Prediction statistics Prediction generally True and false, positives and negatives Quality of a prediction Usefulness of a prediction Prediction goes Bayesian Use of prediction statistics

Prediction Three major reasons for doing research –To understand the processes of nature –To be able to predict future event –To be able to control future events Three major activities in medical care –To make a diagnosis –To define the prognosis –To intervene and alter the progress of events Clinical prediction –Signs, symptoms, tests results –Diagnosis, prognosis

Types of prediction Using one observation (test) to predict another observation (outcome) –Both test and outcome are continuous measurements e.g. Using age to predict height Regression analysis, curve fitting –Test is a criteria and outcome a measurement e.g. using sex to predict weight Confidence intervals between two means –Both test and outcome are criteria e.g. using the presence of calcification in a mammogram to predict the presence of a carcinoma Prediction statistics –Test is a continuous measurement and outcome a criteria E.g. using body temperature to predict the presence of an infection Receiver Operator Characteristics

Prediction statistics Prediction generally True and false, positives and negatives Quality of a prediction Usefulness of a prediction Prediction goes Bayesian Use of prediction statistics

Prediction statistics To evaluate how one criteria can predict another from data collected The number of cases with different combinations of test and outcome results collated

Prediction statistics Prediction generally True and false, positives and negatives Quality of a prediction Usefulness of a prediction Prediction goes Bayesian Use of prediction statistics

Quality of test Sensitivity : the proportion of test positives amongst those outcome positive Specificity : the proportion of test negatives amongst those outcome negative

Prediction statistics Prediction generally True and false, positives and negatives Quality of a prediction Usefulness of a prediction Prediction goes Bayesian Use of prediction statistics

Usefulness of a test Positive Predictive Value : the proportion of outcome positives amongst those test positive Negative Predictive Value : the proportion of outcome negatives amongst those test negative

Usefulness of a test What the user want to know –How likely will outcome be + if test is + –How likely will outcome be - if test is – Predictive values are prevalence dependent –Positive predictive value is 0 (100%) if prevalence is 1 (100%) and 0 (0%) if prevalence is 0 (0%) –Negative predictive value is 0 (0%) if prevalence is 1 100% and 1 (100%) if prevalence is 0 (0%) –The shape of these curves depend on a complex relationship between Sensitivity, Specificity, and prevalence

Prevalence Positive Predictive Value Negative Predictive Value Sensitivity = 0.8 Specificity = 0.8

Prediction statistics Prediction generally True and false, positives and negatives Quality of a prediction Usefulness of a prediction Prediction goes Bayesian Use of prediction statistics

Prediction as probabilities Pre-test probability = Prevalence Post-test probability (test +) = Positive Predictive Value Post-test probability (test -) = 1 - Negative Predictive Value

Bayes Theorem Perceptions of probability is altered by experience or observations –Final probability = Preconceived probability x Bayes factor Prediction can be presented as an example of Bayes model –Post-test probability = function (pre-test proabability, Bayes factor)

Quality of test as Bayes factor Likelihood Ratio Likelihood Ratio –The ratio of probabilities of getting a positive test, between outcome positives and outcome negatives –The more LR>1, the more likely outcome + –The more LR<1, the less likely outcome - Likelihood Ratio + Test –Likelihood Ratio for those test + –LR+ = Sensitivity / (1 – Specificity) Likelihood Ratio – Test –Likelihood Ratio for those test – –LR - = (1-Sensitivity) / Specificity

Using Likelihood Ratio Converting pre-test probability to Post-test probability

Prediction statistics Prediction generally True and false, positives and negatives Quality of a prediction Usefulness of a prediction Prediction goes Bayesian Use of prediction statistics

The use of prediction statistics Development of diagnostic tools and tests –Tested clinically to evaluate quality This is usually under controlled conditions Often in a high prevalence population to get sufficient sample size –Quality of the test published as Sensitivity and Specificity, or increasingly commonly as Likelihood Ratios Interpretation of statistics –Using local prevalence (pre-test probability) to convert quality measurements into post-test probabilities