Surrogate Covariate Research Articles

Point: Is there a best duration of deep molecular response to achieve therapy-free remission in chronic myeloid leukaemia?

Point: Is there a best duration of deep molecular response to achieve therapy-free remission in chronic myeloid leukaemia?

Geoadditive Quantile Regression Model for Sewer Pipes Deterioration Using Boosting Optimization Algorithm

Proactive management of wastewater pipes requires the development of deterioration models that support maintenance and inspection prioritization. The complexity and the lack of understanding of the deterioration process make this task difficult. A semiparametric Bayesian geoadditive quantile regression approach is applied to estimate the deterioration of wastewater pipe from a set of covariates that are allowed to affect linearly and nonlinearly the response variable. Categorical covariates only affect linearly the response variable. In addition, geospatial information embedding the unknown and unobserved influential covariates is introduced as a surrogate covariate that capture global autocorrelations and local heterogeneities. Boosting optimization algorithm is formulated for variable selection and parameter estimation in the model. Three geoadditive quantile regression models (5%, 50% and 95%) are developed to evaluate the band of uncertainty in the prediction of the pipes scores. The proposed model is applied to the wastewater system of the city of Calgary. The results show that an optimal selection of covariates coupled with appropriate representation of the dependence between the covariates and the response increases the accuracy in the estimation of the uncertainty band of the response variable. The proposed modeling approach is useful for the prioritization of inspections and provides knowledge for future installations. In addition, decision makers will be informed of the probability of occurrence of extreme deterioration events when the identified causal factors, in the 5% and 95% quantiles, are observed on the field.

Ecological analysis of associations between groundwater quality and hypertension and cardiovascular disease in rural Saskatchewan, Canada using Bayesian hierarchical models and administrative health data

Associations between groundwater quality and the prevalence of hypertension and ischemic heart disease were investigated in rural areas of the Canadian province of Saskatchewan. The partially ecological study was analyzed using Bayesian hierarchical models to account for spatial variability in risk. Exposure measures and health outcomes were estimated based on previously collected water quality surveillance data from public water supplies and private wells and administrative health data. Water quality exposures for each study region were estimated by applying geostatistical techniques to arsenic concentrations and principal component (PC) scores. The PC scores summarized groups of parameters measuring either health standards or aesthetic objectives described by the province. Generalized linear mixed models with a log link assessed associations between water quality and observed count of health outcomes relative to the expected value. The Bayesian models contained uncorrelated and spatially correlated random effects for each geographic region. Effect estimates were controlled for sex and age by stratification of case and expected case counts, for smoking by inclusion of sex- and age-specific prevalence of chronic obstructive pulmonary disease as a surrogate covariate, and for education and income by use of census data.There was no evidence for associations between groundwater arsenic concentrations in public or private water supplies and increased risk of hypertension or cardiovascular disease. An increase in the second aesthetic objectives PC score from public supplies was associated with a protective effect against ischemic heart disease. This PC value summarized hardness and magnesium Similarly, an increase in the second aesthetic objectives PC in private supplies was associated with decreased prevalence of hypertension.The results of this study are consistent with others demonstrating a relationship between elevated hardness and magnesium concentrations in drinking water and reduced risk of hypertension and cardiovascular disease. Further investigation is warranted with individual exposure history, particularly with respect to the potential beneficial effect of hard water on the prevalence of hypertension and cardiovascular disease.

Two-phase designs for joint quantitative-trait-dependent and genotype-dependent sampling in post-GWAS regional sequencing.

ABSTRACTWe evaluate two‐phase designs to follow‐up findings from genome‐wide association study (GWAS) when the cost of regional sequencing in the entire cohort is prohibitive. We develop novel expectation‐maximization‐based inference under a semiparametric maximum likelihood formulation tailored for post‐GWAS inference. A GWAS‐SNP (where SNP is single nucleotide polymorphism) serves as a surrogate covariate in inferring association between a sequence variant and a normally distributed quantitative trait (QT). We assess test validity and quantify efficiency and power of joint QT‐SNP‐dependent sampling and analysis under alternative sample allocations by simulations. Joint allocation balanced on SNP genotype and extreme‐QT strata yields significant power improvements compared to marginal QT‐ or SNP‐based allocations. We illustrate the proposed method and evaluate the sensitivity of sample allocation to sampling variation using data from a sequencing study of systolic blood pressure.

A comparison of surrogate endpoints for all cause mortality in men with localized unfavorable-risk prostate cancer.

21 Background: Several surrogates for prostate cancer-specific mortality exist, but whether these are surrogates for all cause mortality (ACM), and how their performance compares, is unknown. We investigated the relative efficacy of 4 candidate surrogates for ACM using the proportion of treatment effect (PTE) metric. Methods: Two-hundred and six men with localized unfavorable-risk prostate cancer were randomized to radiation therapy (RT) or RT and 6 months of androgen-deprivation therapy (ADT) from 1995 to 2001 and followed for a median of 16.62 years. Among the 159 men with no or minimal comorbidity, a significant reduction in the risk of death was observed in those randomized to RT and ADT versus RT alone; these 159 men formed the study cohort. In order to assess whether the candidate surrogated satisfied Prentice’s criteria for surrogacy, Cox regression analyses were performed to assess the risk of death for each of the candidate surrogates and treatment before and after adjusting for prostate-specific antigen (PSA), age at randomization, T category, and Gleason score. Results: PSA nadir > 0.5 ng/mL, PSA doubling time < 9 months and interval to PSA failure < 30 months met Prentice’s criteria for surrogacy (P = 0.01, 0.003, and 0.03 for the surrogate covariate in the multivariable model, respectively) for ACM, while PSA failure did not (P = 0.10). For the three surrogates, the PTE values were 103.86%, 43.09%, and 41.26%, respectively. Conclusions: A PSA nadir value of > 0.5 ng/mL following RT and ADT identified men prior to PSA failure who were at high-risk for death and therefore could be used to select men for entry, at the time of PSA nadir and before PSA failure, onto randomized trials evaluating the impact on survival of salvage ADT with or without agents shown to prolong survival in men with castrate-resistant metastatic prostate cancer. By enriching study cohorts with men who have achieved a surrogate endpoint for ACM, one can enhance the likelihood that the study will be able to observe whether survival is prolonged when novel treatment is added to ADT, as compared to ADT alone, in an abbreviated time period. Clinical Trial Number: NCT00116220

Surrogate End Points for All-Cause Mortality in Men With Localized Unfavorable-Risk Prostate Cancer Treated With Radiation Therapy vs Radiation Therapy Plus Androgen Deprivation Therapy

ImportanceSeveral surrogates for prostate cancer–specific mortality satisfying the Prentice criteria exist, but whether these are surrogates for all-cause mortality, and how their performance compares, is unknown.ObjectiveTo ascertain and compare the performance of 4 candidate surrogates (prostate-specific antigen [PSA] failure, PSA nadir >0.5 ng/mL, PSA doubling time <9 months, and interval to PSA failure <30 months) for all-cause mortality using the proportion of treatment-effect metric.Design, Setting, and ParticipantsFor this randomized clinical trial, 206 men with unfavorable-risk prostate cancer who were seen at a Harvard-affiliated academic hospital or an associated community hospital between December 1, 1995, to April 15, 2001, were identified, randomized to radiation therapy alone or radiation therapy followed by 6 months of androgen deprivation therapy, and followed for a median 16.62 years. This analysis looks at the subgroup of 157 men with minimal comorbidities or no comorbidity (median follow-up, 16.49 months).InterventionsPatients were previously randomized to receive radiation therapy or radiation and 6 months of androgen deprivation therapy.Main Outcomes and MeasuresRisk of all-cause mortality.ResultsOverall, a cohort of 157 men (median [interquartile range] age, 72.43 [68.75-75.53]) with unfavorable-risk prostate cancer and minimal or no comorbidities were selected for this study. Three tested metrics met all 4 Prentice criteria for surrogacy for the surrogate covariate in the adjusted model for all-cause mortality: PSA nadir greater than 0.5 ng/mL (adjusted hazard ratio [aHR], 1.72; 95% CI, 1.17-2.52; P = .01), PSA doubling time less than 9 months (aHR, 2.06; 95% CI, 1.29-3.28; P = .003), and interval to PSA failure less than 30 months (aHR, 1.76; 95% CI, 1.06-2.92; P = .03); while PSA failure did not. For the 3 successful surrogates, the proportion of treatment effect values were 103.86%, 43.09%, and 41.26%, respectively.Conclusions and RelevanceA PSA nadir value of greater than 0.5 ng/mL following radiation and androgen deprivation therapy appears to identify men prior to PSA failure who are at high-risk for death. This could be used to select men for entry at the time of PSA nadir onto randomized trials evaluating the impact on survival of salvage androgen deprivation therapy with or without agents shown to prolong survival in men with castrate-resistant metastatic prostate cancer.Trial Registrationclinicaltrials.gov Identifier: NCT00116220

Regression Analysis for the Additive Hazards Model with Covariate Errors

In this article, general inference procedures are proposed for the additive hazards model when covariates are subject to measurement errors and the errors are non-informative. The methods are not restricted to classical additive error models, but are capable of handling general covariate error structures. They can be applied to studies with either an external or internal validation sample, and also to studies with replicate measurements of the surrogate covariate. The asymptotic properties of the resulting estimators are derived, and simulation studies are conducted to evaluate the performance of the proposed estimators. A real example is provided.

Semiparametric Bayesian Analysis of Nutritional Epidemiology Data in the Presence of Measurement Error

We propose a semiparametric Bayesian method for handling measurement error in nutritional epidemiological data. Our goal is to estimate nonparametrically the form of association between a disease and exposure variable while the true values of the exposure are never observed. Motivated by nutritional epidemiological data, we consider the setting where a surrogate covariate is recorded in the primary data, and a calibration data set contains information on the surrogate variable and repeated measurements of an unbiased instrumental variable of the true exposure. We develop a flexible Bayesian method where not only is the relationship between the disease and exposure variable treated semiparametrically, but also the relationship between the surrogate and the true exposure is modeled semiparametrically. The two nonparametric functions are modeled simultaneously via B-splines. In addition, we model the distribution of the exposure variable as a Dirichlet process mixture of normal distributions, thus making its modeling essentially nonparametric and placing this work into the context of functional measurement error modeling. We apply our method to the NIH-AARP Diet and Health Study and examine its performance in a simulation study.

A Pseudo–Partial Likelihood Method for Semiparametric Survival Regression With Covariate Errors

This article presents an estimator for the regression coefficient vector in the Cox proportional hazards model with covariate error. The estimator is obtained by maximizing a likelihood-type function similar to the Cox partial likelihood. The likelihood function involves the cumulative baseline hazard function, for which a simple estimator is substituted. The method is capable of handling general covariate error structures; it is not restricted to the independent additive error model. It can be applied to studies with either an external or internal validation sample, and also to studies with replicate measurements of the surrogate covariate. The estimator is shown to be consistent and asymptotically normal, and an estimate of the asymptotic covariance matrix is derived. Some extensions to general transformation survival models are indicated. Simulation studies are presented for a setup with a single error-prone binary covariate and a setup with a single error-prone normally distributed covariate. These simulation studies show that the method typically produces estimates with low bias and confidence intervals with accurate coverage rates. Efficiency results relative to fully parametric maximum likelihood are also presented. The method is applied to data from the Framingham Heart Study.

Estimation in the Cox Model with Missing Covariate Data

We consider a Cox model for right-censored survival data when a covariate is missing completely at random and when a continuous surrogate covariate and a complete validation sample are available. The likelihood is approximated using a nonparametric estimation of the missing covariate values and we propose new estimators of the regression parameter and of the cumulative hazard function based on the approximated likelihood. We show that the estimators are n 1/2 -consistent and asymptotically Gaussian and give conditions which ensure that the estimator of the regression parameter has the minimal asymptotic variance in the model with missing covariate data.

Additive Hazards Regression with Covariate Measurement Error

The additive hazards model specifies that the hazard function conditional on a set of covariates is the sum of an arbitrary baseline hazard function and a regression function of covariates. This article deals with the analysis of this semiparametric regression model with censored failure time data when covariates are subject to measurement error. We assume that the true covariate is measured on a randomly chosen validation set, whereas a Surrogate covariate (i.e., an error-prone version of the true covariate) is measured on all study subjects. The Surrogate covariate is modeled as a linear function of the true covariate plus a random error. Only moment conditions are imposed on the measurement error distribution. We develop a class of estimating functions for the regression parameters that involve weighted combinations of the contributions from the validation and nonvalidation sets. The optimal weight can be selected by an adaptive procedure. The resulting estimators are consistent and asymptotically normal with easily estimated variances. Simulation results demonstrate that the asymptotic approximations are adequate for practical use. Illustration with a real medical study is provided.

Exploring Heterogeneity in Randomized Trials Via Meta-Analysis

Meta-analysis of clinical trials with heterogeneous results provides an opportunity to learn a great deal about variations in treatment effectiveness. Rather than computing a single summary estimate of a series of trials, it may be more informative to explore the effect that different study characteristics may make on treatment efficacy. Regression analysis offers a tool for these analyses. This paper outlines and applies hierarchical Bayesian models for this purpose, presenting two examples of meta-regression using summary data, in one of which results are compared with those from analysis of complete individual patient data. When covariates are not readily available, the event rate in the control group can become a surrogate covariate. An empirical study of 115 meta-analyses shows that this control rate is significantly correlated with the odds ratio about 15% of the time. This suggests that investigators should search for the causes of heterogeneity related to patient characteristics and treatment protocols to determine when treatment is most beneficial and that they should plan to study this heterogeneity in clinical trials.

A Semiparametric Mixture Approach to Case-Control Studies with Errors in Covariables

Abstract Methods are devised for estimating the parameters of a prospective logistic model in a case-control study with dichotomous response D that depends on a covariate X. For a portion of the sample, both the gold standard X and a surrogate covariate W are available; however, for the greater portion of the data, only the surrogate covariate W is available. By using a mixture model, the relationship between the true covariate and the response can be modeled appropriately for both types of data. The likelihood depends on the marginal distribution of X and the measurement error density (W|X, D). The latter is modeled parametrically based on the validation sample. The marginal distribution of the true covariate is modeled using a nonparametric mixture distribution. In this way we can improve the efficiency and reduce the bias of the parameter estimates. The results also apply when there is no validation data provided the error distribution is known or estimated from an independent data source. Many of the results also apply to the easier case of prospective sampling.