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Design and analysis of randomised trials with imperfect dichotomous outcomes

   Institute of Cancer and Genomic Sciences

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  Dr Sam Watson  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

Researchers conducting a randomised trial can be faced with the choice of using an expensive error-free outcome measure or a less-costly but less precise alternative. As an example, consider a trial of an intervention to prevent infectious disease. Infection could be confirmed in a lab using PCR-based methods or using an imperfect diagnostic test such as an immunochromatographic assay (a rapid diagnostic test). Lab testing can be expensive, requiring the shipping and freezing of samples, skilled technicians, and the requisite facilities, which may also not be available in low resource settings. The diagnostic test can be administered on location, requires little training, and is low cost. However the diagnostic test is “imperfect”; its performance is typically described by its sensitivity and specificity. Using an imperfect test without appropriate correction for sensitivity and specificity results in a biased estimator for prevalence and incidence. In particular, if p is the true prevalence then our estimator, q, for the prevalence with an imperfect outcome is q = Sensitivity*p + (1-Specificity)*(1-p) – so it should be clear that related measures such as a risk ratio or rate ratio will also be biased as the errors do not cancel out. With correction, estimates will be unbiased but significantly less precise than the error-free outcome with equivalent sample sizes. However, the cost difference between the two may mean that an equivalently precise estimate of a treatment effect could be obtained from a larger trial with an imperfect outcome at a lower cost than a smaller trial with the error-free outcome. A motivating example is a cluster trial of a water, sanitation, and hygiene (WASH) intervention designed to reduce transmission of enteric pathogens. Possible outcomes include PCR testing of stool for enteric infection, rapid diagnostic testing of stool in the field, or participant self-reported diarrhoea. The last outcome can also be considered imperfect as not all infection causes diarrhoea, and uninfected individuals can still have diarrhoea.

This project will consider how best to design trials when there are competing trade-offs between imperfect and perfect outcome measures in terms of sample size and variance inflation, extensions of these concepts to circumstances with unknown sensitivity and specificity and cluster-based trials, and methods of analysis and reporting.

What the studentship will encompass:

The studentship will be a predominantly statistical project involving theoretical statistical analysis supported by computational analysis including simulation-based studies. A re-analysis of previous trial data and epidemiological data will also be used in the research. We expect the studentship to produce papers for submission to peer-reviewed journals to disseminate the research, as well as conference attendance and presentation of the results to international partners to support delivery of trials around the world. The project will be divided into work packages as:

WP1 Reviews of the literature to identify: (i) trials that have used imperfect outcome measures as primary endpoints; (ii) statistical approaches to correcting for imperfect outcomes when estimating prevalence, incidence, and related measures. The former will be restricted as required to produce a coherent body of literature and a practicable review strategy, for example, all trials to use immunochromatographic assays as outcomes, or trials that have used symptom reporting for respiratory illness or other infectious disease as primary outcomes.

WP2 Building on the results from WP1, this work package will encompass examination of the variance inflation factors and ratio of required samples sizes to achieve a desired precision for individual level trials with an imperfect outcome versus an error-free outcome measure. The objective is to identify the optimal trial design under different unit costs for the outcomes. We will consider the cases when the sensitivity and specificity of the outcome measure are both known and unknown. In the latter case we will take a Bayesian approach to average over the distribution of sensitivity and specificity, and so develop computational tools to assess the statistics of interest. Extensions of the results to cluster trial and other settings with correlated observations will also be considered.

WP3 Re-analysis of a cluster randomised trial we are currently conducting in Mali with including both imperfect and perfect outcome measures in the area of evaluation of WASH interventions supported by epidemiological evidence on the performance of such tests, including data from an epidemiological study we have recently concluded in Bangladesh.

The supervision team for the project will be Dr Sam Watson (IAHR), supported by Prof Karla Hemming (IAHR) and Prof Richard Lilford (IAHR) who all work in the area of randomised trial design and analysis. Prof Hemming has expertise in cluster trial design and analysis, particularly stepped wedge trial design and Prof Lilford directs a substantial portfolio of global health research. Dr Sam Watson works on issues of trial design in non-standard and low-resource settings, including geospatial approaches, multiple outcomes and trial arms, and Bayesian methods. All have worked on cluster trials internationally. We expect the candidate will work closely with researchers both in the University of Birmingham and with our international partners, who will provide input and support to the project.

Applicants should hold a postgraduate qualification or first-class undergraduate degree in statistics or a related area that includes a statistical or data analysis component, such as epidemiology or computer science. 


You are applying for a PhD studentship from the MRC TMRP DTP. A list of potential projects and the application form is available online at:

Please complete the form fully. Incomplete forms will not be considered. CVs will not be accepted for this scheme.

Please apply giving details for your first choice project. You can provide details of up to two other TMRP DTP projects you may be interested in at section B of the application form.

Before making an application, applicants should contact the project primary supervisor to find out more about the project and to discuss their interests in the research.

The deadline for applications is 4pm (GMT) 18 February 2022. Late applications will not be considered.

Completed application forms must be returned to: [Email Address Removed]

Informal enquiries may be made to [Email Address Removed]

Funding Notes

Studentships are funded by the Medical Research Council (MRC) for 3 years. Funding will cover tuition fees at the UK rate only, a Research Training and Support Grant (RTSG) and stipend. We aim to support the most outstanding applicants from outside the UK and are able to offer a limited number of bursaries that will enable full studentships to be awarded to international applicants. These full studentships will only be awarded to exceptional quality candidates, due to the competitive nature of this scheme.
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