Summarising predictive ability of a survival model and applications in medical research.

With the molecular revolution in medicine, many new potential prognostic and predictive factors are becoming available. However, whether new factors will lead to substantial improvement in the accuracy of prognostic assessments requires the use of a suitable per formance measure when considering different prognostic models. Several such measures have been proposed for use in survival analysis with a particular emphasis on measures proposed for the Cox proportional hazards model. However, there is no consensus of opinion on this issue. The proposed measures make use of a wide spectrum of techniques from information theory to statistical imputation. No comprehensive systematic summary of these measures has been done, and no adequate comparison of measures, theoretically or in practice, has been reported. This PhD studies the proposed measures systematically. It defines a set of criteria that a measure should possess in the context of survival analysis. Essential aspects of a measure are that it should be consistent under different degrees of censoring and sample size conditions it should also possess properties such as variable and parameter monotonicity. Desirable properties of a measure are robustness and extendability. This thesis compares the existing measures using these criteria discussing their strengths and shortcomings. From a practical point of view, a discussion of why these measures are important and what information they can provide in medical research, practical data analysis, and perhaps most importantly in prognostic modelling is presented. Data has been taken from completed randomised controlled trials in several diseases carried out by MRC Clinical Trials Unit and other research organisations. The measures that have the best properties will be applied to models fitted to these datasets. This allows us to quantify and assess the prognostic ability of the available prognostic factors in several diseases

Three Essays in Public Finance

This dissertation comprises three essays in public finance. The first essay is a research of a theory of trading of club goods and its application to jurisdiction. The essay establishes a model of trading of club goods among clubs, and illustrates its effects on the process and outcome of club formation. Cost function as well as disutility of crowdedness is emphasized and integrated into the process of club formation, after allowing for exchanging club good among clubs. In the process, the essay develops a market for club goods. Then the model is revised and applied to the formation of jurisdictions. The second essay comes out of an interest regarding household demand, poverty and public goods in developing countries. The essay explores household food consumption in Jamaica and estimates the effects of related variables. With Jamaica Survey of Living Conditions 2001 data, the essay estimates an Engel curve which reflects the relation between household food consumption and related variables. What’s more, to investigate the possible neighborhood effect on food consumption, the essay tests and estimates the spatial correlation among neighborhood food consumption. The estimated results can be applied to poverty reduction policy. The third essay extends the theme of poverty, consumption, and government programs by analyzing one other public program—education. Education is closely linked to poverty alleviation. Determining the demand for education and the return to education will help government focus programs aimed at reducing drop-out rates and in the long run, poverty in the country. The essay applies discrete time survival analysis techniques to analyze education duration in Jamaica. Based on Jamaica Survey of Living Conditions 2002, the essay estimates the effects of household, individual and other related covariates on dropout risks of students. The essay compares discrete time Cox model and discrete time logit model and concludes that the two estimations are consistent. The estimation results could be used to predict the effects of changes in the covariates, or be used to predict the dropout risks of particular students in each grade, both of which could provide useful policy implications to improve education in Jamaica

Prognostic factors for epilepsy

Introduction and Aims: Epilepsy is a neurological disorder and is a heterogeneous condition both in terms of cause and prognosis. Prognostic factors identify patients at varying degrees of risk for specific outcomes which facilitates treatment choice and aids patient counselling. Few prognostic models based on prospective cohorts or randomised controlled trial data have been published in epilepsy. Patients with epilepsy can be loosely categorised as having had a first seizure, being newly diagnosed with epilepsy, having established epilepsy or frequent unremitting seizures despite optimum treatment. This thesis concerns modelling prognostic factors for these patient groups, for outcomes including seizure recurrence, seizure remission and treatment failure. Methods: Methods for modelling prognostic factors are discussed and applied to several examples including eligibility to drive following a first seizure and following withdrawal of treatment after a period of remission from seizures. Internal and external model validation techniques are reviewed. The latter is investigated further in a simulation study, the results of which are demonstrated in a motivating example. Mixture modelling is introduced and assessed to better predict whether a patient would achieve remission from seizures immediately, at a later time point, or whether they may never achieve remission. Results: Multivariable models identified a number of significant factors. Future risk of a seizure was therefore obtained for various patient subgroups. The models identified that the chance of a second seizure was below the risk threshold for driving, set by the DVLA, after six months, and the risk of a seizure following treatment withdrawal after a period of remission from seizures was below the risk threshold after three months. Selected models were found to be internally valid and the simulation study indicated that concordance and a variety of imputation methods for handling covariates missing from the validation dataset were useful approaches for external validation of prognostic models. Assessing these methods for a selected model indicated that the model was valid in independent datasets. Mixture modelling techniques begin to show an improved prognostic model for the frequently reported outcome time to 12-month remission. Conclusions: The models described within this thesis can be used to predict outcome for patients with first seizures or epilepsy aiding individual patient risk stratification and the design and analysis of future epilepsy trials. Prognostic models are not commonly externally validated. A method of external validation in the presence of a missing covariate has been proposed and may facilitate validation of prognostic models making the evidence base more transparent and reliable and instil confidence in any significant findings

Statistical evaluation of surrogate outcomes: methodological extensions to ordinal outcomes with applications in acute stroke

Background Surrogate outcomes are measures of treatment effect that can be used to predict treatment effect on the true outcome of interest. Surrogates are valued as they can be used in place of true outcomes to reduce the length, size, or intrusiveness of a clinical trial. However, validation of surrogacy is a conceptually complicated area and much theoretical and practical statistical development has been conducted in recent years. Methods A systematic review was conducted to identify which surrogate evaluation approach was best suited to be extended to ordinal outcomes. I extended a foremost approach to the case where the surrogate, the true clinical outcome, or both are ordinal outcomes. This extension investigated surrogacy at both the trial and individual levels; trial level surrogacy was based on a two stage method. The extension was developed through large simulation studies and used to investigate whether deep venous thromboembolism (DVT) was a surrogate for the ongoing measure of death and disability the Oxford Handicap Scale (OHS), using data from the stroke trial CLOTS3. CLOTS3 was a large multi-centre randomised clinical trial which investigated whether intermittent pneumatic compression (IPC) applied to the legs reduced the occurrence of deep venous thromboembolism (DVT) in stroke clinical trial patients. Results The systematic review identified the information theory approach as the most intuitively and practically worthwhile approach to surrogacy evaluation. I extended this approach to: a binary surrogate and ordinal true outcome (the binary-ordinal setting); the ordinal-binary and the ordinal-ordinal settings. The simulation studies showed that the approach worked well in most scenarios tested. However, trial level surrogacy was impacted by loss of efficiency due to the use of the two stage method. Bias imposed at the trial level by separation of discrete outcomes was effectively dealt with using a penalised likelihood method. The information theory approach for ordinal outcomes identified no surrogate that would predict treatment effect of IPC on the true outcome OHS measured at six months in the stroke trial CLOTS3

Prognostic and surrogate markers for outcome in the treatment of pulmonary tuberculosis

Phase III trials for new tuberculosis treatment regimens require large numbers of participants and can take over five years to complete. A surrogate marker for poor outcome (failure at end of treatment or recurrence following successful treatment), the established endpoint in such trials, could shorten trial duration and reduce trial size. Culture results after two months of treatment have shown the most promise but, prior to this research, no formal evaluation had been performed. In this thesis, culture results during treatment are evaluated as prognostic and surrogate markers for poor outcome using data on 6974 patients from twelve tuberculosis treatment randomised controlled multi-arm trials conducted in East Africa and East Asia. A strong association was found between culture results during treatment and poor outcome. Nevertheless, culture results were not good patient-specific predictors of poor outcome with low sensitivities and specificities. Existing meta-analytic methods for evaluating surrogate markers are not wholly suited to this setting of multi-arm trials with binary true and surrogate endpoints. Extending these methods, the two month culture was found to be a good surrogate marker using data from Hong Kong trials and the three month culture was found to be a good surrogate marker using data from East African trials. These results are an indication that cultures during treatment do capture some of the treatment effect. Further work is needed in understanding the differences between the Hong Kong and East African trials. The meta-analytic methods for evaluating surrogate markers in this thesis included a graphical representation that permitted a clear visual evaluation of the surrogate. Methods developed in this thesis for modelling the relationship between the treatment effects on the true and surrogate endpoints were not satisfactory. The deficiencies were not overcome with the two extensions proposed. Further work is needed in developing a more appropriate model