A comparison of Bayesian and frequentist approaches to incorporating external information for the prediction of prostate cancer risk

How well do polygenic risk scores identify men at high risk for prostate cancer? Systematic review and meta-analysis

OBJECTIVES

Genome-wide association studies have revealed over 200 genetic susceptibility loci for prostate cancer (PCa). By combining them, polygenic risk scores (PRS) can be generated to predict risk of PCa. We summarize the published evidence and conduct meta-analyses of PRS as a predictor of PCa risk in Caucasian men.

PATIENTS AND METHODS

Data were extracted from 59 studies, with 16 studies including 17 separate analyses used in the main meta-analysis with a total of 20,786 cases and 69,106 controls identified through a systematic search of ten databases. Random effects meta-analysis was used to obtain pooled estimates of area under the receiver-operating characteristic curve (AUC). Meta-regression was used to assess the impact of number of single-nucleotide polymorphisms (SNPs) incorporated in PRS on AUC. Heterogeneity is expressed as I² scores. Publication bias was evaluated using funnel plots and Egger tests.

RESULTS

The ability of PRS to identify men with PCa was modest (pooled AUC 0.63, 95% CI 0.62-0.64) with moderate consistency (I² 64%). Combining PRS with clinical variables increased the pooled AUC to 0.74 (0.68-0.81). Meta-regression showed only negligible increase in AUC for adding incremental SNPs. Despite moderate heterogeneity, publication bias was not evident.

CONCLUSION

Typically, PRS accuracy is comparable to PSA or family history with a pooled AUC value 0.63 indicating mediocre performance for PRS alone.

Estimation Parameters of Dependence Meta-Analytic Model: New Techniques for the Hierarchical Bayesian Model

Dependence in meta-analytic models can happen due to the same collected data or from the same researchers. The hierarchical Bayesian linear model in a meta-analysis that allows dependence in effect sizes is investigated in this paper. The interested parameters on the hierarchical Bayesian linear dependence (HBLD) model which was developed using the Bayesian techniques will then be estimated. The joint posterior distribution of all parameters for the hierarchical Bayesian linear dependence (HBLD) model is obtained by applying the Gibbs sampling algorithm. Furthermore, in order to measure the robustness of the HBLD model, the sensitivity analysis is conducted using a different prior distribution on the model. This is carried out by applying the Metropolis within the Gibbs algorithm. The simulation study is performed for the estimation of all parameters in the model. The results show that the obtained estimated parameters are close to the true parameters, indicating the consistency of the parameters for the model. The model is also not sensitive because of the changing prior distribution which shows the robustness of the model. A case study, to assess the effects of native-language vocabulary aids on second language reading, is conducted successfully in testing the parameters of the models.

Comparison of Logistic Regression and Bayesian Networks for Risk Prediction of Breast Cancer Recurrence

Purpose. For individualized follow-up, accurate prediction of locoregional recurrence (LRR) and second primary (SP) breast cancer risk is required. Current prediction models employ regression, but with large data sets, machine-learning techniques such as Bayesian Networks (BNs) may be better alternatives. In this study, logistic regression was compared with different BNs, built with network classifiers and constraint- and score-based algorithms. Methods. Women diagnosed with early breast cancer between 2003 and 2006 were selected from the Netherlands Cancer Registry (NCR) ( N = 37,320). BN structures were developed using 1) Bayesian network classifiers, 2) correlation coefficients with different cutoffs, 3) constraint-based learning algorithms, and 4) score-based learning algorithms. The different models were compared with logistic regression using the area under the receiver operating characteristic curve, an external validation set obtained from the NCR from 2007 and 2008 ( N = 12,308), and subgroup analyses for a high- and low-risk group. Results. The BNs with the most links showed the best performance in both LRR and SP prediction (c-statistic of 0.76 for LRR and 0.69 for SP). In the external validation, logistic regression generally outperformed the BNs in both SP and LRR (c-statistic of 0.71 for LRR and 0.64 for SP). The differences were nonetheless small. Although logistic regression performed best on most parts of the subgroup analysis, BNs outperformed regression with respect to average risk for SP prediction in low- and high-risk groups. Conclusions. Although estimates of regression coefficients depend on other independent variables, there is no assumed dependence relationship between coefficient estimators and the change in value of other variables as in the case of BNs. Nonetheless, this analysis suggests that regression is still more accurate or at least as accurate as BNs for risk estimation for both LRRs and SP tumors.

Informing a Risk Prediction Model for Binary Outcomes with External Coefficient Information

We consider a situation where there is rich historical data available for the coefficients and their standard errors in an established regression model describing the association between a binary outcome variable Y and a set of predicting factors X, from a large study. We would like to utilize this summary information for improving estimation and prediction in an expanded model of interest, Y| X, B. The additional variable B is a new biomarker, measured on a small number of subjects in a new dataset. We develop and evaluate several approaches for translating the external information into constraints on regression coefficients in a logistic regression model of Y| X, B. Borrowing from the measurement error literature we establish an approximate relationship between the regression coefficients in the models Pr(Y = 1| X , β), Pr(Y = 1| X, B, γ) and E(B| X, θ ) for a Gaussian distribution of B. For binary B we propose an alternate expression. The simulation results comparing these methods indicate that historical information on Pr(Y = 1| X , β) can improve the efficiency of estimation and enhance the predictive power in the regression model of interest Pr(Y = 1| X, B, γ). We illustrate our methodology by enhancing the High-grade Prostate Cancer Prevention Trial Risk Calculator, with two new biomarkers prostate cancer antigen 3 and TMPRSS2:ERG.

Weibull regression with Bayesian variable selection to identify prognostic tumour markers of breast cancer survival

As data-rich medical datasets are becoming routinely collected, there is a growing demand for regression methodology that facilitates variable selection over a large number of predictors. Bayesian variable selection algorithms offer an attractive solution, whereby a sparsity inducing prior allows inclusion of sets of predictors simultaneously, leading to adjusted effect estimates and inference of which covariates are most important. We present a new implementation of Bayesian variable selection, based on a Reversible Jump MCMC algorithm, for survival analysis under the Weibull regression model. A realistic simulation study is presented comparing against an alternative LASSO-based variable selection strategy in datasets of up to 20,000 covariates. Across half the scenarios, our new method achieved identical sensitivity and specificity to the LASSO strategy, and a marginal improvement otherwise. Runtimes were comparable for both approaches, taking approximately a day for 20,000 covariates. Subsequently, we present a real data application in which 119 protein-based markers are explored for association with breast cancer survival in a case cohort of 2287 patients with oestrogen receptor-positive disease. Evidence was found for three independent prognostic tumour markers of survival, one of which is novel. Our new approach demonstrated the best specificity.

Multigene panels in prostate cancer risk assessment: a systematic review

PURPOSE

Single-nucleotide polymorphism (SNP) panel tests have been proposed for use in the detection of, and prediction of risk for, prostate cancer and as prognostic indicator in affected men. A systematic review was undertaken to address three research questions to evaluate the analytic validity, clinical validity, clinical utility, and prognostic validity of SNP-based panels.

METHODS

Data sources comprised MEDLINE, Cochrane CENTRAL, Cochrane Database of Systematic Reviews, and EMBASE; these were searched from inception to April 2013. The gray-literature searches included contact with manufacturers. Eligible studies included English-language studies evaluating commercially available SNP panels. Study selection and risk of bias assessment were undertaken by two independent reviewers.

RESULTS

Twenty-one studies met eligibility criteria. All focused on clinical validity and evaluated 18 individual panels with 2 to 35 SNPs. All had poor discriminative ability (overall area under receiver-operator characteristic curves, 58-74%; incremental gain resulting from inclusion of SNP data, 2.5-11%) for predicting risk of prostate cancer and/or distinguishing between aggressive and asymptomatic/latent disease. The risk of bias of the studies, as assessed by the Newcastle Ottawa Scale (NOS) and Quality Assessment of Diagnostic Accuracy Studies (QUADAS) tools, was moderate.

CONCLUSION

The evidence on currently available SNP panels is insufficient to assess analytic validity, and at best the panels assessed would add a small and clinically unimportant improvement to factors such as age and family history in risk stratification (clinical validity). No evidence on the clinical utility of current panels is available.Genet Med 18 6, 535-544.

A genetic-based approach to personalized prostate cancer screening and treatment

PURPOSE OF REVIEW

Recent advances in sequencing technologies have allowed for the identification of genetic variants within germline DNA that can explain a significant portion of the genetic underpinnings of prostate cancer. Despite evidence suggesting that these genetic variants can be used for improved risk stratification, they have not yet been routinely incorporated into routine clinical practice. This review highlights their potential utility in prostate cancer screening.

RECENT FINDINGS

There are now almost 100 genetic variants, called single nucleotide polymorphisms (SNPs) that have been recently found to be associated with the risk of developing prostate cancer. In addition, some of these prostate cancer risk SNPs have also been found to influence prostate specific antigen (PSA) expression levels and potentially aggressive disease.

SUMMARY

Incorporation of panels of prostate cancer risk SNPs into clinical practice offers potential to provide improvements in patient selection for prostate cancer screening; PSA interpretation (e.g. by correcting for the presence of SNPs that influence PSA expression levels; decision for biopsy (using prostate cancer risk SNPs); and possibly the decision for treatment. A proposed clinical algorithm incorporating these prostate cancer risk SNPs is discussed.

A simple-to-use method incorporating genomic markers into prostate cancer risk prediction tools facilitated future validation

OBJECTIVES

To incorporate single-nucleotide polymorphisms (SNPs) into the Prostate Cancer Prevention Trial Risk Calculator (PCPTRC).

STUDY DESIGN AND SETTING

A multivariate random-effects meta-analysis of likelihood ratios (LRs) for 30 validated SNPs was performed, allowing the incorporation of linkage disequilibrium. LRs for an SNP were defined as the ratio of the probability of observing the SNP in prostate cancer cases relative to controls and estimated by published allele or genotype frequencies. LRs were multiplied by the PCPTRC prior odds of prostate cancer to provide updated posterior odds.

RESULTS

In the meta-analysis (prostate cancer cases/controls = 386,538/985,968), all but two of the SNPs had at least one statistically significant allele LR (P < 0.05). The two SNPs with the largest LRs were rs16901979 [LR = 1.575 for one risk allele, 2.552 for two risk alleles (homozygous)] and rs1447295 (LR = 1.307 and 1.887, respectively).

CONCLUSION

The substantial investment in genome-wide association studies to discover SNPs associated with prostate cancer risk and the ability to integrate these findings into the PCPTRC allows investigators to validate these observations, to determine the clinical impact, and to ultimately improve clinical practice in the early detection of the most common cancer in men.

Incorporation of detailed family history from the Swedish Family Cancer Database into the PCPT risk calculator

PURPOSE

A detailed family history provides an inexpensive alternative to genetic profiling for individual risk assessment. We updated the PCPT Risk Calculator to include detailed family histories.

MATERIALS AND METHODS

The study included 55,168 prostate cancer cases and 638,218 controls from the Swedish Family Cancer Database who were 55 years old or older in 1999 and had at least 1 male first-degree relative 40 years old or older and 1 female first-degree relative 30 years old or older. Likelihood ratios, calculated as the ratio of risk of observing a specific family history pattern in a prostate cancer case compared to a control, were used to update the PCPT Risk Calculator.

RESULTS

Having at least 1 relative with prostate cancer increased the risk of prostate cancer. The likelihood ratio was 1.63 for 1 first-degree relative 60 years old or older at diagnosis (10.1% of cancer cases vs 6.2% of controls), 2.47 if the relative was younger than 60 years (1.5% vs 0.6%), 3.46 for 2 or more relatives 60 years old or older (1.2% vs 0.3%) and 5.68 for 2 or more relatives younger than 60 years (0.05% vs 0.009%). Among men with no diagnosed first-degree relatives the likelihood ratio was 1.09 for 1 or more second-degree relatives diagnosed with prostate cancer (12.7% vs 11.7%). Additional first-degree relatives with breast cancer, or first-degree or second-degree relatives with prostate cancer compounded these risks.

CONCLUSIONS

A detailed family history is an independent predictor of prostate cancer compared to commonly used risk factors. It should be incorporated into decision making for biopsy. Compared with other costly biomarkers it is inexpensive and universally available.

Replication of breast cancer susceptibility loci in whites and African Americans using a Bayesian approach

Genome-wide association studies (GWAS) and candidate gene analyses have led to the discovery of several dozen genetic polymorphisms associated with breast cancer susceptibility, many of which are considered well-established risk factors for the disease. Despite attempts to replicate these same variant-disease associations in African Americans, the evaluable populations are often too small to produce precise or consistent results. We estimated the associations between 83 previously identified single nucleotide polymorphisms (SNPs) and breast cancer among Carolina Breast Cancer Study (1993-2001) participants using maximum likelihood, Bayesian, and hierarchical methods. The selected SNPs were previous GWAS hits (n = 22), near-hits (n = 19), otherwise well-established risk loci (n = 5), or located in the same genes as selected variants (n = 37). We successfully replicated 18 GWAS-identified SNPs in whites (n = 2,352) and 10 in African Americans (n = 1,447). SNPs in the fibroblast growth factor receptor 2 gene (FGFR2) and the TOC high mobility group box family member 3 gene (TOX3) were strongly associated with breast cancer in both races. SNPs in the mitochondrial ribosomal protein S30 gene (MRPS30), mitogen-activated protein kinase kinase kinase 1 gene (MAP3K1), zinc finger, MIZ-type containing 1 gene (ZMIZ1), and H19, imprinted maternally expressed transcript gene (H19) were associated with breast cancer in whites, and SNPs in the estrogen receptor 1 gene (ESR1) and H19 gene were associated with breast cancer in African Americans. We provide precise and well-informed race-stratified odds ratios for key breast cancer-related SNPs. Our results demonstrate the utility of Bayesian methods in genetic epidemiology and provide support for their application in small, etiologically driven investigations.

Bayes and base rates: what is an informative prior for actuarial violence risk assessment?

Bayes' theorem describes an axiomatic relationship among marginal and conditional proportions within a single "experiment." In many ways, it has been fruitful to greatly extend this idea to the task of drawing inferences from data much more generally. Commonly, what matters is how all prior knowledge is revised (or not) by new findings resulting in posterior (sometimes "subjective") probabilities. And, to address many important problems, it is sensible to conceive of probability in such subjective terms. However, some commentators in the domain of violence risk assessment have assumed an analogous axiomatic relationship among marginals (i.e., priors in the form of base rates) observed in one study and conditionals (i.e., posteriors in the form of revised rates) expected in a separate study or assessment context. We present examples from our own research to suggest this assumption is generally unwarranted and ultimately an unaddressed empirical matter.

Cancer pharmacogenomics: strategies and challenges

Genetic variation influences the response of an individual to drug treatments. Understanding this variation has the potential to make therapy safer and more effective by determining selection and dosing of drugs for an individual patient. In the context of cancer, tumours may have specific disease-defining mutations, but a patient's germline genetic variation will also affect drug response (both efficacy and toxicity), and here we focus on how to study this variation. Advances in sequencing technologies, statistical genetics analysis methods and clinical trial designs have shown promise for the discovery of variants associated with drug response. We discuss the application of germline genetics analysis methods to cancer pharmacogenomics with a focus on the special considerations for study design.

Using graded response model for the prediction of prostate cancer risk

Disease risk-associated single nucleotide polymorphisms (SNPs) identified from genome-wide association studies (GWAS) have the potential to be used for disease risk prediction. An important feature of these risk-associated SNPs is their weak individual effect but stronger cumulative effect on disease risk. To date, a stable summary estimate of the joint effect of genetic variants on disease risk prediction is not available. In this study, we propose to use the graded response model (GRM), which is based on the item response theory, for estimating the individual risk that is associated with a set of SNPs. We compare the GRM with a recently proposed risk prediction model called cumulative relative risk (CRR). Thirty-three prostate cancer risk-associated SNPs were originally discovered in GWAS by December 2009. These SNPs were used to evaluate the performance of GRM and CRR for predicting prostate cancer risk in three GWAS populations, including populations from Sweden, Johns Hopkins Hospital, and the National Cancer Institute Cancer Genetic Markers of Susceptibility study. Computational results show that the risk prediction estimates of GRM, compared to CRR, are less biased and more stable.