OBGYN MSc Stat Module (2016-2018) :
Contents_5. Predictions and Tests
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 Binary Tests Pre-test and Post-test Probability Receiver Operator Characteristics
The statistics of prediction consists of two major domains.

The first domain is to develop a prediction model, so that one or more observations (tests) can be used to predict an event of interest (outcome). This is often technically complex, and currently a rapidly changing and advancing field of numerical research under the general category of artificial intelligence. This domain is not be covered in this module

The second domain is to evaluate the quality of a particular prediction model, and create an algorithm to use it in the clinical setting. This is the domain that will be covered in this module, and the programs used are in StatPgm 5a. Tests : Binary Tests and StatPgm 5b. Tests : Receiver Operator Characteristics (ROC)

The model The model is to use a Test to predict an outcome

  • The Outcome is an event of interest, and in a test is what we set out to diagnose or predict
    • An outcome can be a measurement. e.g. how tall will the person be when he grows up
    • An outcome can be a set of alternatives. e.g. Is the patient suffering from urinary infection, appendicitis, or food poisoning
    • An outcome can be binary, no/yes, false/true, negative/positive. e.g. Will this delivery require a Caesarean Section
  • The Test is an observation we use to predict an outcome
    • A test can be a measurement. e.g. the mother's height to predict a need for Caesarean Section, the oestrogen level to predict ovulation
    • A test can be binary, no/yes, false/true, negative/positive. e.g. vaginal bleeding to predict Placenta Previa, abnormal nuchal translucency to predict chromosomal abnormality in a baby.
  • The Prediction is any process, logical, mathematical, statistical, that links the test to the outcome
    • Using a measurement test to predict a measurement outcome uses the regression analysis, which is covered in Contents_2b. Correlation and Regression, and will not be further covered here
    • Using a binary test to predict a measurement outcome uses the 95% confidence interval of difference between two groups, which is covered in Contents_3. Comparing Two Groups, and will not be further covered here
    • Binary Test to predict binary outcome. The most commonly used model, will be discussed in detail in this page
    • Measurement test to predict binary outcome, the Receiver Operator Characteristics, will be discussed in detail in this page
Terms commonly used in evaluating tests
  • Outcome is the event of interest we wish to predict.
    • Outcome Positive (OPos) is when the event eventuates.
    • Outcome Negative (ONeg) is when the event fails to eventuates.
  • Test is the observation that we use to predict an Outcome.
    • Test Positive (TPos) in a binary test is when the test result corresponds with what we use to predict Outcome Positive
    • Test Negative (TNeg) in a binary test is when the test result does not correspond with what we use to predict Outcome Positive
  • Reference Data is a selected dataset containing appropriate numbers of OPos and ONeg, which we will use to evaluate the quality of prediction. The number of cases in this set are divided into the following
    • True Positives (TP) is the number of cases that are Test Positive and Outcome Positive
    • False Positives (FP) is the number of cases that are Test Positive but Outcome Negative
    • False Negatives (FN) is the number of cases that are Test Negative but Outcome Positive
    • True Negatives (TN) is the number of cases that are Test Negative and Outcome Negative
    From these the following quality parameters can be calculated
    • True Positive Rate (TPR) is the proportion of Outcome Positives that are also Test Positive. TPR = TP / (TP+FN). The term Sensitivity is the same as True Positive Rate
    • True Negative Rate (TNR) is the proportion of Outcome Negatives that are also Test Negative. TNR = TN / (TN+FP). The term Specificity is the same as True Negative Rate
    • False Positive Rate (FPR) is the proportion of Outcome Negatives that are Test Positive. FPR = FP / (FP+TN) = 1-TNR.
    • False Negative Rate (FNR) is the proportion of Outcome Positives that are Test Negative. FNR = FN / (FN+TP) = 1-TPR.
    • Youden's Index (YI) is a summary indicator of overall quality of prediction, assuming TPR and FPR to be of equal importance. YI = (TPR+TNR)/2
    • Likelihood Ratio for Test Positive (LR+) is the ratio of True and False Positive Rates, LR+ = TPR/FPR, and represents the ratio of probabilities between Outcome Positive and Outcome Negative, when the test is Test Positive
    • Likelihood Ratio for Test Negative (LR-) is the ratio of False and True Negative Rates, LR- = FNR/TNR, and represents the ratio of probabilities between Outcome Positive and Outcome Negative, when the test is Test Negative