In the Low-Birth-Weight Study described in Section 1.6.2, determine the crude odds ratio of smoking (SMOKE) on the outcome low birthweight (LOW). Stratify on RACE and note the odds ratios within the...

In the Low-Birth-Weight Study described in Section 1.6.2, determine the crude odds ratio of smoking (SMOKE) on the outcome low birthweight (LOW). Stratify on RACE and note the odds ratios within the three strata. Do the odds ratios appear to be homogeneous across strata? Compute the Mantel–Haenszel and logit-based estimates of the odds ratio. How do these compare to the crude estimate? Determine whether homogeneity of the odds ratios across strata holds through the use of the chi-square test of homogeneity and the Breslow–Day test. Finally, use a logistic regression analysis to compute the adjusted odds ratio and to determine whether the odds ratios were homogeneous across strata. How do these results compare to the ones you obtained using the more classical categorical data approach?

The example we use to initially illustrate each of the models comes from the Low-Birth-Weight Study (see Section 1.6.2) where we form a four category outcome from birth weight (BWT) using cutpoints: 2500g, 3000g, and 3500g. This example is not typical of many ordinal outcomes that use loosely defined “low,” “medium,” or “high” categorizations of some measurable quantity. Instead, here we explicitly derived this variable from a measured continuous variable. We make use of this fact when we show how the proportional odds model can be derived from the categorization of a continuous variable. In addition some of the exercises are designed to extend this discussion. First, we need to give some thought to the assignment of codes to the outcome variable, as this has implications on the definition of the odds ratio calculated by the various ordinal models.