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entitled 'Medicare: Radiopharmaceutical Purchase Prices for CMS
Consideration in Hospital Outpatient Rate-Setting' which was released
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July 14, 2005:
The Honorable Michael O. Leavitt:
The Secretary of Health and Human Services:
Subject: Medicare: Radiopharmaceutical Purchase Prices for CMS
Consideration in Hospital Outpatient Rate-Setting:
Dear Mr. Secretary:
In our recent report on hospital outpatient drug purchase prices,
Medicare: Drug Purchase Prices for CMS Consideration in Hospital
Outpatient Rate-Setting, we stated that we would issue a subsequent
report with radiopharmaceutical purchase price information.[Footnote 1]
This report contains that information.
Medicare pays hospitals for drugs and other pharmaceutical products
that beneficiaries receive as part of their treatment in hospital
outpatient departments. Specifically, the Centers for Medicare &
Medicaid Services (CMS) in the Department of Health and Human Services
(HHS) uses an outpatient prospective payment system (OPPS) to pay
hospitals fixed, predetermined rates for services. These services
include pharmaceutical products--drugs, biologicals,[Footnote 2] and
radiopharmaceuticals[Footnote 3]--given to beneficiaries in outpatient
settings. When OPPS was first developed as directed by the Balanced
Budget Act of 1997,[Footnote 4] the rates for hospital outpatient
services and drugs and radiopharmaceuticals were based on hospitals'
1996 median costs. However, these rates prompted concerns that payments
to hospitals would not reflect the cost of newly introduced
pharmaceutical products used to treat, for example, cancer, rare blood
disorders, and other serious conditions. In turn, congressional
concerns were raised that beneficiaries might lose access to some of
these products if hospitals avoided providing them because of a
perceived shortfall in payments.
In response to these concerns, the Medicare, Medicaid, and SCHIP
Balanced Budget Refinement Act of 1999 authorized pass-through
payments, which are a way to augment, on a temporary basis, the OPPS
payments for newly introduced pharmaceutical products first used after
1996.[Footnote 5] The Medicare Prescription Drug, Improvement, and
Modernization Act of 2003 (MMA) modified this payment method for some
of these pharmaceutical products.[Footnote 6] As part of the
modification, the MMA defined a new payment category--specified covered
outpatient drugs (SCOD)--which includes many of these newly introduced
pharmaceutical products. The MMA defined a SCOD as a drug or
radiopharmaceutical used in hospital outpatient departments, covered by
Medicare, and for which CMS has established a separate ambulatory
payment classification (APC) group.[Footnote 7] The MMA established a
methodology for CMS to follow in setting payment rates for SCODs in
2004 and 2005. CMS defines SCODs by their Healthcare Common Procedure
Coding System (HCPCS) codes, which CMS assigns to products, supplies,
and services for billing purposes. The MMA also directed us to collect
data on hospitals' acquisition costs of SCODs and to provide
information based on these data to the Secretary of Health and Human
Services for his consideration in setting 2006 Medicare payment
rates.[Footnote 8] The MMA directed us to collect these data by
surveying a large sample of hospitals.
In summary, we obtained from our survey data the average and median
purchase prices for each of nine radiopharmaceutical SCOD categories.
Purchase pricerefers to the price that hospitals pay upon receiving the
product and is the key component of hospital acquisition costs. These
nine categories represent 9 percent of all Medicare spending on SCODs
in the first 9 months of 2004. The purchase price information takes
account of discounts taken at the time hospitals received the product
but excludes any rebates paid subsequent to the receipt of the product.
Background:
Radiopharmaceuticals are primarily used for diagnostic purposes but are
also used in treating some diseases. Radiopharmaceuticals have two
components: a medicine or pharmaceutical agent, which is
nonradioactive, and a radioisotope, which is radioactive. The first
component targets specific places in the body (e.g., brain, liver),
while the second component emits radiation to allow imaging of the
interior of the body.
Hospitals can purchase radiopharmaceuticals in one or more ways. They
can purchase a unit dose or a multidose vial of the product that has
been prepared by a nuclear pharmacy independent of the hospital, or
they can purchase the product's radioactive and nonradioactive
components separately and prepare the radiopharmaceutical in-house. For
example, to acquire Technetium Tc 99m Sestamibi, a radiopharmaceutical
for myocardial imaging, a hospital can either order a ready-to-use unit
dose of the product from an independent nuclear pharmacy or create a
dose in-house after purchasing separately Technetium Tc 99m--the
radioactive component--and a preparation kit that includes the
nonradioactive agent. In a survey conducted by the Society of Nuclear
Medicine and the Society of Nuclear Medicine Technologist Section, 76
percent of hospitals reported that they purchased their
radiopharmaceuticals in unit doses.[Footnote 9]
Scope and Methodology:
In our report on hospital drug prices, we presented results drawn from
our survey data on purchase price information on 53 SCOD drug
categories, for the period July 1, 2003, through June 30, 2004. These
53 SCOD categories represented 86 percent of Medicare spending for
SCODs during the first 9 months of 2004.[Footnote 10] In this report,
we present our survey results for nine radiopharmaceutical SCOD
categories for the period July 1, 2003, through June 30, 2004. These
nine represented 9 percent of Medicare spending for SCODs during the
first 9 months of 2004.[Footnote 11] The previous report and this
report together provide purchase price information on SCODs that
accounted for 95 percent of all Medicare spending on SCODs during the
first 9 months of 2004. We report here the average and median purchase
prices for the nine radiopharmaceutical SCOD categories. The purchase
price information takes account of volume and other discounts, but it
excludes rebates, which manufacturers may give after a hospital has
paid for the radiopharmaceuticals, and payments made to hospitals by
group purchasing organizations, which negotiate prices with
manufacturers on behalf of their member hospitals.
Hospitals' purchase prices of the radiopharmaceutical products included
here were obtained from the same survey that produced the hospital
outpatient drug purchase prices. Specifically, we surveyed 1,400 acute
care, Medicare-certified hospitals,[Footnote 12] expecting that this
would yield responses from about 1,000 hospitals.[Footnote 13] We
conducted the survey from September 27, 2004, through February 22,
2005, and received usable information on radiopharmaceuticals from 808
hospitals, which gave us a response rate of 61 percent.[Footnote 14] We
asked the hospitals to provide price data for SCODs purchased from July
1, 2003, through June 30, 2004. Using our survey data, we calculated
average and median purchase prices of a product's unit dose. To ensure
the soundness of our approach to data collection and analysis, we
obtained comments from an advisory panel of experts in pharmaceutical
economics, pharmacy, medicine, survey sampling, and Medicare payment.
To assess the reliability of our data, we checked for anomalies and
outliers, asked hospitals for clarification as needed, and discussed
technical issues with a nuclear pharmacist. On this basis, we
determined that the data were sufficiently reliable for our purposes.
(For details on our methods, see enc. I.)
Our results have certain limitations. First, despite a large overall
sample size, our estimates of average and median purchase prices are
more precise for radiopharmaceuticals that were purchased by a larger
number of hospitals than for radiopharmaceuticals that were purchased
by relatively few hospitals. Second, we limited our detailed results to
hospitals' purchase prices because we could not fully account for
rebates or payments from group purchasing organizations. Third, the
average and median purchase prices we report refer to a specific time
period and might have increased or decreased since then. In addition,
our estimated purchase prices are based on hospitals' unit dose
purchases only; we do not report prices for the generally less
prevalent forms--multidoses or doses prepared in-house using a kit. We
performed our work according to generally accepted government auditing
standards from March 2004 through July 2005.
Hospitals' Acquisition Costs:
for Selected Radiopharmaceutical SCOD Categories:
The following section presents detailed information on purchase prices-
-the key component of hospital acquisition costs--for certain
radiopharmaceutical SCOD categories for the period July 1, 2003,
through June 30, 2004.[Footnote 15] We also present limited information
on rebates, another component of acquisition costs.
Table 1 contains information on average and median purchase prices. We
order the SCOD categories by their rank in Medicare spending for
radiopharmaceutical SCODs and have identified the SCOD categories by
their HCPCS codes. For each SCOD category, we present both the average
and the median purchase prices, as well as other information that
provides context, including the CMS payment rate. The CMS:
payment rate for 2005 is specified for each HCPCS for a billing unit,
which, for the products in this report, is a dose or is measured in
millicuries (mCi). In table 1, we report the purchase prices by CMS
billing unit.
For two radiopharmaceutical products, our data suggest that it may be
more meaningful to estimate their purchase prices per dose rather than
per billing unit. CMS pays for these radiopharmaceuticals in billing
units defined as a certain number of mCi. However, for each of these
two radiopharmaceuticals, whether hospitals purchased larger doses
(more mCi) or smaller doses (fewer mCi), the price was about the same.
For Q3005--Technetium Tc 99m Mertiatide--the billing unit is one mCi,
yet doses that differed in size (number of mCi) had purchase prices
that were very similar. The two most common doses--5 mCi and 10 mCi--
had average purchase prices of $132.30 and $130.51, respectively.
Similarly, for Q3008--Indium In 111 Pentetreotide--while the billing
unit is 3 mCi, this product's purchase price per dose varied relatively
little with the size of the dose purchased. For the two most common
doses--3 mCi and 6 mCi--the average purchase prices were $1,176.10 and
$1,373.89, respectively.
Table 1: Purchase Prices for Radiopharmaceuticals Accounting for 9
Percent of Medicare Spending on SCODs:
Rank in Medicare spending on radio-pharmaceutical SCODs: 1;
HCPCS code: A9500;
Description: Technetium Tc 99m Sestamibi, per dose;
Medicare spending on SCOD, 2004[A] (in millions): $66.5;
Percent of Medicare spending on SCODs, 2004[A]: 3.4%;
Number of hospitals in sample: 405;
Total number of hospitals[B]: 2,477;
CMS payment rate for 2005[C]: $106.32;
Average purchase price[D]: $75.15;
95% confidence interval of the average purchase price[E]: $73.24 -
77.06;
Median purchase price[F]: $76.47;
95% confidence interval of the median purchase price[E]: $75.58 -
77.85.
Rank in Medicare spending on radio-pharmaceutical SCODs: 2;
HCPCS code: A9502;
Description: Technetium Tc 99m Tetrofosmin, per dose;
Medicare spending on SCOD, 2004[A] (in millions): $38.8;
Percent of Medicare spending on SCODs, 2004[A]: 2%;
Number of hospitals in sample: 174;
Total number of hospitals[B]: 964;
CMS payment rate for 2005[C]: $104.58;
Average purchase price[D]: $70.7;
95% confidence interval of the average purchase price[E]: $67.92 -
73.48;
Median purchase price[F]: $67.59;
95% confidence interval of the median purchase price[E]: $66.23 -
70.98.
Rank in Medicare spending on radio-pharmaceutical SCODs: 3;
HCPCS code: C1775;
Description: Fluorodeoxyglucose (FDG) F18, per dose (4-40 mCi/ml);
Medicare spending on SCOD, 2004[A] (in millions): $32.1;
Percent of Medicare spending on SCODs, 2004[A]: 1.6%;
Number of hospitals in sample: 71;
Total number of hospitals[B]: 687;
CMS payment rate for 2005[C]: $221.11;
Average purchase price[D]: $287.9;
95% confidence interval of the average purchase price[E]: $263.24 -
312.55;
Median purchase price[F]: $272.8;
95% confidence interval of the median purchase price[E]: $261.83 -
308.52.
Rank in Medicare spending on radio-pharmaceutical SCODs: 4;
HCPCS code: C1083;
Description: Yttrium 90 Ibritumomab Tiuxetan, per dose;
Medicare spending on SCOD, 2004[A] (in millions): $7.1;
Percent of Medicare spending on SCODs, 2004[A]: 0.4%;
Number of hospitals in sample: 80;
Total number of hospitals[B]: 130;
CMS payment rate for 2005[C]: $20,948.25;
Average purchase price[D]: $19,614.96;
95% confidence interval of the average purchase price[E]: $19,498.98 -
19,730.95;
Median purchase price[F]: $19,516.70;
95% confidence interval of the median purchase price[E]: $19,459.55 -
19,565.02.
Rank in Medicare spending on radio-pharmaceutical SCODs: 5;
HCPCS code: A9505;
Description: Thallous Chloride TL 201, per mCi;
Medicare spending on SCOD, 2004[A] (in millions): $6.7;
Percent of Medicare spending on SCODs, 2004[A]: 0.3%;
Number of hospitals in sample: 292;
Total number of hospitals[B]: 1,199;
CMS payment rate for 2005[C]: $18.29;
Average purchase price[D]: $17.18;
95% confidence interval of the average purchase price[E]: $16.32 -
18.05;
Median purchase price[F]: $15.49;
95% confidence interval of the median purchase price[E]: $15.06 -
17.06.
Rank in Medicare spending on radio-pharmaceutical SCODs: 6;
HCPCS code: Q3005;
Description: Technetium Tc 99m Mertiatide, per mCig;
Medicare spending on SCOD, 2004[A] (in millions): $6.2;
Percent of Medicare spending on SCODs, 2004[A]: 0.3%;
Number of hospitals in sample: 292;
Total number of hospitals[B]: 1,655;
CMS payment rate for 2005[C]: $31.13;
Average purchase price[D]: $27.4;
95% confidence interval of the average purchase price[E]: $26.47 -
28.34;
Median purchase price[F]: $27.58;
95% confidence interval of the median purchase price[E]: $27.56 -
27.60.
Rank in Medicare spending on radio-pharmaceutical SCODs: 7;
HCPCS code: A9507;
Description: Indium In 111 Capromab Pendetide, per dose;
Medicare spending on SCOD, 2004[A] (in millions): $4.8;
Percent of Medicare spending on SCODs, 2004[A]: 0.2%;
Number of hospitals in sample: 56;
Total number of hospitals[B]: 262;
CMS payment rate for 2005[C]: $1,915.23;
Average purchase price[D]: $1,801.12;
95% confidence interval of the average purchase price[E]: $1,760.80 -
1,841.43;
Median purchase price[F]: $1,841.23;
95% confidence interval of the median purchase price[E]: $1,703.46 -
1,860.22.
Rank in Medicare spending on radio-pharmaceutical SCODs: 8;
HCPCS code: Q3008;
Description: Indium In 111 Pentetreotide, per 3 mCih;
Medicare spending on SCOD, 2004[A] (in millions): $4.5;
Percent of Medicare spending on SCODs, 2004[A]: 0.2%;
Number of hospitals in sample: 193;
Total number of hospitals[B]: 666;
CMS payment rate for 2005[C]: $1,079.00;
Average purchase price[D]: $1,279.55;
95% confidence interval of the average purchase price[E]: $1,198.35 -
1,360.76;
Median purchase price[F]: $1,423.87;
95% confidence interval of the median purchase price[E]: $1,395.49 -
1,437.61.
Rank in Medicare spending on radio-pharmaceutical SCODs: 9;
HCPCS code: A9521;
Description: Technetium Tc 99m Exametazime, per dose;
Medicare spending on SCOD, 2004[A] (in millions): $3.8;
Percent of Medicare spending on SCODs, 2004[A]: 0.2%;
Number of hospitals in sample: 180;
Total number of hospitals[B]: 773;
CMS payment rate for 2005[C]: $778.13;
Average purchase price[D]: $455.59;
95% confidence interval of the average purchase price[E]: $358.29 -
552.89;
Median purchase price[F]: $456.3;
95% confidence interval of the median purchase price[E]: $379.90 -
523.95.
Sources: GAO survey and CMS.
Notes: mCi = millicurie, ml = milliliter:
[A] Medicare spending is for the period January 1, 2004, through
September 30, 2004. The percentage of Medicare spending is based on all
SCODs--both drugs and radiopharmaceuticals.
[B] This estimate of the total number of hospitals in the population is
based on our sample.
[C] This is the payment rate specified for each HCPCS for 2005. It
incorporates CMS's April 2005 update.
[D] This price is based on data provided by the hospitals in our survey
and does not reflect delivery fees or any other ancillary costs
associated with purchasing or administering this product. We asked
hospitals to report prices for drugs purchased from July 1, 2003,
through June 30, 2004. We weighted the prices by the volume purchased
as well as by the sample weights.
[E] The confidence interval measures the precision of the estimate. The
narrower the interval, the greater the precision.
[F] The median purchase price is the midpoint of all prices reported by
hospitals in our sample. This price does not reflect delivery fees or
any other ancillary costs associated with purchasing or administering
this product. Half of the prices reported by hospitals are above the
median and half are below. The median is weighted by volume purchased
and by hospital sample weights.
[G] The billing unit of measure for Q3005, Technetium Tc 99m
Mertiatide, is per mCi. The per mCi purchase price reported is based on
purchase prices for two commonly reported dose sizes, 5 mCi and 10 mCi.
Since in our data the 5 mCi dose is more common than the 10 mCi dose
and the purchase price of a 5 mCi dose and of a 10 mCi dose were
similar, we treated a 10 mCi dose as if it were a 5 mCi dose.
[H] The billing unit of measure for Q3008, Indium In 111 Pentetreotide,
is per 3 mCi. The per mCi purchase price reported is based on purchase
prices for two commonly reported dose sizes, 3 mCi and 6 mCi. Since a 3
mCi dose is the billing unit specified by CMS for Q3008 and since in
our data the purchase price of a 3 mCi dose and of a 6 mCi dose varied
relatively little, we treated a 6 mCi dose as if it were a 3 mCi dose.
[End of table]
In contrast to the detailed purchase price information in table 1, our
information on the rebate component of hospitals' acquisition costs is
limited. About 3 percent of sample hospitals that purchased any of the
nine radiopharmaceuticals reported receiving one or more rebates. Most
of these rebates were directly attributed to specific
radiopharmaceutical SCOD categories. The remaining rebates were for
multiple products and could not be attributed to any single SCOD
category. Most of the rebates came from one company.
Agency Comments and Our Evaluation:
We received comments on a draft of this report from HHS (see enc. II).
HHS stated that paying appropriately for radiopharmaceuticals and the
overhead costs of handling them within the hospital is a priority. HHS
commended our efforts and acknowledged the challenges of accurately
surveying hospitals for radiopharmaceutical acquisition costs. It
stated that we found at least one radiopharmaceutical SCOD for which
rebates may affect its acquisition cost. HHS also stated that it had
concerns regarding the limitations of our study. One concern pertained
to variation in the dosages of radiopharmaceuticals purchased; the
other concern pertained to potential changes in purchase prices since
the time of our data collection. HHS stated that it would take into
account our data on hospital purchase prices in developing 2006
Medicare payment rates for SCODs. HHS added that, in developing payment
rates for 2006 and future years, it considered it important to have a
methodology that can be updated appropriately and that reflects rebates
and other components of radiopharmaceutical acquisition costs.
Despite the limitations that HHS noted, we believe our estimates of
average purchase price for each radiopharmaceutical SCOD category that
we report are sufficiently accurate for use in developing Medicare
rates for SCOD categories. We have clarified our report regarding
rebates: We did not find that one radiopharmaceutical SCOD accounted
for most rebates, but rather that radiopharmaceutical rebates were
relatively rare and that most rebates were attributable to specific
radiopharmaceuticals. Although it is possible for radiopharmaceuticals
in our survey to be purchased in different types of doses--unit doses,
multidoses, and kits for doses prepared in-house--as a practical
matter, most radiopharmaceuticals are purchased as unit doses, and we
have added information on that to the report. In our survey, about 85
percent of hospitals reported purchasing the nine radiopharmaceuticals
listed in table 1 only as unit doses, while about 13 percent reported
purchasing unit doses as well as multidoses, kits for in-house
preparation, or both.[Footnote 16] HHS also expressed concerns about
whether our data are sufficiently current for use in Medicare rate-
setting. If HHS uses our purchase price data in developing SCOD payment
rates, it can mitigate the effect of time lags by adjusting
radiopharmaceutical purchase prices in line with the expected increase
or decrease in hospital drug prices for the coming year. HHS regularly
uses a similar approach in other payment systems, including the
hospital inpatient payment system.
We are sending copies of this report to the Senate Committee on
Finance, the House Committee on Energy and Commerce, and the House
Committee on Ways and Means. We will also make copies available to
others on request. The report is available at no charge on GAO's Web
site at http://www.gao.gov.
If you or your staff have any questions about this report, please
contact me at (202) 512-7119 or steinwalda@gao.gov. Contact points for
our Offices of Congressional Relations and Public Affairs may be found
on the last page of this report. GAO staff who made major contributions
to this report are listed in enclosure III.
Sincerely yours,
Signed by:
A. Bruce Steinwald:
Director, Health Care:
Enclosures - 3:
[End of section]
Enclosure I: Methodology:
This enclosure summarizes the sample design, methods for conducting the
survey and processing data submissions, and the methods we used for
estimating average and median purchase prices of specified covered
outpatient drugs (SCOD). It also names the members of the advisory
panel that commented on our approach to data collection and analysis.
We did our work in accordance with generally accepted government
auditing standards from March 2004 through July 2005.
Sample Design:
We developed a stratified random sample of hospitals. The population
consisted of 3,450 hospitals (1) that had charged Medicare for SCODs
during the first half of 2003 and (2) that were still Medicare
providers on July 1, 2004. To achieve a sample of 1,000 hospitals,
which we determined would meet the Medicare Prescription Drug,
Improvement, and Modernization Act of 2003's (MMA) requirement for a
large sample, we drew a sample of 1,400 hospitals from the population,
on the basis of an expected response rate for all SCODs of 71 percent.
A pilot sample of 48 hospitals was included in the 1,400. (Of the 1,400
hospitals, 1,322 had submitted Medicare claims for radiopharmaceuticals
for the first 6 months of 2003.)
To improve the precision of our estimates of average and median
purchase price, we stratified the sample of hospitals. The objective
was to select strata that would represent very different average
purchase prices for SCODs. Because we did not have a measure of
purchase price at the time we selected the sample, we used total
hospital outpatient SCOD charges to Medicare as a proxy for purchase
price. We used a regression model to identify stratification factors
(such as teaching hospital status) that would maximize the difference
in average purchase price (as proxied by Medicare charges) among
strata. We selected the strata of hospitals as follows. First, we
grouped them into major teaching hospital, nonmajor teaching hospital,
urban nonteaching hospital, and rural nonteaching hospital strata.
Second, within each of these strata, we further divided the hospitals
into several strata depending on the number of unique SCODs that the
hospitals billed for. For example, one stratum contains major teaching
hospitals that billed for fewer than 20 unique SCODs. Third, we placed
small hospitals in a separate stratum to ensure that hospitals with no
or minimal charges for SCODs during the first 6 months of 2003 were
appropriately represented.[Footnote 17]
In our sample design, we defined a major teaching hospital as a
hospital for which the ratio of resident physicians to the average
number of patients was at least 1 to 4 and a nonmajor teaching hospital
as one having a ratio of resident physicians to patients of less than 1
to 4. We defined an urban hospital as one located in a county that was
considered a metropolitan statistical area (as defined by the Office of
Management and Budget) and a rural hospital as one located in a county
that was not considered a metropolitan statistical area. We defined a
small hospital as a hospital for which the total charge amount to
Medicare for SCODs during the first 6 months of 2003 was less than
$10,000. The number of unique SCODs refers to the number of SCODs for
which each hospital submitted Medicare claims during the first 6 months
of 2003. (See table 2.)
Table 2: Characteristics of Sample Strata:
Major teaching hospitals: < 20 unique SCODs;
Hospitals in the population[A]: 75;
Average total charges[B]: $238,949;
Standard deviation of total charges[C]: $320,349;
Neyman allocation for total sample of 1,400[D]: 21;
Target sample of 1,000[E]: 11;
Target response rate in % [F]: 52%.
Major teaching hospitals: 20-39 unique SCODs;
Hospitals in the population[A]: 111;
Average total charges[B]: $861,415;
Standard deviation of total charges[C]: $1,805,586;
Neyman allocation for total sample of 1,400[D]: 111;
Target sample of 1,000[E]: 96;
Target response rate in % [F]: 86%.
Major teaching hospitals: 40-59 unique SCODs;
Hospitals in the population[A]: 96;
Average total charges[B]: $2,297,626;
Standard deviation of total charges[C]: $1,985,026;
Neyman allocation for total sample of 1,400[D]: 96;
Target sample of 1,000[E]: 91;
Target response rate in % [F]: 95%.
Major teaching hospitals: 60+ unique SCODs;
Hospitals in the population[A]: 73;
Average total charges[B]: $6,034,849;
Standard deviation of total charges[C]: $3,703,998;
Neyman allocation for total sample of 1,400[D]: 73;
Target sample of 1,000[E]: 73;
Target response rate in % [F]: 100%.
Nonmajor teaching hospitals: < 20 unique SCODs;
Hospitals in the population[A]: 143;
Average total charges[B]: $196,875;
Standard deviation of total charges[C]: $241,523;
Neyman allocation for total sample of 1,400[D]: 29;
Target sample of 1,000[E]: 16;
Target response rate in % [F]: 55%.
Nonmajor teaching hospitals: 20-39 unique SCODs;
Hospitals in the population[A]: 313;
Average total charges[B]: $714,043;
Standard deviation of total charges[C]: $630,105;
Neyman allocation for total sample of 1,400[D]: 151;
Target sample of 1,000[E]: 94;
Target response rate in % [F]: 62%.
Nonmajor teaching hospitals: 40-59 unique SCODs;
Hospitals in the population[A]: 137;
Average total charges[B]: $1,952,405;
Standard deviation of total charges[C]: $1,222,357;
Neyman allocation for total sample of 1,400[D]: 129;
Target sample of 1,000[E]: 80;
Target response rate in % [F]: 62%.
Nonmajor teaching hospitals: 60+ unique SCODs;
Hospitals in the population[A]: 34;
Average total charges[B]: $5,242,311;
Standard deviation of total charges[C]: $3,410,652;
Neyman allocation for total sample of 1,400[D]: 34;
Target sample of 1,000[E]: 34;
Target response rate in % [F]: 100%.
Urban nonteaching hospitals: < 20 unique SCODs;
Hospitals in the population[A]: 609;
Average total charges[B]: $161,797;
Standard deviation of total charges[C]: $210,080;
Neyman allocation for total sample of 1,400[D]: 99;
Target sample of 1,000[E]: 61;
Target response rate in % [F]: 62%.
Urban nonteaching hospitals: 20-39 unique SCODs;
Hospitals in the population[A]: 428;
Average total charges[B]: $735,416;
Standard deviation of total charges[C]: $728,106;
Neyman allocation for total sample of 1,400[D]: 238;
Target sample of 1,000[E]: 149;
Target response rate in % [F]: 63%.
Urban nonteaching hospitals: 40+ unique SCODs;
Hospitals in the population[A]: 126;
Average total charges[B]: $2,232,851;
Standard deviation of total charges[C]: $1,837,833;
Neyman allocation for total sample of 1,400[D]: 126;
Target sample of 1,000[E]: 110;
Target response rate in % [F]: 87%.
Rural nonteaching hospitals: < 20 unique SCODs;
Hospitals in the population[A]: 730;
Average total charges[B]: $136,618;
Standard deviation of total charges[C]: $141,370;
Neyman allocation for total sample of 1,400[D]: 80;
Target sample of 1,000[E]: 49;
Target response rate in % [F]: 61%.
Rural nonteaching hospitals: 20-39 unique SCODs;
Hospitals in the population[A]: 321;
Average total charges[B]: $672,290;
Standard deviation of total charges[C]: $560,202;
Neyman allocation for total sample of 1,400[D]: 140;
Target sample of 1,000[E]: 86;
Target response rate in % [F]: 61%.
Rural nonteaching hospitals: 40+ unique SCODs;
Hospitals in the population[A]: 53;
Average total charges[B]: $2,072,873;
Standard deviation of total charges[C]: $1,382,985;
Neyman allocation for total sample of 1,400[D]: 53;
Target sample of 1,000[E]: 35;
Target response rate in % [F]: 66%.
Stratum: Small hospitals;
Hospitals in the population[A]: 201;
Average total charges[B]: $3,679;
Standard deviation of total charges[C]: $3,116;
Neyman allocation for total sample of 1,400[D]: 20;
Target sample of 1,000[E]: 15;
Target response rate in % [F]: 75%.
Total;
Hospitals in the population[A]: 3,450;
Neyman allocation for total sample of 1,400[D]: 1,400;
Target sample of 1,000[E]: 1,000;
Target response rate in % [F]: 71%.
Source: GAO.
[A] Hospitals in the population refers to the number of hospitals that
made any claims to Medicare for any SCOD from January 1, 2003, through
June 30, 2003, and were still Medicare-certified hospitals on July 1,
2004.
[B] Total charges are the hospital outpatient charges to Medicare from
January 1, 2003, through June 30, 2003. Average total charges refers to
the average total charges per hospital.
[C] The standard deviation is a measure of variation around the
average.
[D] The Neyman allocation is a method for determining the optimum
sample size, that is, the sample size that results in the greatest
precision.
[E] We expected an achieved sample of 1,000 (an overall response rate
of 71 percent), and we applied the Neyman allocation to determine the
optimum number of hospitals in each stratum. In some strata, the
optimum allocation exceeded the number of hospitals in the population.
In these instances, the excess hospitals were reallocated to the
remaining strata according to the Neyman allocation.
[F] The target response rate is the ratio of the target sample to the
total sample for each stratum.
[End of table]
To determine whether we had selected strata that represented
substantially different average purchase prices for SCODs, we examined
other possible stratification factors and compared the efficiency of
our stratified sample with a simple random sample.[Footnote 18] Other
factors that we examined included hospital size (measured by both
annual discharges and average number of patients), ownership status
(for-profit, nonprofit), whether the hospital billed Medicare for
radiopharmaceuticals, and whether the hospital billed Medicare for
blood products. However, these other factors were highly correlated
with the factors that we had selected and did not significantly improve
the model. Stratification made the sample about 10 times more efficient
than a simple random sample.
To determine the appropriate number of hospitals in each stratum, we
used the Neyman allocation--a method for determining the optimum sample
size, that is, the sample size that results in the greatest precision.
After the sample was selected, we established the optimal allocation of
1,000 hospitals--our target response--among strata, using another
Neyman allocation. We used the results of this second allocation to
establish target response rates by stratum.
Data Collection and Data Processing:
We developed a survey instrument and tested it before sending it to the
entire sample of 1,400 hospitals. We gave hospitals several options for
submitting data, which we extracted from their submissions and put in a
standard format.
After consulting a number of experts, including pharmacists, hospital
administrators, and representatives from industry groups, on methods of
developing and administering the survey, we developed and pretested the
survey instrument with 12 hospitals in June 2004. This initial
instrument was limited to 22 products. As a result of responses to the
pretest, we modified the data collection instrument, and Westat, our
data collection contractor, piloted the revised instrument with 48
hospitals beginning on August 5, 2004. As a result of the pilot, we
clarified certain instructions and made changes in our procedures but
did not significantly change the instrument.
Westat began data collection from the 1,352 hospitals in the sample on
September 27, 2004.[Footnote 19] Key components of the data collection
protocol were as follows:
* a first mailing to the chief executive officer or chief financial
officer of each hospital explaining the survey, followed by a telephone
call to identify the main point of contact;
* a second mailing to the main contact outlining the data that were
needed and describing the options for submitting the data;
* a follow-up telephone call to facilitate the main contact's
understanding of the data collection, provide technical assistance as
needed, and obtain some basic information about the hospital; and:
* telephone calls at regular intervals to remind the hospitals to
submit their data and to provide assistance as needed.
Hospitals could submit data in one of three ways: by uploading
electronic files through the study Web site, by sending an e-mail to
the study address with data attached, or by sending electronic media or
paper submissions through the mail. Electronic submissions took three
forms: downloads from distributors' and suppliers' ordering systems,
extracts from hospitals' own databases, and entries made in a GAO-
supplied Excel form. Paper submissions were most often copies of
invoices.
The contractor performed extensive follow-up. On average, Westat
interviewers called each hospital 8 times before receiving a complete
data submission. Hospitals that were late in responding received 15
calls on average. For drugs, we obtained an overall response rate of 83
percent. For radiopharmaceuticals, we obtained an overall response rate
of 61 percent (based on the 1,322 hospitals in our sample that had
submitted Medicare claims for radiopharmaceuticals for the first 6
months of 2003).
Table 3: Response Rates for Radiopharmaceutical SCODs:
Stratum: Major teaching hospitals: < 20 unique SCODs;
Response rate for radiopharmaceutical SCODs[A]: 42%.
Stratum: Major teaching hospitals: 20-39 unique SCODs;
Response rate for radiopharmaceutical SCODs[A]: 64%[B].
Stratum: Major teaching hospitals: 40-59 unique SCODs;
Response rate for radiopharmaceutical SCODs[A]: 67%[B].
Stratum: Major teaching hospitals: 60+ unique SCODs;
Response rate for radiopharmaceutical SCODs[A]: 59%[B].
Stratum: Nonmajor teaching hospitals: < 20 unique SCODs;
Response rate for radiopharmaceutical SCODs[A]: 69%.
Stratum: Nonmajor teaching hospitals: 20-39 unique SCODs;
Response rate for radiopharmaceutical SCODs[A]: 66%.
Stratum: Nonmajor teaching hospitals: 40-59 unique SCODs;
Response rate for radiopharmaceutical SCODs[A]: 57%.
Stratum: Nonmajor teaching hospitals: 60+ unique SCODs;
Response rate for radiopharmaceutical SCODs[A]: 74%[B].
Stratum: Urban nonteaching hospitals: < 20 unique SCODs;
Response rate for radiopharmaceutical SCODs[A]: 60%.
Stratum: Urban nonteaching hospitals: 20-39 unique SCODs;
Response rate for radiopharmaceutical SCODs[A]: 60%.
Stratum: Urban nonteaching hospitals: 40+ unique SCODs;
Response rate for radiopharmaceutical SCODs[A]: 63%[B].
Stratum: Rural nonteaching hospitals: < 20 unique SCODs;
Response rate for radiopharmaceutical SCODs[A]: 43%.
Stratum: Rural nonteaching hospitals: 20-39 unique SCODs;
Response rate for radiopharmaceutical SCODs[A]: 60%.
Stratum: Rural nonteaching hospitals: 40+ unique SCODs;
Response rate for radiopharmaceutical SCODs[A]: 62%.
Stratum: Small hospitals;
Response rate for radiopharmaceutical SCODs[A]: 100%.
Total;
Response rate for radiopharmaceutical SCODs[A]: 61%.
Source: GAO.
[A] Except where otherwise indicated, we counted as responses all
hospitals that sent usable data on or before January 15, 2005.
[B] We continued to process data received through February 22, 2005,
for certain strata.
[End of table]
We extracted data from hospitals' submissions and placed those data in
a standard format for analysis. In many cases, hospitals submitted data
on all drugs and radiopharmaceuticals purchased--not just SCODs--and
consequently we needed to extract the SCOD drug and radiopharmaceutical
data. Most data were submitted for periods of a day or a month, as we
requested, but 19 hospitals in our sample submitted annual data on
radiopharmaceuticals.
Westat technical staff checked the data for consistency and reviewed
each record to confirm that key information had been included. We
excluded records that lacked key information and trimmed the data to
exclude outliers. On average, 1.8 percent of purchase records were
excluded.
Estimates of SCOD Average and Median Purchase Prices:
This section describes the rationale and method for weighting the
hospital sample data, calculating average purchase price, calculating
median purchase price, and calculating their confidence intervals.
Weighting the Hospital Sample Data:
To estimate hospitals' average and median purchase prices for SCODs,
the sample hospitals' purchase price data are weighted to make them
representative of the population of hospitals from which the sample is
drawn. A survey sample is drawn from a population. To enable data from
the sample to represent data from the population on purchase prices and
other variables, the sample data are weighted: the less likely that a
hospital will be sampled, the larger its weight. For example, if each
hospital has a 1 in 10 probability of being sampled, its sample weight
is 10. That is, each hospital in the sample represents 10 hospitals in
the population. Consequently, if 5 hospitals in a sample buy a
particular drug, and the sample weight is 10, we estimate that 50
hospitals in the population bought that drug. In this report, we refer
to sample weights as "hospital weights." Our sample is stratified, so
all hospitals in a particular stratum (for example, major teaching
hospitals) have the same weight. Since in our sample the probability of
a hospital's being selected varied by stratum, hospitals in different
strata have different weights.
In calculating weights, we took account of two distinctive facts about
our survey: First, our sample is unusual in that we must treat it as a
set of separate samples--one for each SCOD--since the population of
hospitals that buy a drug or radiopharmaceutical in a particular HCPCS
varies depending on the SCOD. Some SCODs are bought by many hospitals,
while others are bought by relatively few hospitals. Second, we lacked
a direct measure of the number of hospitals in the population that
bought a particular SCOD; consequently, we used the number of hospitals
that billed for that SCOD, according to Medicare outpatient claims
data, as a proxy or indirect measure of the population's size.
We calculated the hospital weight as:
W sub jh = N sub jh / R sub jh
where:
* W sub jh denotes the hospital weight for the jth SCOD in the hth
stratum,
* N sub jh denotes the population (the total number of hospitals) that,
according to Medicare outpatient claims, billed for the jth SCOD in the
hth stratum, and:
* R sub jh denotes the total number of hospitals in the hth stratum
that purchased the jth SCOD, according to their survey submissions.
This weight recognizes that not all hospitals responded to our survey,
since the weight's denominator is R sub jh--the number of hospitals
that responded to the survey and indicated that they bought the jth
drug.[Footnote 20]
We made one adjustment to the hospital weight to take account of
unusual circumstances. In some cases, the total number of hospitals in
a stratum that reported purchasing a particular SCOD exceeded our
population estimates. This situation resulted from imperfections in the
Medicare claims data used as a proxy for purchase price. That is, in
these cases R sub jh exceeds N sub jh. Since that situation is
implausible, we adjusted the size of the population derived from
Medicare claims, as follows:
N' sub jh = N sub jh * (R sub jh/M sub jh)
where:
* N' sub jh denotes the adjusted population and:
* M sub jh represents the number of hospitals in the hth stratum that
purchased the jth SCOD, according to their survey submissions, and that
submitted an outpatient claim to Medicare for that drug.
This adjustment makes the size of the adjusted population larger than
the unadjusted population--the number of hospitals that billed Medicare
for the drug. Sampling statisticians call this adjustment "post-
stratification."
Average Purchase Price Using Volume and Hospital Weights:
To summarize hospitals' purchase prices for each SCOD--reflecting
purchases made, in many cases, at different prices and in different
quantities--we calculated an average purchase price for each SCOD. This
average purchase price for a particular SCOD is in effect a weighted
average. To reflect the differences among hospitals in purchase prices
and purchase volumes, we used both the hospital weights and purchase
volume as weighting variables in estimating the average purchase price.
The average purchase price is estimated from our sample data, based on
the following equation:
Y sub j = [Sigma sub h (N sub h/n sub h) Sigma sub i y* sub jhi] /
[Sigma sub h (N sub h/n sub h) Sigma sub i x* sub jhi]
where:
* N sub h represents the total number of hospitals in the hth stratum,
* n sub h represents the size of the sample of hospitals in the hth
stratum,
* y* sub jhi = Sigma sub k y sub jhik, which represents the total
dollar amount summed over all invoice records (k denotes an invoice
record) for the jth SCOD purchased by the ith hospital in the hth
stratum, and:
* x* sub jhi = Sigma k x sub jhik, which represents the total number of
units summed over all invoice records (k denotes an invoice record) for
the jth SCOD purchased by the ith hospital in the hth stratum.
The equation estimates the average purchase price of a SCOD as the
ratio of the total amount purchased in dollars to the total number of
units purchased. For example, a total purchase amount of $50,000 and a
total number of units purchased of 1,000 milligrams yields an average
purchase price of $50 per milligram.
Median Purchase Price Using Volume and Hospital Weights:
In addition to the average purchase price, we calculated the estimated
median of each SCOD's purchase price. To calculate this median, we
first applied volume and hospital weights to each hospital's purchases
of a given SCOD; we then ranked the weighted hospitals' purchase prices
from lowest to highest and selected the midpoint of these prices.
More precisely, the estimated median--based on the population
cumulative density function F for hospital purchase prices--is given
by:
X sub 0.5 = inf { y sub jhik: F(y sub jhik ) greater than or equal to
0.5 },
where:
* X sub 0.5 denotes the median estimate of hospital purchase price for
a particular SCOD,
* y sub jhik denotes the unit purchase price listed in the kth invoice
record submitted in our survey by the ith hospital in the hth stratum,
* F, the cumulative density function, is the probability that the
variable Y takes on a value less than or equal to a particular value
(in this case, y sub jhik),
* inf { a:b } refers to the minimum value of a, which satisfies the
condition specified in b (in this case b is the condition that F(y sub
jhik ) is greater than or equal to 0.5), and:
* the estimated population cumulative density function, F, is defined
as:
F(x) = { Sigma sub h (N sub h / n sub h) Sigma sub i Sigma sub k I(y
sub jhik is less than or equal to x) } / { Sigma sub h (N sub h / n sub
h) Sigma sub i Sigma sub k }
In this equation for F(x), the hospital weights, N sub h/n sub h, enter
in both the numerator and the denominator. The term I (y sub jhik is
less than or equal to x) equals 1 if y sub jhik is less than or equal
to x and is zero otherwise; that is, if the purchase price of a SCOD by
a hospital in the hth stratum is less than or equal to x (any specific
value), this term takes on the value of 1.
Confidence Intervals for Average Purchase Price:
and Median Purchase Price:
To help assess the precision of our estimates of average and median
purchase prices, we calculated confidence intervals for each measure. A
confidence interval gives an estimated range of values, calculated from
sample data (our survey), that is likely to include the true average of
the population (in this case, the average purchase price for a
particular SCOD). As is commonly done, we calculated 95 percent
confidence intervals.[Footnote 21]The narrower the confidence interval
around the average calculated from sample data, the more precise the
estimated average is considered to be.
We obtained the 95 percent confidence intervals of our estimated
average purchase prices by using methods detailed in Cochran[Footnote
22] and Hansen, Hurwitz, and Madow,[Footnote 23] since our estimates
were calculated from our survey--that is, from a stratified
sample.[Footnote 24] To calculate the confidence interval for our
estimates of median prices, we used the equations presented in
Binder[Footnote 25] and Francisco and Fuller.[Footnote 26] We estimated
the average purchase prices, median purchase prices, and the confidence
intervals of both these averages and medians using specialized software
for survey data analysis--SUDAANŽ.[Footnote 27]
Advisory Panel:
To provide us with advice on our methodology for collecting and
analyzing acquisition cost data concerning SCODs, we convened a panel
of experts with experience in pharmaceutical issues or in technical
fields relevant to our survey. The panel met twice: first, to consult
with us on sample design and the survey, and later to review our
preliminary results. The panelists included the chairman, Joseph P.
Newhouse, PhD--John D. MacArthur Professor of Health Policy and
Management, Harvard University; Robert A. Berenson, MD--Senior Fellow,
Urban Institute; Ernst R. Berndt, PhD--Professor of Applied Economics,
Sloan School of Management, Massachusetts Institute of Technology;
Andrea G. Hershey, PharmD--Clinical Coordinator, Pharmacy Residency
Program Director, Union Memorial Hospital (Baltimore, Md.); and Richard
L. Valliant, PhD--Senior Research Scientist, University of Michigan.
[End of section]
Comments from the Department of Health and Human Services:
DEPARTMENT OF HEALTH & HUMAN SERVICES:
Office of Inspector General:
Washington, D.C. 20201:
JUL 8 2005:
Mr. A. Bruce Steinwald:
Director, Health Care:
U.S. Government Accountability Office:
Washington, DC 20548:
Dear Mr. Steinwald:
Enclosed are the Department's comments on the U.S. Government
Accountability Office's (GAO's) draft correspondence entitled,
"Medicare: Radiopharmaceutical Purchase Prices for CMS Consideration in
Hospital Outpatient Rate-Setting" (GAO-05-733R). The comments represent
the tentative position of the Department and are subject to
reevaluation when the final version of this correspondence is received.
The Department appreciates the opportunity to comment on this draft
correspondence before its publication.
Sincerely,
Signed by:
Daniel R. Levinson:
Inspector General:
Enclosure:
The Office of Inspector General (OIG) is transmitting the Department's
response to this draft correspondence in our capacity as the
Department's designated focal point and coordinator for U.S. Government
Accountability Office reports. OIG has not conducted an independent
assessment of these comments and therefore expresses no opinion on
them.
COMMENTS OF THE U.S. DEPARTMENT OF HEALTH AND HUMAN SERVICES ON THE
U.S. GOVERNMENT ACCOUNTABILITY OFFICE'S DRAFT CORRESPONDENCE ENTITLED,
"MEDICARE: RADIOPHARMACEUTICAL PURCHASE PRICES FOR CMS CONSIDERATION IN
HOSPITAL OUTPATIENT RATE-SETTING" (GAO-05-733R):
The Department of Health and Human Services (HHS) appreciates the
opportunity to review the Government Accountability Office's (GAO's)
draft correspondence.
Paying appropriately for radiopharmaceuticals and related overhead
resources under the outpatient prospective payment system is a priority
for HHS, Centers for Medicare & Medicaid Services (CMS). CMS commends
the efforts of GAO and recognizes the challenges of accurately
surveying hospitals for radiopharmaceutical acquisition costs. The data
provided by GAO focused on hospital radiopharmaccutical purchase
prices, which are one component of hospital radiopharmaccutical
acquisition costs. As the report points out, costs for at least one
category of radiopharmaceutical products may be influenced by rebates.
CMS is concerned about some of the limitations about the purchase price
survey noted in the report, such as the variation between unit dosing,
multi-dosing, and doses prepared in-house using a kit. Also, CMS
foresees concerns about the potential for the purchase prices to have
changed since the time period that GAO surveyed hospitals.
As with the GAO report on hospital outpatient drug purchase prices, CMS
will take the survey data into account as we develop the proposed
payment rates for 2006. CMS believes it is important, as we develop the
payment rates for 2006 and future years, to have a methodology that can
be updated in an appropriate manner and that reflects the rebates and
other price concessions that influence radiopharmaceutical acquisition
costs.
[End of section]
GAO Contact and Staff Acknowledgments:
GAO Contact:
A. Bruce Steinwald (202) 512-7119 or steinwalda@gao.gov:
Acknowledgments:
In addition to the contact named above, Phyllis Thorburn, Assistant
Director; Todd Anderson; Hannah Fein; Kaycee Misiewicz; Elizabeth T.
Morrison; Dae Park; Jonathan Ratner; Anna Theisen-Olson; and Mike
Thomas made key contributions to this report.
(290461):
FOOTNOTES
[1] GAO, GAO-05-581R (Washington, D.C.: June 30, 2005).
[2] In this report, the term drugs refers to both drugs and
biologicals. Biologicals are products derived from living sources,
including humans, animals, and microorganisms.
[3] Radiopharmaceuticals are radioactive substances used for diagnostic
or therapeutic purposes.
[4] Pub. L. No. 105-33, § 4523, 111 Stat. 251, 445--450.
[5] Pub. L. No. 106-113, app. F, § 201(b), 113 Stat. 1501A-321, 1501A-
337--1501A-339.
[6] Pub. L. No. 108-173, § 621(a), 117 Stat. 2066, 2307--2310.
[7] Under OPPS, CMS groups services into APCs on the basis of their
clinical and cost similarities. All services that are grouped into the
same APC have the same base payment rate. The MMA required CMS to
establish a separate APC for a pharmaceutical product if the cost per
administration is $50 or more. MMA 117 Stat. 2310. Drugs that cost less
than $50 per administration are bundled with other services for payment
purposes. CMS has interpreted the cost per administration as the median
cost per day.
[8] MMA 117 Stat. 2308. In addition, the MMA required the Medicare
Payment Advisory Commission, known as MedPAC, to report on hospitals'
overhead costs and related expenses for SCODs for the Secretary's
consideration in setting 2006 payment rates. MMA 117 Stat. 2309.
Overhead costs are not part of acquisition costs. MedPAC's mandated
report is Chapter 6, "Payment for pharmacy handling costs in hospital
outpatient departments," in Issues in a Modernized Medicare Program
(Washington, D.C.: MedPAC, June 2005).
[9] See Denise A. Merlino, "Nuclear Medicine Facility Survey: SNM 2003
Survey Reporting on 2002 Cost and Utilization," Journal of Nuclear
Medicine Technology, vol. 32, no. 4 (2004), 215-219.
[10] See GAO-05-581R.
[11] In this report, the term SCOD includes both pharmaceutical
products that currently meet the definition of SCODs and those that do
not meet the definition now but may be considered SCODs in the future.
[12] Forty-eight of these hospitals were in our pilot survey, which
began on August 5, 2004.
[13] We contracted for data collection and much of the data processing
with a large survey firm with experience in conducting health care
surveys.
[14] Of the 1,400 hospitals, 1,322 had submitted Medicare claims for
radiopharmaceuticals for the first 6 months of 2003.
[15] Although SCODs by definition are used in hospital outpatient
departments, the data we received from hospitals may represent
radiopharmaceuticals that were used for both inpatients and outpatients
and for Medicare and non-Medicare patients.
[16] Less than 2 percent of hospitals reported purchasing only
multidoses, kits, or both.
[17] Even if these hospitals did not have charges for SCODs in the
first 6 months of 2003, they might have made purchases for SCODs after
that time period. Therefore, it was important to include them in the
sample.
[18] We measured efficiency by the size of the reduction in sample
variation.
[19] We also used data from the 48 hospitals in the pilot survey, for a
total sample of 1,400 hospitals.
[20] Our formulation of the hospital weight is an adaptation of the
usual formulation, in which N sub jh is divided by n sub jh , the
number of hospitals in the hTH stratum that purchased the jTH SCOD.
Unlike R sub jh, n sub jh includes hospitals that did not respond to
the survey and consequently is not appropriate for our purpose.
[21] If independent samples are taken repeatedly from the same
population, and a confidence interval calculated for each sample, then
a certain percentage of the intervals will include the unknown average
for the population. The confidence interval is often calculated so that
the percentage is 95 percent.
[22] W.G. Cochran, Sampling Techniques, 3RD ed., Wiley Series in
Probability and Mathematical Statistics, section 11.7 (New York, N.Y.:
John Wiley & Sons, 1977), 303.
[23] M.H. Hansen, W.N. Hurwitz, and W.G. Madow, Sample Survey Methods
and Theory, vol. I, Methods and Applications, Wiley Publications in
Statistics, sections 6.6 and 6.7 (New York, N.Y.: John Wiley & Sons,
Inc., 1953), 252-259.
[24] More precisely, this is a stratified cluster sample. "Cluster"
refers to the set of invoice records (for a given SCOD) reported by a
hospital. The size of a cluster varied widely among hospitals--from 1
invoice record for a given SCOD to over 800 records.
[25] D.A. Binder, "Use of Estimating Functions for Interval Estimation
from Complex Surveys," Proceedings of the Survey Research Methods
Section, American Statistical Association (1991).
[26] C.A. Francisco and W.A. Fuller, "Quantile Estimation with a
Complex Survey Design," Annals of Statistics, 19 (1991), 454-469.
[27] B.V. Shah, B.B. Barnwell, and G.S. Bieler, SUDAAN: User's Manual,
Release 7.5, vols. 1 and 2 (Research Triangle Park, N.C.: Research
Triangle Institute, 1997). SUDAANŽ is a registered trademark of the
Research Triangle Institute.