Calculation of roc curves in multidimensional likelihood ratio based screening with Down's syndrome as a special case

1998 ◽  
Vol 5 (2) ◽  
pp. 57-62 ◽  
Author(s):  
S O Larsen ◽  
M Christiansen ◽  
B Nørgaard-Pedersen
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Programming Language ◽  
A Priori ◽  
Roc Curves ◽  
Likelihood Ratios ◽  
Screening Performance ◽  
Log Likelihood ◽  
Special Knowledge ◽  
Special Case

Objectives The development of algorithms and computer programs for the analysis of screening performance in situations with multiple normally (Gaussian) distributed selection markers and a priori risks depending on a stratification of the population. Methods The S-PLUS programming language was used to construct programs producing distributions of log likelihood ratios based on the Monte Carlo simulation. These distributions were used to construct programs for the calculation of roc curves, including a possible stratification of the population. Results S-PLUS programs for the analysis of screening performance are listed and described. The programs can be used without any special knowledge of S-PLUS. An example of the use of the programs is given.

scholarly journals Determining patient abdomen thickness from a single digital radiograph with a computational model: clinical results from a proof of concept study

2020 ◽  
Vol 93 (1111) ◽  
pp. 20200010
Author(s):  
Mark Worrall ◽  
Sarah Vinnicombe ◽  
David Sutton
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Computational Model ◽  
A Priori ◽  
Clinical Results ◽  
A Priori Knowledge ◽  
Proof Of Concept ◽  
Radiographic Image ◽  
X Ray ◽  
Digital Radiograph

Objective: A computational model has been created to estimate the abdominal thickness of a patient following an X-ray examination; its intended application is assisting with patient dose audit of paediatric X-ray examinations. This work evaluates the accuracy of the computational model in a clinical setting for adult patients undergoing anteroposterior (AP) abdomen X-ray examinations. Methods: The model estimates patient thickness using the radiographic image, the exposure factors with which the image was acquired, a priori knowledge of the characteristics of the X-ray unit and detector and the results of extensive Monte Carlo simulation of patient examinations. For 20 patients undergoing AP abdominal X-ray examinations, the model was used to estimate the patient thickness; these estimates were compared against a direct measurement made at the time of the examination. Results: Estimates of patient thickness made using the model were on average within ±5.8% of the measured thickness. Conclusion: The model can be used to accurately estimate the thickness of a patient undergoing an AP abdominal X-ray examination where the patient’s size falls within the range of the size of patients used to create the computational model. Advances in knowledge: This work demonstrates that it is possible to accurately estimate the AP abdominal thickness of an adult patient using the digital X-ray image and a computational model.

Graphical presentation of distributions of risk in screening

2005 ◽  
Vol 12 (3) ◽  
pp. 155-160 ◽  
Author(s):  
J K Morris ◽  
N J Wald
Keyword(s):  
Relative Frequency ◽  
Gaussian Approximation ◽  
Gaussian Model ◽  
Likelihood Ratios ◽  
Frequency Distributions ◽  
Risk Estimates ◽  
Screening Performance ◽  
Log Likelihood ◽  
Standard Deviations ◽  
Screening Marker

Objective: The screening performance of tests involving multiple markers is usually presented visually as two Gaussian relative frequency distributions of risk, one curve relating to affected and the other to unaffected individuals. If the distribution of the underlying screening markers is approximately Gaussian, risk estimates based on the same markers will usually also be approximately Gaussian. However, this approximation sometimes fails. Here we examine the circumstances when this occurs. Setting: A theoretical statistical analysis. Methods: Hypothetical log Gaussian relative distributions of affected and unaffected individuals were generated for three antenatal screening markers for Down's syndrome. Log likelihood ratios were calculated for each marker value and plots of the relative frequency distributions were compared with plots of Gaussian distributions based on the means and standard deviations of these log likelihood ratios. Results: When the standard deviations of the distributions of a perfectly Gaussian screening marker are similar in affected and unaffected individuals, the distributions of risk estimates are also approximately Gaussian. If the standard deviations differ materially, incorrectly assuming that the distributions of the risk estimates are Gaussian creates a graphical anomaly in which the distributions of risk in affected and unaffected individuals plotted on a continuous risk scale intersect in two places. This is theoretically impossible. Plotting the risk distributions empirically reveals that all individuals have an estimated risk above a specified value. For individuals with more extreme marker values, the risk estimates reverse and increase instead of continuing to decrease. Conclusion: It is useful to check whether a Gaussian approximation for the distribution of risk estimates based on a screening marker is valid. If the value of the marker level at which risk reversal occurs lies within the set truncation limits, these may need to be reset, and a Gaussian model may be inappropriate to illustrate the risk distributions.

scholarly journals Corrigendum to ``Descriptive Measures of Poisson-Lomax Distribution''

2020 ◽  
Vol 43 (2) ◽  
pp. 345-353
Author(s):  
Khushnoor Khan
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Probability Distribution ◽  
Programming Language ◽  
Numerical Results ◽  
Due Diligence ◽  
Mean Values ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
The Mean

This corrigendum focuses on the correction of numerical results derived from Poisson-Lomax Distribution (PLD) originally proposed by Al-Zahrani & Sagor (2014). Though the mathematical properties and derivations by Al-Zahrani & Sagor (2014) were immaculate but during the execution ofthe R codes using Monte Carlo simulation some anomalies occurred in the calculation of the mean values. The same  anomalies are addressed in thepresent corrigendum. The outcome of the corrigendum will provide basic guidelines for the academia and reviewers of various journals to match thenumerical results with the shape of the probability distribution under study. The results will also emphasize the fact that code writing is a cumbersome process and due diligence be exercised in executing the codes using any programming language. Relevant R codes are appended in Appendix 'A'.

scholarly journals A Simple Strategy for Mitigating the Effect of Data Variability on the Identification of Active Chemotypes from High-Throughput Screening Data

2007 ◽  
Vol 12 (2) ◽  
pp. 276-284 ◽  
Author(s):  
Stephen R. Johnson ◽  
Ramesh Padmanabha ◽  
Wayne Vaccaro ◽  
Mark Hermsmeier ◽  
Angela Cacace ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
High Throughput ◽  
High Throughput Screening ◽  
A Priori ◽  
Response Curves ◽  
Simple Strategy ◽  
Data Variability ◽  
The Individual ◽  
Protein Supply

Among the several goals of a high-throughput screening campaign is the identification of as many active chemotypes as possible for further evaluation. Often, however, the number of concentration response curves (e.g., IC50s or Kis) that can be collected following a primary screen is limited by practical constraints such as protein supply, screening workload, and so forth. One possible approach to this dilemma is to cluster the hits from the primary screen and sample only a few compounds from each cluster. This introduces the question as to how many compounds must be selected from a cluster to ensure that an active compound is identified, if it exists at all. This article seeks to address this question using a Monte Carlo simulation in which the dependence of the success of sampling is directly linked to screening data variability. Furthermore, the authors demonstrate that the use of replicated compounds in the screening collection can easily assess this variability and provide a priori guidance to the screener and chemist as to the extent of sampling required to maximize chemotype identification during the triage process. The individual steps of the Monte Carlo simulation provide insight into the correspondence between the percentage inhibition and eventual IC50 curves.

scholarly journals Maximum logq Likelihood Estimation for Parameters of Weibull Distribution and Properties: Monte Carlo Simulation

2021 ◽  
Author(s):  
Mehmet Niyazi Cankaya ◽  
Roberto Vila
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Weibull Distribution ◽  
Mean Squared Error ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Likelihood Method ◽  
P Value ◽  
Test Statistic ◽  
Log Likelihood

Abstract The maximum logq likelihood estimation method is a generalization of the known maximum log likelihood method to overcome the problem for modeling non-identical observations ( inliers and outliers). The parameter $q$ is a tuning constant to manage the modeling capability. Weibull is a flexible and popular distribution for problems in engineering. In this study, this method is used to estimate the parameters of Weibull distribution when non-identical observations exist. Since the main idea is based on modeling capability of objective function p(x; ʘ) = logq [f(x; ʘ)], we observe that the finiteness of score functions cannot play a role in the robust estimation for inliers . The properties of Weibull distribution are examined. In the numerical experiment, the parameters of Weibull distribution are estimated by logq and its special form, log , likelihood methods if the different designs of contamination into underlying Weibull distribution are applied. The optimization is performed via genetic algorithm. The modeling competence of p(x; ʘ) and insensitiveness to non-identical observations are observed by Monte Carlo simulation. The value of $q$ can be chosen by use of the mean squared error in simulation and the $p$ -value of Kolmogorov - Smirnov test statistic used for evaluation of fitting competence. Thus, we can overcome the problem about determining of the value of $q$ for real data sets.

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