Pedigree analysis package (PAP) vs. MORGAN: Model selection and hypothesis testing on a large pedigree

The MORGAN package of programs is compared to a commonly used package, PAP, with respect to model selection in segregation analysis of a quantitative trait. MORGAN uses Monte Carlo Markov chain (MCMC) methods to estimate the likelihood, whereas both versions of PAP used employ an approximation to the likelihood for the mixed model. Comparisons are done by using results obtained from simulated data. All simulations were done on the same 232-member pedigree using data generated under each of several variations of models, which included different combinations of environmental, polygenic, and major gene components. PAP, version 4.0, and MORGAN gave similar results with respect to model selection for the majority of situations, suggesting that MCMC methods provide a computationally tractable approach for analysis of more complex models that cannot be analyzed by more direct computational methods. PAP, version 3.0, gave somewhat more disparate results compared with either PAP version 4.0 or MORGAN. Both MORGAN and the two versions of PAP confirmed that the major gene component is much easier to detect in the presence of some dominance. All three packages frequently falsely accepted the polygenic model when there was high residual heritability. Genet. Epidemiol. 15:355–369,1998. © 1998 Wiley-Liss, Inc.     

Identifying influential observations in Bayesian models by using Markov chain Monte Carlo

In statistical modelling, it is often important to know how much parameter estimates are influenced by particular observations. An attractive approach is to re-estimate the parameters with each observation deleted in turn, but this is computationally demanding when fitting models by using Markov chain Monte Carlo (MCMC), as obtaining complete sample estimates is often in itself a very time-consuming task. Here we propose two efficient ways to approximate the case-deleted estimates by using output from MCMC estimation. Our first proposal, which directly approximates the usual influence statistics in maximum likelihood analyses of generalised linear models (GLMs), is easy to implement and avoids any further evaluation of the likelihood. Hence, unlike the existing alternatives, it does not become more computationally intensive as the model complexity increases. Our second proposal, which utilises model perturbations, also has this advantage and does not require the form of the GLM to be specified. We show how our two proposed methods are related and evaluate them against the existing method of importance sampling and case deletion in a logistic regression analysis with missing covariates. We also provide practical advice for those implementing our procedures, so that they may be used in many situations where MCMC is used to fit statistical models.     

核心家系中数量性状遗传方差分量模型的研究

目的 研究核心家系中带协变量的数量性状的遗传方差分量模型，探索数量性状的遗传因素和环境因素作用大小的分析方法。方法 将线性涨合模型应用于核心家系资料，根据核心家系成员的遗传关系建立遗传方差分量模型，运用SAS软件中的Mixed模块和WinBUGS软件进行参数估计，分析各影响因素作用大小。结果 模拟研究表明REML法和MCMC法都可得到近似无偏的参数估计。REML法计算耗时较少，但该法对各参数的区间估计具有一定的局限性，而MCMC法可方便地得到各参数的可信区间。结论 该模型可应用于实际家系资料，分析遗传因素和环境因素对数量表型的影响大小。     

核心家系中质量性状遗传方差分量模型的研究

目的研究核心家系中带协变量的质量性状的遗传方差分量模型,定量地评价遗传因素和环境因素对质量性状的作用。方法将广义线性混合模型应用于核心家系资料建立遗传方差分量模型,运用MCMC方法进行参数估计。结果模拟研究表明大样本时MCMC法可得到近似无偏的参数估计。结论该方法可应用于家系资料,分析遗传因素和环境因素对质量表型的影响大小。     

A Practical ANOVA Approach for Uncertainty Analysis in Population-Based Disease Microsimulation Models

Objectives

To provide a practical approach for calculating uncertainty intervals and variance components associated with initial-condition and dynamic-equation parameters in computationally expensive population-based disease microsimulation models.

MCMC收敛性诊断的方差比法及其应用

目的探讨方差比法在MCMC收敛性诊断中的应用以及收敛性诊断的重要性,以期为贝叶斯统计方法的研究和MCMC的应用提供有用的参考及帮助.方法为演示方差比法诊断的结果,对一个正态混合分布的MCMC计算实例进行诊断,诊断结果由WinBUGS软件和CODA软件给出.结果方差比法诊断结果反映出当没有对数据进行事先分组时,MCMC模拟结果经10000次迭代没有达到收敛状态,此时参数的MCMC估计值有较大偏倚.结论方差比法能够对尚未收敛的马尔科夫链给出较为明确的诊断,其诊断结果简单明了易于应用.     

A statistical procedure for the estimation of accuracy parameters in interlaboratory studies

Interlaboratory studies are conducted to estimate the accuracy of methods of laboratory measurements. The standard parameters used to describe this accuracy are the repeatability and the reproducibility. Usually variance components models are used to estimate these parameters. If the model assumptions are violated the resulting estimates for reproducibility and repeatability may, however, be biased. A new method of residual analysis in variance components models--developed by the author--may be used to detect violations of the model assumptions. If the residual analysis indicates that the model assumptions are violated, a simple robust method--which makes fewer assumptions--may be used for the estimation of accuracy parameters. The application of this residual analysis is demonstrated using data of an interlaboratory study. Graphical methods play an important role in the evaluation of the residuals. The analysis of the residuals uses methods similar to those used for the analysis of Studentized residuals in the linear model. The estimates obtained by the variance components model and the simple robust method are compared. The results of the residual analysis may be used to decide which of the two estimates can be considered more appropriate. The necessity of residual analysis in the analysis of interlaboratory studies by variance components models is pointed out. Potential hazards inherent to residual analysis in variance components models are discussed. Conclusions for the analysis of interlaboratory studies are drawn.     

Computationally efficient multipoint linkage analysis on extended pedigrees for trait models with two contributing major Loci

We have developed a computationally efficient method for multipoint linkage analysis on extended pedigrees for trait models having a two-locus quantitative trait loci (QTL) effect. The method has been implemented in the program, hg_lod, which uses the Markov chain Monte Carlo (MCMC) method to sample realizations of descent patterns conditional on marker data, then calculates the trait likelihood for each realization by efficient exact computation. Given its computational efficiency, hg_lod can handle data on large pedigrees with a lot of unobserved individuals, and can compute accurate estimates of logarithm of odds (lod) scores at a much larger number of hypothesized locations than can any existing method. We have compared hg_lod to lm_twoqtl, the first publically available linkage program for trait models with two major loci, using simulated data. Results show that our method is orders of magnitude faster while the accuracy of QTL localization is retained. The efficiency of our method also facilitates analyses with multiple trait models, for example, sensitivity analysis. Additionally, since the MCMC sampling conditions only on the marker data, there is no need to resample the descent patterns to compute likelihoods under alternative trait models. This achieves additional computational efficiency.     

Sensitivity analysis of longitudinal normal data with drop-outs

We propose to perform a sensitivity analysis to evaluate the extent to which results from a longitudinal study can be affected by informative drop-outs. The method is based on a selection model, where the parameter relating the dropout probability to the current observation is not estimated, but fixed to a set of values. This allows to evaluate several hypotheses for the degree of informativeness of the drop-out process. Expectation and variance of missing data, conditional on the drop-out time are computed, and a stochastic EM algorithm is used to obtain maximum likelihood estimates. Simulations show that when the drop-out parameter is correctly specified, unbiased estimates of the other parameters are obtained, and coverage percentages of their confidence intervals are close to their theoretical value. More interestingly, misspecification of the drop-out parameter does not considerably alter these results. This method was applied to a randomized clinical trial, designed to demonstrate non-inferiority of an inhaled corticosteroid in terms of bone density, compared with a reference treatment. Sensitivity analysis showed that the conclusion of non-inferiority was robust against different hypotheses for the drop-out process.     

Comparison of variance estimation approaches in a two-state Markov model for longitudinal data with misclassification

We examine the behaviour of the variance-covariance parameter estimates in an alternating binary Markov model with misclassification. Transition probabilities specify the state transitions for a process that is not directly observable. The state of an observable process, which may not correctly classify the state of the unobservable process, is obtained at discrete time points. Misclassification probabilities capture the two types of classification errors. Variance components of the estimated transition parameters are calculated with three estimation procedures: observed information, jackknife, and bootstrap techniques. Simulation studies are used to compare variance estimates and reveal the effect of misclassification on transition parameter estimation. The three approaches generally provide similar variance estimates for large samples and moderate misclassification. In these situations, the resampling methods are reasonable alternatives when programming partial derivatives is not appealing. With smaller chains or higher misclassification probabilities, the bootstrap method appears to be the best choice.     

Epidemiologic evaluation of measurement data in the presence of detection limits

Quantitative measurements of environmental factors greatly improve the quality of epidemiologic studies but can pose challenges because of the presence of upper or lower detection limits or interfering compounds, which do not allow for precise measured values. We consider the regression of an environmental measurement (dependent variable) on several covariates (independent variables). Various strategies are commonly employed to impute values for interval-measured data, including assignment of one-half the detection limit to nondetected values or of "fill-in" values randomly selected from an appropriate distribution. On the basis of a limited simulation study, we found that the former approach can be biased unless the percentage of measurements below detection limits is small (5-10%). The fill-in approach generally produces unbiased parameter estimates but may produce biased variance estimates and thereby distort inference when 30% or more of the data are below detection limits. Truncated data methods (e.g., Tobit regression) and multiple imputation offer two unbiased approaches for analyzing measurement data with detection limits. If interest resides solely on regression parameters, then Tobit regression can be used. If individualized values for measurements below detection limits are needed for additional analysis, such as relative risk regression or graphical display, then multiple imputation produces unbiased estimates and nominal confidence intervals unless the proportion of missing data is extreme. We illustrate various approaches using measurements of pesticide residues in carpet dust in control subjects from a case-control study of non-Hodgkin lymphoma.     

Interpretable inference on the mixed effect model with the Box–Cox transformation

We derived results for inference on parameters of the marginal model of the mixed effect model with the Box–Cox transformation based on the asymptotic theory approach. We also provided a robust variance estimator of the maximum likelihood estimator of the parameters of this model in consideration of the model misspecifications. Using these results, we developed an inference procedure for the difference of the model median between treatment groups at the specified occasion in the context of mixed effects models for repeated measures analysis for randomized clinical trials, which provided interpretable estimates of the treatment effect. From simulation studies, it was shown that our proposed method controlled type I error of the statistical test for the model median difference in almost all the situations and had moderate or high performance for power compared with the existing methods. We illustrated our method with cluster of differentiation 4 (CD4) data in an AIDS clinical trial, where the interpretability of the analysis results based on our proposed method is demonstrated. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust fit of Bayesian mixed effects regression models with application to colony forming unit count in tuberculosis research

Early bactericidal activity of tuberculosis drugs is conventionally assessed using statistical regression modeling of colony forming unit (CFU) counts over time. Typically, most CFU counts deviate little from the regression curve, but gross outliers due to erroneous sputum sampling are occasionally present and can markedly influence estimates of the rate of change in CFU count, which is the parameter of interest. A recently introduced Bayesian nonlinear mixed effects regression model was adapted to offer a robust approach that accommodates both outliers and potential skewness in the data. At its most general, the proposed regression model fits the skew Student t distribution to residuals and random coefficients. Deviance information criterion statistics and compound Laplace‐Metropolis marginal likelihoods were used to discriminate between alternative Bayesian nonlinear mixed effects regression models. We present a relatively easy method to calculate the marginal likelihoods required to determine compound Laplace‐Metropolis marginal likelihoods, by adapting methods available in currently available statistical software. The robust methodology proposed in this paper was applied to data from 6 clinical trials. The results provide strong evidence that the distribution of CFU count is often heavy tailed and negatively skewed (suggesting the presence of outliers). Therefore, we recommend that robust regression models, such as those proposed here, should be fitted to CFU count.     

Segregation analysis of quantitative traits in nuclear families: comparison of three program packages

Segregation analysis frequently is used to test for the presence of major gene effects and to estimate the various genetic and environmental components contributing to diseases. Recent advances in both theoretical models and computational algorithms have provided a number of new programs for performing segregation analyses. We compared two newer programs: REGC (part of the package "SAGE") and FISHER/MENDEL with an older established program (PAP) to determine relative accuracy in recovering parameter values and asymptotic standard errors, ability to discriminate between alternative transmission models, and execution speeds. Each program was applied to a set of computer simulations of a quantitative trait generated under a variety of genetic models. The results of these comparisons indicated that all the programs provided very similar parameter estimates, but that they differed in their abilities to identify the correct mode of transmission. In our simulations, PAP more often led to the selection of the correct transmission model, whereas REGC frequently indicated the presence of a major gene in simulations of purely polygenic transmission. Relative speeds for the programs differed, and their rank ordering varied with the complexity of the model being fitted. Although REGC was the fastest program for fitting a major gene or mixed model, it was by far the slowest program for estimating parameters in a sporadic or polygenic model.     

What to add to nothing? Use and avoidance of continuity corrections in meta‐analysis of sparse data

OBJECTIVES: To compare the performance of different meta-analysis methods for pooling odds ratios when applied to sparse event data with emphasis on the use of continuity corrections. BACKGROUND: Meta-analysis of side effects from RCTs or risk factors for rare diseases in epidemiological studies frequently requires the synthesis of data with sparse event rates. Combining such data can be problematic when zero events exist in one or both arms of a study as continuity corrections are often needed, but, these can influence results and conclusions. METHODS: A simulation study was undertaken comparing several meta-analysis methods for combining odds ratios (using various classical and Bayesian methods of estimation) on sparse event data. Where required, the routine use of a constant and two alternative continuity corrections; one based on a function of the reciprocal of the opposite group arm size; and the other an empirical estimate of the pooled effect size from the remaining studies in the meta-analysis, were also compared. A number of meta-analysis scenarios were simulated and replicated 1000 times, varying the ratio of the study arm sizes. RESULTS: Mantel-Haenszel summary estimates using the alternative continuity correction factors gave the least biased results for all group size imbalances. Logistic regression was virtually unbiased for all scenarios and gave good coverage properties. The Peto method provided unbiased results for balanced treatment groups but bias increased with the ratio of the study arm sizes. The Bayesian fixed effect model provided good coverage for all group size imbalances. The two alternative continuity corrections outperformed the constant correction factor in nearly all situations. The inverse variance method performed consistently badly, irrespective of the continuity correction used. CONCLUSIONS: Many routinely used summary methods provide widely ranging estimates when applied to sparse data with high imbalance between the size of the studies' arms. A sensitivity analysis using several methods and continuity correction factors is advocated for routine practice.     

Expected value of sample information for Weibull survival data

Expected value of sample information (EVSI) involves simulating data collection, Bayesian updating, and re-examining decisions. Bayesian updating in Weibull models typically requires Markov chain Monte Carlo (MCMC). We examine five methods for calculating posterior expected net benefits: two heuristic methods (data lumping and pseudo-normal); two Bayesian approximation methods (Tierney & Kadane, Brennan & Kharroubi); and the gold standard MCMC. A case study computes EVSI for 25 study options. We compare accuracy, computation time and trade-offs of EVSI versus study costs. Brennan & Kharroubi (B&K) approximates expected net benefits to within +/-1% of MCMC. Other methods, data lumping (+54%), pseudo-normal (-5%) and Tierney & Kadane (+11%) are less accurate. B&K also produces the most accurate EVSI approximation. Pseudo-normal is also reasonably accurate, whilst Tierney & Kadane consistently underestimates and data lumping exhibits large variance. B&K computation is 12 times faster than the MCMC method in our case study. Though not always faster, B&K provides most computational efficiency when net benefits require appreciable computation time and when many MCMC samples are needed. The methods enable EVSI computation for economic models with Weibull survival parameters. The approach can generalize to complex multi-state models and to survival analyses using other smooth parametric distributions.     

Metamodels of bias in Cox proportional-hazards and logistic regressions with heteroscedastic measurement error under group-level exposure assessment

In occupational epidemiology, group-based exposure assessment entails estimating the average exposure level in a group of workers and assigning the average to all members of the group. The assigned exposure values can be used in epidemiological analyses and have been shown to produce virtually unbiased relative-risk estimates in many situations. Although the group-based exposure assessment continues to be used widely, it is unclear whether it produces unbiased relative-risk estimates in all circumstance, specifically in Cox proportional-hazards and logistic regressions when between-worker variance is not constant but proportional to the true group mean. This question is important because (i) between-worker variance has been shown to differ among exposure groups in occupational epidemiological studies and (ii) recent theoretical work has suggested that bias may exist in such situations. We conducted computer simulations of occupational epidemiological studies to address this question and analysed simulation results using 'metamodelling'. The results indicate that small-to-negligible bias can be expected to result from heteroscedastic between-worker variance. Cox proportional-hazards models can produce attenuated risk estimates, while logistic regression may result in overestimation of risk gradient. Bias caused by ignoring the heteroscedastic measurement error is unlikely to be large enough to alter the conclusion about the direction of exposure-disease association in occupational epidemiology.     

Inference for the median residual life function in sequential multiple assignment randomized trials

In survival analysis, median residual lifetime is often used as a summary measure to assess treatment effectiveness; it is not clear, however, how such a quantity could be estimated for a given dynamic treatment regimen using data from sequential randomized clinical trials. We propose a method to estimate a dynamic treatment regimen‐specific median residual life (MERL) function from sequential multiple assignment randomized trials. We present the MERL estimator, which is based on inverse probability weighting, as well as, two variance estimates for the MERL estimator. One variance estimate follows from Lunceford, Davidian and Tsiatis' 2002 survival function‐based variance estimate and the other uses the sandwich estimator. The MERL estimator is evaluated, and its two variance estimates are compared through simulation studies, showing that the estimator and both variance estimates produce approximately unbiased results in large samples. To demonstrate our methods, the estimator has been applied to data from a sequentially randomized leukemia clinical trial. Copyright © 2013 John Wiley & Sons, Ltd.     

A semi-parametric estimate of extra-Poisson variation for vital rates

We introduce a method for estimating overdispersion in Poisson models for vital rates. We assume smoothness conditions on the counts to obtain pointwise variance estimates that we combine to obtain an estimate of the overdispersion parameter. We create confidence intervals about the observed rates using this estimate and an approximation based on the gamma distribution. The advantage of this method is that the estimates of the superpopulation rates do not depend on the smoothness assumption, yet when this assumption is met we obtain approximately unbiased estimates of the overdispersion parameter. Thus, we may calculate confidence intervals for vital rates under an overdispersed Poisson model without making parametric assumptions on the mean rates. © 1997 John Wiley & Sons, Ltd.     

Proportional hazards model with random effects

We propose a general proportional hazards model with random effects for handling clustered survival data. This generalizes the usual frailty model by allowing a multivariate random effect with arbitrary design matrix in the log relative risk, in a way similar to the modelling of random effects in linear, generalized linear and non-linear mixed models. The distribution of the random effects is generally assumed to be multivariate normal, but other (preferably symmetrical) distributions are also possible. Maximum likelihood estimates of the regression parameters, the variance components and the baseline hazard function are obtained via the EM algorithm. The E-step of the algorithm involves computation of the conditional expectations of functions of the random effects, for which we use Markov chain Monte Carlo (MCMC) methods. Approximate variances of the estimates are computed by Louis' formula, and posterior expectations and variances of the individual random effects can be obtained as a by-product of the estimation. The inference procedure is exemplified on two data sets.