captures between treatment variability i. The F statistic has two degrees of freedom.

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If increased HDL is a consequence of alcohol consumption and part of the mechanism by which it lowers the risk of heart disease, then it is not a confounder. Similarly a confounder can also be a preventive factor for the disease. If one focuses on how prevalence changes within any particular maternal age group looking moore side to side, it is zex that increasing birth order does not correlate with the prevalence of Down syndrome.

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Keep in mind that this analysis does not consider any other "risk factors" besides birth order. Rothman points out that a good way to sort this out is to look at both effects simultaneously, as in the graph below. Not surprisingly, since most diseases have multiple contributing causes risk factorsthere are many possible confounders. The test statistic is a measure that allows us to assess whether the differences among the sample means numerator are more than would be expected by chance if the null hypothesis is true.

Hypothesis testing - analysis of variance (anova)

A 5th born child appears to have roughly a 4-fold increase in risk of being born with Down syndrome. While this can represent a barrier to testing a particular hypothesis, it is also an opportunity to dissect the many determinants and to define their relative importance. Or, if the age distribution is similar in the exposure groups being compared, then age will not cause confounding.

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