How to test whether the change among surveys in one group is equal to the change in the other groups?

1. Scenery

We have a table below:

	NHES (S1)	N I (S2)	N II (S3)	N III (S4)	N IV (S5)	Change (C)
BMI Group	High Cholesterol (%> 240 mg/dl)
< style=""> (G1)	27.1	22.3	22.1	13.8	15.2	-11.9 (C1)
25.0 – (G2)	39.2	33.1	31.2	23.3	18.7	-20.5 (C2)
> 30 (G3)	38.9	33.1	31.5	23.0	17.9	-21.0 (C3)

Age and sex-adjusted trends in CVD risk factors, by level of obesity and survey year in the

We want to know: Ho: C1 = C3.

2. Algorithm Solution

Recall:

Y= α*(S5, G1) + β₁*(S1) + β₂*(S2) + β₃*(S3) + β₄*(S4) + β₅*(G2) + β₆*(G3)

+ β₇*(S1, G2) + β₈* (S1, G3) + β₉*(S2, G2) + β₁₀*(S2, G3) + β₁₁*(S3, G2)

+ β₁₂*(S3, G3) + β₁₃*(S3, G2) + β₁₄*(S3, G3)

And: Prevalence of high cholesterol in NHES (S1) among persons with normal BMI (G1)

[S1-G1] = α + β₁ = 27.1, and

[S5-G1] = α = 15.2, then

C1 = [S5-G1] - [S1-G1] = 15.2 – 27.1 = -11.9

Also:

[S1-G3] = α + β₁ + β₆ + β₈ = 38.9, and

[S5-G3] = α + β₆ = 17.9, then

C3 = [S5-G3] - [S1-G3] = -21.0

So:

When we test whether C1 = C3, we are going to test:

α - (α + β₁) = (α + β₆) – (α + β₁ + β₆ + β₈),

i.e. β₈ = 0

Same for others:

To test C1 = C2, we are going to test, β₇ = 0

3. Implementation

Using PROC RLOGIST:

proc rlogist data= all;

  nest survey3 strata3 psu3/psulev=3 MISSUNIT;

  weight mecwgt3;

  subpopn age >19;

  subgroup bmigrp agegrp sex survey3 WHITE BMIADHOC;

  levels 3 3 2 5 2 2;

  model High_chol = bmigrp agegrp sex survey3 bmigrp*survey3;

  reflevel survey3 =5 agegrp =1 bmigrp=1;

  pred_eff bmigrp=(1,0,0)*survey3=(1,0,0,0,-1) /name="Survey: first versus last in BMI<25";

  pred_eff bmigrp=(0,1,0)*survey3=(1,0,0,0,-1)/name="Survey: first versus last in 25<BMI<30";

  pred_eff bmigrp=(0,0,1)*survey3=(1,0,0,0,-1)/name="Survey: first versus last in BMI>30";

  PREDMARG BMIGRP SURVEY3 BMIGRP*SURVEY3;

  PRINT BETA P_BETA PREDMRG SEPRDMRG P_PMCON PRMGCON SEPMCON

  /PREDMRGFMT=f7.3 PRMGCONFMT=F7.3 SEPMCONFMT=F7.3;

RUN;

SUDAAN will give us these beta and p value for beta:

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variable beta p value

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BMIGRP,

BY NHES & NHANES

1, 1 0.00 .

1, 2 0.00 .

1, 3 0.00 .

1, 4 0.00 .

1, 5 0.00 .

2, 1 0.33 0.0483 <- b=""> ß7

2, 2 0.32 0.0414

2, 3 0.24 0.1284

2, 4 0.41 0.0130

2, 5 0.00 .

3, 1 0.37 0.0181 <- b=""> ß8

3, 2 0.38 0.0156

3, 3 0.30 0.0350

3, 4 0.44 0.0021

3, 5 0.00 .

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