Robust non-linear mixed modelling of longitudinal PSA levels after prostate cancer treatment

Methods for the evaluation of biomarkers in patients with kidney and liver diseases: multicentre research programme including ELUCIDATE RCT

Background

Protein biomarkers with associations with the activity and outcomes of diseases are being identified by modern proteomic technologies. They may be simple, accessible, cheap and safe tests that can inform diagnosis, prognosis, treatment selection, monitoring of disease activity and therapy and may substitute for complex, invasive and expensive tests. However, their potential is not yet being realised.

Design and methods

The study consisted of three workstreams to create a framework for research: workstream 1, methodology – to define current practice and explore methodology innovations for biomarkers for monitoring disease; workstream 2, clinical translation – to create a framework of research practice, high-quality samples and related clinical data to evaluate the validity and clinical utility of protein biomarkers; and workstream 3, the ELF to Uncover Cirrhosis as an Indication for Diagnosis and Action for Treatable Event (ELUCIDATE) randomised controlled trial (RCT) – an exemplar RCT of an established test, the ADVIA Centaur® Enhanced Liver Fibrosis (ELF) test (Siemens Healthcare Diagnostics Ltd, Camberley, UK) [consisting of a panel of three markers – (1) serum hyaluronic acid, (2) amino-terminal propeptide of type III procollagen and (3) tissue inhibitor of metalloproteinase 1], for liver cirrhosis to determine its impact on diagnostic timing and the management of cirrhosis and the process of care and improving outcomes.

Results

The methodology workstream evaluated the quality of recommendations for using prostate-specific antigen to monitor patients, systematically reviewed RCTs of monitoring strategies and reviewed the monitoring biomarker literature and how monitoring can have an impact on outcomes. Simulation studies were conducted to evaluate monitoring and improve the merits of health care. The monitoring biomarker literature is modest and robust conclusions are infrequent. We recommend improvements in research practice. Patients strongly endorsed the need for robust and conclusive research in this area. The clinical translation workstream focused on analytical and clinical validity. Cohorts were established for renal cell carcinoma (RCC) and renal transplantation (RT), with samples and patient data from multiple centres, as a rapid-access resource to evaluate the validity of biomarkers. Candidate biomarkers for RCC and RT were identified from the literature and their quality was evaluated and selected biomarkers were prioritised. The duration of follow-up was a limitation but biomarkers were identified that may be taken forward for clinical utility. In the third workstream, the ELUCIDATE trial registered 1303 patients and randomised 878 patients out of a target of 1000. The trial started late and recruited slowly initially but ultimately recruited with good statistical power to answer the key questions. ELF monitoring altered the patient process of care and may show benefits from the early introduction of interventions with further follow-up. The ELUCIDATE trial was an ‘exemplar’ trial that has demonstrated the challenges of evaluating biomarker strategies in ‘end-to-end’ RCTs and will inform future study designs.

Conclusions

The limitations in the programme were principally that, during the collection and curation of the cohorts of patients with RCC and RT, the pace of discovery of new biomarkers in commercial and non-commercial research was slower than anticipated and so conclusive evaluations using the cohorts are few; however, access to the cohorts will be sustained for future new biomarkers. The ELUCIDATE trial was slow to start and recruit to, with a late surge of recruitment, and so final conclusions about the impact of the ELF test on long-term outcomes await further follow-up. The findings from the three workstreams were used to synthesise a strategy and framework for future biomarker evaluations incorporating innovations in study design, health economics and health informatics.

Trial registration

Current Controlled Trials ISRCTN74815110, UKCRN ID 9954 and UKCRN ID 11930.

Funding

This project was funded by the NIHR Programme Grants for Applied Research programme and will be published in full inProgramme Grants for Applied Research; Vol. 6, No. 3. See the NIHR Journals Library website for further project information.

Modelling disease progression in relapsing-remitting onset multiple sclerosis using multilevel models applied to longitudinal data from two natural history cohorts and one treated cohort

BACKGROUND

The ability to better predict disease progression represents a major unmet need in multiple sclerosis (MS), and would help to inform therapeutic and management choices.

OBJECTIVES

To develop multilevel models using longitudinal data on disease progression in patients with relapsing-remitting MS (RRMS) or secondary-progressive MS (SPMS); and to use these models to estimate the association of disease-modifying therapy (DMT) with progression.

DESIGN

Secondary analysis of three MS cohorts.

SETTING

Two natural history cohorts: University of Wales Multiple Sclerosis (UoWMS) cohort, UK, and British Columbia Multiple Sclerosis (BCMS) cohort, Canada. One observational DMT-treated cohort: UK MS risk-sharing scheme (RSS).

PARTICIPANTS

The UoWMS database has > 2000 MS patients and the BCMS database (as of 2009) has > 5900 MS patients. All participants who had definite MS (RRMS/SPMS), who reached the criteria set out by the Association of British Neurologists (ABN) for eligibility for DMT [i.e. age ≥ 18 years, Expanded Disability Status Scale (EDSS) score of ≤ 6.5, occurrence of two or more relapses in the previous 2 years] and who had at least two repeated outcome measures were included: 404 patients for the UoWMS cohort and 978 patients for the BCMS cohort. Through the UK MS RSS scheme, 5583 DMT-treated patients were recruited, with the analysis sample being the 4137 who had RRMS and were eligible and treated at baseline, with at least one valid EDSS score post baseline.

MAIN OUTCOME MEASURES

EDSS score observations post ABN eligibility.

METHODS

We used multilevel models in the development cohort (UoWMS) to develop a model for EDSS score with time since ABN eligibility, allowing for covariates and appropriate transformation of outcome and/or time. These methods were then applied to the BCMS cohort to obtain a 'natural history' model for changes in the EDSS score with time. We then used this natural history model to predict the trajectories of EDSS score in treated patients in the UK MS RSS database. Differences between the progression predicted by the natural history model and the progression observed at 6 years' follow-up for the UK MS RSS cohort were used as indicators of the effectiveness of the DMTs. Previously developed utility scores were assigned to each EDSS score, and differences in utility also examined.

RESULTS

The model best fitting the UoWMS data showed a non-linear increase in EDSS score over time since ABN eligibility. This model fitted the BCMS cohort data well, with similar coefficients, and the BCMS model predicted EDSS score in UoWMS data with little evidence of bias. Using the natural history model predicts EDSS score in a treated cohort (UK MS RSS) higher than that observed [by 0.59 points (95% confidence interval 0.54 to 0.64 points)] at 6 years post treatment.

LIMITATIONS

Only two natural history cohorts were compared, limiting generalisability. The comparison of a treated cohort with untreated cohorts is observational, thus limiting conclusions about causality.

CONCLUSIONS

EDSS score progression in two natural history cohorts of MS patients showed a similar pattern. Progression in the natural history cohorts was slightly faster than EDSS score progression in the DMT-treated cohort, up to 6 years post treatment.

FUTURE WORK

Long-term follow-up of randomised controlled trials is needed to replicate these findings and examine duration of any treatment effect.

FUNDING DETAILS

The National Institute for Health Research Health Technology Assessment programme.

Early diagnosis of gestational trophoblastic neoplasia based on trajectory classification with compartment modeling

BACKGROUND

In randomized clinical trials or observational studies, it is common to collect biomarker values longitudinally on a cohort of individuals. The investigators may be interested in grouping individuals that share similar changes of biomarker values and use these groups for diagnosis or therapeutic purposes. However, most classical model-based classification methods rely mainly on empirical models such as splines or polynomials and do not reflect the physiological processes.

METHODS

A model-based classification method was developed for longitudinal biomarker measurements through a pharmacokinetic model that describes biomarker changes over time. The method is illustrated using data on human Chorionic Gonadotrophic Hormone measurements after curettage of hydatidiform moles.

RESULTS

The resulting classification was linked to the evolution toward gestational trophoblastic neoplasia and may be used as a tool for early diagnosis. The diagnostic accuracy of the pharmacokinetic model was more reproducible than the one of a purely mathematical model that did not take into account the biological processes.

CONCLUSION

The use of pharmacokinetic models in model-based classification approaches can lead to clinically useful classifications.

Estimating the optimal threshold for a diagnostic biomarker in case of complex biomarker distributions

BACKGROUND

Estimating the optimal threshold (and especially the confidence interval) of a quantitative biomarker to be used as a diagnostic test is essential for medical decision-making. This is often done with simple methods that are not always reliable. More advanced methods work well but only for biomarkers with very simple distributions. In fact, biomarker distributions are often complex because of a natural heterogeneity in marker expression and other heterogeneities due to various disease stages, laboratory equipments, etc. Methods are required to estimate a biomarker optimal threshold in case of heterogeneity and complex distributions.

METHODS

A previously described Bayesian method developed for normally distributed biomarkers is applied to two flexible distributions; namely, a Student-t and a mixture of Dirichlet processes. Here, numerical studies assess the adequacy of the previous method with both distributions. Two applications are presented: the diagnosis of treatment failure after prostate cancer treated by ultrasound and the early diagnosis of cancers of the upper aerodigestive tract.

RESULTS

Bayesian inference provided reliable credible intervals in terms of bias and coverage probability. The two distributions analysed gave meaningful clinical interpretations in both applications.

CONCLUSIONS

Reliable methods can be used to estimate a biomarker optimal threshold, even in case of complex distributions.

A Bayesian approach to analyze energy balance data from lactating dairy cows

The objective of the present investigation was to develop a Bayesian framework for updating and integrating covariate information into key parameters of metabolizable energy (ME) systems for dairy cows. The study addressed specifically the effects of genetic improvements and feed quality on key parameters in current ME systems. These are net and metabolizable energy for maintenance (NE(M) and ME(M), respectively), efficiency of utilization of ME for milk production (k(L)) and growth (k(G)), and efficiency of utilization of body stores for milk production (k(T)). Data were collated from 38 studies, yielding 701 individual cow observations on milk energy, ME intake, and tissue gain and loss. A function based on a linear relationship between milk energy and ME intake and correcting for tissue energy loss or gain served as the basis of a full Bayesian hierarchical model. The within-study variability was modeled by a Student t-distribution and the between-study variability in the structural parameters was modeled by a multivariate normal distribution. A meaningful relationship between genetic improvements in milk production and the key parameters could not be established. The parameter k(L) was linearly related to feed metabolizability, and the slope predicted a 0.010 (-0.0004; 0.0210) change per 0.1-unit change in metabolizability. The effect of metabolizability on k(L) was smaller than assumed in present feed evaluation systems and its significance was dependent on collection of studies included in the analysis. Three sets of population estimates (with 95% credible interval in parentheses) were generated, reflecting different degrees of prior belief: (1) Noninformative priors yielded 0.28 (0.23; 0.33) MJ/(kg(0.75)d), 0.55 (0.51; 0.58), 0.86 (0.81; 0.93) and 0.66 (0.58; 0.75), for NE(M), k(L), k(G), and k(T), respectively; (2) Introducing an informative prior that was derived from a fasting metabolism study served to combine the most recent information on energy metabolism in modern dairy cows. The new estimates of NE(M), k(L), k(G) and k(T) were 0.34 (0.28; 0.39) MJ/(kg(0.75)d), 0.58 (0.54; 0.62), 0.89 (0.85; 0.95), and 0.69 (0.60; 0.79), respectively; (3) finally, all informative priors were used that were established from literature, yielding estimates for NE(M), k(L), k(G), and k(T) of 0.29 (0.11; 0.46) MJ/(kg(0.75)d), 0.60 (0.54; 0.70), 0.70 (0.50; 0.88), and 0.80 (0.67; 0.97), respectively. Bayesian methods are especially applicable in meta-analytical studies as information can enter at various stages in the hierarchical model.

A Bayesian method to estimate the optimal threshold of a longitudinal biomarker

The objective of this study was to develop methods to estimate the optimal threshold of a longitudinal biomarker and its credible interval when the diagnostic test is based on a criterion that reflects a dynamic progression of that biomarker. Two methods are proposed: one parametric and one non-parametric. In both the cases, the Bayesian inference was used to derive the posterior distribution of the optimal threshold from which an estimate and a credible interval could be obtained. A numerical study shows that the bias of the parametric method is low and the coverage probability of the credible interval close to the nominal value, with a small coverage asymmetry in some cases. This is also true for the non-parametric method in case of large sample sizes. Both the methods were applied to estimate the optimal prostate-specific antigen nadir value to diagnose prostate cancer recurrence after a high-intensity focused ultrasound treatment. The parametric method can also be applied to non-longitudinal biomarkers.