This is a report I wrote for a case study.

1. Hospital and Physician Quality
Ran Zhou
Introduction
This report is aimed at examining the data from the Centers for Medicare and Medicaid
Services to estimate the performance of each hospital and performance of each physician. The
performance of the hospitals and the physicians are both influenced by the fixed effects, the
region of the hospital and the procedure the hospital or the phisician provides, which means
that the mortality rate can be influenced by the region and procedure in general. However,
the performance varies between hopitals and between physicians, so random effects for each
hospital and each physician are good for estimating the cluster-level(hospital and physician)
differences.
Model
We consider fitting a generalized linear mixed model with fixed effects for each combination
of region and procedure type and random effects for each hopital and each physician only
on the intercept. The performance is measured by the mortality rate with 30 days of the
procedure. The model in the equation form is:
logit(Pr(Yijk = 1)) = β0 + β1Region + β2Procedure + β3Region × Procedure + b0i + b0ij
where Yijk = 1 if patient k treated by physician j in hospital i died within 30 days, and we
assume b0i, b0ij ∼ N(0, σ2
). The model was estimated using a Bayesian approach, with a
prior N(0, 1) on each element of β and independent half-t priors with scale 10 and df=3 on
the two variance components. After fitting the model combining the prior distributions and
the observed data, 4000 posterior samples sampled from the posterior distributions of each β
and each random effect are collected for further analysis.
Analysis
1. Variance of Hospitals vs. Variance of physicians
Table 1 shows the point and interval estimates of the variances of the random effects on both
1

2. Point Estimate Interval Estimate
hospital 0.0126 (0, 0.0703)
physician 0.1375 (0.0814, 0.218)
*
Table 1: Variance of Hospital and
Variance of Physician
hospital level and physician level. The posterior
estimated variance of the random effects of the
physicians is higher than that of the hospitals,
which means that, the difference in performance
among hospitals is not as much as the differnce
in performance among physicians.
2. Mortality Rate Comparison among Regions
The plot below shows the posterior medians and 95% credible intervals of odds ratios
comparing the odds of death in each region to that in region Queens for procedure CABG
and procedure Valve or Valve/CABG. An example of how to interpret the odds ratios and
the credible intervals is:
• For region Western NY - Rochester, the posterior median and the credible interval for
CABG is 1.6817 and (0.9367, 3.1489), meaning that, when the procedure is CABG,
mostly the odds of death for region Western NY - Rochester is 1.6817 times of the odds
of death for region Queens, and 95% of the posterior odds ratio falls between (0.9367,
3.1489).
• For region Western NY - Rochester, the posterior median and the credible interval for
Valve or Valve/CABG is 2.0061 and (1.1235, 3.5774), meaning that, when the procedure
is Valve or Valve/CABG, mostly the odds of death for region Western NY - Rochester
is 2.0061 times of the odds of death for region Queens, and 95% of the posterior odds
ratio falls between (1.1235, 3.5774).
CABG Valve or Valve/CABG
1 2 3 4 1 2 3 4
Bronx
Capital District
Central NY
Kings
Manhattan
NY Metro − Long Island
NY Metro − New Rochelle
Staten Island
Western NY − Buffalo
Western NY − Rochester
Odds Ratio
Region
Odds Ratios of Death in Each Region vs. Queens
for Each Procedure
We can see that Queens region has a better performance or lower mortality rate than all
the other regions for procedure Valve or Valve/CABG, and region Queens also has a better
performance or lower mortality rate than all the other regions except for region NY Mero-New
Rochelle for procedure CABG.
Additionally, comparing the overall odds ratios between the two procedures, we can see that
procedure Valve or Valve/CABG in general have higher odds ratios of death comparing
2

3. each regions to region Queens (posterior medians for procedure Valve or Valve/CABG are
closer to 2, and posterior medians for procedure CABG are closer to 1.5), which means that
the advance of region Queens for procedure Valve or Valve/CABG is higher than that of
procedure CABG. Also comparing with region Queens, Bronx, Manhattan, NY Metro - Long
Island, Staten Island and Western NY - Rochester perform worser for procedure Valve or
Valve/CABG than procedure CABG; Capital District, Central NY, Kings, and Western NY -
Buffalo have similar performace for both procedure relative to region Queens; and NY Metro -
New Rochelle perform better than region Queens on procedure CABG but worse than region
Queens on procedure Valve or Valve/CABG.
3. Mortality Rate Comparison among Physicians - Mortality Ratio
Plot/Table
The 6 plots are showing the estimates of the ratio of the model-predicted mortality rate
to the expected mortality rate for each physician in each hospital. Each physician has a
ratio estimates for the two procedures, and the hospitals that the physicians belong to
are seperated by difference colors. Expected mortality rate is important here in analyzing
physician performance because some physicians may have more unhealthy patients, leading
to a higher mortality rate than those physicians having more healthy patients. Thus a ratio
greater than 1 in these plots represents the physician is doing worse than expected given the
illness of his or her patients, and a ratio less than 1 represents the physician is doing better
than expected.
Some ratios have a large credible interval, such as Weinstein S in hospital Montefiore - Moses
and Chen J M in hospital NYP- Columbia Presby. This is because that the physician in that
hospital does not have much cases in the data (both of them only have 1 case) and the model
was not able to make a good estimation based on such a small sample size.
CABG Valve or Valve/CABG
0 5 10 15 0 5 10 15
Graver L | 1
Manetta F | 1
Meyer D B | 1
Palazzo R | 1
Parnell V | 1
Scheinerman S J | 1
Lang S | 2
Bello R A | 3
D Alessandro D A | 3
Deanda A | 3
Derose J J | 3
Goldstein D J | 3
Michler R E | 3
Weinstein S | 3
Bello R A | 4
D Alessandro D A | 4
Derose J J | 4
Goldstein D J | 4
Michler R E | 4
Bennett E | 5
Britton L | 5
Depan H | 5
Miller S | 5
Abbott A E | 6
Canavan T | 6
El Amir N | 6
Singh C | 6
Depan H | 7
Reich H | 7
Singh C | 7
Kelley J | 8
Lancey R A | 8
Mortality Rate Ratio
Physician
hospital
LIJ Medical Center
NY Hospital − Queens
Montefiore − Moses
Montefiore − Weiler
Albany Medical Center
Champ.Valley Phys Hosp
Ellis Hospital
M I Bassett Hospital
Ratio of
Predicted Mortality Rate vs.Expected Mortality Rate
for Each Physician in Each Hospital [1]
3

4. CABG Valve or Valve/CABG
0 1 2 3 4 5 0 1 2 3 4 5
Bennett E | 9
Canavan T | 9
Depan H | 9
Reich H | 9
Saifi J | 9
El Amir N | 10
Joyce F | 10
Kelley J | 10
Green G R | 11
Marvasti M | 11
Nazem A | 11
Rosenberg J | 11
Zhou Z | 11
Wong K | 12
Yousuf M | 12
Fink G W | 13
Lutz C J | 13
Abrol S | 14
Crooke G | 14
Jacobowitz I | 14
Lahey S J | 14
Ribakove G | 14
Saunders P | 14
Stephens G A | 14
Vaynblat M | 14
Ciaburri D | 15
Tortolani A | 15
Burack J H | 16
Ko W | 16
Lee D C | 16
Tak V M | 16
Mortality Rate Ratio
Physician
hospital
St. Peters Hospital
St. Elizabeth Med Ctr
St. Josephs Hospital
Unitd Hlth Svcs−Wilson
Univ.Hosp−SUNY Upstate
Maimonides Medical Ctr
NY Methodist Hospital
Univ.Hosp−Brooklyn
Ratio of
Predicted Mortality Rate vs.Expected Mortality Rate
for Each Physician in Each Hospital [2]
CABG Valve or Valve/CABG
0 5 10 0 5 10
Balsam L B | 17
Crooke G | 17
Culliford A | 17
Deanda A | 17
Loulmet D F | 17
Ribakove G | 17
Schwartz C F | 17
Geller C M | 18
Hoffman D | 18
Ko W | 18
Tranbaugh R | 18
Ciuffo G B | 19
Gorki H | 19
Loulmet D F | 19
Patel N C | 19
Plestis K A | 19
Subramanian V | 19
Adams D H | 20
Anyanwu A C | 20
Chikwe J Y | 20
Ciuffo G B | 20
DiLuozzo G | 20
Filsoufi F | 20
Griepp R | 20
Nguyen K | 20
Reddy R C | 20
Stelzer P | 20
Tannous H J | 20
Zias E | 20
Balaram S K | 24
Swistel D | 24
Mortality Rate Ratio
Physician
hospital
Bellevue Hospital Ctr
Beth Israel Med Ctr
Lenox Hill Hospital
Mount Sinai Hospital
St. Lukes at St. Lukes
Ratio of
Predicted Mortality Rate vs.Expected Mortality Rate
for Each Physician in Each Hospital [3]
Table 2 following the 6 ratio plots shows the top 5% and the bottom 5% physicians having
the posterior probability that the ratio is greater than 1. Since the results for physicians
with small case numbers may be confounding in determining the true top 5% and bottom
5%. I removed the physicians with case number less than 3. The table together with the six
mortality rate plots will be used for answering the following question.
(1) Dr. Tortolani Performance - Advice Hospital NY Methodist Hospital
NY Methodist Hospital is concerned about the performance of Dr. Tortolani. He is one of
the only two physicians in this hospital. Based on the posterior results, Dr. Tortolani in NY
Methodist Hospital has a higher mortality rate than expected for both of the procedures,
4

5. CABG Valve or Valve/CABG
0 5 10 15 20 0 5 10 15 20
Argenziano M | 21
Chen J M | 21
Naka Y | 21
Quaegebeur J | 21
Smith C | 21
Stewart A S | 21
Takayama H | 21
Williams M R | 21
Chen J M | 22
Ciaburri D | 22
Girardi L | 22
Isom O | 22
Krieger K | 22
Lang S | 22
Naka Y | 22
Salemi A | 22
Tortolani A | 22
Balsam L B | 23
Crooke G | 23
Culliford A | 23
Deanda A | 23
Galloway A | 23
Grossi E | 23
Loulmet D F | 23
Mosca R S | 23
Ribakove G | 23
Schwartz C F | 23
Zias E | 23
Esposito R | 25
Hall M | 25
Hartman A | 25
Kalimi R | 25
Pogo G | 25
Vatsia S | 25
Mortality Rate Ratio
Physician
hospital
NYP− Columbia Presby.
NYP− Weill Cornell
NYU Hospitals Center
North Shore Univ Hosp
Ratio of
Predicted Mortality Rate vs.Expected Mortality Rate
for Each Physician in Each Hospital [4]
CABG Valve or Valve/CABG
1 2 3 1 2 3
Hartman A | 26
Kalimi R | 26
Manetta F | 26
Bercow N | 27
Colangelo R | 27
Fernandez H A | 27
Lamendola C | 27
Robinson N | 27
Taylor J | 27
Bilfinger T | 28
Gupta S | 28
McLarty A | 28
Rosengart T | 28
Seifert F | 28
Goncalves J A | 29
Kokotos W J | 29
Schubach S | 29
Lundy E F | 30
Salenger R | 30
Bhutani A K | 31
Ciaburri D | 31
Sarabu M | 31
Shahani R | 31
Zakow P | 31
Lafaro R | 32
Lansman S | 32
Malekan R | 32
Saunders P | 32
Spielvogel D | 32
Mortality Rate Ratio
Physician
hospital
Southside Hospital
St. Francis Hospital
Univ.Hosp−Stony Brook
Winthrop Univ. Hosp
Good Sam − Suffern
Vassar Bros. Med Ctr
Westchester Med Ctr
Ratio of
Predicted Mortality Rate vs.Expected Mortality Rate
for Each Physician in Each Hospital[5]
which is shown in the second mortality ratio plot. The predicted mortality rate of
Dr. Tortolani in NY Methodist Hospital is around 1.5 times higher than the expected
mortality rate for procedure Valve or Valve/CABG, and 1.8 times higher than the expected
mortality rate for procecure CABG. Since Dr. Tortolani is one of the only two physicians in
NY Methodist Hospital, it is hard to make a comparison. When analyzing the performance of
Dr. Tortolani, we can also refer to the mortality ratio from hospital NYP-Weill Cornell shown
in the fourth mortality ratio plot, in which the predicted mortality rate of Dr. Tortolani
in hospital NYP-Weill Cornell is around 5 times higher than the expected mortality rate
for procedure Valve or Valve/CABG, and 3 times higher than the expected mortality rate
for procedure CABG. The posterior estimates show that Dr. Tortolani perform even worse
in hospital NYP-Weill Cornell than NY Methodist Hospital. Additionally, in hospital
NYP-Weill Cornell, he is one of the 9 physicians, and six of them have predicted mortality
5

6. CABG Valve or Valve/CABG
0 2 4 6 0 2 4 6
Asgarian K T | 33
McGinn J | 33
Nabagiez J P | 33
Rosell F M | 33
Aldridge J | 34
Ashraf M | 34
Grosner G | 34
Picone A | 34
Bell−Thomson J | 35
Downing S W | 35
Picone A | 35
Aldridge J | 36
Bell−Thomson J | 36
Downing S W | 36
Lico S | 36
Aldridge J | 37
Ashraf M | 37
Picone A | 37
Nast E | 38
Raudat C W | 38
Becker E J | 39
Cheeran D | 39
Kirshner R | 39
Alfieris G | 40
Hicks G | 40
Knight P | 40
Massey H | 40
Mortality Rate Ratio
Physician
hospital
Staten Island UnivHosp
Buffalo General Hosp
Erie County Med Ctr
Mercy Hospital
Millard Fillmore Hosp
Arnot Ogden Med Ctr
Rochester General Hosp
Strong Memorial Hosp
Ratio of
Predicted Mortality Rate vs.Expected Mortality Rate
for Each Physician in Each Hospital[6]
Physician Hospital Procedure Posterior Median Credible Interval Probability
Top 5%
Tortolani A NYP- Weill Cornell Valve or Valve/CABG 5 ( 2.6446, 8.3298 ) 4.7912724
Loulmet D F Lenox Hill Hospital CABG 3 ( 2.6856, 8.0919 ) 4.7417775
Reddy R C Mount Sinai Hospital CABG 262 ( 1.598, 3.5293 ) 2.4039046
Reddy R C Mount Sinai Hospital Valve or Valve/CABG 362 ( 1.4013, 2.8297 ) 2.0203586
Tortolani A NYP- Weill Cornell CABG 4 ( 1.7553, 5.8565 ) 3.2905105
Schwartz C F Bellevue Hospital Ctr Valve or Valve/CABG 27 ( 1.5895, 4.3659 ) 2.6333642
Ciuffo G B Mount Sinai Hospital Valve or Valve/CABG 174 ( 1.3915, 3.2882 ) 2.1701689
Deanda A NYU Hospitals Center Valve or Valve/CABG 5 ( 1.4162, 4.2961 ) 2.5215007
Picone A Erie County Med Ctr CABG 22 ( 1.4136, 4.4005 ) 2.5985714
Knight P Strong Memorial Hosp Valve or Valve/CABG 1000 ( 1.199, 2.1054 ) 1.6058438
Argenziano M NYP- Columbia Presby. Valve or Valve/CABG 388 ( 1.2117, 2.4967 ) 1.7576248
Stelzer P Mount Sinai Hospital CABG 43 ( 1.3128, 3.59 ) 2.2308289
McLarty A Univ.Hosp-Stony Brook CABG 102 ( 1.2515, 3.4725 ) 2.1106008
D Alessandro D A Montefiore - Weiler Valve or Valve/CABG 4 ( 1.2686, 3.3938 ) 2.0983952
Argenziano M NYP- Columbia Presby. CABG 150 ( 1.1821, 2.6834 ) 1.8105605
Knight P Strong Memorial Hosp CABG 529 ( 1.1608, 2.3954 ) 1.6889650
Swistel D St. Lukes at St. Lukes Valve or Valve/CABG 473 ( 1.1662, 2.2623 ) 1.6409176
Ciuffo G B Lenox Hill Hospital Valve or Valve/CABG 14 ( 1.2863, 3.608 ) 2.2482856
Bottom 5%
Bennett E St. Peters Hospital Valve or Valve/CABG 442 ( 0.3423, 0.91 ) 0.5738937
Graver L LIJ Medical Center Valve or Valve/CABG 453 ( 0.341, 0.9033 ) 0.5703277
Malekan R Westchester Med Ctr Valve or Valve/CABG 167 ( 0.2428, 0.8441 ) 0.4657696
Taylor J St. Francis Hospital Valve or Valve/CABG 876 ( 0.4442, 0.9066 ) 0.6423340
Lansman S Westchester Med Ctr CABG 207 ( 0.2237, 0.8355 ) 0.4387923
Kalimi R Southside Hospital CABG 57 ( 0.2915, 0.8264 ) 0.5068509
Fernandez H A St. Francis Hospital CABG 360 ( 0.3555, 0.8648 ) 0.5687830
Malekan R Westchester Med Ctr CABG 115 ( 0.1827, 0.7441 ) 0.3794448
Jacobowitz I Maimonides Medical Ctr Valve or Valve/CABG 427 ( 0.3057, 0.8218 ) 0.5204003
Spielvogel D Westchester Med Ctr CABG 335 ( 0.2245, 0.7439 ) 0.4166268
Kalimi R North Shore Univ Hosp CABG 259 ( 0.2878, 0.731 ) 0.4677355
Girardi L NYP- Weill Cornell Valve or Valve/CABG 927 ( 0.3691, 0.8131 ) 0.5610520
Sarabu M Vassar Bros. Med Ctr Valve or Valve/CABG 424 ( 0.2382, 0.734 ) 0.4356546
Scheinerman S J LIJ Medical Center Valve or Valve/CABG 347 ( 0.2124, 0.6883 ) 0.3953530
Spielvogel D Westchester Med Ctr Valve or Valve/CABG 576 ( 0.2596, 0.6946 ) 0.4324956
Palazzo R LIJ Medical Center Valve or Valve/CABG 259 ( 0.1744, 0.6624 ) 0.3603454
Michler R E Montefiore - Weiler CABG 9 ( 0.1328, 0.5122 ) 0.2727945
Lang S NYP- Weill Cornell CABG 6 ( 0.1174, 0.4417 ) 0.2339727
*
Table 2: Predicted Mortality Rate and Expected Mortality Rate Ratio
6

7. rate either smaller or similar to the expected mortality rate.
(2) Physician Performance in NYP- Columbia Presby.
The physician performance in NYP- Columbia Presby is shown in the fourth mortality ratio
plot. Two physicians, Chen J M and Quaegebeur J, are shown in the plot having a high
mortality ratio median an credible interval for procedure Valve or Valve/CABG, meaning
physician procedure cases
Argenziano M CABG 150
Argenziano M Valve or Valve/CABG 388
Chen J M Valve or Valve/CABG 1
Naka Y CABG 298
Naka Y Valve or Valve/CABG 580
Quaegebeur J Valve or Valve/CABG 2
Smith C CABG 114
Smith C Valve or Valve/CABG 674
Stewart A S CABG 178
Stewart A S Valve or Valve/CABG 558
Takayama H CABG 75
Takayama H Valve or Valve/CABG 126
Williams M R CABG 150
Williams M R Valve or Valve/CABG 445
* Table 3: Information of Hospital NYP-
Columbia Presby
that predicted mortality rate is much higher than
the ecpected. However, Chen J M only have 1 case
in the data and Quaegebeur J only have two cases
(shown in Table 3), which means that the posterior
estimate is not reliable and we need more cases
to further examine the performance of these two
physicians. Although they have a high mortality
rate ratio, we should not be concerned about their
performance for now. Other than these two physi-
cians, Physician Argenziano M, physician Naka Y,
and physician Stewart A S have predicted mortal-
ity rate higher than the expected mortality rate
for both of the procedure. Since they have a lot of
cases shown in Table 3, we have strong evidence to
say that these three physicians shoud be concerned
about if needed.
(3) Salary Issue of Dr. Ciaburri and Best Clinician
Dr. Ciaburri is arguing for a salary increase with the reason that he has the best mortality rate
score in the state. After checking his record in the data, we see in Table 4 that Dr. Ciaburri
is working/has worked in three hospitals and indeed has zero observed death rates for all
the three hospitals. However, the performance of a physician is not only determined by the
observed death rate, it also incorporates the procedure type, the region, which hospital the
physician is working in and how many cases has the physician finished. For example, when
the observed number of death is 0, if the physician is in a region or hospital that has more
unhealthy patients or worse condition, or if the physician has finished more cases, or if the
physician has performed more harder procedures, or if the physician has a higher expected
hospital region procedure cases death obsrate exprate
NY Methodist Hospital Kings CABG 65 0 0 2.22
NY Methodist Hospital Kings Valve or Valve/CABG 117 0 0 3.43
NYP- Weill Cornell Manhattan CABG 1 0 0 1.00
NYP- Weill Cornell Manhattan Valve or Valve/CABG 2 0 0 2.79
Vassar Bros. Med Ctr NY Metro - New Rochelle CABG 1 0 0 0.60
Vassar Bros. Med Ctr NY Metro - New Rochelle Valve or Valve/CABG 1 0 0 0.60
* Table 4: Information of Dr. Ciaburri
7

8. mortality rate but lower predicted mortality rate, then we can say that the physician has
a better performance. Since he has only performed 65 CABG procedures and 117 Valve or
Valve/CABG procedures in NY Methodist Hospital, and fewer in the other two hospitals, we
cannot determine Dr. Ciaburri has the best mortality rate score.
In order to determine the best clinician, I would limit the clinicians to those who has
performed at least 100 cases for at least one procedure, since the more a clinician have
finished a procedure, the better he/she can be. Then I will look at the physicians among the
bottom 5% having posterior probability exceeding 1, because this posterior result incorporates
the impact of region, procedure, hospital and the expected mortality rate. I will also look at
the observed mortality rate. Then the best clinician I choose is Palazzo R. He has performed
259 Valve or Valve/CABG cases. He is among the four physicians with probability of posterior
mortality rate is higher than expected mortality rate equal to 0, and has the lowest observed
mortality rate when limiting the clinicians to those who has performed at least 100 cases for
at least one procedure.
4. Mortality Rate Comparison among Hospitals
We have to first define an expected mortality rate for each hospital. I use average expected
mortality rate for each procedure as the hospital expected motality rate. When calculating
the predicted posterior probabilities, I only add the random effect on the fixed effect to
combine information across physicians. Then the hospital-specific ratio and 95% credible
intervals are shown below.
CABG Valve or Valve/CABG
0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0
LIJ Medical Center
NY Hospital − Queens
Montefiore − Moses
Montefiore − Weiler
Albany Medical Center
Champ.Valley Phys Hosp
Ellis Hospital
M I Bassett Hospital
St. Peters Hospital
St. Elizabeth Med Ctr
St. Josephs Hospital
Unitd Hlth Svcs−Wilson
Univ.Hosp−SUNY Upstate
Maimonides Medical Ctr
NY Methodist Hospital
Univ.Hosp−Brooklyn
Bellevue Hospital Ctr
Beth Israel Med Ctr
Lenox Hill Hospital
Mount Sinai Hospital
NYP− Columbia Presby.
NYP− Weill Cornell
NYU Hospitals Center
St. Lukes at St. Lukes
North Shore Univ Hosp
Southside Hospital
St. Francis Hospital
Univ.Hosp−Stony Brook
Winthrop Univ. Hosp
Good Sam − Suffern
Vassar Bros. Med Ctr
Westchester Med Ctr
Staten Island UnivHosp
Buffalo General Hosp
Erie County Med Ctr
Mercy Hospital
Millard Fillmore Hosp
Arnot Ogden Med Ctr
Rochester General Hosp
Strong Memorial Hosp
Odds Ratio
Region
Odds Ratios of Death in Each Region vs. Queens
for Valve or Valve/CABG
8

9. Hospital Procedure Cases Probability
LIJ Medical Center Valve or Valve/CABG 1167 0.02950
Westchester Med Ctr Valve or Valve/CABG 1348 0.04675
Vassar Bros. Med Ctr Valve or Valve/CABG 1135 0.05175
Winthrop Univ. Hosp Valve or Valve/CABG 1320 0.14125
North Shore Univ Hosp CABG 1272 0.14675
* Table 5: 5-High-Achieving Hospitals
When analyzing the 5-high-
achieving and 5-low-achieving
hospitals, I use similar ap-
proach as what I did for find-
ing the best clinician. For
high-achieving hospital, I first
limit the hospitals to those
Hospital Procedure Cases Probability
Mount Sinai Hospital CABG 930 0.97650
St. Lukes at St. Lukes Valve or Valve/CABG 614 0.97225
NYP- Columbia Presby. CABG 965 0.96000
Bellevue Hospital Ctr Valve or Valve/CABG 628 0.93925
St. Lukes at St. Lukes CABG 348 0.93575
* Table 6: 5-Low-Achieving Hospitals
with at least 1000 cases for
at least 1 procedure. Then
I find the hospitals with low
probability of having the pre-
dicted mortality rate higher
than the expected mortality
rate and in top 5. The 5-high-
achieving hospitals are shown
in Table 5. Similarly, I limit the 5-low-achieving hospitals to those with less than 1000 cases,
and then choose the bottom 5 of probabilities of predicted mortality greater than expected
mortality. The results are shown in Table 6.
Conclusion
The most simple way of analyzing performance of hospitals and physicians for this dataset
is by comparing the obseved mortality rate and expected mortality rate directly. However,
this method is not enough for incoporate other factors, such as the condition of the regioin
a hospital belongs to and the condition of a procudure. These information is essential in
determining the performance since difference region may have different illness prevalence,
and difference procedure may have different effect in treating the illness. Observed mortality
rate does not reflect those information.
Modeling also allows us to consider cluster level difference. In such case, we can also
incorporate the difference among hospitals and the difference among physicians. Since
some hospitals may have better techniques, and some physicians may have more and better
experience.
Additionally, by getting the posterior sample from the gaussian linear mixer model, we can
have a posterior distribution for each parameter, and thus for the interested statistics. With
this distribution we would be able to know how certain we are about the estimation and
to further determine if we would like to trust the estimation or not. This also reflect my
analysis of the salary issue of Dr. Ciaburri, in which I stated that number of cases is also
important. If a physician have more cases, then the posterior distribution is more certered at
the median value since we have more evidence, otherwise, the posterior distribution will be
more spread, leading to a very uncertain prediction. This is also the reason that with the
same observed death rate, we say that the physician who have more cases perform better
instead of the two physicians have the same performance.
9