Paul Gustafson

An overview of robust Bayesian analysis

SummaryRobust Bayesian analysis is the study of the sensitivity of Bayesian answers to uncertain inputs. This paper seeks to provide an overview of the subject, one that is accessible to statisticians outside the field. Recent developments in the area are also reviewed, though with very uneven emphasis.

Measurement error and misclassification in statistics and epidemiology: impacts and Bayesian adjustments.

INTRODUCTION Examples of Mismeasurement The Mismeasurement Phenomenon What is Ahead? THE IMPACT OF MISMEASURED CONTINUOUS VARIABLES The Archetypical Scenario More General Impact Multiplicative Measurement Error Multiple Mismeasured Predictors What about Variability and Small Samples? Logistic Regression Beyond Nondifferential and Unbiased Measurement Error Summary Mathematical Details THE IMPACT OF MISMEASURED CATEGORICAL VARIABLES The Linear Model Case More General Impact Inferences on Odds-Ratios Logistic Regression Differential Misclassification Polychotomous Variables Summary Mathematical Details ADJUSTMENT FOR MISMEASURED CONTINUOUS VARIABLES Posterior Distributions A Simple Scenario Nonlinear Mixed Effects Model: Viral Dynamics Logistic Regression I: Smoking and Bladder Cancer Logistic Regression II: Framingham Heart Study Issues in Specifying the Exposure Model More Flexible Exposure Models Retrospective Analysis Comparison with Non-Bayesian Approaches Summary Mathematical Details ADJUSTMENT FOR MISMEASURED CATEGORICAL VARIABLES A Simple Scenario Partial Knowledge of Misclassification Probabilities Dual Exposure Assessment Models with Additional Explanatory Variables Summary Mathematical Details FURTHER TOPICS Dichotomization of Mismeasured Continuous Variables Mismeasurement Bias and Model Misspecification Bias Identifiability in Mismeasurement Models Further Remarks APPENDIX: BAYES-MCMC INFERENCE Bayes Theorem Point and Interval Estimates Markov Chain Monte Carlo Prior Selection MCMC and Unobserved Structure REFERENCES

Association Between Use of Interferon Beta and Progression of Disability in Patients With Relapsing-Remitting Multiple Sclerosis

CONTEXT Interferon beta is widely prescribed to treat multiple sclerosis (MS); however, its relationship with disability progression has yet to be established. OBJECTIVE To investigate the association between interferon beta exposure and disability progression in patients with relapsing-remitting MS. DESIGN, SETTING, AND PATIENTS Retrospective cohort study based on prospectively collected data (1985-2008) from British Columbia, Canada. Patients with relapsing-remitting MS treated with interferon beta (n = 868) were compared with untreated contemporary (n = 829) and historical (n = 959) cohorts. MAIN OUTCOME MEASURES The main outcome measure was time from interferon beta treatment eligibility (baseline) to a confirmed and sustained score of 6 (requiring a cane to walk 100 m; confirmed at >150 days with no measurable improvement) on the Expanded Disability Status Scale (EDSS) (range, 0-10, with higher scores indicating higher disability). A multivariable Cox regression model with interferon beta treatment included as a time-varying covariate was used to assess the hazard of disease progression associated with interferon beta treatment. Analyses also included propensity score adjustment to address confounding by indication. RESULTS The median active follow-up times (first to last EDSS measurement) were as follows: for the interferon beta-treated cohort, 5.1 years (interquartile range [IQR], 3.0-7.0 years); for the contemporary control cohort, 4.0 years (IQR, 2.1-6.4 years); and for the historical control cohort, 10.8 years (IQR, 6.3-14.7 years). The observed outcome rates for reaching a sustained EDSS score of 6 were 10.8%, 5.3%, and 23.1% in the 3 cohorts, respectively. After adjustment for potential baseline confounders (sex, age, disease duration, and EDSS score), exposure to interferon beta was not associated with a statistically significant difference in the hazard of reaching an EDSS score of 6 when either the contemporary control cohort (hazard ratio, 1.30; 95% CI, 0.92-1.83; P = .14) or the historical control cohort (hazard ratio, 0.77; 95% CI, 0.58-1.02; P = .07) were considered. Further adjustment for comorbidities and socioeconomic status, where possible, did not change interpretations, and propensity score adjustment did not substantially change the results. CONCLUSION Among patients with relapsing-remitting MS, administration of interferon beta was not associated with a reduction in progression of disability.

On Model Expansion, Model Contraction, Identifiability and Prior Information: Two Illustrative Scenarios Involving Mismeasured Variables

When a candidate model for data is nonidentifiable, conventional wisdom dictates that the model must be simplified somehow, in order to gain identifiability. We explore two scenarios involving mismeasured variables where in fact model expansion, as opposed to model contraction, might be used to obtain an identifiable model. We compare the merits of model contraction and model expansion. We also investigate whether it is necessarily a good idea to alter the model for the sake of identifiability. In particular, we compare the properties of estimators obtained from identifiable models to those of estimators obtained from nonidentifiable models in tandem with crude prior information. Both asymptotic theory and simulations with MCMC-based estimators are used to draw comparisons. A technical point which arises is that the asymptotic behaviour of a posterior mean from a nonidentifiable model can be investigated using standard asymptotic theory, once the posterior mean is described in terms of the identifiable part of the model only.

Large hierarchical Bayesian analysis of multivariate survival data.

Failure times that are grouped according to shared environments arise commonly in statistical practice. That is, multiple responses may be observed for each of many units. For instance, the units might be patients or centers in a clinical trial setting. Bayesian hierarchical models are appropriate for data analysis in this context. At the first stage of the model, survival times can be modelled via the Cox partial likelihood, using a justification due to Kalbfleisch (1978, Journal of the Royal Statistical Society, Series B 40, 214-221). Thus, questionable parametric assumptions are avoided. Conventional wisdom dictates that it is comparatively safe to make parametric assumptions at subsequent stages. Thus, unit-specific parameters are modelled parametrically. The posterior distribution of parameters given observed data is examined using Markov chain Monte Carlo methods. Specifically, the hybrid Monte Carlo method, as described by Neal (1993a, in Advances in Neural Information Processing 5, 475-482; 1993b, Probabilistic inference using Markov chain Monte Carlo methods), is utilized.

Expanding access to HAART: a cost-effective approach for treating and preventing HIV.

Objective:HIV continues to present a substantial global health burden. Given the high direct medical costs associated with the disease, prevention of new transmission is an important element in limiting economic burden. In addition to providing therapeutic benefit, treatment with HAART has potential to prevent transmission of HIV. The objective in this study was to perform an economic evaluation of the incremental net benefit associated with an intervention to expand treatment with HAART in British Columbia, Canada. Design:A mathematical model describing transmission of HIV, integrated with a microsimulation model describing the clinical and economic course of HIV. Methods:The primary outcome was the incremental net benefit of expanding treatment with HAART from 50 to 75% of clinically eligible individuals in British Columbia, assuming a willingness-to-pay threshold of US

Neonatal intensive care unit characteristics affect the incidence of severe intraventricular hemorrhage.

50 000 per quality-adjusted life year. Direct medical costs included were antiretroviral and nonantiretroviral medications, hospitalizations, physician visits, and laboratory tests. The mathematical and microsimulation models were based on patient characteristics observed in British Columbia. Longitudinal data described health services utilization, clinical progression, and survival for all individuals receiving treatment for HIV in British Columbia. Results:Over 30 years, the HAART expansion scenario was associated with a net benefit of US

Bayesian propensity score analysis for observational data

900 million (95% confidence interval US

A sensitivity analysis using information about measured confounders yielded improved uncertainty assessments for unmeasured confounding

493 million to 1.45 billion). Conclusion:Increasing the HAART treatment rate from 50 to 75% of clinically eligible individuals in British Columbia appears to be a cost-effective strategy based on this model. These cost-effectiveness results are consistent with public health objectives: all individuals who are eligible for an established life-saving treatment should receive it.

Local sensitivity of inferences to prior marginals

Objectives:The incidence of intraventricular hemorrhage (IVH), adjusted for known risk factors, varies across neonatal intensive care units (NICU)s. The effect of NICU characteristics on this variation is unknown. The objective was to assess IVH attributable risks at both patient and NICU levels. Study Design:Subjects were <33 weeks’ gestation, <4 days old on admission in the Canadian Neonatal Network database (all infants admitted in 1996–97 to 17 NICUs). The variation in severe IVH rates was analyzed using Bayesian hierarchical modeling for patient level and NICU level factors. Results:Of 3772 eligible subjects, the overall crude incidence rates of grade 3–4 IVH was 8.3% (NICU range 2.0–20.5%). Male gender, extreme preterm birth, low Apgar score, vaginal birth, outborn birth, and high admission severity of illness accounted for 30% of the severe IVH rate variation; admission day therapy-related variables (treatment of acidosis and hypotension) accounted for an additional 14%. NICU characteristics, independent of patient level risk factors, accounted for 31% of the variation. NICUs with high patient volume and high neonatologist/staff ratio had lower rates of severe IVH. Conclusions:The incidence of severe IVH is affected by NICU characteristics, suggesting important new strategies to reduce this important adverse outcome.