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SUDAAN FAQ 
How do I analyze survey data with a probability proportional to size sampling design?

This example is taken from Levy and Lemeshow's Sampling of Populations.

page 350 cluster sampling with unequal probabilities:  probability proportional to size sampling
This example uses the hospslct data set.

proc descript data = hospslct filetype=sas design = wr means totals;
  nest drawing/psulev = 1;
  weight wstar;
  var lifethrt dxdead;
run;

Number of observations read    :     50    Weighted count :    50056
Denominator degrees of freedom :      4

Variance Estimation Method: Taylor Series (WR)
by: Variable, One.

-----------------------------------------------------
|                 |                  |
| Variable        |                  | One
|                 |                  | 1            |
-----------------------------------------------------
|                 |                  |              |
| LIFETHRT        | Sample Size      |           50 |
|                 | Weighted Size    |     50056.00 |
|                 | Total            |      6006.72 |
|                 | SE Total         |      1001.12 |
|                 | Mean             |         0.12 |
|                 | SE Mean          |         0.02 |
-----------------------------------------------------
|                 |                  |              |
| DXDEAD          | Sample Size      |           50 |
|                 | Weighted Size    |     50056.00 |
|                 | Total            |      2002.24 |
|                 | SE Total         |      1226.12 |
|                 | Mean             |         0.04 |
|                 | SE Mean          |         0.02 |
-----------------------------------------------------

proc ratio data = hospslct filetype = sas design = wr;
  nest drawing / psulev =1;
  weight wstar;
  numer dxdead;
  denom lifethrt;
run;

Number of observations read    :     50    Weighted count :    50056
Denominator degrees of freedom :      4

Variance Estimation Method: Taylor Series (WR)
by: Variable, One.

---------------------------------------------------
|                 |                  |
| Variable        |                  | One
|                 |                  | 1          |
---------------------------------------------------
|                 |                  |            |
| DXDEAD/LIFETHRT | Sample Size      |         50 |
|                 | Weighted Size    |   50056.00 |
|                 | Weighted X-Sum   |    6006.72 |
|                 | Weighted Y-Sum   |    2002.24 |
|                 | Ratio Est.       |       0.33 |
|                 | SE Ratio         |       0.23 |
---------------------------------------------------

Page 353 cluster sampling with unequal probabilities:   probability proportional to size sampling

data hspslct2;
  set hospslct;
  /*n is 50*/
  /*N_i is admiss*/
  /* X is 7087, the total number of life-threating conditions across all the hospitals*/
  /*X_i is tl, the total number of life-threating conditions for each hospital*/
  if hospno = 2 then  tl = 785; 
  if hospno = 5 then  tl = 3404; 
  if hospno = 9 then  tl = 778; 
  w2star = (admiss/50)*(7087/tl);
run;

proc descript data = hspslct2 filetype = sas means totals;
  nest drawing/psulev=1;
  weight w2star;
  var lifethrt dxdead;
run;

Number of observations read    :     50    Weighted count :    51345
Denominator degrees of freedom :      4
Variance Estimation Method: Taylor Series (WR)
by: Variable, One.

-----------------------------------------------------
|                 |                  |
| Variable        |                  | One
|                 |                  | 1            |
-----------------------------------------------------
|                 |                  |              |
| LIFETHRT        | Sample Size      |           50 |
|                 | Weighted Size    |     51345.00 |
|                 | Total            |      6259.18 |
|                 | SE Total         |      1277.32 |
|                 | Mean             |         0.12 |
|                 | SE Mean          |         0.02 |
-----------------------------------------------------
|                 |                  |              |
| DXDEAD          | Sample Size      |           50 |
|                 | Weighted Size    |     51345.00 |
|                 | Total            |      1760.47 |
|                 | SE Total         |      1079.04 |
|                 | Mean             |         0.03 |
|                 | SE Mean          |         0.02 |
-----------------------------------------------------

proc ratio data = hspslct2 filetype = sas;
  nest drawing/psulev=1;
  weight w2star;
  numer dxdead;
  denom lifethrt;
run;

Number of observations read    :     50    Weighted count :    51345
Denominator degrees of freedom :      4
Variance Estimation Method: Taylor Series (WR)
by: Variable, One.

---------------------------------------------------
|                 |                  |
| Variable        |                  | One
|                 |                  | 1          |
---------------------------------------------------
|                 |                  |            |
| DXDEAD/LIFETHRT | Sample Size      |         50 |
|                 | Weighted Size    |   51345.00 |
|                 | Weighted X-Sum   |    6259.18 |
|                 | Weighted Y-Sum   |    1760.47 |
|                 | Ratio Est.       |       0.28 |
|                 | SE Ratio         |       0.21 |
---------------------------------------------------

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