Caesarean Section Project : HK 2017 1
Overview
Why / Why not
Focus
Technology
Progress
Discussions
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 Why and why not : should we continue or abandon project
 Focus : what is the project trying to do
 Technology : What are the basic methodologies
 Progress : Where have we got to
 Discussions : Where do we go from here
Why
Why not
 CS Rates
 Everyone agrees that CS has complications
 CS rate continues to increase
 Much auditing, but no mechanism to control CS rate
 A bad experience
 Neonatal cardiac surgery mortality = 15%
 New surgeon, 8 deaths in first 13 cases, 62%
 Binomial Test p=0.0002, 95%CI=35% to 88%
 Hospital banned surgeon
 Ban overturned on appeal, patient's high risks not considered
 Journal review
 Much clinical audits published
 None include risk assessment in detail
 Many CUSUM papers are not CUSUM
 No CUSUM and Risk evaluation links
 Artificial intelligence in Medicine
 Controversy between algorithmic or pattern recognition
 Bayesian model used extensively in medical diagnosis
 Audit may be a model to evaluate Bayesian statistics
 Statistically based clinical research irrelevant
 Guidelines precludes decision making
 Major advances by statistics already made
 Data from a single hospital cannot be generalized
 Laboratory and technology based research more useful
 Methodology uncertain
 Basic Bayesian probability already ancient technology
 Audit methodologies complex and controversial
 Clinicians are not statisticians
 Effort not cost effective
 Steep learning curve
 Attention to details needed to get it right
 Editors may not favour results
 Retrospective data
 Definition of clinical events not made by researchers
 Significant volume of missing data
 No one is interested
 Most junior staff have no academic ambition
 Most senior staff already have their own research interest
 Nurses and midwives focussed on caring
About
Order
Publications
 The question
 Can we combine Bayesian Probability and CUSUM
 Can we create a new clinical tool
 Will it have sufficient quality to be useful
 Framework of audit
 Yearly summary and overview
 Continuous using CUSUM (Bernoulli distribution)
 Continuous monitoring and reporting on quality at technician level
 Early alert to changing trends
 Statistically robust method of selecting outlier for qualitative review
 Continuous adjustment of bench mark using risk profile of cases being audited
 Structure of research
 Adapt Pattern Probability model of Bayesian Probability
 Testing multivariate Bayesian model
 Adapt Known CUSUM for Bernoulli distribution (Binary)
 Modify fixed bench mark risk to dynamically changing risks
 Identify risk factor
 Background : age, height, BMI, parity, previous CS
 Morbidity : diabetes, hypertension, APH
 Baby : malpresentation, suspected fetal compromise
 Identify Environmental factor
 Seasonal, weekdays, hours
 Induction, duration of labour
 Categorizing risks
 Prepartum decisions : Prelabour CS, induction, spontaneous labour
 Intrapartum decisions : Intrapartum CS, vaginal delivery
 Bayesian probability
 Adjust risks for each patient
 Validate individual risks with overall CS rate
 CUSUM audit
 Straight forward CUSUM assuming static risk level
 Adjusted CUSUM with continuously changing risk levels
Possible publications
 Epidemiology of CS
 Bayesian prediction of CS
 CUSUM audit of Caesarean section
 Comparing static with variable risks, methodological paper
 Early identification of changing trends, clinical paper
 Cost effectiveness of selecting outlier cases for qualitative review
Bayes
CUSUM
Baysian Probability : The Pattern Probability Model
 A modification of the clinical decision making
Posttest probability = function(Pretest probability, odds ratio)
 Allows multiple tests. Posttest probability after one test becomes pretest probability of the next test
 Proviso : no within class correlation between predictors
Advantages of Pattern Probability
 Tolerance of missing data, able to draw conclusions with only available data
 Indifferent to order of information input
 Regardless of initial probability assumption, conclusions rapidly adapted to incoming data
Published use of Pattern Probability in medical diagnosis
 Warner first proposed the method in 1961, congenital heart disease
 Overall applied it to classification of psychiatric illness, 1972
 de Dombal popularised it for surgery, appendicitis, 1987
 Others since
Limitations of Pattern Probability
 Domain specific
 Unable to process outside of clearly defined alternatives
 Unable to predict outliers
CUSUM Overall
 Quality evaluation for manufacturing
 Detects small but persistent departure from a bench mark
 Models depend on different statistical distribution
 We use the model for Bernoulli distribution, binary data
Logic of CUSUM
 Bench mark of in control proportion defined
 Tolerance of departure defined
 Decision line for alert calculated
 CUSUM continuously calculated as data become available
 CUSUM value moves towards decision line with positive item
 CUSUM value moves away from decision line with negative item
 Alert issued when CUSUM crosses decision line
Weakness of CUSUM when used clinically
 CUSUM is designed for manufacturing industry
 It assumes uniform production
 It defines a static bench mark, based on a static risk
 It does not cater to variable risks common in clinical situations
Main point of project
 Inserting variable risk to the bench mark
 Does this improve CUSUM
Summary
Data
Bayesian Probability
Check Bayes Results
CUSUM
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Summary
 Obstetric record 20112015 downloaded, cleaned, and prepared for analysis
 Only singlton live birth are included
 Initial analysis results promising
 Ethics Committee application started
 Delivery::Year($ar) : 2011=7115, 2012=6992, 2013=6060, 2014=6680, 2015=6617
 Age::G($ar) : Error=0, <17=35, 1725=3973, 2630=10455, 3135=13062, 3640=5188, >40=751
 Height::G($ar) : Error=400, <146=269, 146150=2242, 151155=7732, 156160=11960, >160=10861
 BMI::G($ar) : Error=1897, <21=700, 2125=13830, 2630=13740, 3135=2842, >35=455
 Parity::G($ar) : Error=0, Primip=7012, PrevCS=21520, Multip=4932
 Diabetes::G($ar) : Error=0, yes=3118, no=30346
 Hypertension::G($ar) : Error=0, yes=1033, no=32431
 APH::G($ar) : Error=0, yes=765, no=32699
 Malpresentation::G($ar) : Error=0, yes=1119, no=32345
 FetalCompromise::G($ar) : Error=0, yes=1316, no=32148
 Gestation::G($ar) : Error=7, <36=1255, 3639=21667, 40=7107, &ft;40=3428
 Induction::G($ar) : Error=0, yes=5734, no=27730 no includes PCS
 MOD::G($ar) : Error=0, PCS=4264, ICS=3524, VD=25676
 ElectedMOD::G($ar) : Error=0, PCS=4264, Induction=5662, SponLab=23538
 LabouredMOD::G($ar) : Error=4264, ICS=3524, VD=25676 Error are PCS
 BirthWeight::G($ar) : Error=0, <=2.5=2304, <2.53.5=24563, <3.54.0=5770, >4.0=827
 FirstStage::G($ar) : Error=5485, 1<6Hr=15143, 6<12Hr=8838, 12<18Hr=3055, 18<24Hr=794, 24+Hr=149 Error includes first stage<15min
 SecondStage::G($ar) : Error=7735, <30min=20206, 30<60min=2836, 60<90min=1381, 90<120min=733, 120+min=573 Error include second stage <1min
 Apgar::G($ar) : Error=79, <5=53, 5+=33332
 Sex::G($ar) : Error=1, Male=17309, Female=16154
PrePartum
Intrapartum
PCS=prepartum CS
P(θx,π), last column = posttest risks
Age : Prepartum CS increases with age, 2.9% to 24.9%
 Count  P(xθ)  P(θx)  P(θx,π) 
 PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab 
<17  1  4  30  0.0002  0.0007  0.0013  0.1059  0.3189  0.5753  0.0286  0.1143  0.8571 
1725  179  679  3115  0.042  0.1199  0.1323  0.1427  0.4076  0.4498  0.0451  0.1709  0.784 
2630  948  1748  7759  0.2223  0.3087  0.3296  0.2583  0.3587  0.383  0.0907  0.1672  0.7421 
3135  1842  2209  9011  0.432  0.3901  0.3828  0.3585  0.3238  0.3177  0.141  0.1691  0.6899 
3640  1107  880  3201  0.2596  0.1554  0.136  0.4711  0.2821  0.2468  0.2134  0.1696  0.617 
>40  187  142  422  0.0439  0.0251  0.0179  0.5049  0.2887  0.2064  0.249  0.1891  0.5619 
Total  4264  5662  23538 
Height : Prepartum CS decreases with being taller, 25.2% to 11.3%
 Count  P(xθ)  P(θx)  P(θx,π) 
 PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab 
<146  68  50  151  0.0161  0.0089  0.0065  0.5113  0.2818  0.2068  0.2522  0.1846  0.5632 
146150  368  379  1495  0.0871  0.0672  0.0644  0.3981  0.3073  0.2946  0.1637  0.1678  0.6686 
151155  1057  1318  5357  0.2501  0.2338  0.2309  0.3499  0.327  0.323  0.1363  0.1691  0.6946 
156160  1502  1968  8490  0.3554  0.3491  0.3659  0.332  0.3261  0.3419  0.1252  0.1633  0.7115 
>160  1231  1923  7707  0.2913  0.3411  0.3322  0.302  0.3536  0.3444  0.113  0.1757  0.7113 
Total  4226  5638  23200 
BMI : Prepartum CS increases with BMI, 7.9% to 18.1%. So with induction, 14.9% to 25.2%
 Count  P(xθ)  P(θx)  P(θx,π) 
 PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab 
<21  55  115  530  0.0138  0.0208  0.024  0.2356  0.3552  0.4093  0.0794  0.159  0.7616 
2125  1474  2130  10226  0.3704  0.386  0.4633  0.3037  0.3165  0.3799  0.1077  0.149  0.7434 
2630  1885  2467  9388  0.4737  0.4471  0.4254  0.3519  0.3321  0.316  0.1387  0.1738  0.6875 
3135  484  688  1670  0.1216  0.1247  0.0757  0.3778  0.3872  0.235  0.1726  0.2349  0.5926 
>35  81  118  256  0.0204  0.0214  0.0116  0.3816  0.4009  0.2175  0.1805  0.2518  0.5677 
Total  3979  5518  22070 
Parity : Previous CS has high prepartum CS, 15.8%. Primip has high induction rate, 22.3%
 Count  P(xθ)  P(θx)  P(θx,π) 
 PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab 
Primip  544  1565  4903  0.1276  0.2764  0.2083  0.2084  0.4514  0.3402  0.0776  0.2232  0.6992 
PrevCS  3399  3245  14876  0.7971  0.5731  0.632  0.3981  0.2862  0.3156  0.1579  0.1508  0.6913 
Multip  321  852  3759  0.0753  0.1505  0.1597  0.1953  0.3904  0.4143  0.0651  0.1727  0.7622 
Total  4264  5662  23538 
Diabetes : Diabetes has higer prepartum CS, 18.2% to 12.2%, also induction, 26% to 16%
 Count  P(xθ)  P(θx)  P(θx,π) 
 PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab 
yes  567  812  1739  0.133  0.1434  0.0739  0.3796  0.4094  0.2109  0.1818  0.2604  0.5577 
no  3697  4850  21799  0.867  0.8566  0.9261  0.3272  0.3233  0.3495  0.1218  0.1598  0.7183 
Total  4264  5662  23538 
Hypertension : Hypertension has higer prepartum CS, 25% to 12.4%, also induction, 45.5% to 16%
 Count  P(xθ)  P(θx)  P(θx,π) 
 PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab 
yes  258  470  305  0.0605  0.083  0.013  0.3867  0.5305  0.0828  0.2498  0.455  0.2953 
no  4006  5192  23233  0.9395  0.917  0.987  0.3304  0.3225  0.3471  0.1235  0.1601  0.7164 
Total  4264  5662  23538 
APH : APH has higer prepartum CS, 39% to 12.1%
 Count  P(xθ)  P(θx)  P(θx,π) 
 PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab 
yes  298  116  351  0.0699  0.0205  0.0149  0.6638  0.1946  0.1416  0.3895  0.1516  0.4588 
no  3966  5546  23187  0.9301  0.9795  0.9851  0.3213  0.3384  0.3403  0.1213  0.1696  0.7091 
Total  4264  5662  23538 
Malpresentation : Malpresentation has higer prepartum CS, 72.5% to 10.7%, but lower induction, 2% to 17.4%
 Count  P(xθ)  P(θx)  P(θx,π) 
 PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab 
yes  811  22  286  0.1902  0.0039  0.0122  0.9222  0.0188  0.0589  0.7248  0.0197  0.2556 
no  3453  5640  23252  0.8098  0.9961  0.9878  0.2899  0.3565  0.3536  0.1068  0.1744  0.7189 
Total  4264  5662  23538 
Suspected Fetal Compromise : higher prepartum CS, 19.2% to 12.5%, also higher induction, 60.8% to 14.5%
 Count  P(xθ)  P(θx)  P(θx,π) 
 PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab 
yes  278  881  290  0.0652  0.1556  0.0123  0.2797  0.6675  0.0529  0.1919  0.608  0.2001 
no  3986  4781  23248  0.9348  0.8444  0.9877  0.3379  0.3052  0.357  0.1245  0.1493  0.7262 
Total  4264  5662  23538 
Gestation : Prepartum CS higher preterm, and induction higher post term
 Count  P(xθ)  P(θx)  P(θx,π) 
 PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab  PCS  Induction  SponLab 
<36  288  63  904  0.0676  0.0111  0.0384  0.5769  0.0951  0.328  0.2295  0.0502  0.7203 
3639  3737  2912  15018  0.8766  0.5145  0.6381  0.432  0.2535  0.3145  0.1725  0.1344  0.6931 
40  122  740  6245  0.0286  0.1307  0.2654  0.0674  0.3078  0.6248  0.0172  0.1041  0.8787 
>40  116  1945  1367  0.0272  0.3436  0.0581  0.0634  0.8011  0.1354  0.0338  0.5674  0.3987 
Total  4263  5660  23534 
Contents of Intrapartum : 141
ICS = Intrapartum CS
Age : Intrapartum CS increases with age, 5.9% to 20.4%
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
<17  2  32  0.0006  0.0012  0.3129  0.6871  0.0588  0.9412 
1725  309  3485  0.0877  0.1357  0.3925  0.6075  0.0814  0.9186 
2630  1038  8469  0.2946  0.3298  0.4717  0.5283  0.1092  0.8908 
3135  1470  9750  0.4171  0.3797  0.5235  0.4765  0.131  0.869 
3640  590  3491  0.1674  0.136  0.5518  0.4482  0.1446  0.8554 
>40  115  449  0.0326  0.0175  0.6511  0.3489  0.2039  0.7961 
Total  3524  25676 
Height : Intrapartum CS decreases when taller, 27.8% to 9.7%
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
<146  56  145  0.0161  0.0057  0.7374  0.2626  0.2782  0.7218 
146150  339  1535  0.0972  0.0605  0.6163  0.3837  0.1806  0.8194 
151155  942  5733  0.2702  0.2261  0.5444  0.4556  0.1409  0.8591 
156160  1216  9242  0.3488  0.3645  0.489  0.511  0.1161  0.8839 
>160  933  8697  0.2676  0.343  0.4383  0.5617  0.0967  0.9033 
Total  3486  25352 
BMI : Intrapartum CS increases with BMI, 9.3% to 78%
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
<21  47  598  0.014  0.0247  0.3617  0.6383  0.0722  0.9278 
2125  1141  11215  0.3396  0.4629  0.4232  0.5768  0.0915  0.9085 
2630  1611  10244  0.4795  0.4228  0.5314  0.4686  0.1347  0.8653 
3135  478  1880  0.1423  0.0776  0.6471  0.3529  0.201  0.799 
>35  83  291  0.0247  0.012  0.6728  0.3272  0.2201  0.7799 
Total  3360  24228 
Parity : Multipara without previous CS=3.3%, with previous CS=13.2%, primip=15.1%
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
Primip  979  5489  0.2778  0.2138  0.5651  0.4349  0.1514  0.8486 
PrevCS  2391  15730  0.6785  0.6126  0.5255  0.4745  0.1319  0.8681 
Multip  154  4457  0.0437  0.1736  0.2011  0.7989  0.0334  0.9666 
Total  3524  25676 
Diabetes : Marginally higher in diabetes, 15.5% to 11.7%
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
yes  396  2155  0.1124  0.0839  0.5724  0.4276  0.1552  0.8448 
no  3128  23521  0.8876  0.9161  0.4921  0.5079  0.1174  0.8826 
Total  3524  25676 
Hypertension : higher with hypertension, 30.6% to 11.6%
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
yes  237  538  0.0673  0.021  0.7625  0.2375  0.3058  0.6942 
no  3287  25138  0.9327  0.979  0.4879  0.5121  0.1156  0.8844 
Total  3524  25676 
APH : higher with APH, 30% to 11.8%
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
yes  140  327  0.0397  0.0127  0.7572  0.2428  0.2998  0.7002 
no  3384  25349  0.9603  0.9873  0.4931  0.5069  0.1178  0.8822 
Total  3524  25676 
Malpresentation : higher with malpresentation, 87.7% to 11.3%
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
yes  270  38  0.0766  0.0015  0.981  0.019  0.8766  0.1234 
no  3254  25638  0.9234  0.9985  0.4805  0.5195  0.1126  0.8874 
Total  3524  25676 
Suspected Fetal Compromise : marginally higher, 16.6% to 11.9%
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
yes  194  977  0.0551  0.0381  0.5913  0.4087  0.1657  0.8343 
no  3330  24699  0.9449  0.9619  0.4955  0.5045  0.1188  0.8812 
Total  3524  25676 
Gestation : higher before 36w, 25.5%, and postterm, 19.7%, compared with 9.9% and 12.2% near term
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
<36  246  721  0.0698  0.0281  0.7132  0.2868  0.2545  0.7455 
3639  1775  16155  0.504  0.6293  0.4447  0.5553  0.099  0.901 
40  849  6136  0.2411  0.239  0.5021  0.4979  0.1216  0.8784 
>40  652  2660  0.1851  0.1036  0.6411  0.3589  0.1969  0.8031 
Total  3522  25672 
Induction : higher with induction, 19.5% to 10.3%
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
yes  1104  4558  0.3133  0.1775  0.6383  0.3617  0.195  0.805 
no  2420  21118  0.6867  0.8225  0.455  0.545  0.1028  0.8972 
Total  3524  25676 
First Stage : increases with length of first stage, 5.7% to 49.3%
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
1<6Hr  663  14460  0.2532  0.5707  0.3074  0.6926  0.0574  0.9426 
6<12Hr  802  8034  0.3063  0.3171  0.4914  0.5086  0.1171  0.8829 
12<18Hr  816  2238  0.3117  0.0883  0.7792  0.2208  0.3263  0.6737 
18<24Hr  274  520  0.1047  0.0205  0.8361  0.1639  0.4117  0.5883 
24+Hr  63  86  0.0241  0.0034  0.8764  0.1236  0.4932  0.5068 
Total  2618  25338 
Second Stage: increases with length of second stage, 1.6% to 83.3%
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
<30min  26  20143  0.0909  0.7928  0.1029  0.8971  0.0155  0.9845 
30<60min  38  2798  0.1329  0.1101  0.5468  0.4532  0.1421  0.8579 
60<90min  19  1362  0.0664  0.0536  0.5534  0.4466  0.1454  0.8546 
90<120min  37  696  0.1294  0.0274  0.8252  0.1748  0.3933  0.6067 
120+min  166  407  0.5804  0.016  0.9731  0.0269  0.8326  0.1674 
Total  286  25406 
Birth weight, Apgar score, and sex are shown for interest only. They should be excluded from analysis because
 Their value not known at the time of decision making
 Birth weight is correlated and probably tautological to gestation
 Apgar score is an outcome and not a risk factor
Birth weight
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
<=2.5  375  1462  0.1064  0.0569  0.6514  0.3486  0.2041  0.7959 
>2.53.5  2222  19272  0.6305  0.7506  0.4565  0.5435  0.1034  0.8966 
>3.54.0  763  4435  0.2165  0.1727  0.5562  0.4438  0.1468  0.8532 
>4.0  164  507  0.0465  0.0197  0.7021  0.2979  0.2444  0.7556 
Total  3524  25676 
Apgar
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
<5  13  21  0.0037  0.0008  0.8181  0.1819  0.3816  0.6184 
5+  3511  25576  0.9963  0.9992  0.4993  0.5007  0.1204  0.8796 
Total  3524  25597 
Sex
 Count  P(xθ)  P(θx)  P(θx,π) 
 ICS  VD  ICS  VD  ICS  VD  ICS  VD 
Male  1928  13192  0.5471  0.5138  0.5157  0.4843  0.1275  0.8725 
Female  1596  12483  0.4529  0.4862  0.4823  0.5177  0.1134  0.8866 
Total  3524  25675 
 Each data point a group with a calculated risk in percent to nearest whole number
 x axis = calculated risk for the group
 y axis = actual % of calculated risk for the group
 Prepartum decisions : Good correlation between calculated risk and actual percentage of outcome
 Some, but poor quality correlation in Intrapartum outcomes
 Suspect many cases without duration of first and second stage
 Effect of many risk factors already influenced prepartum decisions, so may have less predictability here
All Cases
Delivery Time
Working Hours
Night
We will use Prepartum CS (pcs) from 2011, in order of delivery, to demonstrate CUSUM
 Too much data
 Variability over time of day and day of week
Actual number and percent of prepartum CS according to the time of delivery
 PCS rate high during working hours
 PCS rate low at night.
Grp  n  mean(%)  SD  SE  95%CI Mean  0:befor_9am  149  36.9  29.7  2.5  32.1  41.7  1:9am6pm  3831  32.0  25.9  0.4  31.2  32.8  2:after_6pm  284  33.4  26.9  1.6  30.3  36.6 
Calculated risk level similar in 3 groups
Grp  Grp  Difference(%)  95% CI  0:befor_9am  1:9am6pm  4.9  0.6  9.2  0:befor_9am  2:after_6pm  3.4  1.7  8.6  1:9am6pm  2:after_6pm  1.4  4.6  1.7 
Calculated risks of cases with prepartum CS
 Those delivered at night and those delivered during working hours are significantly different
 Differences however are small
Conclusions
 Overall CUSUM too confusing
 CUSUM for different time of delivery required
CUSUM for prepartum CS during working hours
 Fixed bench mark (left)
 Bench mark rate 20% (0.2)
 Alert 1.5 x bench mark, 30% (0.3)
 Variable bench mark (right)
 Bench mark rate at start 20% (0.2)
 Bench mark varies according to calculated risk in each case
 Alert 1.5 x current bench mark
First 250 deliveries in 2011 for greater detail
 Alert line using p=0.05, p=0.02, p=0.01
 CUSUM resets when p=0.01 alert line crossed
Conclusion
 Prepartum CS rate during working hours exceeds 20%, reaching 30%
 Statistically very interesting
 Clinically, because most prepartum CS are planned and carried out during working hours
 Plot shows the math only
CUSUM for prepartum CS at night time (midnight  9am)
 Fixed bench mark (left)
 Bench mark rate 3% (0.03)
 Alert 1.5 x bench mark, 4.5% (0.045)
 Alert sets at p=0.05, p=0.03, and p=0.01
 Variable bench mark (right)
 Bench mark rate at start 3% (0.03)
 Bench mark varies according to calculated risk in each case
 Alert 1.5 x current bench mark
Conclusion
 Prepartum CS rate at night rarely exceed 3% and never exceed 4.5% in 2011
 The rate is lower than the calculated risk level of the cases
 The pattern is statistically clear, but the cause remains to be found
 Possibly, actions are posponed until day time
 Plot shows the math only
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About Project
Achievement So Far
Controversies
Actions and Decisions
 Bayesian probability reduces multiple risk indicators to a single one
 Using Bayesian risk in an audit
 Adjusts a proposed bench mark by risk profiles of cases being audited
 Provides a more realistic bench mark
 Use of CUSUM to audit clinical outcome and decisions
 Once set up, it requires no special expertise
 Continuous and immediate results are available from computers
 outliers can be statistically identified to quantitative review
 Adding Bayesian probability to CUSUM
 Fixed risk works for industrial production but not clinical care
 Risk levels in clinical situations are not fixed
 Changing bench mark dynamically with Bayesian risk provides a more realistic bench mark for clinical audit
 We have a very large data base
 20112015, may be more
 Quality of data good. Some data missing but workable
 The statistics methodology seems workable
 The basic methods are time tested and accepted
 Modification and combining the methods are new and basis of this project
 Results of initial analysis seems to make sense
Bayesian vs Logistic Regression
CUSUM with Variable Risk
Logistic Regression
 Frequentist statistics : Estimating an underlying invariant truth
 Assumes an invariant relationship between all parameters
 Assumes correlations between predictors
 Assumes outcomes dependent on predictors
 Regression model : combination of predictors (independent variables) to predict outcomes (dependent variables)
 Works best with binary outcomes
 The results are static, best estimate of an invariant underlying truth
Bayesian Probability
 Bayesian : Logical methods to handle information
 Assumes the frequencies of outcomes variable
 Assumes absence of intragroup correlations between predictors
 Assumes predictors depend on outcomes
 Three step model :
 Step 1 : Assess relationship with individual predictors as dependent on outcome, P(xθ)
 Step 2 : Combine multiple relationship of P(xθ)
 Step 3 : Inserts prehoc probability to produce expected probability, P(θx,π)
 No limit to number of outcomes
 The results from multiple steps are tools and resources, used flexibly for different purposes and in different environments
 Modification of standard and accepted CUSUM for proportions
 Replace p0, static expected proportion when process in control, with variable expected risk
 Replace p1, static proportion of tolerated limit, with static tolerated ratio of variable expected risk
 Replace h, static alert line calculated at the beginning of audit, with a variable h, recalculated with every input
 Reset of p0, p1, and h to expected levels uninfluenced by data
 When CUSUM crosses the zero (0) value, as in fixed CUSUM model
 When CUSUM crosses the calculated h value, to avoid the stabalizing effect of long term averaging
 Controversy
 The only new thing in the whole project
 Method seems logical, but not validated
 Hope this can be published, and becomes accepted
 A decision and plan to move ahead
 Who to be involved
 who to do what
 How to avoid stalling and loss of communication
 Literature search
 Review of more current use of Bayesian methods in clinical research
 Review of current clinical audit methodologies
 Get the proper references for technical terms
 12 months of prospective data, every delivery
 Outcomes of interest
 Additional predictors, definition of predictors
 parameters for subgroup analysis
 Booked/unbooked
 HK/mainland
 Name of decision maker, rank, experience
 Stated indications, evidence of indications
 Requests
 May need a full time recorder ? with midwifery qualification
 To review every delivery and check data
 To interview staff to fill in the gaps
 For 7000 deliveries a year, roughly 20 deliveries a day
 List of possible papers
 Epidemiology
 Prediction and risk evaluation
 Audit
 Technical papers o Bayes and CUSUM
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