Healthsciences.ncsa.illinois.edu
nature publishing group
Application of Software Design Principles and
Debugging Methods to an Analgesia Prescription
Reduces Risk of Severe Injury From Medical Use
of Opioids
SM Belknap1–6, H Moore4,5, SA Lanzotti7, PR Yarnold8, M Getz6, DL Deitrick7, A Peterson9,
J Akeson10, T Maurer10, RC Soltysik11, GA Storm12 and I Brooks13
a prescription is a health-care program implemented by a physician or other qualified practitioner in the form
of instructions that govern the plan of care for an individual patient. although the algorithmic nature of prescriptions
is axiomatic, this insight has not been applied systematically to medication safety. We used software design principles
and debugging methods to create a "patient-oriented prescription for analgesia" (popa), assessed the rate and extent
of adoption of popa by physicians, and conducted a statistical process control clinical trial and a subsidiary cohort
analysis to evaluate whether popa would reduce the rate of severe and fatal opioid-associated adverse drug events
(aDes). We conducted the study in a population of 153,260 hospitalized adults, 50,576 (33%) of whom received
parenteral opioids. hospitalwide, the use of popa increased to 62% of opioid prescriptions (diffusion half-life = 98 days),
while opioid-associated severe/fatal aDes fell from an initial peak of seven per month to zero per month during the
final 6 months (P < 0.0016) of the study. in the nested orthopedics subcohort, the use of popa increased the practice
of recording pain scores (94% vs. 72%, P < 0.00001) and the use of adjuvant analgesics (95% vs. 40%, P < 0.00001) and
resulted in fewer opioid-associated severe aDes than routine patient-controlled analgesia (pCa) (0% vs. 2.7%, number
needed to treat (nnT) = 35, P < 0.015). The widespread diffusion of popa was associated with a substantial hospitalwide
decline in opioid-associated severe/fatal aDes.
Hospitalized patients are subjected to an average of more than one depression accounts for only 2% of hospital ADEs but 12.3% of
medication error each day;1 adverse drug events (ADEs) cause life-threatening ADEs4 and 25% of fatal ADEs.5
more than 770,000 patient injuries or deaths annual y in US hospi-
We hypothesized that the application of software design prin-
tals (http://www.ahrq.gov/qual/aderia/aderia.htm); an estimated ciples and debugging methods to a prescription would reduce the
30–40% of patients receive health care inconsistent with the avail-
rate of severe and fatal ADEs. To test this hypothesis, we created
able scientific evidence; and 20–25% of patients receive health care and debugged a "Patient-oriented Prescription for Analgesia"
that is either unnecessary or actual y harmful.2 Among hospital-
(POPassessed the rate and extent of its adoption
ized adults, opioid ADEs are more common than any other class3 by physicians, and conducted a statistical process control clinical
and are disproportionately severe: opioid-associated respiratory trial and subcohort analysis in hospitalized adults.
1Division of General Internal Medicine, Department of Medicine, Northwestern University Feinberg School of Medicine, Chicago, Illinois, USA; 2Department of
Molecular Pharmacology and Biologic Chemistry, Northwestern University Feinberg School of Medicine, Chicago, Illinois, USA; 3Robert H. Lurie Cancer Center,
Northwestern University Feinberg School of Medicine, Chicago, Illinois, USA; 4Department of Medicine, University of Illinois College of Medicine at Peoria, Peoria,
Illinois, USA; 5Section of Clinical Pharmacology, Department of Biomedical and Therapeutic Sciences, University of Illinois College of Medicine at Peoria, Peoria, Illinois,
USA; 6Department of Medicine, OSF Saint Francis Medical Center, Peoria, Illinois, USA; 7Quality Management, OSF Saint Francis Medical Center, Peoria, Illinois, USA;
8Department of Emergency Medicine, Northwestern University Feinberg School of Medicine, Chicago, Illinois, USA; 9Nursing Service, OSF Saint Francis Medical Center,
Peoria, Illinois, USA; 10Department of orthopedics, OSF Saint Francis Medical Center, Peoria, Illinois, USA; 11Jesse Brown VA Medical Center, Chicago, Illinois, USA;
12Pharmacy Service, OSF Saint Francis Medical Center, Peoria, Illinois, USA; 13National Center for Supercomputing Applications, University of Illinois at
Urbana–Champaign, Urbana, Illinois, USA. Correspondence: SM Belknap (Received 27 June 2007; accepted 22 January 2008; advance online publication 19 March 2008.
CliniCal pharmaCology & TherapeuTiCs VOLUME 84 NUMBER 3 SEPTEMBER 2008
Patient–oriented Prescription for Analgesia (Adult Program)
Procedure/Cause of Pain _
Note: To override default values (in parentheses), enter substitute values in spaces. Default values are for adults weighing more than 40 kg. To delete an order, cross it out & initial.
DISCONTINUE all previous Opioids, Benzodiazepines, Antiemetics, & NSAIDs
Adjuvant Analgesia (Check one of the following options)
First dose only:
Ketorolac(Toradol) i.v. or subcut. (15) _mg, & then
• If unable to take oral meds:
Ketorolac i.v. or subcut. (15) _mg every 6 hrs. STOP after 3 days.
• If able to take oral meds:
Ibuprofen p.o. (600) _mg every 6 hrs. STOP after (3) _days.
Non-NSAID Option:
Acetaminophen rectally or p.o. (975) _mg every 6 hrs.
Programmed Opioid Analgesia for Abbott PCA Model 4100 (Checking box activates full protocol)
Fentanyl 50 micrograms/mL by subcutaneous (subcut.) infusion with portless PCA tubing through 0.22 micron in-line filter.
• Initial Dose
If this protocol is started in PACU, follow anesthesiologist's post-surgical orders while patient in PACU.
If started on floor & if pain score is 8 cm or greater, give (50) _micrograms subcut,
one dose only.
(25) _micrograms/hr
(If left blank, dose defaults to 25 micrograms/hr.)
DO NOT INCREASE continuous
Fentanyl dose rate more often than once every 24 hours.
• PCA (On-demand)
(If left blank, dose defaults to 25 micrograms with each patient demand.)
• 4 Hour Dose Limit
75% of (Continuous + On-demand doses)
Adjust 4 hour dose limit whenever dose changes.
•
Breakthrough pain: If pain score is 8 cm or greater, INCREASE on-demand dose by (10) _micrograms; reassess in 1 hour.
Repeat 3 times. If pain score is 8 cm or greater on 3 consecutive assessments then notify physician.
•
Taper:
STOP on-demand dose after (3 days) _(Alternatively, enter a stop date)
& then REDUCE continuous dose rate every 4 hours by (10) _micrograms.
•
Minimal pain:
If the visual analogue pain score is 2 cm or less on any 3 consecutive assessments,REDUCE on-demand dose by (10) _micrograms.
•
Oversedation:
If oversedated, hold continuous & on-demand
Fentanyl doses for 4 hrs, then restart continuous
Fentanyl at 1/2 prior dose rate & on–demand
Fentanyl at 1/2 prior dose; reassess at 1 hour & 2 hours.
If unarousable or respiration depressed, (e.g., resp. rate less than 6/min or O2 saturation less than 92%),
then STOP
Fentanyl & give
Naloxone(Narcan) 0.1 mg i.v. every 2–5 mins up to 4 times until awake.
Notify physician
after giving first dose of naloxone.
• p.r.n. Constipation: PEG Standard Solution (Miralax) p.o. 240 mL p.r.n. once daily when tolerating fluid diet.
Senna Standard Extract p.o. 1 to 4 tablets p.r.n. twice daily when tolerating fluids.
• p.r.n. Nausea:
Mild nausea:
Metoclopramide (Reglan) i.v. or subcut. 5 to 10 mg p.r.n. every 8 hrs.
Severe nausea or vomiting:
Droperidol (Inapsine) i.v. or subcut. 1.25 to 2.5 mg p.r.n. every 8 hrs.
If patient continues to vomit 2 hours after receiving Droperidol then notify physician.
• p.r.n. Pruritis:
Diphenhydramine (Benadryl) subcut., i.v., or p.o. 10 to 25 mg p.r.n. every 8 hrs.
Use a 10 cm. Visual Analogue Pain Scale (such as CAT Pain Gauge) for all pain assessments; do not substitute alternate scale.
Measure & Record Visual Analogue Pain Score with each vital sign recording; reassess 1 hour after each fentanyl dose change.
Cutaneous O saturation measures every 4 hours while patient lethargic or sleeping.
Patient–oriented Prescription for Analgesia (Adult Program) v1.1 Revised 20 Sepember 2001
Physician's ID #
Figure 1 Patient-oriented Prescription for Analgesia (Adult Program) v1.1 after debugging. This is the current version of POPA. The CAT pain scale mentioned
in "monitoring orders" is a mechanical visual analog pain scale manufactured by Caterpillar. (Although the protocol specifies droperidol, prochlorperazine was
substituted for droperidol after a Food and Drug Administration–mandated addition of a black box warning to the droperidol package insert.)
Quarterly purchases of POPA cartridges
Quarterly purchases of POPA cartridges
n(
t ) =
1 +
e−�
t−�
Severe or fatal opioid-associated adverse drug events
Figure 2 Diffusion of Patient-oriented Prescription for Analgesia (POPA)
Figure 3 Diffusion of Patient-oriented Prescription for Analgesia (POPA) in
in the hospital and effect on opioid-associated severe/fatal adverse drug
the hospital and effect on opioid-associated severe/fatal adverse drug events
events. This shows the optimal fit of the logistic growth equation to quarterly
(ADEs). (
a) Quarterly hospitalwide purchases of POPA cartridges over time.
hospitalwide purchases of POPA cartridges. These empty glass and silicone
(
b) A u-type process control run chart (σ = 3) for hospitalwide
rubber patient–controlled analgesia pump cartridges were filled with
opioid-associated severe/fatal ADEs. As the use of POPA became more
fentanyl solution by our pharmacy and used solely for POPA. The diffusion
widespread, opioid-associated severe/fatal ADEs became less common.
half-life of the use of POPA in hospital prescriptions was 98 days.
LCL, lower control limit; UCL, upper control limit.
VOLUME 84 NUMBER 3 SEPTEMBER 2008
www.nature.com/cpt
below the run chart centerline for the final 16 consecutive months
Diffusion of POPA use among prescribers
(
P < 0.0037), and eventual y falling to zero events per month for
POPA is the prescription shown The hospitalwide the final 6 consecutive months of the study (
P < 0.0016).
diffusion half-life for adoption of POPA by prescribers was
The substantial decline in the rate of severe/fatal opioid-associ-
98 days and. By the end of the study period, ated ADEs does not correspond to zero risk, because adherence to
POPA accounted for 62% of all parenteral opioid prescriptions POPA safety practices was not universa) and unidenti-
fied hazards may remain. The fall in the rate of opioid-associated
severe/fatal ADEs is unlikely to be a result of performance expec-
statistical process control trial in full cohort
tation (Hawthorne effect)6 given the consistency, magnitude, and
of hospitalized adults
sustained duration of this decline across al hospital services, the
During the study period, 4,453 ADEs were reported, including 503 accompanying 45% decline in the use of opioids, the increase in
opioid-associated ADEs above the causality threshold (Naranjo adjuvant analgesic drug use, and the increased frequency of assess-
score > 4), 74 of which were severe and three of which were fatal. ment of pain severity, hemoglobin oxygen saturation, and level of
The run chart showed two transitions, first from an out-of-control consciousness. There were no severe or fatal ADEs associated with
process to an in-control process, then to an in-control process the adjuvant analgesics ketorolac, ibuprofen, and acetaminophen,
with a lower central tendencyEvent rates were higher consistent with prior reports that risk of ketorolac-associated gas-
than the upper control limit during 3 months in 1997, indicating trointestinal bleeding or acute renal failure is negligible at doses
special causes of variation—identified as opioid polypharmacy, <150 mg/day given for <5 days.7,8 The run charts for antibiotics
failure to reduce opioid dose during oversedation or respiratory and anticoagulants/thrombolytics—drug classes for which there
depression, and inappropriate meperidine use. Between 1998 had been no specific medication safety improvement effort—
and 2002, there was a reduction in the frequency of these special showed no decrease in severe/fatal ADEs over the same interval
causes of variation, leading to the opioid ADE rate remaining middle and bottom panel, respectively).
within control limits. The increasing use of POPA and its sub-
As measured in fentanyl equivalents (FEs), hospitalwide use
routines in the full hospital cohort was associated with a decline of all parenteral opioids, including fentanyl, hydromorphone,
over time in severe/fatal opioid-associated ADEs, from a peak of morphine, and meperidine showed an initial rise from
seven events per month in September 1997 to a rate consistently 48 g FE in 1997 to a peak of 73.4 g FE in the year 2000, coinciding
table 1 Attributes of patients, type of surgery, pain management, and outcomes in the nested cohort of 496 orthopedic
surgery patients
univariates
pCa (N =245)
popa (N = 251)
Difference (95% Ci)
Patient attributes Mean age (years)
2.2 (0.1 to 4.3)
P < 0.027
*
Mean weight (kg)
0.3 (−3.7 to 4.3)
P < 0.92
−1.3 (−9.8 to 7.2)
P < 0.99
1.3 (−7.2 to 9.8)
P < 0.99
Surgery Knee surgery (%)
−8.4 (−17 to 0.001)
P < 0.062
8.4 (−0.001 to 17)
P < 0.062
Bilateral surgery (%)
−5.3 (−10.5 to 0.0)
P < 0.072
Surgical revision (%)
0 (−6.0 to 6.0)
P < 0.90
Pain management Pain scored (%)
P < 0.00001
**
Adjuvant analgesic (%)
55.1 (48.6 to 61.7)
P < 0.00001
**
Pain scored and adjuvant analgesic (%)
P < 0.00001
**
Outcomes Severe/fatal ADE (%)
−2.7 (−4.7 to −0.7)
P < 0.0077
**
Pain score (0–10)
0.1 (-0.4 to 0.6)
P < 0.18
−3.3 (−11.9 to 5.3)
P < 0.47
Length of stay (days)
−0.13 (−0.46 to 0.20)
P < 0.27
Patients given POPA were demographically similar to patients given routine PCA, were more likely to have a recorded pain score and more likely to get an adjuvant analgesic,
and were less likely to have a severe ADE. Mean pain scores, rate of nausea, and duration of hospitalization were similar. Compared with routine morphine PCA, use of POPA
was associated with significantly fewer severe/fatal ADEs. Compared with hip surgery or bilateral knee surgery, unilateral knee surgery was a significant predictor of
opioid-associated severe ADE; we had made no a priori hypothesis regarding the effect of type of surgery on risk. ESS, measure of effect strength for sensitivity (0 = chance,
100 = perfect intergroup discrimination);8 type I error rate is exact (permutation)
P value estimated via 10,000 Monte Carlo experiments.8
ADE, adverse drug event; PCA, patient-controlled analgesia; POPA, Patient-oriented Prescription for Analgesia; PV, predictive value achieved by the analysis.8
*Statistically significant but unstable in jackknife validity analysis.
**Statistically significant and stable in jackknife validity analysis.
CliniCal pharmaCology & TherapeuTiCs VOLUME 84 NUMBER 3 SEPTEMBER 2008
Severe or fatal opioid-associated adverse drug events
table 3 Outcomes (severe/fatal adverse drug events) and risk
factors in the nested cohort of 496 orthopedic surgery patients
given either POPA or routine morphine PCA
risk factor for s/F aDe
pV (%) ess (%) P value
Univariable optimal discriminate analysis
Use of PCA instead of POPA
P < 0.0069
*
Knee surgery vs. hip surgery
P < 0.049
*
Unilateral surgery
P < 0.63
Severe or fatal anticoagulant and
Unilateral knee surgery
P < 0.030
*
antithrombotic-associated adverse drug events
Revision surgery
P < 0.99
P < 0.71
Maximum pain score day 1 (0–10)
P < 0.63
P < 0.61
Multiple opioids prescribed
P < 0.68
Adjuvant analgesic omitted
P < 0.037
*
Pain not scored OR adjuvant
P < 0.017
*
Severe or fatal antibiotic-associated adverse drug events
analgesic omitted
P < 0.019
**
P < 0.25
P < 0.30
Length of stay (days)
P < 0.53
Classification tree analysis
73.1
P < 0.04
***
Use of standard PCA instead
P < 0.0065†
Figure 4 Comparison of trends in the rates of occurrence of severe/fatal
adverse drug events (ADEs) associated with (
a) opioids, (
b) thrombolytics/
Unilateral knee surgery node
P < 0.019†
anticoagulants, and (
c) antibiotics. The increasing use of Patient-oriented
Prescription for Analgesia (POPA) and its subroutines in the hospital cohort
was associated with a statistically significant decline in severe/fatal
496 Orthopedic patients
opioid-associated ADEs. By way of comparison, there were no statistically significant changes in the rates of severe/fatal ADEs associated with anticoagulants/thrombolytics or with antibiotics over the same period.
LCL, lower control limit; UCL, upper control limit.
P < 0.0065
251 POPA Pts.
245 PCA Pts.
table 2 trends in annual hospitalwide parenteral opioid use
in grams of fentanyl equivalents
P < 0.019
annual opioid use in grams of fentanyl equivalents
109 had hip or B/L
Fentanyl morphine hydromorphone meperidine Total
Patients being managed with POPA had a significantly lower rate of opioid-associated
severe/fatal ADEs than did patients on routine PCA. Statistical results are reported as mean values or percentages (for ordered and categorical attributes, respectively).
Calculations of the predictive value, effect strength for sensitivity (ESS), and generalized exact (permutation)
P value were based on the resultant optimal
discriminant analysis (ODA) model. ESS is a normed statistic on which 0 =
As measured in fentanyl equivalents, hospitalwide use of all parenteral opioids,
discrimination expected by chance, and 100 = perfect intergroup discrimination.
including fentanyl, hydromorphone, morphine, and meperidine, showed a rise from
All reported
P values are nondirectional. Type I error rate (
P value) is an exact
1997 to 2000, coinciding with an effort to improve the efficacy of pain management,
(permutation)
P estimated through 10,000 Monte Carlo experiments. The optimal
and then a fall from 2000 to 2002, coinciding with the rapid diffusion of POPA use
classification tree analyemploys both the classical nondirectional Fisher's
among prescribers, a consequent displacement of morphine and meperidine by
exact test58 and resampling calculations.
fentanyl and a generalized reduction of opioid doses on account of coadministration
ADE, adverse drug event; PCA, patient-controlled analgesia; POPA, Patient-oriented
of adjuvant ketorolac, ibuprofen, and acetaminophen. As POPA uses fentanyl
Prescription for Analgesia; Pts., patients; PV, predictive value achieved by the analysis;
exclusively, the increasing use of POPA resulted in the increasing use of fentanyl in
S/F ADE, severe/fatal ADE.
the hospital. Opioids were given both as discrete doses and as continuous infusions.
*Statistically significant and stable in jackknife validity analysis.56
**Statistically
A typical discrete dose of fentanyl is 25 µg. Therefore, the 21.2 g of fentanyl dispensed
significant but unstable in jackknife validity analysis.56
***Statistically significant by
in 2002 would correspond to 848,000 discrete doses of 25 µg of fentanyl.
sequentially rejective Sidak Bonferroni–type procedure for multiple comparisons.
POPA, Patient-oriented Prescription for Analgesia.
†Statistically significant by nondirectional Fisher's exact test.57
VOLUME 84 NUMBER 3 SEPTEMBER 2008
www.nature.com/cpt
table 4 severe opioid-associated ADes in a nested cohort of orthopedic patients treated with PCA
sex
pain score
los aDe description
Respiratory arrest
Naloxone, full recovery
Respiratory arrest (O2 Sat. 83%)
Naloxone, full recovery
Respiratory depression (O2 Sat. 66%)
Naloxone, full recovery
Respiratory depression
Naloxone, full recovery
Respiratory depression, mechanical ventilation, PCA D/Ced, full recovery
Respiratory depression, mechanical ventilation PCA D/Ced, full recovery
Respiratory arrest, airway obstruction
Cerebellar infarction, ataxia
Each of these seven life-threatening events among routine morphine PCA orthopedic patients had a Naranjo score >4. There were no severe or fatal events in patients treated with POPA. Only one of the seven patients with a severe opioid-associated ADE had both a recorded pain score and was given an adjuvant analgesic. There were no severe or fatal ADEs associated with drugs other than opioids in the orthopedic surgery cohort.
ADE, adverse drug event; LOS, hospital length of stay in days; PCA, patient-controlled analgesia; POPA, Patient-oriented Prescription for Analgesia.
with an effort to improve the efficacy of pain management, and one had both a recorded pain score and received an adjuvant
then fell by 45% to 40.7 g FE in 2002, coinciding with the rapid analgesic, and none had been treated with POP
diffusion of POPA use among prescribers, displacement of mor-
In multivariate analysis a strong, statistically significant two-
phine and meperidine by fentanyl, and a generalized reduction variable classification tree model consisting of analgesia pre-
of opioid use due to coadministration of the adjuvant analge-
scription (routine morphine PCA vs. POPA) and the type of
sic drugs ketorolac, ibuprofen, and acetaminophen. As POPA surgical procedure (unilateral knee surgery vs. hip surgery or
uses fentanyl exclusively, the increasing use of POPA resulted in bilateral knee surgery) emerged for prediction of severe opioid-
increasing use of fentanyl in the hospital, from 9.3 g in 1997 to associated ADEs. Analgesia prescription (morphine PCA) was
21.2 g in Of the 77 opioid-associated ADEs, there the first attribute loading in the classification tree model, and
were 2 fatal and 11 severe meperidine-associated ADEs. Eight the type of surgical procedure (unilateral knee surgery) was
of these thirteen meperidine-associated events were character-
the second attribute loading. Effect strength for sensitivity is a
ized by seizures or psychosis due to accumulation of the toxic standardized measure of effect strength, where 0 = chance and
metabolite normeperidine in patients with diminished kidney 100 = perfect intergroup discrimination. For this model, effect
function. Over the study period, use of ketorolac increased by strength for sensitivity was 73.1%, indicating a very strong sig-
71%, use of meperidine declined by 69%, and the recording of at nal. The individual components of the model were statistically
least one pain score increased from <1 to >50% of the patients. significant by Fisher's exact test and the type I error rate of the
Even when not explicitly prescribed, there was a notable increase overall model was confirmed as statistical y significant (
P < 0.04,
in the use of adjuvant analgesics, sedation monitoring, and pain using a sequentially rejective Sidak Bonferroni–type
scoring for non-POPA patients—particularly in hospital units procedure for multiple comparisons.
where POPA was used extensively. However, this informal use
remained less prevalent than the formal use of these safety prac-
tices among POPA patients (
Physicians usually rely on memory and write extemporaneous
prescriptions. Occasionally, physicians use standard order sets
exposure–effect optimal discriminant analysis
or templates,9–11 but these are rarely derived explicitly and pre-
in orthopedic surgery cohort
cisely from scientific evidence,12,13 often violate principles of
The 251 POPA patients and 245 routine morphine patient-con-
good software design, and are not verifiably debugged. Standard
trolled analgesia (PCA) patients were demographically similar order sets or templates have been shown to improve compliance
), and were in a single hospital unit staffed by the same with drug therapy recommendations in some settings14 but not
nurses and pharmacists, and were attended by the same sur-
in others.15 Prescription bugs in standard order sets can cause
geons. POPA patients were more likely to have their pain scores catastrophic medication errors.16 We are unaware of any earlier
recorded (94% vs. 72%, NNT = 4.7) and to be given round-the-
study of the effects of prescription design and debugging on
clock adjuvant analgesia (95% vs. 40%, NNT = . patient outcomes.
Patients given round-the-clock adjuvant analgesia were less likely
The apparent simplicity of prescriptions is deceptive, as the pre-
to have a severe opioid-associated ADE (
P < . scriber's terse instructions rely implicitly on subroutines: toxi city
POPA patients were less likely than routine morphine PCA and efficacy monitoring, pharmaceutical compounding, phar-
patients to have a severe opioid-associated ADE (0/251 vs. 7/245, macy and nursing practices, operating instructions, laboratory
P < 0.007, NNT = 35,. No POPA patient required resus-
methods, and standard operating procedures. Neglect of scientific
citation with the opioid antagonist naloxone or had hemoglobin evidence, poor design, and lack of adequate debugging of pre-
saturation measurements <92%. Of the seven orthopedic surgery scriptions and their subroutines likely account for their erratic
patients with severe opioid-associated ADEs, six were women, and occasionally fatal effects. The recognition of the algorith-
five were morbidly obese, all had unilateral knee surgery, only mic nature of prescriptions compels the application of software
CliniCal pharmaCology & TherapeuTiCs VOLUME 84 NUMBER 3 SEPTEMBER 2008
design principles and debugging methods to their improvement.17 are analgesia prescription (POPA vs. morphine PCA), procedure (uni-
Competent programmers begin with detailed software specifica-
lateral knee surgery, bilateral knee surgery, unilateral hip surgery, or
tions, write modular, reusable code,18 and devote substantial time bilateral hip surgery), weight, age, sex, revision surgery vs. initial surgery,
and effort to debugging.19 Developing Computerized Physician use of visual analog pain scale, use of adjuvant analgesics, use of mul-
tiple opioids, pain score, nausea, and length of hospital stay
Order Entry (CPOE) software with the understanding that pre-
We also identified a multivariate model for prediction of severe/fatal
scriptions are programs and not mere text, may lead to improved opioid-associated ADEs.
drug therapy performance in terms of safety, efficacy, and cost.
There has been no method to ensure the rapid, reliable transla-
software design and debugging of POPA. The design and debugging of
tion of detailed knowledge about drug safety, efficacy, and cost POPA was informed by literature reports of opioid-associated hazards,
errors, and defects, and by failure mode, effect, and criticality analysis
into clinical practice. Clinical practice guidelines have been vari-
ously criticized as being vague, untested, nonrigorous,20 obsoles-
of events in our hospital. The most common bugs in non-POPA analgesia
cent,21 and largely ignored by physicians.22 Physician education prescriptions in our hospital were: failure to monitor patient oxygenation
alone does not improve patient safety.23 There is little evidence and level of consciousness, failure to reduce opioid dose in the pres-
that crew resource management training through simulation ence of respiratory depression or oversedation, omission of a round-the-
clock adjuvant analgesic, omission of pain severity assessments, failure to
reduces the rate of medication errors.24 CPOE may increase prompt opioid dose escalation for uncontrol ed pain, simultaneous use of
the error rate25 and may not reduce the rate of ADEs when the multiple opioids, simultaneous use of opioids and other sedating drugs,
prescriptions contained in the CPOE system are not properly and inappropriate use of meperidine.
designed and debugged.26 Hospital quality-assurance programs
We have earlier described27 our use of the balanced-scorecard
may identify many drug therapy flaws, but often fail to translate method28 to manage the tradeoffs between important drug therapy
outcomes. For example, concern about opioid-associated ADEs may
this knowledge into improved practice.
cause underdosing and inadequate analgesia.29 The balanced scorecard
It is possible for a physician to order drug therapy without con-
for POPA includes the parameters severe/fatal ADE rate, visual analog
sulting relevant research articles, clinical practice guidelines, expert pain score, duration of hospitalization, and adoption rate of POPA by
opinions, textbooks, or lectures. However, a physician cannot order prescribers. The software specification for POPA required a decrease in
drug therapy without a prescription. The prescription is located on severe/fatal ADEs with no offsetting increase in pain scores or duration
of hospitalization.
the critical path between intent and practice. Well-formed, widely
Our first design goal for POPA was to improve the detection of and
used prescriptions exert beneficial effects through reduction of response to patient oversedation and respiratory depression by imple-
clinical process variation, familiarity to clinicians, and displace-
menting periodic assessments of respiratory rate, cutaneous hemoglobin
ment of unsafe or ineffective practices. When properly designed O2 saturation, and level of consciousness. In POPA, these assessments are
and debugged, prescriptions provide a conduit through which linked to explicit criteria prompting opioid dose reduction. A mechani-
cal visual analog pain scale30 was specified to identify patients requiring
evidence-based medical knowledge can reliably reach patients. opioid dose changes. Our second design goal was to increase the use of
Our experience has been that clinicians who use these prescrip-
round-the-clock adjuvant analgesia, with parenteral ketorolac,31,32 oral
tions provide assiduous peer review, compelling the translation of ibuprofen,33 or oral or rectal acetaminophen,34 as coadministration of
new medical knowledge into improved prescriptions.
these drugs reduces the required opioid dose and the consequent risk
We have shown here that sound prescription design fol owed by of respiratory depression. Our third design goal was to displace unsafe
opioids such as meperidine with fentanyl. Fentanyl is a synthetic, high
iterative cycles of hazard identification and debugging can reduce potency opioid with high lipid solubility, a rapid intercompartmental
the rate of severe patient injury by eliminating prescription bugs clearance, no active or toxic metabolites, high µ1-opioid selectivity, lack
that are a root cause of opioid-associated ADEs. As POPA does of tissue irritation, and minimal myocardial depressant or vasodilatory
not depend on resources that are unique to our hospital, we expect effects. The pharmacokinetic properties of fentanyl minimize hysteresis
that POPA is widely applicable. The new discipline of algorithmic between dose and effect, facilitating titration of demand35 and basal36
fentanyl doses, thereby minimizing mismatch of pain severity and opioid
medicine we introduce here provides a conceptual basis for sur-
effect. Fentanyl has been underused among hospitalized adults because
mounting the intransigent implementation barriers that impede of the lack of a suitable algorithm.
translation of medical knowledge into clinical practice.
Other notable features of POPA include administration of fentanyl
through the subcutaneous route, use of a basal continuous fentanyl dose,
avoidance of drugs that interact with fentanyl, and nested control loops
The setting is OSF Saint Francis Medical Center (Peoria, IL), a 731-bed
for fentanyl dosing—an inner loop of on-demand PCA, and an outer
tertiary care academic medical center and the primary teaching hospital
loop of nurse-adjusted fentanyl dose based on assessment of pain and
for the University of Illinois Col ege of Medicine at Peoria. The principal
oversedation. The subcutaneous route is more easily established and reli-
experiment is a statistical process control trial in the cohort consisting
ably maintained than the intravenous route, avoiding the severe pain or
of all 153,260 adults (18 years or older) hospitalized from January 1997
oversedation that can occur when loss of intravenous access requires
ad
to December 2002, 50,576 (33%) of whom received parenteral opioids.
hoc intramuscular or oral opioid administration. Subcutaneous fenta-
The exposure variable is monthly POPA usage over the interval January
nyl is safe, effective, and has pharmacokinetics similar to intravenous
1997 to December 2002. The effect variable is the monthly hospitalwide
administration.37–40 The use of a basal continuous fentanyl dose provides
number of severe and fatal opioid ADEs during the interval January 1997
an "opioid floor," avoiding severe pain when there are long intervals
to December 2002.
between on-demand doses, as occur during sleep. Using an established
The subsidiary experiment is a cohort study of 496 orthopedic surgery
model41 over a range of pharmacokinetic parameter values, we ran
patients, consisting of all 251 patients who were prescribed POPA and al
simulations42 of fentanyl kinetics after subcutaneous administration43
245 patients who were prescribed routine intravenous morphine PCA
to determine default fentanyl dose and dose increments for POPA. The
during the study period. For the univariate analyses, the effect variable
default fentanyl doses are 25 µg/h continuous and 25 µg as per demand,
is the number of severe or fatal opioid ADEs. The exposure variables
with a lockout time of 15 min and a 4-h dose limit of 75% of the unlimited
VOLUME 84 NUMBER 3 SEPTEMBER 2008
www.nature.com/cpt
maximal dose. Subcutaneous fentanyl PCA was administered through an
We assessed ADE causality using the Naranjo scale,50 a validated
Abbott PCA Model 4100 pump (Abbott Laboratories, North Chicago, IL),
instrument having a high interrater reliability51 and objective signs
a 0.22 µm inline filter, and a Sof-set subcutaneous catheter.
such as pulse oximetry, resuscitative use of naloxone, and respiratory
All prescriptions (physicians' orders) in our hospital were either hand-
arrest. A Naranjo score >4 was considered to be above the causality
written or verbal. POPA prescriptions were ordered on a standard paper
threshold. We graded the adverse event as mild, moderate, severe, or
formWe performed an additional comparative assessment of
fatal. Events were considered severe if patients had an opioid-associated
POPA in the orthopedic surgery subcohort because there had been a high
ADE requiring life-saving intervention, such as unplanned intensive care
preintervention rate of opioid ADEs among these patients. The routine
unit transfer, unplanned use of resuscitative dose of naloxone (≥0.4 mg),
morphine PCA protocol used as a comparator for this assessment was an
nonelective endotracheal intubation, or noninvasive ventilation. Support-
established practice at our medical center, was based on a widely accepted
ive data included low cutaneous hemoglobin O2 saturation, documenta-
protocol,44 and also was ordered on a standard form.
tion of unarousability, favorable response to naloxone or discontinuation
POPA was tested and refined in clinical scenarios with experienced
of opioids, and clinician assessment.
clinicians and during treatment of 250 patients in five debugging cycles,
Nurse quality managers, clinical pharmacists, and physician abstrac-
using direct observation, clinician interviews, and medical record reviews
tor/evaluators were trained to abstract ADE data. Competence was
to identify and eliminate prescription bugs. Nurses often omitted evalua-
maintained by periodic refresher training and cross-validation by
tion of patient's pain, oxygenation, and sedation in other opioid prescrip-
expert reviewers. We periodically calculated Cohen's
κ scores for
tions because of their perception that these evaluations did not improve
causality and severity assessments, and confirmed a high inter-rater
patient safety or comfort. Thus, POPA provides explicit instructions
reliability for these assessments among evaluators in our hospital as
whereby the nurse can use their evaluations to adjust fentanyl dosing
earlier described.52 We used the MIDAS+ medical information soft-
or take other appropriate action. Conventional dose titration of opioids
ware (Midas+ Care Management System, Version 6.1r5; ACS Health-
requires physician–nurse or physician–pharmacist communication for
care Solutions/Midas+, Tucson, AZ) to collate hospital ADEs, identify
each dose change, often resulting in long delays. With POPA, dose titra-
hazard and error patterns, and track progress. An abstractor/evaluator
tion occurs with minimal delay, lessening the risk of a mismatch between
who was blinded to information regarding routine ADE evaluation
pain severity and opioid dose.
conducted a separate abstraction and evaluation for all 496 patients
Other POPA bug fixes during these debugging cycles included exten-
who received either POPA or routine PCA after major orthopedic hip
sive editing of POPA text for accuracy and clarity based on direct obser-
or knee surgery from January 1998 to December 2002.
vation of clinical encounters and on clinician feedback, use of defaults to
avoid ambiguity when a prescriber does not specify an initial value, and
protocols to transition between POPA and other opioid prescriptions.
Statistical process control analysis: Severe/fatal opioid-associated ADEs
In software design terms, POPA is modular, has well-defined interfaces,
were col ated by month and analyzed with a u-type process control chart
and minimizes tight coupling For example, by default, the
using
Statview 5.0 (SAS Institute, Cary, NC). Exact
P values were calcu-
first order in POPA discontinues previously prescribed opioids, benzo-
lated by resampling with a standard Poisson model using Mathematica
diazepines, and other sedatives, as to avoid interactions with fentanyl.
5.2 (Wolfram Research, Champaign, IL).
Analysis of diffusion of innovation: We used Mathematica 5.2 to calcu-
implementation of POPA. We established the baseline 12 months prior
late POPA's hospitalwide diffusion half-life by optimal fit of the logistic
to introduction of POPA by disseminating information about analgesia
growth equation to quarterly POPA cartridge purchases as obtained from
safety and efficacy to clinicians through established channels, including
hospital pharmacy purchase data53,54 In order to facilitate
one-on-one discussions, conferences, grand rounds, department and
an approximate comparison of opioid prescription trends, we express
committee meetings, newsletters, brochures, and practice guidelines.
the amounts of morphine, meperidine, and hydromorphone as grams of
We established the intervention by providing education and training
FE using the equivalency relations: fentanyl 100 µg = morphine 10 mg =
about POPA to all nurses, physicians, and pharmacists through brief in-
meperidine 80 mg = hydromorphone 1.3 mg.
service training sessions and distribution of supportive written materials.
Orthopedic surgery cohort analysis: Exact
P values for the univariate
POPA was then made available to prescribers, who were free to choose
analyses were calculated using resampling or Fisher's exact test. The mul-
POPA or other analgesia prescription at their discretion. Analgesia man-
tivariate nonlinear model for predicting which of the patients would have
agement for both POPA and routine analgesia was provided by the pri-
a severe or fatal opioid-associated ADE was calculated by conducting
mary service and not by a special analgesia service.
hierarchical y optimal classification tree analysis.55 The type I error rate
evaluation of POPA. We chose a statistical process control trial design
for the overall model was ensured at
P < 0.05 using a sequential y rejective
instead of a randomized control ed trial design because statistical process
Sidak Bonferroni–type procedure for multiple comparisons. The uni-
control trials have greater statistical power, are more ethical y acceptable
variate analyses and classification tree analysis were carried out using
when the beneficial effect of the test article has high plausibility, require
Optimal Data Analysis56
fewer resources, are minimal y disruptive of clinical practice, cause less
distortion of underlying clinical processes, and are less susceptible to nul
This study was funded by Food and Drug Administration grant FD-R-000887,
bias.45–49 Also, the Deming–Shewart plan-do-study-act loops (http://
Caterpil ar and OSF Saint Francis Medical Center. S.M.B. was supported in part
deming.eng.clemson.edu/pub/den/deming_map.htm) used in statistical
by an American Heart Association grant and by American Cancer Society grant
process control bear a felicitous correspondence to the iterative debug-
RS-GHP-05-215-01-CPPB. The OSF Saint Francis Medical Center Pharmacy
ging cycles used by computer programmers.
and Therapeutics Committee provided oversight for the POPA drug therapy
Our hospital has an amnesty policy that prohibits disciplinary action
improvement project. The Peoria Community Institutional Review Board
against physicians, nurses, pharmacists, and other health-care work-
approved the chart review and data analysis necessary for evaluation of the
ers who voluntarily report medication errors. Our hospital also has a
POPA project. Caterpillar manufactured the mechanical visual analog scales
program to identify drug therapy flaws, including hazards and failures,
to our specifications. We thank Dr Tim Miller for his support.
medication errors, and ADEs. ADE detection methods included concur-
rent review of hospital records by nurse quality managers with respect to
COnFliCt OF inteRest
resuscitations, unplanned intensive care unit transfers, and nonelective
The authors declared no conflict of interest.
endotracheal intubation or noninvasive ventilation, perievent discontinu-
2008 American Society for Clinical Pharmacology and Therapeutics
ation of drugs, unplanned use of antidotes, toxicology laboratory reports,
1. Aspden, P., Wolcott. J., Bootman, J.L. & Cronenwett, L.R. (eds.).
Preventing
and ADE voicemail hotline reports. An ADE was defined as "an injury
Medication Errors: Crossing the Quality Chasm Committee on Identifying and
related to the medical use of a drug."3
Preventing Medication Errors (National Academies Press, Washington, DC, 2007).
CliniCal pharmaCology & TherapeuTiCs VOLUME 84 NUMBER 3 SEPTEMBER 2008
2. Eccles, M., Grimshaw, J., Walker, A., Johnston, M. & Pitts, N. Changing the
31. Gillies, G., Kenny, G., Bullingham, R. & McArdle, C. The morphine sparing
behavior of healthcare professionals: the use of theory in promoting the
effect of ketorolac tromethamine. A study of a new, parenteral non-steroidal
uptake of research findings.
J. Clin. Epidemiol. 58, 107–112 (2005).
anti-inflammatory agent after abdominal surgery.
Anaesthesia 42, 727–731
3. Bates, D.W.
et al. Incidence of adverse drug events and potential adverse
drug events. Implications for prevention. ADE Prevention Study Group.
JAMA
32. Parker, R.K., Holtmann, B., Smith, I. & White, P.F. Use of ketorolac after lower
274, 29–34 (1995).
abdominal surgery. Effect on analgesic requirement and surgical outcome.
4. Shapiro, S., Slone, D., Lewis, G.P. & Jick, H. Fatal drug reactions among medical
Anesthesiology 80, 6–12 (1994).
inpatients.
JAMA 216, 467–472 (1971).
33. Dahl, V., Raeder, J.C., Drosdal, S., Wathne, O. & Brynildsrud, J. Prophylactic
5. Porter, J. & Jick, H. Drug-related deaths among medical inpatients.
JAMA
oral ibuprofen or ibuprofen-codeine versus placebo for postoperative
237, 879–881 (1977).
pain after primary hip arthroplasty.
Acta Anaesthesiol. Scand. 39, 323–326
6. Franke, R.H. & Kaul, J.D. The Hawthorne experiments: first statistical
interpretation.
Am. Sociol. Rev. 43, 623–643 (1978).
34. Delbos, A. & Boccard, E. The morphine-sparing effect of propacetamol in
7. Strom, B.L.
et al. Parenteral ketorolac and risk of gastrointestinal and operative
orthopedic postoperative pain.
J. Pain Symptom. Manage. 10, 279–286
site bleeding. A postmarketing surveillance study.
JAMA 275, 376–382 (1996).
8. Feldman, H.I.
et al. Parenteral ketorolac: the risk for acute renal failure.
Ann.
35. Camu, F., Van Aken, H. & Bovill, J.G. Postoperative analgesic effects of three
Intern. Med. 126, 193–199 (1997).
demand-dose sizes of fentanyl administered by patient-controlled analgesia.
9. Elsberry, V.A., Paxinos, J. & Harris, L.M. Preprinted physician's order form for
Anesth. Analg. 87, 890–895 (1998).
parenteral nutrient orders.
Am. J. Hosp. Pharm. 35, 779, 782 (1978).
36. Berde, C.B., Lehn, B., Yee, J.D., Sethna, N.F. & Russo, D. Patient-controlled
10. Honda, D.H., Jansen, J.R., Minor, D.R. & Good, J.W. Preprinted physician's order
analgesia in children and adolescents: a randomized, prospective comparison
form for intravenous cisplatin therapy.
Am. J. Hosp. Pharm. 36, 742–743 (1979).
with intramuscular morphine for postoperative analgesia.
J. Pediatr. 118,
11. Kowalsky, S.F., Echols, R.M. & Peck, F. Jr. Preprinted order sheet to enhance
460–466 (1991).
antibiotic prescribing and surveillance.
Am. J. Hosp. Pharm. 39, 1528–1529
37. Hunt, R., Fazekas, B., Thorne, D. & Brooksbank, M. A comparison of
subcutaneous morphine and fentanyl in hospice cancer patients.
J. Pain
12. Dranitsaris, G., Leung, P. & Warr, D. Implementing evidence based antiemetic
Symptom Manage. 18, 111–119 (1999).
guidelines in the oncology setting: results of a 4-month prospective
38. Watanabe, S., Pereira, J., Hanson, J. & Bruera, E. Fentanyl by continuous
intervention study.
Support. Care Cancer 9, 611–618 (2001).
subcutaneous infusion for the management of cancer pain: a retrospective
13. Fonarow, G.C.
et al. Influence of a performance-improvement initiative on
study.
J. Pain Symptom Manage. 16, 323–326 (1998).
quality of care for patients hospitalized with heart failure: results of the
39. Mercadante, S., Caligara, M., Sapio, M., Serretta, R. & Lodi, F. Subcutaneous
Organized Program to Initiate Lifesaving Treatment in Hospitalized Patients
fentanyl infusion in a patient with bowel obstruction and renal failure.
J. Pain
With Heart Failure (OPTIMIZE-HF).
Arch. Intern. Med. 167, 1493–1502 (2007).
Symptom Manage. 13, 241–244 (1997).
14. Girotti, M.J., Fodoruk, S., Irvine-Meek, J. & Rotstein, O.D. Antibiotic handbook
40. Paix, A.
et al. Subcutaneous fentanyl and sufentanil infusion substitution for
and pre-printed perioperative order forms for surgical antibiotic prophylaxis:
morphine intolerance in cancer pain management.
Pain 63, 263–269 (1995).
do they work?
Can. J. Surg. 33, 385–388 (1990).
41. Bjorkman, S., Wada, D.R. & Stanski, D.R. Application of physiologic models to
15. Aswapokee, N., Vaithayapichet, S. & Komoltri, C. The failure of a preprinted
predict the influence of changes in body composition and blood flows on
order form to alter physicians' antimicrobial prescribing pattern.
J. Med. Assoc.
the pharmacokinetics of fentanyl and alfentanil in patients.
Anesthesiology
Thai. 75, 223–230 (1992).
88, 657–667 (1998).
16. Cohen, M.R. & Davis, N.M. Developing safe and effective preprinted physician's
42. Belknap, S.M. The Chicago Kinetic Simulator: a Mathematical program for the
order forms.
Hosp. Pharm. 27, 508, 513, 528 (1992).
simulation and optimization of mathematical models.
Math. J. 1, 68–86 (1991).
17. Minsky, M. Why programming is a good medium for expressing poorly
43. Miller, R.S., Peterson, G.M., Abbott, F., Maddocks, I., Parker, D. & McLean, S.
understood and sloppily formulated ideas. In
Design and Planning II (eds.
Plasma concentrations of fentanyl with subcutaneous infusion in palliative
Krampen, M. & Seitz, P.) 120–125 (Visual Committee Books, Hasting House, NY,
care patients.
Br. J. Clin. Pharmacol. 40, 553–556 (1995).
44. Lehmann, K.A. Patient controlled analgesia for postoperative pain. In
18. Dijkstra, E.W. Go-to statement considered harmful.
Commun. ACM 11,
Advances in Pain Research and Therapy (eds. Benedetti, C., Chapman, C.R. &
147–148 (1968).
Girou, G.) 297–324 (Raven Press, New York, 1984).
19. Gruenberger, F. Program testing and validating.
Datamation 14, 39–47 (1968).
45. Diaz, M. & Neuhauser, D. Pasteur and parachutes: when statistical process
20. Weingarten, S. Practice guidelines and prediction rules should be subject to
control is better than a randomized controlled trial.
Qual. Saf. Health Care
careful clinical testing.
JAMA 277, 1977–1978 (1997).
14, 140–143 (2005).
21. Shekelle, P.G.
et al. Validity of the Agency for Healthcare Research and Quality
46. Berwick, DM. Continuous improvement as an ideal in health care.
N. Engl.
clinical practice guidelines: how quickly do guidelines become outdated?
J. Med. 320, 53–56 (1989).
JAMA 286, 1461–1467 (2001).
47. Laffel, G. & Blumenthal, D. The case for using industrial quality management
22. Cabana, M.D.
et al. Why don't physicians follow clinical practice guidelines?
science in health care organizations.
JAMA 262, 2869–2873 (1989).
A framework for improvement.
JAMA 282, 1458–1465 (1999).
48. Blumenthal, D. Quality of health care. Part 4: the origins of the quality-of-care
23. Neale, G., Vincent, C. & Darzi, S.A. The problem of engaging hospital doctors in
debate.
N. Engl. J. Med. 335, 1146–1149 (1996).
promoting safety and quality in clinical care.
J.R. Soc. Health 127, 87–94 (2007).
49. Norberg, A., Christopher, N.C., Ramundo, M.L., Bower, J.R. & Berman, S.A.
24. Nishisaki, A., Keren, R. & Nadkarni, V. Does simulation improve patient safety?
Contamination rates of blood cultures obtained by dedicated phlebotomy vs
Self-efficacy, competence, operational performance, and patient safety.
intravenous catheter.
JAMA 289, 726–729 (2003).
Anesthesiol. Clin. 25, 225–236 (2007).
50. Naranjo, C.A.
et al. A method for estimating the probability of adverse drug
25. Tamuz, M. & Harrison, M.I. Improving patient safety in hospitals: contributions
reactions.
Clin. Pharmacol. Ther. 30, 239–245 (1981).
of high-reliability theory and normal accident theory.
Health Serv. Res.
51. Nebeker, J.R., Barach, P. & Samore, M.H. Clarifying adverse drug events: a
41, 1654–1676 (2006).
clinician's guide to terminology, documentation, and reporting.
Ann. Intern.
26. Nebeker, J.R., Hoffman, J.M., Weir, C.R., Bennett, C.L. & Hurdle, J.F. High rates
Med. 140, 795–801 (2004).
of adverse drug events in a highly computerized hospital.
Arch. Intern. Med.
52. Hafner, J.W. Jr, Belknap, S.M., Squillante, M.D. & Bucheit, K.A. Adverse drug events
165, 1111–1116 (2005).
in emergency department patients.
Ann. Emerg. Med. 39, 258–267 (2002).
27. Graumlich, J.F., Belknap, S.M., Bullard, S.A., Storm, G.A., Brunsman, K.S. &
53. Ryan, B. & Gross, N.C. The diffusion of hybrid corn in two Iowa communities.
Howerton, J.A. Pharmaceutical care of postoperative nausea and vomiting:
Rural Sociol. 8, 15–24 (1943).
balanced scorecard for outcomes.
Pharmacotherapy 20, 1365–1374 (2000).
54. Coleman, J., Menzel, H. & Katz, E. Social processes in physicians' adoption of
28. Kaplan, R.S. & Norton, D.P. The balanced scorecard—measures that drive
a new drug.
J. Chronic Dis. 9, 1–19 (1959).
performance
Harv. Bus. Rev. 70, 71–79 (1992).
55. Yarnold, P.R., Soltysik, R.C. & Bennett, C.L. Predicting in-hospital mortality of
29. Desbiens, N.A.
et al. Pain and satisfaction with pain control in seriously ill
patients with AIDS-related
Pneumocystis carinii pneumonia: an example of
hospitalized adults: findings from the SUPPORT research investigations. For
hierarchically optimal classification tree analysis.
Stat. Med. 16, 1451–1463
the SUPPORT investigators. Study to Understand Prognoses and Preferences
for Outcomes and Risks of Treatment.
Crit. Care Med. 24, 1953–1961 (1996).
56. Yarnold, P.R. & Soltysik, R.C.
Optimal Data Analysis: A Guidebook With Software
30. Price, D.D., Bush, F.M., Long, S. & Harkins, S.W. A comparison of pain
for Windows. (APA Books, Washington, DC, 2004).
measurement characteristics of mechanical visual analogue and simple
57. Fisher, R.A. On the interpretation of χ2 from contingency tables, and the
numerical rating scales.
Pain 56, 217–226 (1994).
calculation of P.
J. R. Stat. Soc. 85, 87–94 (1922).
VOLUME 84 NUMBER 3 SEPTEMBER 2008
www.nature.com/cpt
Source: http://healthsciences.ncsa.illinois.edu/pubs/Algorithmic_Medicine.pdf
II FORUM ECONOMICO DEL MEDITERRANEO Roma, 25–26 febbraio 2010 Documentazione di supporto A cura del Settore Crediti Corporate Presenza e operatività del sistema bancario italiano nei Paesi della Sponda Sud del Mediterraneo ed altri elementi di approfondimento su questioni economico-finanziarie
Indicators of ADHD symptoms FECHA DE RECEPCIÓN: 23 de junio in virtual learning context using FECHA DE APROBACIÓN: 17 de julio Pp. 22-37 machine learning technics Laura Patricia Mancera Valetts* Indicadores de síntomas ADHD en Silvia Margarita Baldiris Navarro** el contexto de aprendizaje virtual,