Example 63.2: PPS Selection of Two Units Per Stratum

The SURVEYSELECT Procedure

Example 63.2: PPS Selection of Two Units Per Stratum

A state health agency plans to conduct a state-wide survey of a variety of different hospital services. The agency plans to select a probability sample of individual discharge records within hospitals using a two-stage sample design. First stage units are hospitals, and second stage units are patient discharges during the study time period. Hospitals are stratified first according to geographic region and then by rural/urban type and size of hospital. Two hospitals are selected from each stratum with probability proportional to size. This example describes hospital selection for this survey using PROC SURVEYSELECT.

The data set HospitalFrame contains all hospitals in the first geographical region of this state.

   data HospitalFrame;
      input Hospital$ Type$ SizeMeasure @@;
      if (SizeMeasure < 20) then Size='Small ';
         else if (SizeMeasure < 50) then Size='Medium';
         else Size = 'Large ';   
   datalines;
   034 Rural  0.870   107 Rural  1.316
   079 Rural  2.127   223 Rural  3.960
   236 Rural  5.279   165 Rural  5.893
   086 Rural  0.501   141 Rural 11.528
   042 Urban  3.104   124 Urban  4.033
   006 Urban  4.249   261 Urban  4.376
   195 Urban  5.024   190 Urban 10.373 
   038 Urban 17.125   083 Urban 40.382
   259 Urban 44.942   129 Urban 46.702
   133 Urban 46.992   218 Urban 48.231
   026 Urban 61.460   058 Urban 65.931
   119 Urban 66.352
   ;

In the SAS data set HospitalFrame, the variable Hospital identifies the hospital. The variable Type equals `Urban' if the hospital is located in an urbanized area, and `Rural' otherwise. The variable SizeMeasure contains the hospital's size measure, which is constructed from past data on service utilization for the hospital together with the desired sampling rates for each service. This size measure reflects the amount of relevant survey information expected from the hospital. Refer to Drummond et al. (1982) for details on this type of size measure. The variable Size equals `Small', `Medium', or `Large', depending on the value of the hospital's size measure.

The following PROC PRINT statements display the data set Hospital Frame.

   title1 'Hospital Utilization Survey';
   title2 'Sampling Frame, Region 1';
   proc print data=HospitalFrame;
   run;

Output 63.2.1: Sampling Frame

Hospital Utilization Survey

Sampling Frame, Region 1

Obs	Hospital	Type	SizeMeasure	Size
1	034	Rural	0.870	Small
2	107	Rural	1.316	Small
3	079	Rural	2.127	Small
4	223	Rural	3.960	Small
5	236	Rural	5.279	Small
6	165	Rural	5.893	Small
7	086	Rural	0.501	Small
8	141	Rural	11.528	Small
9	042	Urban	3.104	Small
10	124	Urban	4.033	Small
11	006	Urban	4.249	Small
12	261	Urban	4.376	Small
13	195	Urban	5.024	Small
14	190	Urban	10.373	Small
15	038	Urban	17.125	Small
16	083	Urban	40.382	Medium
17	259	Urban	44.942	Medium
18	129	Urban	46.702	Medium
19	133	Urban	46.992	Medium
20	218	Urban	48.231	Medium
21	026	Urban	61.460	Large
22	058	Urban	65.931	Large
23	119	Urban	66.352	Large

The following PROC SURVEYSELECT statements select a probability sample of hospitals from the HospitalFrame data set, using a stratified design with PPS selection of two units from each stratum.

   title1 'Hospital Utilization Survey';
   proc surveyselect data=HospitalFrame method=pps_brewer
         seed=48702 out=SampleHospitals;
      size SizeMeasure;
      strata Type Size notsorted;
      run;

The STRATA statement names the stratification variables Type and Size. The NOTSORTED option specifies that observations with the same STRATA variable values are grouped together but are not necessarily sorted in alphabetical or increasing numerical order. In the HospitalFrame data set, Size = `Small' precedes Size = `Medium'.

In the PROC SURVEYSELECT statement, the METHOD=PPS_BREWER option requests sample selection by Brewer's method, which selects two units per stratum with probability proportional to size. The SEED=48702 option specifies '48702' as the initial seed for random number generation. The SIZE statement specifies the size measure variable. It is not necessary to specify the sample size with the N= option, since Brewer's method always selects two units from each stratum.

Figure 63.2.2 displays the output from PROC SURVEYSELECT. A total of 8 hospitals were selected from the 4 strata. The data set SampleHospitals contains the selected hospitals.

Output 63.2.2: Sample Selection Summary

Hospital Utilization Survey

The SURVEYSELECT Procedure

Selection Method	Brewer's PPS Method
Size Measure	SizeMeasure
Strata Variables	Type
	Size

Input Data Set	HOSPITALFRAME
Random Number Seed	48702
Stratum Sample Size	2
Number of Strata	4
Total Sample Size	8
Output Data Set	SAMPLEHOSPITALS

The following PROC PRINT statements display the sample hospitals.

   title1 'Hospital Utilization Survey';
   title2 'Sample Hospitals, Region 1';
   proc print data=SampleHospitals;
   run;

Output 63.2.3: Sample Hospitals

Hospital Utilization Survey

Sample Selected by Stratified PPS Design

Obs	Type	Size	Hospital	SizeMeasure	SelectionProb	SamplingWeight	JtSelectionProb
1	Rural	Small	079	2.127	0.13516	7.39868	0.01851
2	Rural	Small	236	5.279	0.33545	2.98106	0.01851
3	Urban	Small	006	4.249	0.17600	5.68181	0.01454
4	Urban	Small	195	5.024	0.20810	4.80533	0.01454
5	Urban	Medium	133	46.992	0.41357	2.41795	0.11305
6	Urban	Medium	218	48.231	0.42448	2.35584	0.11305
7	Urban	Large	026	61.460	0.63445	1.57617	0.31505
8	Urban	Large	058	65.931	0.68060	1.46929	0.31505

The variable SelectionProb contains the selection probability for each hospital in the sample. The variable JtSelectionProb contains the joint probability of selection for the two sample hospitals in the same stratum. The variable SamplingWeight contains the sampling weight component for this first stage of the design. The final-stage weight components, which correspond to patient record selection within hospitals, can be multiplied by the hospital weight components to obtain the overall sampling weights.

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