Likelihood Ratio Method and Algorithmic Differentiation: Fast Second Order Greeks

2014 ◽  
Author(s):  
Luca Capriotti
Keyword(s):  
Likelihood Ratio ◽  
Second Order ◽  
Ratio Method ◽  
Algorithmic Differentiation ◽  
Likelihood Ratio Method

Predicting Fetal Chromosome Anomalies in the First Trimester Using Pregnancy Associated Plasma Protein-A: A Comparison of Statistical Methods

1993 ◽  
Vol 32 (02) ◽  
pp. 175-179 ◽  
Author(s):  
B. Brambati ◽  
T. Chard ◽  
J. G. Grudzinskas ◽  
M. C. M. Macintosh
Keyword(s):  
Logistic Regression ◽  
General Population ◽  
Likelihood Ratio ◽  
False Positive ◽  
False Positive Rate ◽  
Ratio Method ◽  
Detection Rates ◽  
Gaussian Distributions ◽  
Positive Rate ◽  
Likelihood Ratio Method

Abstract:The analysis of the clinical efficiency of a biochemical parameter in the prediction of chromosome anomalies is described, using a database of 475 cases including 30 abnormalities. A comparison was made of two different approaches to the statistical analysis: the use of Gaussian frequency distributions and likelihood ratios, and logistic regression. Both methods computed that for a 5% false-positive rate approximately 60% of anomalies are detected on the basis of maternal age and serum PAPP-A. The logistic regression analysis is appropriate where the outcome variable (chromosome anomaly) is binary and the detection rates refer to the original data only. The likelihood ratio method is used to predict the outcome in the general population. The latter method depends on the data or some transformation of the data fitting a known frequency distribution (Gaussian in this case). The precision of the predicted detection rates is limited by the small sample of abnormals (30 cases). Varying the means and standard deviations (to the limits of their 95% confidence intervals) of the fitted log Gaussian distributions resulted in a detection rate varying between 42% and 79% for a 5% false-positive rate. Thus, although the likelihood ratio method is potentially the better method in determining the usefulness of a test in the general population, larger numbers of abnormal cases are required to stabilise the means and standard deviations of the fitted log Gaussian distributions.

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