Re: Centering (was Re: Missing covariates)

From: "Perez Ruixo, Juan Jose [JanBe]" <JPEREZRU@janbe.jnj.com> Subject: Re: Centering (was Re: Missing covariates) Date: Mon, 30 Jul 2001 13:08:26 +0200 Dear Alan and all, Now, I think everybody agree with centering approach for quantitative covariates, also when they are sampled with different strategies. But, I don't think the same is true for categorical covariates. In this setting, we can distinguish nominal (for instance, pharmaceutical form: solution, capsule or tablet; or sex) and ordinal (for instance, disease progresion: grade I, II, III or IV; or APGAR scale) covariates. This type of covariates cannot be treated as special continous covariates with special sampling values. Quantitative covariates are from interval (for instance, temperature) or ratio (for instance, age) metric scale, and additive or additive and multiplicative operations with them are allowed, respectively. For this reasons, centering approach can be used independently of sampling strategy. Categorical covariates aren't from metric scale. In nominal covariates only equality operations are allowed, and in ordinal covariates equality and order operations are possible. By definition, additive and multiplicative operations are not applicable. For this reasons, centering approach must be avoided. A special case is ordinal covariates with a lot of values (for instance, APGAR). If you assume asummed that the "distance" between 6 and 7 scores is the same as between 10 and 11 scores, usually, it's possible to treat this covariate as a quantitative with an interval metric scale and then, centering approach can be usefull. But this assumption is hardly applicable for covariates with a few scores like disease progression covariates. Usually, the "distance" between grade I and II scores is not the same than III to IV scores. Allan's example shows how the slope of a linear regression model with categorical data is affected by the codification used, as I said in my last email. In that example, the real difference between male and female weight is 10.85 (SE: 1.39). I agree we can get this value from codification like sexf0 or sexf2, but no sexf1 or sexf3. In last examples, we need to multiply by 2 for getting the confidence interval of the real difference between male and female. Sexf0 and sexf2 represents two different types of codification. The sexf0 codification is named "reference cell coding" or "partial method" and, sexf2 codification is named "deviations from mean coding" or "marginal method". The choice of the covariates codification depends of the effect that you want to fit. Now, we can consider the pharmaceutical form covariate. If I want to estimate the absorption rate constant difference between capsule and solution and, also the difference between tablet and solution, I will use two dummy covariates with reference cell coding (D1: solution = 0 and capsule = 1; D2 solution = 0 and table = 1). But, if I wish to compare the capsule absorption rate with respect to the mean of absorption rate of all pharmaceuticaI forms, I will use deviation from mean coding. If I have the same number of data for every pharmaceutical form, I could code: solution = -1, capsule = 1 and tablet = 0. If the number of categories increases, the complexity of codification increases too. This situation doesn't happen with reference cell coding. Moreover, in health sciences, the reference cell coding is the most oftenly used codification because the regression coefficients are very easy to interpret. In sexf0 example, the intercept have a direct meaning, it's the weight average for category 0 and it's independent of the ratio male to female. It doesn't happen the same with sexf2. Moreover, if the male to female ratio is not equal to 1:1, it's neccesary to modify appropiately the values for codifications with deviations from mean coding, otherwise the intercept will be affected and won't represent the weigth average of male and female. Thanks, Juan Jose Perez Ruixo Global Clinical Pharmacokinetics and Clinical Pharmacodynamics Department. Jassen Research Foundation Turnhoutsweg, 30 B-2340 Beerse Belgium Telephone: +032 / 14 60 75 08 Fax: +032 / 14 60 58 34 E-mail: jperezru@janbe.jnj.com