Propensity score-based diagnostics for categorical response regression models

For binary or categorical response models, most goodness-of-fit statistics are based on the notion of partitioning the subjects into groups or regions and comparing the observed and predicted responses in these regions by a suitable chi-squared distribution. Existing strategies create this partition based on the predicted response probabilities, or propensity scores, from the fitted model. In this paper, we follow a retrospective approach, borrowing the notion of balancing scores used in causal inference to inspect the conditional distribution of the predictors, given the propensity scores, in each category of the response to assess model adequacy. We can use this diagnostic under both prospective and retrospective sampling designs, and it may ascertain general forms of misspecification. We first present simple graphical and numerical summaries that can be used in a binary logistic model. We then generalize the tools to propose model diagnostics for the proportional odds model. We illustrate the methods with simulation studies and two data examples: (i) a case-control study of the association between cumulative lead exposure and Parkinson's disease in the Boston, Massachusetts, area and (ii) and a cohort study of biomarkers possibly associated with diabetes, from the VA Normative Aging Study.

BAYESIAN SHRINKAGE METHODS FOR PARTIALLY OBSERVED DATA WITH MANY PREDICTORS

Motivated by the increasing use of and rapid changes in array technologies, we consider the prediction problem of fitting a linear regression relating a continuous outcome Y to a large number of covariates X , eg measurements from current, state-of-the-art technology. For most of the samples, only the outcome Y and surrogate covariates, W , are available. These surrogates may be data from prior studies using older technologies. Owing to the dimension of the problem and the large fraction of missing information, a critical issue is appropriate shrinkage of model parameters for an optimal bias-variance tradeoff. We discuss a variety of fully Bayesian and Empirical Bayes algorithms which account for uncertainty in the missing data and adaptively shrink parameter estimates for superior prediction. These methods are evaluated via a comprehensive simulation study. In addition, we apply our methods to a lung cancer dataset, predicting survival time (Y) using qRT-PCR ( X ) and microarray ( W ) measurements.

Investigating parent of origin effects (POE) and anticipation in Irish Lynch syndrome kindreds

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Background: Genetic diseases associated with dynamic mutations often display parent-of-origin effects (POE) in which the risk of disease depends on the sex of the parent from whom the disease allele was inherited. Genetic anticipation describes the progessively earlier onset and increased severity of disease in successive generations of a family. Previous studies have provided limited evidence for and against both POE effect and anticipation in Lynch syndrome (LS). We sought evidence for a specific POE effect and anticipation in Irish LS families. Methods: Affected parent-child pairs (APCPs) (N = 53) were evaluated from LS kindreds (N = 20) from two hospital-based registries and one cancer genetic centre. POE were investigated by studying the ages at diagnosis in the offspring of affected parent-child pairs. Anticipation was assessed by a paired t-test, and bivariate Huang and Vieland model. Results: See Table. Paired t-test revealed anticipation with children developing cancer mean 11.8 years earlier than parents, and 12.7 years using the Huang and Vieland model (p < 0.001). Conclusions: These data demonstrate a similar age at diagnosis among all offspring of affected mothers that was indistinguishable from affected fathers. Affected sons of affected mothers were diagnosed with cancer almost 3 years younger than female offspring; however, this finding failed to reach statistical significance. Evidence of anticipation was suggested in this cohort, emphasizing the importance of early-onset screening. Addition LS families are under review and updated data will be presented at the meeting. [Table: see text]

Investigating parent of origin effects (POE) and anticipation in Irish Lynch syndrome kindreds

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Background: Genetic diseases associated with dynamic mutations often display parent-of-origin effects (POEs) in which the risk of disease depends on the sex of the parent from whom the disease allele was inherited. Genetic anticipation describes the progressively earlier onset and increased severity of disease in successive generations of a family. Previous studies have provided limited evidence for and against both POE effect and anticipation in Lynch syndrome. We sought evidence for a specific POE effect and anticipation in Irish Lynch syndrome families. Methods: Affected parent-child pairs (APCPs) (N = 53) were evaluated from kindreds (N = 20) from two hospital-based registries of MMR mutation carriers. POE were investigated by studying the ages at diagnosis in the offspring of affected parent-child pairs. Anticipation was assessed using the bivariate Huang and Vieland model. Results: Paired t-test revealed anticipation with children developing cancer mean 11.8 years earlier than parents, and 12.7 years using the Veiland and Huang bivariate model (p < 0.001). Conclusions: These data demonstrate a similar age at diagnosis among all offspring of affected mothers that was indistinguishable from affected fathers. Affected sons of affected mothers were diagnosed with cancer almost 3 years younger than female offspring; however, this finding failed to reach statistical significance. Genetic anticipation was present in this cohort of LS families, emphasizing the importance of early-onset screening. An additional 60 LS kindreds are under review and updated data will be presented at the meeting. [Table: see text]

Incorporating auxiliary information for improved prediction in high-dimensional datasets: an ensemble of shrinkage approaches

With advancement in genomic technologies, it is common that two high-dimensional datasets are available, both measuring the same underlying biological phenomenon with different techniques. We consider predicting a continuous outcome Y using X, a set of p markers which is the best available measure of the underlying biological process. This same biological process may also be measured by W, coming from a prior technology but correlated with X. On a moderately sized sample, we have (Y,X,W), and on a larger sample we have (Y,W). We utilize the data on W to boost the prediction of Y by X. When p is large and the subsample containing X is small, this is a p>n situation. When p is small, this is akin to the classical measurement error problem; however, ours is not the typical goal of calibrating W for use in future studies. We propose to shrink the regression coefficients β of Y on X toward different targets that use information derived from W in the larger dataset. We compare these proposals with the classical ridge regression of Y on X, which does not use W. We also unify all of these methods as targeted ridge estimators. Finally, we propose a hybrid estimator which is a linear combination of multiple estimators of β. With an optimal choice of weights, the hybrid estimator balances efficiency and robustness in a data-adaptive way to theoretically yield a smaller prediction error than any of its constituents. The methods, including a fully Bayesian alternative, are evaluated via simulation studies. We also apply them to a gene-expression dataset. mRNA expression measured via quantitative real-time polymerase chain reaction is used to predict survival time in lung cancer patients, with auxiliary information from microarray technology available on a larger sample.

Investigating parent of origin effects (POE) and anticipation in Irish Lynch Syndrome kindreds

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Background: Genetic diseases associated with dynamic mutations often display parent-of-origin effects (POEs) in which the risk of disease depends on the sex of the parent from whom the disease allele was inherited. Genetic anticipation describes the progressively earlier onset and increased severity of disease in successive generations of a family. We sought evidence for a specific POE effect in Lynch syndrome families by studying the ages at diagnosis in the offspring of affected parent-child pairs. In addition, a paired t-test and a specifically developed bivariate statistical approach were used to assess a possible role of anticipation. Methods: Affected parent-child pairs (APCPs) (N = 53) were evaluated from kindreds (N = 20) with known germline MMR mutations. Differences in the mean age of LS associated cancer diagnosis were compared between various groups via t-tests: all p-values were 2-sided. Different group comparisons include: (1) unique parental ages (mothers vs. fathers) (2) affected offspring ages (mothers vs. fathers (3) age of affected female offspring (mothers vs. fathers (4) age of affected male offspring (mothers vs. fathers. Results: There were no statistically significant differences in diagnosis of offspring or parents. Sons of affected mothers were more likely to be affected than daughters of affected mothers. However, the affected cohort/study number is small and while affected sons of affected mothers were diagnosed with cancer almost 3 years younger than female offspring (39.7 vs 42.5), this finding failed to reach clinical significance. Comparison in age at diagnosis in 53 affected parent-child pairs with Lynch syndrome associated malignancies Conclusions: These data demonstrate a similar age at diagnosis among all offspring of affected mothers that was indistinguishable from affected fathers. This study will be expanded to recruit more eligible affected parent child pairs to increase the power of this evaluation. The Veiland & Huang algorithm will be used to compare mean ages of affected parents and children.

Bayesian modeling for genetic anticipation in presence of mutational heterogeneity: a case study in Lynch syndrome

Genetic anticipation, described by earlier age of onset (AOO) and more aggressive symptoms in successive generations, is a phenomenon noted in certain hereditary diseases. Its extent may vary between families and/or between mutation subtypes known to be associated with the disease phenotype. In this article, we posit a Bayesian approach to infer genetic anticipation under flexible random effects models for censored data that capture the effect of successive generations on AOO. Primary interest lies in the random effects. Misspecifying the distribution of random effects may result in incorrect inferential conclusions. We compare the fit of four-candidate random effects distributions via Bayesian model fit diagnostics. A related statistical issue here is isolating the confounding effect of changes in secular trends, screening, and medical practices that may affect time to disease detection across birth cohorts. Using historic cancer registry data, we borrow from relative survival analysis methods to adjust for changes in age-specific incidence across birth cohorts. Our motivating case study comes from a Danish cancer register of 124 families with mutations in mismatch repair (MMR) genes known to cause hereditary nonpolyposis colorectal cancer, also called Lynch syndrome (LS). We find evidence for a decrease in AOO between generations in this article. Our model predicts family-level anticipation effects that are potentially useful in genetic counseling clinics for high-risk families.

A review of statistical methods for testing genetic anticipation: looking for an answer in Lynch syndrome

Anticipation, manifested through decreasing age of onset or increased severity in successive generations, has been noted in several genetic diseases. Statistical methods for genetic anticipation range from a simple use of the paired t-test for age of onset restricted to affected parent-child pairs to a recently proposed random effects model which includes extended pedigree data and unaffected family members [Larsen et al., 2009]. A naive use of the paired t-test is biased for the simple reason that age of onset has to be less than the age at ascertainment (interview) for both affected parent and child, and this right truncation effect is more pronounced in children than in parents. In this study, we first review different statistical methods for testing genetic anticipation in affected parent-child pairs that address the issue of bias due to right truncation. Using affected parent-child pair data, we compare the paired t-test with the parametric conditional maximum likelihood approach of Huang and Vieland [1997] and the nonparametric approach of Rabinowitz and Yang [1999] in terms of Type I error and power under various simulation settings and departures from the modeling assumptions. We especially investigate the issue of multiplex ascertainment and its effect on the different methods. We then focus on exploring genetic anticipation in Lynch syndrome and analyze new data on the age of onset in affected parent-child pairs from families seen at the University of Michigan Cancer Genetics clinic with a mutation in one of the three main mismatch repair (MMR) genes. In contrast to the clinic-based population, we re-analyze data on a population-based Lynch syndrome cohort, derived from the Danish HNPCC-register. Both datasets indicate evidence of genetic anticipation in Lynch syndrome. We then expand our review to incorporate recently proposed statistical methods that consider family instead of affected pairs as the sampling unit. These prospective censored regression models offer additional flexibility to incorporate unaffected family members, familial correlation and other covariates into the analysis. An expanded dataset from the Danish HNPCC-register is analyzed by this alternative set of methods.