Physician Staffing for the VA Volume II, Supplementary Papers (1992) / Chapter Skim
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Section IV: Further Examination of the Empirically Based Physician Staffing Models
Section IV: Further Examination of the Empirically Based Physician Staffing Models
Pages 467-530
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From page 469... ...
The primary purpose of this concluding section of the Supplementary Papers is to examine further the statistical validity of selected physician staffing models presented in chapter 4. In addition, for a subset of these models a certain physician productivity index frequently derived in microeconomic analyses of input-output relationships the Marginal productivitys of an input-will be developed; this index will be used to investigate the output gain expected from incremental increases in physician staffing in a given patient care setting.
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From page 470... ...
PCAs: inpatient care-medicine, surgery, psychiatry, neurology, rehabilitation medicine, and spinal cord injury; ambulatory care-medicine, surgery, psychiatry, neurology, rehabilitation medicine, and other physician services (including emergency care and admitting & screening) ; and long-term care-nursing home and intermediate care.
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From page 471... ...
Both the PF and the IPF deal with only a portion of total physician FTEE at the VAMC, albeit a very important and quantitatively significant portion in each case. The fraction of physician FTEE allocated to patient care only the focus of the PF variant will vary by specialty and facility, of course, but it rarely falls below 65 percent and generally lies in the 7~95 percent range (see Table 9.1 in Volume I)
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From page 472... ...
Rather, it may provide some insight into whether the PF model from which it is derived is a reasonable representation of the production process. All analyses below focus either on the PFs estimated for inpatient medicine, inpatient surgery, or inpatient psychiatry, or on the IPFs estimated for the specialty groupings of medicine, surgery, or psychiatry.
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From page 473... ...
= the annual rate of production of workload in PCA j of VAMC i; {Staffphys~} = a set of variables, each of which takes the form Staffphys~ = the amount of FREE allocated to direct patient care in PCA j of VAMC i for staff physicians based in cost center k, where each k corresponds to one of the 11 specialty groups examined here in detail; {ConPhys'} = a set of variables for physicians under contract to VAMC i, such that ConPhys~ = the contract physician FTEE from specialty k devoted to PCA j; {Res~f} = a set of variables to account for the net productive contribution of residents, with each variable of the form Rest,, = the amount of postgraduate year y resident FTEE allocated to PCA j at VAMC i; = for non-VA physicians who perform consulting and attending duties on a fee-for-visit basis, the amount of FTEE allocated to PCA j at VAMC i;
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From page 474... ...
is a nonstochastic determinant of the dependent variable, workload; thus, it is assumed ipso facto that inputs and outputs are not jointly determined in a mutually interactive fashion. In production models of the profit-maximizing firm, inputs and output are jointly determined, in theory; hence, single equation approaches are problematic, yielding biased model estimates unless special assumptions are imposed (which is often the case)
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From page 475... ...
Rather, it is assumed that each VAMC attempts to meet its patient care mission in a way that balances several concerns: that eligible veterans are treated in a timely manner; that the quality of care is acceptable; and that budget, other resource, and administrative constraints are met. Consistent with this, it is assumed for the PF analysis that a VAMC adjusts inputs and workload in a step-sequence process: Subject to resource and budget availability, the VAMC sets input levels for each fiscal year in accordance with projected workload.
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From page 476... ...
The IPF's underlying assumption is that the amount of physician ['lEE from a given specialty required for patient care and resident education is a function of the volume of patient care workload to be produced, the number of residents to be taught on the PCAs, and possibly other factors influencing the relationship among workload, resident education, and staff physician requirements. From a cause-and-effect standpoint, the basic behavioral assumption in the IPF variant (in contrast with the PF)
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From page 477... ...
where = across all PCAs at VAMC i, the total amount of specialty k staff physician and contract physician [-lhE devoted to patient care and resident education; {W~} = a set of workload variables, each of the form Wit = the level of workload on PCA j of VAMC i associated with specialty k {Rests} = a set of variables, each of the form Resin, = the amount of postgraduate year y resident FTEE at VAMC i in specialty k; {DIPPY} = a set of variables, each of the form NAP, = the amount of Al BE of nonphysician practitioner type m associated with the PCA-related activities of physicians in specialty k at VAMC i; Prodfact ~= one or more variables for factors influencing the productive efficiency of specialty k physicians at VAMC i; ERRORS = the random~rror term for specialty k at VAMC i. Originally, the general specification of the IPF also included variables for nurses and support staff.
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From page 478... ...
Patient care and resident education typically dominate these activities. Because the PCA-related part of research FTEE cannot be separated from total research t-1'EE in the current data systems and because most research occurs off the PCAs, research is excluded from the IPF equation; to derive total physician t-1'~E through an IPF (or a PF)
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From page 479... ...
Since the number of observations for a given model was small (ranging from about 80 to 160) relative to the number of potential variables, a predetermined list of candidate variables was made, including interaction terms, based on assumptions about the workload production process.
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From page 480... ...
for any variable not in the model. Three Estimated PFs The general framework for these estimated PF equations is captured in Equation 4.9.
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From page 481... ...
; FTEE of residents PGY 4 and above allocated to this PCA; social worker FTEE allocated to this PCA; = support-staff FTEE divided by total b1 EE for physicians involved in hands-on delivery of care in the inpatient medicine PCA, defined to include internists, surgeons, psychiatrists, neurologists, and rehabilitation medicine
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From page 482... ...
; (MED MD x FELLOWS) = an interaction term for the joint influence of VA staff internists and fellows on the rate of workload production in this PCA; N Inpatient Surgery = the number of inpatient medicine PCAs (equivalent to the number of VA medicine services)
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From page 483... ...
HGROUP2 (MED MD x OTHER_MD) 483 total P-1 EE allocated to inpatient surgery PCA by VA staff physicians not in medicine, surgery, psychiatry, neurology, or rehabilitation medicine cost centers; nursing-staff [-1 EE divided by total FTEE for physicians involved in handson delivery of care in the inpatient surgery PCA, defined to include internists, surgeons, psychiatrists, neurologists, and rehabilitation medicine physicians (hereafter, this variable will be labeled more succinctly, ~nursingstaff WEE per total physician FTEE in this PCA.)
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From page 484... ...
with R2 = 0.874 and N = 141 W = ln[BDOC' + 1] = the natural logarithm of total bed{lays of care, plus 1, produced in the inpatient psychiatry PCA during the fiscal year; HGROUP4 = a categorical variable assuming a value of 1 if the facility is in RAM Group 4 (mid-size general unaffiliated VAMC)
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From page 485... ...
For example, Wit in Equation 4.10 becomes simply W For computational reasons only, all workload variables are divided by the constant 10,000; this affects the absolute size of the corresponding coefficient estimate but not its algebraic sign or statistical significance.
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From page 486... ...
. The CAPWWU total covers not only ambulatory medicine, but also the other physician services PCA because the latter includes the emergency unit and admitting & screening, important clinic stops with heavy internist involvement.
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From page 487... ...
across all PCAs, plus total surgeon FTEE allocated to resident training, plus 1; SURWWU = total surgery WWUs produced dunug the fiscal year across all inpatient PCAs (divided by 10,0001; and SURCAPWWU = total CAPWWUs produced during He fiscal year in the ambulatory surgery PCA (divided by 10,000~.
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From page 488... ...
across all PCAs, plus total psychiatrist FTEE allocated to residency training, plus 1; PSYWWU = total psychiatry Wows during the fiscal year across all inpatient PCAs (divided by 10,000) ; PSYCAPWWU = total CAPWWUs during the fiscal year in the ambulatory psychiatry PCA; and INSOCW = total inpatient social worker P-lEE.
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From page 489... ...
residuals plotted against the corresponding predicted values of the dependent variable; studentized residuals have been normalized in a way that enhances one's ability to detect systematic trends. If the classical assumptions about ERROR hold, a randomlooking plot should result.
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From page 490... ...
embodied in the original model. The second issue refers specifically to the fact that the best-fitting, clinically plausible PF or IPF that emerged from the original sample provides a better .fit~ to that particular sample than it would typically to any other, equally plausible sample-for example, the sample of variable values that will appear next year.
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From page 491... ...
The first six tables consider, in turn, the six equations, summarizing for each PF or IPF the frequency with which each of its independent variables appears in 100 subsequent models estimated from 100 successive bootstrap samples that were drawn (with replacement) from the original sample.
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From page 492... ...
Not surprisingly, the overall performance of the variables in each equation was roughly in accord with the equation's goodness of fit, as indexed by R2. Of the 31 independent variables in the three PFs, all but 3 (all in the Inpatient Medicine PF)
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From page 493... ...
Each test sample was used as follows. First, the independent variable values for each test-sample VAMC were substituted into the right-hand-side of the MED PF equation estimated with the training sample, thus yielding a predicted workload value for that test site.
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From page 494... ...
classification of patient care; the panel questioned whether DRGs offered the appropriate framework for measuring psychiatry workload. Regarding the second case, the use of clinic stops rather than CAPW~Us led to a significantly better fitting PF.
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From page 495... ...
· MED IPF-In this case, the workload substitution was three-fold: inpatient medicine BDOC replaced aggregate medicine WWUs; the sum of clinic stops for the ambulatory medicine and ambulatory "other physician services PCAs replaced the sum of CAPWWUs for these two PCAs; and total BDOC for the nursing home and intermediate care PCAs replaced total RUGWWUs. With these changes, R2 in fact increased (from 0.583 to 0.603)
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From page 496... ...
, consider now the marginal product of the internist in the VA systemwide Average or Most typical. inpatient medicine PCA.
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From page 497... ...
But note that W defined as the natural logarithm of total WWUs, plus 1, produced in the inpatient medicine PCA, is in fact a nonlinear function of workload.
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From page 498... ...
. One can also infer that, in FY 1989, the addition of one psychiatrist or surgeon Al BE to the inpatient psychiatry or surgery PCA, respectfully, could have lead, on average, to a markedly larger increase in workload than a corresponding unit increase in the internist in the statistically typical inpatient medicine PCA.
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From page 499... ...
Significant m<0.05) Original- in 100 Sample Bootstrap Origmal- Standard Sample Variable Sample Mean Deviation Models MED_MD 5.34 3.24 100 (MED_MD)
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From page 500... ...
Significant ~<0.05) Original- ~ 100 Sample Bootstrap Onginal- Standard Sample Variable Sample Mean Deviation Models SUR_MD 3.94 2.38 100 (SUR_MD)
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From page 501... ...
Significant m<0.05) Original- in 100 Sample Bootstrap Original- Standard Sample Variable Sample Mean Deviation Models PSY_MD 3.86 3.45 100 RESIDENTS 2.09 2.45 100 (PSY_MD*
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From page 502... ...
Significant ~0.05) Original- in 100 Sample Bootstrap Ongmal- Standard Sample VanableSample Mean Deviation Models MEDWW[J0.28 0.17 100 MEDCAPWWU373.26 236.58 82 MEDRUGWWU5.39 4.99 68 FELLOWS7.25 8.49 69 HGROUP20.21 0.41 58 HGROUP30.29 0.46 67 HGROUP40.11 0.31 76 HGROUP50.16 0.37 62 HGROUP60.13 0.34 63 (MEDWWU*
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From page 503... ...
F7JRTHER ~llNAnON OF THE EBPSM TABLE 5 Replicabili~of the ~Final. Surgery IPF: Backward-Elimination Regression Analysis of 100 Bootstrap Samples with Regressor Domain Consisting of Final Model Variables 503 Variable Onginal Sample Original- Standard Sample Mean Deviation 9Ii Times Stat.
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From page 504... ...
504 PHYSlCUN STAFFING FOR THE Vie-VOLUME TABLE 6 Replicabilityof the ~Final. Psychiatry IPF: Backward Elimination Regression Analysis of 100 Bootstrap Samples with Regressor Domain Consisting of Final Model Variables Variable Original Sample Original- Standard Sample Mean Deviation % Times Stat.
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From page 505... ...
Based on Backward Elimination Regressions Using 100 Bootstrap Samples with Regressor Domain Consisting of Final Model Variables. Original Sample R
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From page 506... ...
~ ~ c] 111 Z ~ I ~ ~ A ~ ~ ~ ~ ~ ~ ~ J FIGURE ~ Inpatient Medicine PF Residuals Plot IL a a' J - 0 ~ o o lo: IL - to
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From page 507... ...
. N to 1 1 1 ~ ~ ~ ~ ~ z FIGURE 2 Patient Surgery PF Residuals Plot 507 co m 3 0 a a: lo
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From page 508... ...
,,,, I,,,,,,,,, I,, .,,,,,, I, ~ |,} ~_ O I I ~I U] 1~ ~ ~ 111 Z ~ ~ A I1J O 1E b1 0 ~ O ~ < J 0 FIGURE 3 Inpatient Psychiatry PF Residuals Plot _ N _ _ ~ o - a'
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From page 509... ...
~# # # ~ # , , IL a m > lo o tar _ ~ ~N O 1 0 ~ ~ ~ IIJ Z 1~ ~ Jo I8J C! ~ 111 0 ~ O :~ < J 0 FIGURE 4 Inpatient Neurology PF Residuals Plot 509 .
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From page 510... ...
510 FUR7~ ~nvEmG`lno~ OF DIE APSE # ~ ~ · ~ - .,,,,, ~r ~S os - =c3~z - ~ - o =~0~0~< Jo FIGURE 5 depart Rehabilitation Medicine PF Residuals Plot bit
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From page 511... ...
-- - ~ '''''',,t'''''''''4 ,., ,,,.,.,,' ,,,., _ ~ CU U] ~ ~ 0 ~ A ~ ~ ~ ~ 0 PIGIJRE 6 Spinal Cord Injury PF Residuals Plot 511 a, J @ ~ gl
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From page 512... ...
. mu ~ 0 1 ~I I 01 =~z' - ~O =~0~O FIGURE 7 Ambulatory Medicine PF Residuals Plot ',~ Manor OF ME ERPSM #.
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From page 514... ...
. In m ~0 ~N ~In 0 ~ ~ ~ ~ Z ~ ~ ~ to ~ ~ ~ ~ ~ ~ ~ < J In FIGURE 9 Ambulatory Psychiatry PF Residuals Plot oo _ ~
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From page 515... ...
# # ° ~ .., ,.,.~.,.,,,.,. ~it- _ ~ 0 N ~ O ~ t11 Be 1~ :~ O 111 Z ~ ~ to IIJ O tE 111 ~ ~ O ~ ~ ~ 0 FIGURE 10 Ambulatory Neurology PF Residuals Plot 515 a' 0 ~ n.
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From page 516... ...
516 ~U~ ItlVESTIGAlION OF ME EBpSw ~me # t" Act ~ #me ~ .# # [ #"e j! # t | # S # |# ~# e ~ W-~ ~e - -t al ~ 0~ ~ ~ ~ ~ ~ ~ z ~ ~ ~ ~ ~ ~ ~ In ~ ~ ~ ~ A ~ FIGURE 11 Ambulatory Rehabilitation Medicine PF Residuals Plot o , ~ ~ £
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From page 517... ...
## ~Be at Ad # # ~ 1 : # ~ # # .# # # # ~ ~ ~ He ~ .e ~ # PI _ ~ :~ to o _ ~ O01 ~ ~ O lit Z 1~ ~ ~D t! : 111 0 ~ D ~ < J 03 to _ N FIGURE 12 Ambulatory Other Physician Services PF Residuals Plot 517
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From page 518... ...
~1 01 ~ ~ ~ ~ Z ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ < # ~, , . , , ~ FIGURE 13 Nursing Home PF Residuals Plot IL o ID a, 0
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From page 519... ...
.,,,,,,, ,.,,,,,,,,,,,,,. ~· - ~ ~o , ~ C, oe ~ ~ 0 ~ z ~ ~ ~ ~ c, ~ ~ In ~ c, ~ < A rat FIGURE 14 Idtermediate Care PF Residuals Plot 519 _ , ~ 8
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From page 520... ...
## # .. ## o I ~I -0 · C ~ -~ N ~ ~ · ~ _ ~ ~ ~ i' ~ PIGURB 15 Medicine IPF Residuals Plot _ - N o 0 :]
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From page 521... ...
~ #. t # .# ~ ~ .,,,,,,,,,.,,,,,,,,, ,.,,,, ~ o , I ~ ~ ~ oo ~ ~ ~ o C ~ ~ ~ o ~CE ~ ~ ~ ~ ~ ~ A' ~ FIGURE 16 Surgery IPF Residuals Plot 521 3
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From page 522... ...
i ~# # # a' # 1 ~ `' 1~. ~ ~ ~ ., ,.,,, ,,,.,,,,,,,,, .,,,,,,,,.,,, ,.,,.,,.,,,.,, , - o o o C ~ ~ ~ o FIGURE 17 Psychiatry IPF Residuals Plot
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From page 523... ...
, , , ,,,., a. m ~ ~ , I my I Or 0 m ~ ~ ~ 0 c ~ ~ N ~ ~ ~ · A ~ .0 ~ ~ ~ O FIGURE 18 Neurology IPF Residuals Plot 523 _ o 0 ~ _ · ~ o _ o D O O _ O
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From page 524... ...
o 0~ ·01 0 ~ :] ~ a C ~ ~ N ~ ~ a ~ ~ ~ ~ ~ ~ ~ FIGURE 19 Rehabilitation Medicine IPF Residuals Plot o
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From page 526... ...
# .# #. # ~ # ~ # ~ # ~ ~ ~ O 111 Z ~ ~ ~ ID O ~ lIJ ~ ~ O ~ ~ J al FIGI1}lE 21 Anesthesiology IPF Residuals Plot F7~ IN~SU=nON OF HE E:BP5QU # # # # ~# # _ L m o 40 _ ~ _" ~ IL _ N O -4 ~ O · O 0 ~ o - O m o 'a O
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From page 527... ...
.. 1 1 _ MU ~ O I -- :~= ~ C~- ~ a~ ~ ~ a-~0 :~ a FIGURE 22 I^boratory Medicine IPF Residuals Plot 527 - m 3
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From page 528... ...
· · ~ o o o 1 1 1 0 ~ ~ ~OC ~ ~N O ~ ~81 ~ ~:] 81 ~ FIGURE 23 Diagnostic Radiology IPF Residuals Plot - m - o
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From page 529... ...
. 0 N - 4 0 0 ~ ~ O ell Z 1 ~J ell D tE Ill 0 l-1 0 ~ < _1 @1 FIGURE 24 Nuclear Medicine IPF Residuals Plot 529 N _ e O to _ ~ o z elf o m eO to a:
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From page 530... ...
o _ r\ ~0 ~m ~ it: # # l 8] ~ ~0 c ~ ~N O ~· 0 ~ ~ ~81 FIGURE 25 Radiation Oncology IPF Residuals Plot o o at: 1 a Ir a to a _ ~ o o u a
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