Description

Computes measures of diagnostic test performance from count data presented in a 2 × 2 table.

Usage

n_{D+ | T+}: Number of outcome positive, test positive individuals.
n_{D- | T+}: Number of outcome negative, test positive individuals.
n_{D+ | T-}: Number of outcome positive, test negative individuals.
n_{D- | T-}: Number of outcome negative, test negative individuals.

References

Altman DG, Machin D, Bryant TN, Gardner MJ (2000). Statistics with Confidence, second edition. British Medical Journal, London, pp. 28 - 29.

Brown L, Cai T, Dasgupta A (2001). Interval estimation for a binomial proportion. Statistical Science 16: 101 - 133.

Clopper C, Pearson E (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26: 404 - 413.

Collett D (2003). Modelling Binary Data. Chapman & Hall/CRC, Boca Raton Florida, pp. 24.

Rothman KJ (2012). Epidemiology An Introduction. Oxford University Press, London, pp. 164 - 175.

Simel D, Samsa G, Matchar D (1991). Likelihood ratios with confidence: Sample size estimation for diagnostic test studies. Journal of Clinical Epidemiology 44: 763 - 770.

Wilson EB (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association 22: 209 - 212.

Examples

A new diagnostic test

A new diagnostic test was trialled on 1586 patients. Of 744 patients that were disease positive, 670 were test positive. Of 842 patients that were disease negative, 640 were test negative. What is the diagnostic sensitivity, specificity and positive likelihood ratio of the new test?

Apparent prevalence: 0.55 (95% CI 0.53 to 0.57)
True prevalence: 0.47 (95% CI 0.44 to 0.49)

Sensitivity: 0.90 (95% CI 0.88 to 0.92)
Specificity: 0.76 (95% CI 0.73 to 0.79)

Positive predictive value: 0.77 (95% CI 0.74 to 0.80)
Negative predictive value: 0.90 (95% CI 0.87 to 0.92)

Positive likelihood ratio: 3.75 (95% CI 3.32 to 4.29)
Negative likelihood ratio: 0.13 (95% CI 0.11 to 0.16)

Description

Computes the post-test probability of disease given the pre-test probability and sensitivity and specificity of the diagnostic test.

Usage

Se: Diagnostic sensitivity of the test.
Sp: Diagnostic specificity of the test.

References

Caraguel C, Vanderstichel R (2013). The two-step Fagan's nomogram: ad hoc interpretation of a diagnostic test result without calculation. Evidence Based Medicine 18: 125 - 128.

Hunink M, Glasziou P (2001). Decision Making in Health and Medicine - Integrating Evidence and Values. Cambridge University Press, pp. 128 - 156.

Examples

Hypothyroidism in dogs

You are presented with a dog with lethargy, exercise intolerance, weight gain and bilaterally symmetric truncal alopecia. You are suspicious of hypothyroidism and take a blood sample to measure basal serum thyroxine (T4).

You believe that around 5% of dogs presented to your clinic with a signalment that includes general debility have hypothyroidism. The serum T4 has a sensitivity of 0.89 and specificity of 0.85 for diagnosing hypothyroidism in the dog. The laboratory reports a serum T4 concentration of 18.0 nmol/L (reference range 19.0 to 58.0 nmol/L) which you interpret as a `positive' test result. What is the post-test probability that this dog is hypothyroid?

Positive likelihood ratio: 5.93
Post-test probability of outcome: 0.24

There is a 0.24 chance that your patient is actually hypothyroid based on the serum T4 test results.

Description

Calculates the sensitivity and specificity of two or three diagnostic tests interpreted in series or parallel.

Usage

Details

For series interpretation a subject is declared test positive if both of the tests performed return a positive result. For parallel interpretation a subject is declared test positive if one of the tests performed return a positive result. Intepreting test results in series increases diagnostic specificity. Interpreting test results in parallel increases diagnostic sensitivity.

For the two test situation covariance for positive and negative test results accounts for the situation where test results might be `similar' due to the agent (e.g., antibody, antigen) they detect. For example, the results of two ELISAs are likely to be similar because they detect an individual's immune response to the presence of an anitgen.

References

Dohoo I, Martin S, Stryhn H (2009). Veterinary Epidemiologic Research. AVC Inc Charlottetown, Prince Edward Island, Canada.

Gardner I, Stryhn H, Lind P, Collins M (2000). Conditional dependence between tests affects the diagnosis and surveillance of animal diseases. Preventive Veterinary Medicine 45: 107 - 122.

Jones G, Johnson W, Hanson T, Christensen R (2010). Identifiability of models for multiple diagnostic testing in the absence of a gold standard. Biometrics 66: 855 - 863. DOI: 10.1111/j.1541-0420.2009.01330.x.

Martin S, Meek A, Willeberg P (1987). Veterinary Epidemiology Principles and Methods. Iowa State University Press Ames.

McClure C, Hammell K, Stryhn H, Dohoo I, Hawkins L (2005). Application of surveillance data in evaluation of diagnostic tests for infectious salmon anemia. Diseases of Aquatic Organisms 63: 119 - 127. DOI: 10.3354/dao063119.

Toft N, Akerstedt J, Tharaldsen J, Hopp P (2007). Evaluation of three serological tests for diagnosis of Maedi-Visna virus infection using latent class analysis. Veterinary Microbiology 120: 77 - 86.

Examples

An IFAT and PCR are to be used to diagnose infectious salmon anaemia (IFA). The diagnostic sensitivity and specificity of the IFAT is 0.784 (95% CI 0.716 to 0.842) and 0.951 (95% CI 0.930 to 0.967), respectively. The diagnostic sensitivity and specificity of the PCR is 0.926 (95% CI 0.877 to 0.960) and 0.979 (95% CI 0.964 to 0.989), respectively. It is known that the two tests are dependent, with positive and negative covariances of 0.035 and -0.001. What is the expected sensitivity and specificity if the tests are to interpreted in parallel?

Interpreting test results in parallel and accounting for the lack of test indepdendence returns a diagnostic sensitivity of 0.949 and diagnostic specificity of 0.903.

Description

A function to return shape1 and shape2 parameters for a beta distribution, based on expert elicitation.

Usage

The beta distribution has two parameters: shape1 and shape2, corresponding to a and b in the original version of BetaBuster. If r equals the number of times an event has occurred after n trials, shape1 = (r + 1)} and shape2} = {(n - r + 1)}.

References

Christensen R, Johnson W, Branscum A, Hanson TE (2010). Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians. Chapman and Hall, Boca Raton.

Gardner I, Stryhn H, Lind P, Collins M (2000). Conditional dependence between tests affects the diagnosis and surveillance of animal diseases. Preventive Veterinary Medicine 45: 107 - 122.

Su C-L, Johnson W (2014) Beta Buster. Software for obtaining parameters for the Beta distribution based on expert elicitation. URL: https://cadms.vetmed.ucdavis.edu/diagnostic/software.

Examples

Diagnostic tests

If a scientist is asked for their best guess for the diagnostic sensitivity of a particular test and the answer is 0.90, and if they are also willing to assert that they are 80% certain that the sensitivity is greater than 0.75, what are the shape1 and shape2 parameters for a beta distribution satisfying these constraints?

Shape1: 9.875.
Shape2: 1.986.

Description

Calculates shape and scale parameters for the gamma distribution.

Usage

References

Examples

Description

Computes apparent prevalence and true prevalence on the basis of diagnostic test results. Two methods are used to estimate true prevalence: (1) the Rogan-Gladen estimator; and (2) Bayesian methods.

Usage

Se: Diagnostic sensitivity of the test.
Sp: Diagnostic specificity of the test.
TP: True prevalence.

Details

This function uses apparent prevalence, test sensitivity and test specificity to estimate true prevalence (after Rogan and Gladen, 1978). Confidence intervals for the apparent and true prevalence estimates are based on code provided by Reiczigel et al. (2010).

If apparent prevalence is less than (1 - diagnostic test specificity) the Rogan Gladen estimate of true prevalence will be less than zero and if the apparent prevalence is greater than the diagnostic test sensitivity the Rogan Gladen estimate of true prevalence will be greater than one (Speybroeck et al. 2012). In this case Bayesian estimates of true prevalence should be used, noting that the Bayesian estimates are based on a prior estimate of true prevalence and its uncertainty (Messam et al., 2008).

This function computes Rogan-Gladen and Bayesian estimates of true prevalence. Bayesian estimates are computed using JAGS (Plummer 2003).

References

Agresti A, Coull BA (1998). Approximate is better than 'exact' for interval estimation of binomial proportions. American Statistician 52: 119 - 126.

Blaker H (2000). Confidence curves and improved exact confidence intervals for discrete distributions. Canadian Journal of Statistics 28: 783 - 798.

Clopper CJ, Pearson ES (1934). The use of confidence of fiducial limits illustrated in the case of the binomial. Biometrika 26: 404 - 413.

Gardener IA, Greiner M (1999). Advanced Methods for Test Validation and Interpretation in Veterinary Medicince. Freie Universitat Berlin, ISBN 3-929619-22-9; 80 pp.

Messam L, Branscum A, Collins M, Gardner I (2008) Frequentist and Bayesian approaches to prevalence estimation using examples from Johne's disease. Animal Health Research Reviews 9: 1 - 23.

Plummer M (2003) JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In: Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003), Vienna, Austria, pp. 1 - 10.

Reiczigel J, Foldi J, Ozsvari L (2010). Exact confidence limits for prevalence of disease with an imperfect diagnostic test. Epidemiology and Infection 138: 1674 - 1678.

Rogan W, Gladen B (1978). Estimating prevalence from results of a screening test. American Journal of Epidemiology 107: 71 - 76.

Speybroeck N, Devleesschauwer B, Joseph L, Berkvens D (2012). Misclassification errors in prevalence estimation: Bayesian handling with care. International Journal of Public Health DOI:10.1007/s00038-012-0439-9.

Sterne TE (1954). Some remarks on confidence or fiducial limits. Biometrika 41: 275 - 278.

Examples

Brucellosis

A simple random sample of 150 cows from a herd of 2560 is taken. Each cow is given a screening test for brucellosis which has a sensitivity of 96% and a specificity of 89%. Of the 150 cows tested 45 were positive to the screening test. What is the estimated prevalence of brucellosis in this herd (and its 95% confidence interval)?

The apparent prevalence of brucellosis in this herd is 30 (95% CI 23 to 38) cases per 100 cows at risk. The estimated true prevalence of brucellosis in this herd is 22 (95% CI 14 to 31) cases per 100 cows at risk.

Description

Calculates the probability of that a group of surveillance units are free of disease given a set of negative test results.

Usage

References

Martin P, Cameron A, Greiner M (2007). Demonstrating freedom from disease using multiple complex data sources 1: A new methodology based on scenario trees. Preventive Veterinary Medicine 79: 71 - 97.

Martin P, Cameron A, Barfod K, Sergeant E, Greiner M (2007). Demonstrating freedom from disease using multiple complex data sources 2: Case study - classical swine fever in Denmark. Preventive Veterinary Medicine 79: 98 - 115.

Examples

One hundred and twenty cattle are tested for brucellosis using a test with a diagnostic sensitivity of 0.80. All return a negative result. What is the probability that this group of cattle are free of disease for a design prevalence of 0.01 and an uninformed prior probability disease freedom of 0.50?

If 120 cattle are tested for brucellosis using a test with diagnostic sensitivity of 0.80 we can be 0.724 confident that the prevalence of disease is not greater than 0.01 assuming the prior (pre-test) probability of disease in this group is 0.50.