Introduction
Programs needed for predictions are
Statistics of prediction follows the following processes
 A Test is a measurement or observation we use to predict an outcome
 An Outcome is the eventuality we are trying to predict
 A prediction is usually stated in probability terms, how likely is the outcome to eventuate
 Examples :
 We use Antepartum Haemorrhage as a Test to predict the probability of an Outcome, Placenta Previa
 We use Maternal Height as a Test to predict the probability of an Outcome, needing a C.S.
Outcomes
 Can be a continuous measurement. e.g. How long will the labour be
 Regression is the usual statistical model use to predict continuous measurement
 Not covered in this workshop
 Can be Binary, a no/yes outcome. e.g. Placenta previa, Caesarean Section, Neonatal Death
Tests
 Can be Binary, a no/yes test. e.g. Antepartum Haemorrhage, Unengaged head
 Can be a measurement. e.g. Maternal Height, Biparietal Diameter, Birth weight, Gestational age
Binary Predictors or Tests
Definitions for Data
 The quality of a test is estimated from data
 Data can be obtained either retrospectively from records, or prospectively by survey
 To ensure sufficient power, similar number of outcome positive and negative cases are
obtained.
 When data are collected, each case can be classified according to
 Outcome Positive or Negative
 Test Positive or Negative
An example : using antepartum Haemorrhage as a test to predict presence of Placenta previa.
 Placenta Previa  No Placenta previa  Total 
APH  True Positive TP=12  False Positive FP=5  Test Positive=12+5=17 
No APH  False Negative FN=13  True Negative TN=20  Test Negative=13+20=33 
Total  Outcome Positive=12+13=25  Outcome Negative=5+20=25  Total=50 
Quality of a Test
True Positive Rate (TPR)
 Probability (%) of Test Positive amongst all those that are outcome Positive
 In Our Example, How many of those with Placenta Previa also have APH
 TPR = True Positive / Outcome Positive = TP / (TP+FN) = 12 / (12+13) = 12/25 = 0.48 (48%)
 48% of those with placenta previa have APH
False Positive Rate (FPR)
 Probability (%) of Test Positive amongst all those that are outcome Negative
 In Our Example, How many of those with no Placenta Previa have APH
 FPR = False Positive / Outcome Negative = FP / (FP+TN) = 5 / (5+20) = 5/25 = 0.2 (20%)
 20% of those with no placenta previa has APH
True Negative Rate (TNR)
 Probability (%) of Test Negative amongst all those that are outcome Negative
 In Our Example, How many of those with no Placenta Previa also have no APH
 TNR = True Negative / Outcome Negative = TN / (FP+TN) = 20 / (5+20) = 20/25 = 0.8 (80%)
 Another way of calculation : TNR = 1FPR = 10.2 = 0.8 (80%)
 80% of those with no placenta previa do not have APH
False Negative Rate (FNR)
 Probability (%) of Test Negative amongst all those that are outcome Positive
 In Our Example, How many of those with Placenta Previa have no APH
 FNR = False Negative / Outcome Positive = FN / (FN+TP) = 13 / (13+7) = 13/25 = 0.52 (52%)
 Another way of calculation : FNR = 1TPR = 10.48 = 0.52 (52%)
 52% of those with placenta previa do not have APH
The Youden Index : A measurement of the overall quality of the test
 Youden Index = True Positive Rate  False Positive Rate. YI = TPR  FPR
 A perfect test will have TPR=1 and FPR=0, so YI = 1
 A perfect test that is the wrong way around will have FPR=1 and TPR=0, so YI = 1
 A useless test will have TPR=FPR, so YI=0
 From our data YI = TPRFPR = 0.480.2 = 0.28
Parameters for clinical use
These helps the clinicians to decide how to interpret a test result
Likelihoo Ratio for Test Positive (LR+)
 The ratio of Outcome Positive to Outcome Negative when the test is positive
 In Our Example, The ratio of the probability of Placenta previa to no placenta previa if Antepartum Haemorrhage occured
 LR+ = TPR / FPR = 0.48 / 0.2 = 2.4
 When antenatal haemorrhage is present, placenta praevia is 2.4 time (240%) as likely as no placenta praevia
Likelihoo Ratio for Test Negative (LR)
 The ratio of Outcome Positive to Outcome Negative when the test is negative
 In Our Example, The ratio of the probability of Placenta previa to no placenta previa when there is no Antepartum Haemorrhage
 LR = FNR / TNR = (1TPR) / (1FPR) = (10.48) / (10.2) = 0.52 / 0.8 = 0.65
 When antenatal haemorrhage is absent, placenta praevia is 0.65 times 65% as likely as no placenta praevia
Pretest and posttest probability
Once we have the Likelihood Ratios, we can use them in the future in the clinical situation
Pretest probability
 What we think the probability of Outcome Positive is, before we know the test
 We may know this from statistics collected in the past. e.g. We know that Placenta Previa occurs in
about 1% of out obstetric population (Pretest Probability = 0.01)
 We may not know, and use a general figure for unlikely, a probability of 5% (Pretest Probability = 0.05)
 We may decide it is as likely as not, and use 50% (Pretest Probability = 0.5)
 For our example, we will use 1% (0.01)
Posttest probability
 What we think the probability of Outcome Positive is, after we know the results of the test
 The method of calculation was established by Thomas Bayes, and generally termed Baysian Probability
 The calcultyion is as follows (explain only, no need to memorize is)
 Pretest odd = Pretest probability / (1  Pretest probability)
 Posttest odd = pretest odd * Likelihood Ratio
 Posttest probability = posttest odd / (1 + posttest odd)
Using our example to demonstrate the calculations
 The PreTest Probability is 1% (0.01)
 PreTest Odd = 0.01 / (10.01) = 0.0101
 When antepartum Haemorrhage is seen (Test Positive)
 The Likelihoo Ratio for Test Positive LR+ = 2.4
 Posttest odd = pretest odd * LR+ = 0.0101 * 2.4 = 0.024
 Posttest probability = posttest odd / (1 + posttest odd) = 0.024 / (1.024) = 0.024 (2.4%)
 the presence of antepartum haemorrhage increases the probability of placenta praevia from 1% to 2.4%
 When no antepartum Haemorrhage is seen (Test Negative)
 The Likelihoo Ratio for Test Positive LR = 0.65
 Posttest odd = pretest odd * LR+ = 0.0101 * 0.65 = 0.0066
 Posttest probability = posttest odd / (1 + posttest odd) = 0.0066 / (1.0066) = 0.0065 (0.7%)
 the absence of antepartum haemorrhage reduces the probability of placenta praevia from 1% to 0.7%
Now, if we work in an Obstetric Complication ward, and 30% of our mothers have placenta previa
 The PreTest Probability is 30% (0.3)
 PreTest Odd = 0.3 / (10.3) = 0.4286
 When antepartum Haemorrhage is seen (Test Positive)
 The Likelihoo Ratio for Test Positive LR+ = 2.4
 Posttest odd = pretest odd * LR+ = 0.4286 * 2.4 = 1.0286
 Posttest probability = posttest odd / (1 + posttest odd) = 1.0286 / (2.0286) = 0.507 (50.7%)
 the presence of antepartum haemorrhage increases the probability of placenta praevia from 30% to 50.7%
 When no antepartum Haemorrhage is seen (Test Negative)
 The Likelihoo Ratio for Test Positive LR = 0.65
 Posttest odd = pretest odd * LR+ = 0.4286 * 0.65 = 0.2786
 Posttest probability = posttest odd / (1 + posttest odd) = 0.2786 / (1.2786) = 0.2179 (21.8%)
 the absence of antepartum haemorrhage reduces the probability of placenta praevia from 30% to 21.8%
When there is more than one test
 We start with what we think the background probability is (Pretest Probability)
 The Likelihood Ratio of our first test produces the first Posttest Probability
 This PostTest Probability then becomes the Pretest Probability for the second Test
 The Likelihood Ratio of our second test produces the second Posttest Probability
 When using multiple tests, and providing the tests are independent of each other
 We can make probability estimates as the test results become available
 The same set of tests will produce the same estimate of probability, regardless of the order they are included
 There is no limit to the number of tests. The more tests we have, the more precise our probability extimate becomes
Receiver Operator Characteristics
Exercise
 Died  Lived 
Total  195  203 
Low Apgar Score  93  10 
High Apgar Score  102  193 
Q1. In a study using an Apgar Score at 5 minute of below 5 as low Apgar Score, the relationship between low Apgar
Score and subsequent neonatal death are shown in the table to the right.
Using Low Apgar Score as a test to predict neonatal death, calculate the True Positive
Rate, False Positive Rate, Likelihood Ratio Test Positive, and Likelihood Ratio Test Negative Values.
A 1. Click to show contents
True Positive Rate TPR = 93/195 = 0.4769
False Positive Rate FPR = 10 / 203 = 0.0493
Likelihood Ratio for test positive LR+ = 0.4769/0.0493 = 9.6815
Likelihood Ratio for test negative LR = (10.4769) / (10.0493) = 0.5502
 Died  Lived 
Total  300  267 
Respiratory Distress  200  25 
No Respiratory Distress  100  175 
Q2. In a study of babies admitted to the neonatal unit, the relationship between
respiratory distress and neonatal death are as shown in the table to the right.
Using respiratory distress as a test to predict neonatal death, calculate the True Positive
Rate, False Positive Rate, Likelihood Ratio Test Positive, and Likelihood Ratio Test Negative Values.
A 2. Click to show contents
True Positive Rate TPR = 200/300 = 0.6667
False Positive Rate FPR = 25 / 175 = 0.125
Likelihood Ratio for test positive LR+ = 0.6667/0.125 = 5.3333
Likelihood Ratio for test negative LR = (10.6667) / (10.125) = 0.381
Q3. Using the data in Q1 and Q2, estimate the probability of neonatal death
 When low Apgar Score and Respiratory Distress are both absent
 When low Apgar Score is present and Respiratory Distress is absent
 When low Apgar Score is absent and Respiratory Distress is present
 When low Apgar Score and respiratory distress are present
Calculate these if our overall death rate in the neonatal unit is 2%, 5%, or 10%
A 3. Click to show contents
Pretest probability = 0.02 (2%)
 Low Apgar Score absent, LR = 0.5502, postprobability= 0.0111 (1.1%)
 With pretest probability = 0.0111
 Respiratory distress absent, LR = 0.381, posttest probability = 0.0043 (0.4%)
 Respiratory distress Present, LR+ = 5.3333, posttest probability = 0.0565 (5.7%)
 Low Apgar Score present, LR+ = 9.6815, postprobability= 0.165 (16.5%)
 With pretest probability = 0.165
 Respiratory distress absent, LR = 0.381, posttest probability = 0.07 (7.0%)
 Respiratory distress Present, LR+ = 5.3333, posttest probability = 0.5131 (51.3%)
Pretest probability = 0.05 (5%)
 Low Apgar Score absent, LR = 0.5502, postprobability= 0.0281 (2.8%)
 With pretest probability = 0.0281
 Respiratory distress absent, LR = 0.381, posttest probability = 0.0109 (1.1%)
 Respiratory distress Present, LR+ = 5.3333, posttest probability = 0.1336 (13.4%)
 Low Apgar Score present, LR+ = 9.6815, postprobability= 0.3376 (33.8%)
 With pretest probability = 0.3376
 Respiratory distress absent, LR = 0.381, posttest probability = 0.1626 (16.3%)
 Respiratory distress Present, LR+ = 5.3333, posttest probability = 0.7311 (73.1%)
Pretest probability = 0.1 (10%)
 Low Apgar Score absent, LR = 0.5502, postprobability= 0.0576 (5.8%)
 With pretest probability = 0.0576
 Respiratory distress absent, LR = 0.381, posttest probability = 0.0228 (2.3%)
 Respiratory distress Present, LR+ = 5.3333, posttest probability = 0.2458 (24.6%)
 Low Apgar Score present, LR+ = 9.6815, postprobability= 0.5182 (51.8%)
 With pretest probability = 0.5182
 Respiratory distress absent, LR = 0.381, posttest probability = 0.2907 (29.1%)
 Respiratory distress Present, LR+ = 5.3333, posttest probability = 0.8515 (85.2%)
Height  TPR  FPR  LR+  LR  YI 
162.0cms  1.00  0.96  1.04  0.00  0.04 
161.5cms  1.00  0.92  1.09  0.00  0.08 
161.0cms  1.00  0.84  1.19  0.00  0.16 
160.0cms  0.96  0.84  1.14  0.25  0.12 
159.0cms  0.96  0.76  1.26  0.17  0.20 
158.5cms  0.92  0.68  1.35  0.25  0.24 
158.0cms  0.92  0.48  1.92  0.15  0.44 
157.5cms  0.88  0.48  1.83  0.23  0.40 
157.0cms  0.88  0.40  2.20  0.20  0.48 
156.5cms  0.80  0.36  2.22  0.31  0.44 
156.0cms  0.68  0.36  1.89  0.50  0.32 
155.5cms  0.60  0.24  2.50  0.53  0.36 
155.0cms  0.60  0.20  3.00  0.50  0.40 
154.0cms  0.48  0.20  2.40  0.65  0.28 
153.5cms  0.40  0.12  3.33  0.68  0.28 
153.0cms  0.36  0.04  9.00  0.67  0.32 
152.5cms  0.28  0.04  7.00  0.75  0.24 
152.0cms  0.28  0.00  0.00  0.72  0.28 
151.5cms  0.24  0.00  0.00  0.76  0.24 
151.0cms  0.20  0.00  0.00  0.80  0.20 
150.5cms  0.16  0.00  0.00  0.84  0.16 
150.0cms  0.12  0.00  0.00  0.88  0.12 
149.0cms  0.08  0.00  0.00  0.92  0.08 
147.5cms  0.00  0.00  0.00  1.00  0.00 
Q4. The Likelihood ratios for
various maternal height values to predict Caesarean Section are presented in the table to the right.
 Calculate the probability of Caesarean Section for women who are
 157cms or more in height
 less than 155cms in height
 Calculate these in
 in a HA hospital where overall C.S. rate is 25%
 in a private hospital where the overall C.S. rate is 40%
A 4. Click to show contents
In public hospital, overall C.S. rate = 25%, pretest probability = 0.25
 For women 157 or more LR = 0.23, posttest probability = 0.0712 (7.1%)
 For women less than 155cms LR+ = 3.0, posttest probability = 0.5 (50%)
In private hospital, overall C.S. rate = 40%, pretest probability = 0.4
 For women 157 or more LR = 0.23, posttest probability = 0.1328 (13.3%)
 For women less than 155cms LR+ = 3.0, posttest probability = 0.6667 (66.7%)


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