PubMed Health⌕ Search
Home/Archive/PubMed

PubMed · 9855436

Mathematical modelling of effectiveness.

A R McLean
View original source ↗Export metadata ↓

Abstract

The effectiveness of a vaccine can be broadly defined as a practical measure of its costs and benefits when used in a community setting. What then is the relationship between a vaccine's efficacy and its effectiveness? Effectiveness certainly includes efficacy, but also encompasses secondary effects of vaccination, long-term efficacy of a vaccine (beyond that measured in conventional efficacy trials), the impact of vaccinating against one strain upon cross-reacting infections, costs of vaccination programmes and logistic considerations for vaccine delivery. This paper considers some of the biological determinants of effectiveness namely; secondary effects, long-term efficacy and competitive interactions amongst strains. Mathematical models of the transmission dynamics of infection and its disruption by vaccination are used as tools to help unravel some of the complexities that may arise when making interventions in non-linear biological systems.

Explore related subjects

Clinical Trials as TopicCommunicable Disease ControlCross ReactionsHumansMathematicsModels, BiologicalTime FactorsVaccinesJournal Article

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

A R McLean. 1998. Mathematical modelling of effectiveness.. https://pubmed.ncbi.nlm.nih.gov/9855436/

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

PubMed2008

On the exact interval estimation for the difference in paired areas under the ROC curves.

An important measure for comparison of accuracy between two diagnostic procedures is the difference in paired areas under the receiver operating characteristic (ROC) curves. Non-parametric and maximum likelihood methods have been proposed for interval estimation for the difference in paired areas under ROC curves. However, these two methods are asymptotic procedures and their performance in finite sample sizes has not been thoroughly investigated. We propose to use the concept of generalized pivotal quantities (GPQs) to construct an exact confidence interval for the difference in paired areas under ROC curves. A simulation study is conducted to empirically investigate the probability coverage and expected length of the three methods for various combinations of sample sizes, values of the area under the ROC curve and correlations. Simulation results demonstrate that the exact confidence interval based on the concept of GPQs provides not only sufficient probability coverage but also reasonable expected length. Numerical examples using published data sets illustrate the proposed method.

Clinical Trials as Topic↗
PubMed2007

An efficient test for the analysis of dichotomized variables when the reliability is known.

A difference in an outcome variable between the treatment groups in a trial does not necessarily mean that there is a difference in the number of patients who experience relevant improvement on that variable. When the relevant improvement corresponds with an outcome or change in outcome that exceeds a certain threshold, the outcome variable can be dichotomized. A responder is a patient whose outcome exceeds the threshold. Comparisons can be made between the number of responders in the two treatment groups using logistic regression, or some other method to evaluate binary outcomes. An important disadvantage of this approach is the loss of power. In general, it is more efficient to test the difference between the mean values. We developed a statistical test that compares response rates for a dichotomized variable. It requires that an estimate of the reliability of the outcome variable is available. Simulations showed that the test was valid and robust over a wide range of distributions and sample sizes. The power was greater than the power of a chi(2) test, which would enable substantial reduction in the sample size.

Clinical Trials as Topic↗
PubMed2007

Sample size determination for logistic regression revisited.

There is no consensus on the approach to compute the power and sample size with logistic regression. Some authors use the likelihood ratio test; some use the test on proportions; some suggest various approximations to handle the multivariate case. We advocate the use of the Wald test since the Z-score is routinely used for statistical significance testing of regression coefficients. The null-variance formula became popular from early studies, which contradicts modern software, which utilizes the method of maximum likelihood estimation (MLE), when the variance of the MLE is estimated at the MLE, not at the null. We derive general Wald-based power and sample size formulas for logistic regression and then apply them to binary exposure and confounder to obtain a closed-form expression. These formulas are applied to minimize the total sample size in a case-control study to achieve a given power by optimizing the ratio of controls to cases. Approximately, the optimal number of controls to cases is equal to the square root of the alternative odds ratio. Our sample size and power calculations can be carried out online at www.dartmouth.edu/ approximately eugened.

Clinical Trials as Topic↗