A markov regression model for the analysis of the postpartum lactational amenorrhea

Failure time data represent a particular case of binary longitudinal data. The corresponding analysis of the effect of explanatory covariates repeatedly collected over time on the failure rate has been largely facilitated by the Cox semi-parametric regression model. However, neither the interpretation of the estimated parameters associated with time-dependent covariates is straight-forward, nor does this model fully account for the dynamics of the effect of a covariate over time. Markovian regression models appear as complementary tools to address these specific issues from the predictive point of view. We illustrate these aspects using data from the WHO multicenter study, which was designed to analyze the relation between the duration of postpartum lactational amenorrhea and the breastfeeding pattern. One of the main advantage of this approach applied to the field of reproductive epidemiology was to provide a flexible tool, easily and directly understood by clinicians and fieldworkers, for simulating situations, which were still unobserved, and to predict their effects on the duration of amenorrhea.     

Estimation of sample selection bias models

Econometric models with sample selection biases are widely used in various fields of economics, such as labor economics. The Maximum Likelihood Estimator (MLE) is seldom used to estimate models because of computational difficulty, while Heckman's two-step estimator is widely used to estimate these models. However, Heckman's two-step estimator sometimes performs poorly. In this paper, methods of calculating the MLE are analysed, and finite sample properties of the MLE and Heckman's two-step estimator are compared using Monte Carlo experiments and empirical examples.     

Estimation of sample selection bias models

Econometric models with sample selection biases are widely used in various fields of economics, such as labor economics. The Maximum Likelihood Estimator (MLE) is seldom used to estimate models because of computational difficulty, while Heckman's two-step estimator is widely used to estimate these models. However, Heckman's two-step estimator sometimes performs poorly. In this paper, methods of calculating the MLE are analysed, and finite sample properties of the MLE and Heckman's two-step estimator are compared using Monte Carlo experiments and empirical examples.     

Bayesian predictive inference of a finite population proportion under selection bias

We show how to infer about a finite population proportion using data from a possibly biased sample. In the absence of any selection bias or survey weights, a simple ignorable selection model, which assumes that the binary responses are independent and identically distributed Bernoulli random variables, is not unreasonable. However, this ignorable selection model is inappropriate when there is a selection bias in the sample. We assume that the survey weights (or their reciprocals which we call ‘selection’ probabilities) are available, but there is no simple relation between the binary responses and the selection probabilities. To capture the selection bias, we assume that there is some correlation between the binary responses and the selection probabilities (e.g., there may be a somewhat higher/lower proportion of positive responses among the sampled units than among the nonsampled units). We use a Bayesian nonignorable selection model to accommodate the selection mechanism. We use Markov chain Monte Carlo methods to fit the nonignorable selection model. We illustrate our method using numerical examples obtained from NHIS 1995 data.     

Screening opportunity bias in case-control studies of cancer screening

In case-control evaluations of cancer screening, subjects who have died from the cancer in question (cases) are compared with those who have not (controls) with respect to screening histories. This method is subject to a rather subtle bias, among others, whereby the cases have greater opportunity to have been screened than the controls. In this paper, we propose a method of correction for this bias. We demonstrate its use on two case-control studies of mammographic screening for breast cancer.     

Impact evaluation of job training programmes: selection bias in multilevel models

This paper focuses on the evaluation of a job training programme composed of several different courses. The aim is to evaluate the impact of the programme for the participants with respect to non-participants, paying attention to possible differences in the effectiveness between the courses. The analysis is based on discrete data with a hierarchical structure. Multilevel modelling is the natural choice in this setting, but the results may be severely affected by selection bias. We propose a two-step procedure, which suits both the hierarchical structure and the observational nature of data. The method selects the appropriate control group, using standard results of the propensity score methodology. A suitable multilevel model is formulated, and the dependence of the results on the amount of non-random sample selection is analysed within a likelihood-based framework. As a result, rankings for comparative performances are obtained, adjusted for the amount of plausible selection bias. The procedure is illustrated with reference to a data set about a job training programme organized in Italy in the late 1990s.     

Reducing bias in ecological studies: an evaluation of different methodologies

Summary.  Statistical methods of ecological analysis that attempt to reduce ecological bias are empirically evaluated to determine in which circumstances each method might be practicable. The method that is most successful at reducing ecological bias is stratified ecological regression. It allows individual level covariate information to be incorporated into a stratified ecological analysis, as well as the combination of disease and risk factor information from two separate data sources, e.g. outcomes from a cancer registry and risk factor information from the census sample of anonymized records data set. The aggregated individual level model compares favourably with this model but has convergence problems. In addition, it is shown that the large areas that are covered by local authority districts seem to reduce between-area variability and may therefore not be as informative as conducting a ward level analysis. This has policy implications because access to ward level data is restricted.     

A meta-analytic framework to adjust for bias in external control studies

While randomized controlled trials (RCTs) are the gold standard for estimating treatment effects in medical research, there is increasing use of and interest in using real-world data for drug development. One such use case is the construction of external control arms for evaluation of efficacy in single-arm trials, particularly in cases where randomization is either infeasible or unethical. However, it is well known that treated patients in non-randomized studies may not be comparable to control patients—on either measured or unmeasured variables—and that the underlying population differences between the two groups may result in biased treatment effect estimates as well as increased variability in estimation. To address these challenges for analyses of time-to-event outcomes, we developed a meta-analytic framework that uses historical reference studies to adjust a log hazard ratio estimate in a new external control study for its additional bias and variability. The set of historical studies is formed by constructing external control arms for historical RCTs, and a meta-analysis compares the trial controls to the external control arms. Importantly, a prospective external control study can be performed independently of the meta-analysis using standard causal inference techniques for observational data. We illustrate our approach with a simulation study and an empirical example based on reference studies for advanced non-small cell lung cancer. In our empirical analysis, external control patients had lower survival than trial controls (hazard ratio: 0.907), but our methodology is able to correct for this bias. An implementation of our approach is available in the R package ecmeta .     

An m-estimation-based model selection criterion with a data-oriented penalty

In Wu and Zen (1999), a linear model selection procedure based on M-estimation is proposed, which includes many classical model selection criteria as its special cases, and it is shown that the selection procedure is strongly consistent for a variety of penalty functions. In this paper, we will investigate its small sample performances for some choices of fixed penalty functions. It can be seen that the performance varies with the choice of the penalty. Hence, a randomized penalty based on observed data is proposed, which preserves the consistency property and provides improved performance over a fixed choice of penalty functions.     

An exact upper limit for the variance bias in a carry-over model with correlated errors

The analysis of crossover designs assuming i.i.d. errors leads to biased variance estimates whenever the true covariance structure is not spherical. As a result, the OLS F-test for the equality of the direct effects of the treatments is not valid. Bellavance et al. [1996. Biometrics 52, 607–612] use simulations to show that a modified F-test based on an estimate of the within subjects covariance matrix allows for nearly unbiased tests. Kunert and Utzig [1993. JRSS B 55, 919–927] propose an alternative test that does not need an estimate of the covariance matrix. Instead, they correct the F-statistic by multiplying by a constant based on the worst-case scenario. However, for designs with more than three observations per subject, Kunert and Utzig (1993) only give a rough upper bound for the worst-case variance bias. This may lead to overly conservative tests. In this paper we derive an exact upper limit for the variance bias due to carry-over for an arbitrary number of observations per subject. The result holds for a certain class of highly efficient balanced crossover designs.     

An asymptotic distribution-free selection procedure for a two-way layout problem

This paper deals with an asymptotic distribution-free subset selection procedure for a two-way layout problem. The treatment effect with the largest unknown value is of interest to us. The block effect is a nuisance parameter in this problem. The proposed procedure is based on the Hodges-Lehmann estimators of location parameters. The asymptotic relative efficiency of the proposed procedure with the normal means procedure is evaluated. It is shown that the proposed procedure has a high efficiency.     

Impact of selection bias on the evaluation of clusters of chemical compounds in the drug discovery process

Expert opinion plays an important role when selecting promising clusters of chemical compounds in the drug discovery process. Indeed, experts can qualitatively assess the potential of each cluster, and with appropriate statistical methods, these qualitative assessments can be quantified into a success probability for each of them. However, one crucial element often overlooked is the procedure by which the clusters are assigned to/selected by the experts for evaluation. In the present work, the impact such a procedure may have on the statistical analysis and the entire evaluation process is studied. It has been shown that some implementations of the selection procedure may seriously compromise the validity of the evaluation even when the rating and selection processes are independent. Consequently, the fully random allocation of the clusters to the experts is strongly advocated. Copyright © 2014 John Wiley & Sons, Ltd.     

Bias in meta-analysis due to outcome variable selection within studies

Although bias in meta-analysis arising from selective publication has been studied, within-study selection has received little attention. Chronic diseases often have several possible outcome variables. Methods based on the size of the effect allow results from studies with different outcomes to be combined. However, the possibility of selective reporting of outcomes must be considered. The effect of selective reporting on estimates of the size of the effect and significance levels is presented, and sensitivity analyses are suggested. Substantial publication bias could arise from multiple testing of outcomes in a study, followed by selective reporting. Two meta-analyses, on anthelminth therapy and a treatment for incontinence, are reassessed allowing for within-study selection, as it is clear that more outcomes had been measured than were reported. The sensitivity analyses show that the robustness of the anthelminth results is dependent on what assumption one makes about the reporting strategy for the largest trial. The possible influence of correlation between within-child measurements was such that the conclusions could easily be reversed. The effect of a mild assumption on within-trial selection alone could alter general recommendations about the treatment for incontinence.     

An alternative to model selection in ordinary regression

The weaknesses of established model selection procedures based on hypothesis testing and similar criteria are discussed and an alternative based on synthetic (composite) estimation is proposed. It is developed for the problem of prediction in ordinary regression and its properties are explored by simulations for the simple regression. Extensions to a general setting are described and an example with multiple regression is analysed. Arguments are presented against using a selected model for any inferences.     

Large sample bias of maximum likeihood estimates from a series of sparse ixj tables

For a large series of IxJ tables, each containing two observations, the bias of the maximum likelihood estimates of log linear partial association parameters is shown to be equal to the parameters, regardless of the size of I and J. The partial association considered is that between row and column variables; the three way interactions are assumed to be O. This is a generalization of Andersen's results (1973a, 1973b) for a series of 2x2 tables.     

Tracing studies and analysis of the effect of loss to follow-up on mortality estimation from patient registry data

Summary. Before patient registries are used for studies of the long-term mortality that is associated with chronic medical conditions, the potential bias resulting from patients who become lost to follow-up must be investigated. A study design, used for a systemic lupus erythematosus patient registry, is described. The design involves tracing patients who are defined as 'lost to follow-up' according to specific criteria. This provides supplementary information on the mortality experience of patients who are lost to (regular) follow-up. Some methods of analysis are described, based on comparing the mortality experience of patients when under regular follow-up with the experience of patients after they are deemed to be lost to follow-up. The effect of loss to follow-up, death reporting and visits to the clinic on estimation procedures is illustrated and recommendations are made for patient registries which are to be used in mortality studies.     

Progression-free survival in oncological clinical studies: Assessment time bias and methods for its correction

Progression-free survival (PFS) is a frequently used endpoint in oncological clinical studies. In case of PFS, potential events are progression and death. Progressions are usually observed delayed as they can be diagnosed not before the next study visit. For this reason potential bias of treatment effect estimates for progression-free survival is a concern. In randomized trials and for relative treatment effects measures like hazard ratios, bias-correcting methods are not necessarily required or have been proposed before. However, less is known on cross-trial comparisons of absolute outcome measures like median survival times. This paper proposes a new method for correcting the assessment time bias of progression-free survival estimates to allow a fair cross-trial comparison of median PFS. Using median PFS for example, the presented method approximates the unknown posterior distribution by a Bayesian approach based on simulations. It is shown that the proposed method leads to a substantial reduction of bias as compared to estimates derived from maximum likelihood or Kaplan–Meier estimates. Bias could be reduced by more than 90% over a broad range of considered situations differing in assessment times and underlying distributions. By coverage probabilities of at least 94% based on the credibility interval of the posterior distribution the resulting parameters hold common confidence levels. In summary, the proposed approach is shown to be useful for a cross-trial comparison of median PFS.