Ming‐Hui Chen

The marginal likelihood is commonly used for comparing different evolutionary models in Bayesian phylogenetics and is the central quantity used in computing Bayes Factors for comparing model fit. A popular method for estimating marginal likelihoods, the harmonic mean (HM) method, can be easily computed from the output of a Markov chain Monte Carlo analysis but often greatly overestimates the marginal likelihood. The thermodynamic integration (TI) method is much more accurate than the HM method but requires more computation. In this paper, we introduce a new method, steppingstone sampling (SS), which uses importance sampling to estimate each ratio in a series (the "stepping stones") bridging the posterior and prior distributions. We compare the performance of the SS approach to the TI and HM methods in simulation and using real data. We conclude that the greatly increased accuracy of the SS and TI methods argues for their use instead of the HM method, despite the extra computation needed.

PURPOSE: To examine the impact of marital status on stage at diagnosis, use of definitive therapy, and cancer-specific mortality among each of the 10 leading causes of cancer-related death in the United States. METHODS: We used the Surveillance, Epidemiology and End Results program to identify 1,260,898 patients diagnosed in 2004 through 2008 with lung, colorectal, breast, pancreatic, prostate, liver/intrahepatic bile duct, non-Hodgkin lymphoma, head/neck, ovarian, or esophageal cancer. We used multivariable logistic and Cox regression to analyze the 734,889 patients who had clinical and follow-up information available. RESULTS: Married patients were less likely to present with metastatic disease (adjusted odds ratio [OR], 0.83; 95% CI, 0.82 to 0.84; P < .001), more likely to receive definitive therapy (adjusted OR, 1.53; 95% CI, 1.51 to 1.56; P < .001), and less likely to die as a result of their cancer after adjusting for demographics, stage, and treatment (adjusted hazard ratio, 0.80; 95% CI, 0.79 to 0.81; P < .001) than unmarried patients. These associations remained significant when each individual cancer was analyzed (P < .05 for all end points for each malignancy). The benefit associated with marriage was greater in males than females for all outcome measures analyzed (P < .001 in all cases). For prostate, breast, colorectal, esophageal, and head/neck cancers, the survival benefit associated with marriage was larger than the published survival benefit of chemotherapy. CONCLUSION: Even after adjusting for known confounders, unmarried patients are at significantly higher risk of presentation with metastatic cancer, undertreatment, and death resulting from their cancer. This study highlights the potentially significant impact that social support can have on cancer detection, treatment, and survival.

BACKGROUND: We evaluated whether men at risk for death from prostate cancer after radical prostatectomy can be identified using information available at diagnosis. METHODS: We studied 1095 men with localized prostate cancer to assess whether the rate of rise in the prostate-specific antigen (PSA) level--the PSA velocity--during the year before diagnosis, the PSA level at diagnosis, the Gleason score, and the clinical tumor stage could predict the time to death from prostate cancer and death from any cause after radical prostatectomy. RESULTS: As compared with an annual PSA velocity of 2.0 ng per milliliter or less, an annual PSA velocity of more than 2.0 ng per milliliter was associated with a significantly shorter time to death from prostate cancer (P<0.001) and death from any cause (P=0.01). An increasing PSA level at diagnosis (P=0.01), a Gleason score of 8, 9, or 10 (P=0.02), and a clinical tumor stage of T2 (P<0.001) also predicted the time to death from prostate cancer. For men with an annual PSA velocity of more than 2.0 ng per milliliter, estimates of the risk of death from prostate cancer and death from any cause seven years after radical prostatectomy were also influenced by the PSA level, tumor stage, and Gleason score at diagnosis. CONCLUSIONS: Men whose PSA level increases by more than 2.0 ng per milliliter during the year before the diagnosis of prostate cancer may have a relatively high risk of death from prostate cancer despite undergoing radical prostatectomy.

Missing data is a major issue in many applied problems, especially in the biomedical sciences. We review four common approaches for inference in generalized linear models (GLMs) with missing covariate data: maximum likelihood (ML), multiple imputation (MI), fully Bayesian (FB), and weighted estimating equations (WEEs). There is considerable interest in how these four methodologies are related, the properties of each approach, the advantages and disadvantages of each methodology, and computational implementation. We examine data that are missing at random and nonignorable missing. For ML, we focus on techniques using the EM algorithm, and in particular, discuss the EM by the method of weights and related procedures as discussed by Ibrahim. For MI, we examine the techniques developed by Rubin. For FB, we review approaches considered by Ibrahim et al. For WEE, we focus on the techniques developed by Robins et al. We use a real dataset and a detailed simulation study to compare the four methods.

Abstract We consider Bayesian methods for right-censored survival data for populations with a surviving (cure) fraction. We propose a model that is quite different from the standard mixture model for cure rates. We provide a natural motivation and interpretation of the model and derive several novel properties of it. First, we show that the model has a proportional hazards structure, with the covariates depending naturally on the cure rate. Second, we derive several properties of the hazard function for the proposed model and establish mathematical relationships with the mixture model for cure rates. Prior elicitation is discussed in detail, and classes of noninformative and informative prior distributions are proposed. Several theoretical properties of the proposed priors and resulting posteriors are derived, and comparisons are made to the standard mixture model. A real dataset from a melanoma clinical trial is discussed in detail.