Please note : the data presented in all course material for the statistical module are
generated by computers to demonstrate the methodologies, and should not be confused with
actual clinical information
Introduction
Exercises
Prediction of neonatal Death : 4 related questions
Questions 1_1 : Low Apgar Scores : click to show contents
 Died  Lived 
Total  195  203 
Low Apgar Score  93  10 
High Apgar Score  102  193 
We wish to us the Apgar Score 5 minutes after birth as a predictor of neonatal death. We define a low Apgar Score as less than 5.
We review our medical records and collected 195 babies who died neonatally and 203 that did not died, and reviewed their Apgar Scores. The results are as shown in the table to the right.
 Calculate the True and False Positive and Negative Rates using low Apgar Scores to predict neonatal death
 Calculate the Likelihood Ratios for Test Positive (low Apgar Score) and Test Negative (high Apgar Score)
 Calculate the probability of neonatal death for low and high Apgar Scores in a hospital where the neonatal death rate is 1%, 5%, and 10%.
Answers 1_1 : click to show contents
Using low Apgar Score to predict neonatal death based on the data provided
 The True Positive Rate = 0.4769 (47.7%)
The False Positive Rate FPR = 0.0493 (4.9%)
The False Negative Rate FNR = 0.5231 (52.3%)
The True Negative Rate TNR = 0.9507 (55.1%)
 The Likelihood Ratio for Test Positive (Low Apgar Score) = 9.6815
The Likelihood Ratio for Test Negative (high Apgar Score) = 0.5502
 In a hospital with a neonatal death rate of 1% (Pretest Probability = 0.01)
The probability of neonatal death when low Apgar Score is present = 0.0891 (8.9%)
The probability of neonatal death when low Apgar Score is absent = 0.0055 (0.6%)
 In a hospital with a neonatal death rate of 5% (Pretest Probability = 0.05)
The probability of neonatal death when low Apgar Score is present = 0.3376 (33.8%)
The probability of neonatal death when low Apgar Score is absent = 0.0281 (2.8%)
 In a hospital with a neonatal death rate of 10% (Pretest Probability = 0.1)
The probability of neonatal death when low Apgar Score is present = 0.5182 (51.8%)
The probability of neonatal death when low Apgar Score is absent = 0.0576 (5.8%)
Questions 1_2 : Tachypnoea and neonatal death : click to show contents
Questions 1_3 : Birth weight and neonatal death : click to show contents
Questions 1_4 : Sequential Prediction of Neonatal Death : click to show contents
Prediction of success in IVF : 4 related questions
Questions 2_1 : Laboratory quality and IVF success: click to show contents
 Success  Failure 
Total  195  203 
High Quality  78  31 
Low Quality  117  172 
We wish to predict the success rate (per cycle) of IVF from different laboratories. A high quality laboratory has formally qualified staff with defined duties, carrying out best practice protocols, and instituted quality assurance. A poor quality laboratory lack these formal quality related practices.
We sample successful and failed cycles from different laboratories, and obtained the data as shown in the table to the right.
 Calculate the True and False Positive and Negative Rates using high quality to predict success in IVF
 Calculate the Likelihood Ratios for Test Positive (high quality) and Test Negative (low quality)
 Calculate the probability of IVF success in populations where the overall success rate is 10%, 20%, 30%, and 40%
Answers 2_1 : click to show contents
Using quality of the laboratory to predict successful IVF
 The True Positive Rate = 0.4 (40.0%)
The False Positive Rate FPR = 0.1527 (15.3%)
The False Negative Rate FNR = 0.6 (60.0%)
The True Negative Rate TNR = 0.8473 (84.7%)
 The Likelihood Ratio for Test Positive (high quality laboratory) = 2.6194
The Likelihood Ratio for Test Negative (low quality laboratory) = 0.7081
 In a population of expected 10% success rate (Pretest Probability = 0.1)
The probability of success in a high quality laboratory = 0.2254 (22.5%)
The probability of success in a low quality laboratory = 0.0729 (7.3%)
 In a population of expected 20% success rate (Pretest Probability = 0.2)
The probability of success in a high quality laboratory = 0.3957 (39.6%)
The probability of success in a low quality laboratory = 0.1504 (15.0%)
 In a population of expected 30% success rate (Pretest Probability = 0.3)
The probability of success in a high quality laboratory = 0.5289 (52.9%)
The probability of success in a low quality laboratory = 0.2328 (23.3%)
 In a population of expected 40% success rate (Pretest Probability = 0.4)
The probability of success in a high quality laboratory = 0.6359 (63.6%)
The probability of success in a low quality laboratory = 0.3207 (32.1%)
Questions 2_2 : Cinical complexity and IVF Success : click to show contents
 Success  Failure 
Total  300  267 
Simple  100  25 
Complex  200  175 
Success rate in IVF depends to some extent on the causes of infertility. Patients can be classified as having a simple causation, such as tubal obstruction, or complex with multiple causes, previous failures, and complications.
We wish to predict IVF success using the patient's clinical background, and collected data from our records, the results are shown in the table to the right.
 Calculate the True and False Positive and Negative Rates using simple clinical background to predict IVF
 Calculate the Likelihood Ratios for Test Positive (simple) and Test Negative (complex)
 Calculate the probability of IVF success for simple and complex clinical background in a population with expected success rate of 10%, 20%, 30%, and 40%.
Answers 2_2 : click to show contents
Using simple or complex clinical background to predict IVF success
 The True Positive Rate = 0.3333 (33.3%)
The False Positive Rate FPR = 0.125 (12.5%)
The False Negative Rate FNR = 0.6667 (66.7%)
The True Negative Rate TNR = 0.875 (87.5%)
 The Likelihood Ratio for Test Positive (simple) = 2.6667
The Likelihood Ratio for Test Negative (complex) = 0.7619
 In a population with an overall success rate of 10% (Pretest Probability = 0.1)
The probability of success with a simple clinical background = 0.2286 (22.9%)
The probability of success with a complex clinical background = 0.078 (7.8%)
 In a population with an overall success rate of 20% (Pretest Probability = 0.2)
The probability of success with a simple clinical background = 0.4 (40.0%)
The probability of success with a complex clinical background = 0.16 (16.0%)
 In a population with an overall success rate of 30% (Pretest Probability = 0.3)
The probability of success with a simple clinical background = 0.5333 (53.3%)
The probability of success with a complex clinical background = 0.2462 (24.6%)
 In a population with an overall success rate of 40% (Pretest Probability = 0.4)
The probability of success with a simple clinical background = 0.64 (64.0%)
The probability of success with a complex clinical background = 0.3368 (33.7%)
Questions 2_3 : Age and IVF success : click to show contents
Questions 2_4 : Sequential Prediction of IVF Success : click to show contents
