The simplest way of accomplishing a probability sample is a one-step process, or one stage sampling, by making random picks directly from a sampling frame containing a complete and current listing of all the persons in the population. However, this is impractical for most large populations, because it would result in a geographically dispersed sample which is difficult and expensive to implement. In addition, a complete and current list of population elements, such as HIV infected persons in care, may not be available. Fortunately, the construction of such a list is not required in order to develop a probability sample. Sampling can be accomplished by constructing a probability sample in stages, i.e., by making a series of random picks from each of a hierarchical series of sampling frames (e.g., geographic areas, health care providers, patients); these picks must be made in such a way that each selection is linked to a selection made in the previous sampling stage by virtue of having the frame for that pick be defined by the elements included in the previous selection.

The HIV Cost and Services Utilization Study (HCSUS) used a multistage probability sample of persons in care for HIV disease in the 48 contiguous United States in 1996, demonstrating that such an approach is feasible for studying HIV disease [3]. In the HCSUS, the hierarchy was as follows: 1) participants were selected from a complete list of patients being cared for by their provider, 2) providers were selected from a complete list of providers in their area, and 3) areas were selected from a complete list of all such areas in the United States. The MMP uses many of the features of the HCSUS sample design in developing a nationally representative probability sample of non-institutionalized persons receiving outpatient care for HIV infection in the 50 United States, the District of Columbia and Puerto Rico.

The separately funded cities/counties are Chicago, IL; Houston, TX; Los Angeles County, CA; New York City, NY; Philadelphia, PA; and San Francisco, CA. The decision not to directly pick these cities was driven by a secondary goal of providing statewide data to participating state health departments. This was accomplished by folding the six cities/counties into the five states that contain them for the purposes of first stage sampling only (i.e., not for purposes of administering the project). This yielded 52 PSUs. The decision to sample 20 of the 52 PSUs was made based on funding availability and face validity rather than on any statistical argument.

In MMP, a systematic sampling with a random start was used to generate a random stratified proportional to size sample. In order to improve the reliability of the final sample, the PSUs were stratified into five groups - four geographic and one by size, then ordered by the PSU’s measure of size (MOS). The MOS is an estimate of the number of persons in the population of interest that are contained in each unit of a sampling frame. For the first stage of MMP, the MOS were the CDC estimates of the number of adults and children living with AIDS at the end of 2002, current as of November 24, 2003. Although the target population for MMP is all persons diagnosed with HIV in care in the US, at the time the first stage was developed, there was no data system that collected information on HIV infected persons in care. Therefore, the estimated number of persons living with AIDS was used as a proxy measure of PSU size.

The systematic sampling procedure was as follows. We first created a list or pseudo-population of patients grouped by PSUs, arrayed by stratum and size. For example, if the largest PSU in the first stratum (PSU #1) had 1000 cases, then patients 1 to 1000 would be labeled “PSU #1;” and if PSU #2 had 2130 cases, then patients 1001 to 3130 would be labeled “PSU #2.”

Selection proceeds by picking a random start at the beginning of the list and then taking uniform steps forward through it. In MMP, the initial pick was to be a patient in the first 5% of the list with subsequent steps each being 5% forward through the list; 5% having been chosen because we wished to sample 20 PSUs. The PSU containing each patient picked in this procedure is included. Since the steps each contain 5% of the total cases, at least one step must fall among the patients that represent any PSU that has more than 5% of the total cases. These large PSUs are sampled with certainty. The process is iterative. The cases in certainty PSUs are removed, the step size recalculated based on the number of available and required PSUs, and the additional PSUs to be sampled with certainty are identified and removed. The cycle repeats until no further PSUs were sampled with certainty.

Describing the particular choices made in the MMP sample will elucidate this approach. The total number of cases, that is, the sum of the MOS, across all 52 PSUs was 384,070. Five percent of this total is 19,204. Thus any PSU with at least 19,204 cases was to be sampled with certainty. Four PSUs had at least this many cases: California, Florida, New York, and Texas (Table 1).

We then excluded the four certainty PSUs, recalculated the total number of cases, and redefined the criteria for PSUs that would also be sampled with certainty. Sixteen PSUs remained to be sampled from 48 remaining PSUs. So, any PSU with at least 6.25%, or 12,473 of the remaining 199,569 cases, was to be sampled with certainty. Four PSUs had at least this many cases: Georgia, Illinois, New Jersey and Pennsylvania. Twelve PSUs remained to be sampled from the remaining 44 PSUs. So, any PSU containing at least 8.3%, or 11,860 of the remaining 142,321 cases was to be sampled with certainty. No PSUs contained this many cases, so no further PSUs were sampled with certainty.

The remaining 12 PSUs were to be sampled PPS in a stratified manner. This was accomplished by recreating the list according to stratum and size as described above, using the cases from the remaining 44 PSUs. Selecting randomly from such as list results in a sample that is: a) PPS because the proportion of entries that are grouped under a PSU reflects the proportion of cases contained in that PSU, and b) stratified because of the specific ordering.

We grouped the states into five strata: four based on region and one that grouped together states with few cases. The stratum of states with few cases was formed to minimize how many PSUs with few cases were included. Sampling cases from PSUs that contain very few cases is difficult and expensive to implement, so we defined a stratum of “small” PSUs in such a way that only one PSU would be sampled from that stratum. Since 12 PSUs were to be sampled, a stratum containing PSUs with close to but less than the “step” value of 8.3% (11,860) of all cases would likely contribute one PSU but could not contribute two or more to the sample. To define this stratum, the smallest PSU was chosen and PSUs were added from the list (taking the next smallest and so on) until the total number of included cases was smaller than 11,860 but as large as possible. In this manner, 18 PSUs containing 11,118 were chosen for the small state stratum; adding the next smallest would have resulted in 12,915 cases in this stratum.

The remaining 26 PSUs (defined as “medium” size) were divided into four geographical strata based on the Census definitions of geographic regions: the Northeast region contained Census divisions New England and Middle Atlantic (states: CT, MA); Midwest contained Census divisions East North Central and West North Central (states: WI, MN, IN, MO, MI, OH); South contained Census divisions South Atlantic, East South Central and West South Central as well as Puerto Rico (states: AR, OK, KY, MS, AL, TN, SC, LA, NC, VA, DC, MD, PR); and West contained Census divisions Mountain and Pacific (states: OR, NV, CO, AZ, WA).

The geographic strata were ordered: Northeast, Midwest, South and West and then were followed by the small PSU stratum to form the pseudo population list. Within each stratum, the PSUs were ordered by size. In order to preclude possible sampling periodicity by size, within Northeast the PSUs were ordered smallest to largest; within Midwest largest to smallest; within South smallest to largest; within West largest to smallest; and within the small PSU stratum smallest to largest. The sampling frame resulting from the determination of the certainty picks, and from the stratification and ordering of the remaining PSUs, is shown in Table 1.

PSUs eligible to be one of 12 picked by random PPS selection are listed after the certainty PSUs, beginning with Connecticut. As implied above, the initial pick had to be within the first 8.3% or 11,860 cases. A random number of 0.878 was chosen, thus identifying a random start of 0.878 x 11,860, or 10,413. Case number 10,413 is contained within Massachusetts, which therefore was the first randomly selected PSU. Stepping though the list at intervals of 11,860 resulted in the selection of one state in the Northeast, two each in the Midwest and the West, six in the South and, as anticipated, one from the grouping of states with few cases. Areas with “Yes” in the Sampled column in Table 1 comprise the final sample of states.

A variety of sources were used to identify facilities providing HIV care (including the number of individuals in care at those institutions). These included the HIV/AIDS Reporting System (HARS) databases, laboratory reporting databases and other local databases, including AIDS Drug Assistance Program and Medicaid databases. The HARS was the best source for identifying HIV care providers. It is the current version of the reporting system that all states have used for surveillance of new AIDS cases since 1985 and, since at least 2005, all new cases of HIV infection [4,5]. In 2005, when the first facility sampling frames were constructed, 18 of the 20 states conducting MMP had HIV viral load and/or CD4 reporting of any value or of all tests performed.

For the 2005 pilot data collection cycle, the following types of facilities were included on the facility sampling frame: outpatient and inpatient care facilities; Veterans Administration facilities; and state or local prisons and jails that met the definition of providing HIV care. The following types of facilities were not included: emergency departments (because they do not provide sufficient information on the standard of care), HIV counseling and testing sites and laboratories (which report HIV infection, but do not provide medical care for HIV infection), Federal prisons, military bases and institutions (project areas have no jurisdiction to obtain their medical records), and pediatric facilities (unless they provided HIV medical care to persons age 18 and older).

For the 2007 and subsequent data collection cycles, two other exclusions were made from the facility sampling frame to focus predominately on patients receiving outpatient care. It was decided not to include inpatient facilities or prisons or jails on the facility sampling frame. Inpatient facilities were excluded since they do not provide primary medical care for HIV infection. HIV-infected patients could have interfaced with inpatient care facilities for a variety of reasons. It would be prohibitively difficult to recruit providers who do not typically provide HIV care (but who may have prescribed antiretroviral medications or ordered CD4 counts or HIV viral load tests during the patient’s inpatient stay). In addition, the likelihood of finding and recruiting patients who had only one encounter with the provider at an inpatient facility would be much lower than that for patients who have an ongoing relationship with a regular HIV care provider. In some instances, such as hospice or care in long term care facilities, primary medical care is provided; however, this care is different from outpatient care provided by other facilities on the facility sampling frame. Prisons and jails as providers of HIV care were excluded from the sampling frame because these facilities are not able to be accessed in all project areas due to Institutional Review Board (IRB) and other issues.

Once the lists of facilities from HARS and each of the supplemental sources were obtained, cleaned, and standardized, they were combined into a single facility sampling frame (FSF) for each project area, on which each facility only appears only once. Any outpatient facility that met the MMP facility definition and was a known provider of HIV medical care during the recent time periods used for each data source was eligible to be included on the FSF.Facilities that had not seen a patient with HIV during the time frame estimated patient loads (EPLs) were obtained (i.e., they had an EPL of 0) were included on the FSF, but patients were not sampled from these facilities.

Facilities are sampled in the second stage in a manner analogous to the PSUs in the first stage. To accomplish PPS sampling at this stage, an EPL of adult HIV infected patients in each facility was also needed on the frame.The EPL is an estimate of the actual number of eligible patients that will be seen at a facility during the PDP for a given data collection cycle. In 2007, for each data source from which EPLs could be derived, a 4 month EPL was created using the most recent data from each data source as well as from facility contacts to accurately reflect the patient load for the January 1 through April 30, 2007 PDP. Data were obtained either from a data run or other record-based source or as a less precise estimate, typically provided by facility staff. A matrix, or table, of EPLs from each data source was constructed for all eligible facilities, and this matrix was used to create the FSF, which in turn was used to select facilities for the previous data collection cycles. During this step, the quality of the different EPLs obtained across the various data sources was evaluated in order to determine, for each facility, which EPL was the most accurate to use for facility sampling.

A sampled patient’s overall selection probability is the product of the three stage-specific selection probabilities. It is desirable that this overall probability of selection be uniform. Such uniformity will result in greater statistical efficiency because there would be minimal variation in point estimates derived from the information that patients contributed. The result is that confidence limits for estimates derived from MMP data will thus be minimized. Facilities with very low EPLs, or small facilities, are problematic in this regard because achieving uniform selection probability may require the selection of more patients than they actually have. In MMP, this was handled by linking known small facilities to larger ones to create linked ‘facilities’ with combined EPLs that met or exceeded a minimum value.

Facilities designated as small were linked to one or more other facilities so that the small facility is selected for the sample only if the facilities to which it is linked also are selected. The desired minimum EPL across each project area ranges between 40 and 80, and depend in part on the distribution of EPLs across the entire FSF for that project area. Minimum values of 40 to 80 have been determined to be optimal for selecting the facility sample across project areas based on anticipated design effects and distributions of facility sizes.

In project areas of large geographic size, or with variations in facility attributes by region, this linkage was performed within pre-specified sub-regions to facilitate efficient use of project area resources during data collection, as well as to ensure facilities from every sub-region were selected.

Electronic files containing the FSF from each project area were sent to CDC using the CDC’s Secure Data Network (SDN). All files sent to CDC are stripped of identifying information for each facility; facilities are identified only by unique numeric facility identification (ID) number, assigned by the project area. Facility ID numbers for all project areas are made unique by adding a 4-digit project area code in front of the assigned 4-digit facility ID number. The number of facilities sampled in each project area varied from 25 in Houston and Los Angeles to 68 in California (Table 2). In Delaware a census of all 21 eligible facilities was used as the second stage sample. In other project areas, facilities were randomly sampled from among all facilities on the FSF. In the five states containing cities/counties that are separately funded for surveillance, a larger number of facilities was sampled in the second stage of sampling in order to provide more useful local data to the separately funded areas. Specifically, separate samples of facilities were selected within each of the six separately funded cities/counties as well as elsewhere in those states.

Of the 828 facilities sampled and eligible, 582 participated. Because this was a strict probability sample, no replacement facilities were sampled. Furthermore, in those project areas with lower facility response rates the sample size was not increased because of the strict probability sampling protocol. This might be considered in future years. Facility participation rates ranged from 65% to 100%, with a median of 91.4%.

At the end of the PDP, health department MMP staff request a list from each sampled facility of all HIV-infected adults who received medical care (defined as any visit to the facility for medical care or prescription of medications, including refill authorizations and immunizations) during the PDP. Patients are eligible for inclusion on the patient sampling frame if they were HIV infected, at least 18 years of age at the beginning of the PDP, and received care at a sampled and participating facility during the PDP.

Facilities construct patient lists using International Classification of Diseases (ICD-9 or ICD-10) codes for procedures, tests or prescriptions during the PDP, or in smaller facilities by reviewing appointment logs.

Patients are eligible for selection only at their first reported visit to the facility during the PDP to ensure that multiple visits to the same facility do not lead to multiple opportunities for selection. As facilities use different mechanisms to identify eligible patients, the lists are not unduplicated across facilities. To account for multiplicity - multiple patient visits to different facilities during the PDP - the interview includes questions about the number of different facilities visited during the PDP to allow for the adjustment of the multiplicity of probability of selection in the weighting process. Without this, persons visiting more facilities would have higher probabilities of selection which could lead to estimation bias.

For each facility, the actual count of patients seen during the entire PDP derived from a facility’s patient list will differ from the selected best EPL used to construct the FSF. EPLs were obtained for a 4-month period, which should closely match the number of patients on the patient lists obtained for the 4 month PDP.

Patient sampling is conducted as soon as all patient lists have been received from the participating facilities. The file containing lists of HIV-infected patients seen during the PDP at all participating facilities is used to select the patient sample. The selected participant ID numbers are returned to the project area via the CDC’s SDN after patient sampling has been completed; this set of participant IDs comprises the entire patient sample for the project area.

It was determined that 400 is the minimum sample size for a state to obtain total population estimates with an acceptable level of precision (assuming a moderate design effect [of between 2 and 4], or increase in variance of estimates due to using a multistage sampling design). This sample size was assigned to most of the states with the lowest AIDS prevalence. Sample sizes for states with moderate to high AIDS prevalence were determined based on the distribution of cases among the 20 sampled states and the 6 separately funded cities/counties in those states, in order to achieve a national sample size of approximately 10,000. States that have large numbers of prevalent AIDS cases were allocated larger sample sizes (California 1300; Florida 800; Illinois 500; New Jersey 500; New York 1000; Pennsylvania 500; and Texas 800). These project area sample sizes will allow national estimates at an acceptable level of precision (assuming a moderate design effect) for subpopulations as small as 5% of the total population of interest. Table 2 outlines the patient sample size selected for each MMP project area. Although patient sample sizes of 800 and 400 were selected for Florida and Maryland, respectively, errors in the estimation of patient loads during facility sampling frame construction resulted in reduced patient sample sizes in these areas. Patient selection was accomplished by systematic random sampling within facility. Changes in the probability of selection by oversampling in facilities with lower response rates were not attempted in order to maintain a constant probability of selection across all facilities in order to handle patient multiplicity.

It should be noted that in all stages of selection, the probability nature of the sample allows the computation of required probabilities of selection for selected patients:

Probability of Selection (Patient_i) = P1 x P2 x P3x M, where

P1 = the probability of selection for the state

P2 = the probability of selection for the facility associated with the i^th selected patient

P3 = the probability of selection for the i^th selected patient within the facility containing the patient.

M = the number of facilities the patient reports visiting during the population definition period.