Example 89.2 PPS Selection of Two Units per Stratum

This example describes hospital selection for a survey by using PROC SURVEYSELECT. A state health agency plans to conduct a statewide survey of a variety of different hospital services. The agency plans to select a probability sample of individual discharge records within hospitals by using a two-stage sample design. First-stage units are hospitals, and second-stage units are patient discharges during the study 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.

The data set HospitalFrame contains all hospitals in the first geographical region of the 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 urban 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. See Drummond et al. (1982) for details about 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 and produce Output 89.2.1:

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

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

title1 'Hospital Utilization Survey';
title2 'Stratified PPS Sampling';
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 names SizeMeasure as the size measure variable. It is not necessary to specify the sample size with the N= option, because Brewer’s method always selects two units from each stratum.

Output 89.2.2 displays the output from PROC SURVEYSELECT. A total of eight hospitals were selected from the four strata. The data set SampleHospitals contains the selected hospitals.

The following PROC PRINT statements display the sample hospitals and produce Output 89.2.3:

title1 'Hospital Utilization Survey';
title2 'Sample Selected by Stratified PPS Design';
proc print data=SampleHospitals;
run;

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.