Question

9.11

Table C.13 Anorexia data

Ben-Tovim et al. (1979) report a case-control study to test hypothesis that anorexic people tend to overestimate their true waist measurements.Eight anorexic women were identified from a hospital in-patient unit and compared with 11 non-anorexic adolescent schoolgirls. The outcome variable used to compare cases and controls was the body perception index,

BPI = 100 * (perceived waistwidth)/ (true waist width)

The data collected were as follows:

Subject number	Waist width (cm)
Cases	True	Perceived	BPI
1	22.6	29.5	130.5
2	19.2	30.6	159.6
3	21.9	31.1	142.0
4	23.4	28.1	119.9
5	22.9	32.7	143.0
6	19.1	37.1	194.0
7	21.4	32.9	153.7
8	28.3	33.5	118.2
Controls
9	24.9	32.9	132.3
10	16.6	27.9	168.1
11	22.0	28.7	130.5
12	22.2	34.1	153.6
13	21.4	33.9	158.4
14	19.1	39.3	206.0
15	18.2	36.9	202.7
16	21.4	31.4	146.5
17	17.6	40.4	229.5
18	20.0	34.6	172.8
19	24.3	31.8	130.9

(i) Estimate the mean BPI for cases and for controls

(ii) Compare the two distributions (cases and controls) using boxplots.

(iii) Do your results in (i) and (ii) support the prior hypothesis the researchers,that cases have a lower BPI? Consider the danger involved in carrying out a one-sided test,as this prior hypothesis might suggest.Test the null hypothesis that cases and controls have the same BPI,using a two-sided test.

(iv) One possible confounding variable in this example is true width,since the relative error in perception (that is, the BPI) might differ with increasing body size.Plot BPI against true width ,marking cases and controls with different symbols or colours.Does BPI seem to change with true width? If so,how?Does it appear that a different regression line will be required for cases and controls?

(v) From a general linear model,test the effect of case-control status adjusted for true width.

(vi) Write down the equation of the fitted bivariate model from (v).Find the mean true width.Hence compute the least-square means (adjusted for true width) for cases and controls.

(vii) Fit the simple linear regression of (a) BPI on true width ,(b) case-control status on true width .Find the (raw) residuals from (a) and (b) and fit the simple linear regression of the (a) residuals on the (b) residuals.Compare the slope parameter from this model with that for case-control status in (vi).You sholud find a close relationship: why?

(viii) Compare the results in (v) and (vii) with those in (ii) and (iii).What effect has adjustment for true width had?Are there any other potential confounding variables that might be worth considering,were data available?

Answer 1