Independence Estimating Equations for Controlled Clinical Trials with Small Sample Sizes

Objectives: The application of independence estimating equations (IEE) for controlled clinical trials (CCTs) has recently been discussed, and recommendations for its use have been derived for testing hypotheses. The robust estimator of variance has been shown to be liberal for small sample sizes. Therefore a series of modifications has been proposed. In this paper we systematically compare confidence intervals (CIs) proposed in the literature for situations that are common in CCTs.

Methods: Using Monte-Carlo simulation studies, we compared the coverage probabilities of CIs and non-convergence probabilities for the parameters of the mean structure for small samples using modifications of the variance estimator proposed by Mancl and de Rouen [7], Morel et al. [8] and Pan [3].

Results: None of the proposed modifications behave well in each investigated situation. For parallel group designs with repeated measurements and binary response the method proposed by Pan maintains the nominal level. We observed non-convergence of the IEE algorithm in up to 10% of the replicates depending on response probabilities in the treatment groups. For comparing slopes with continuous responses, the approach of Morel et al. can be recommended.

Conclusions: Results of non-convergence probabilities show that IEE should not be used in parallel group designs with binary endpoints and response probabilities close to 0 or 1. Modifications of the robust variance estimator should be used for sample sizes up to 100 clusters for CI estimation.

Tutorial on Microarray Gene Expression Experiments

Objectives: With the collection of articles presented in this special issue, we aim at educating interested statisticians and biometricians on the one hand as well as biologists and medical researchers on the other with respect to basic necessities in planning, conducting and analyzing microarray gene expression experiments. The reader should get comprehensive directions to understand both the overall structure of this approach as well as the decisive details, which enable – or thwart – a meaningful data analysis.

Methods: For a one-day workshop with tutorial character we brought together experts in design, conduct and analysis of microarray gene expression experiments who prepared a series of comprehensive lessons. These contributions were then reworked into a series of introductory articles and bundled in form and content as a Special Topic.

Results: It was possible to present a tutorial overview of the field. The interested reader was able to learn the basic necessities and was referred to further references for details on the possible alternatives. A recipe style all-embracing plan, covering all eventualities and possibilities was not only beyond the scope of an introductory tutorial-like presentation, but was also not yet agreed upon by the scientific society.

Conclusions: It proved feasible to find a framework for integrating the interdisciplinary approaches to the challenging field of gene expression analysis with microarrays, hopefully contributing to a rapid and comprehensive introduction for novices.

Sample Selection for Microarray Gene Expression Studies

Objectives: The choice of biomedical samples for microarray gene expression studies is decisive for both validity and interpretability of results. We present a consistent, comprehensive framework to deal with the typical selection problems in microarray studies.

Methods: Microarray studies are designed either as case-control studies or as comparisons of parallel groups from cohort studies, since high levels of random variation in the experimental approach thwart absolute measurements of gene expression levels. Validity and results of gene expression studies heavily rely on the appropriate choice of these study groups. Therefore, the so-called principles of comparability, which are well known from both clinical and epidemiological studies, need to be applied to microarray experiments.

Results: The principles of comparability are the study-base principle, the principle of deconfounding and the principle of comparable accuracy in measurements. We explain each of these principles, show how they apply to microarray experiments, and illustrate them with examples. The examples are chosen as to represent typical stumbling blocks of microarray experimental design, and to exemplify the benefits of implementing the principles of comparability in the setting of micro-array experiments.

Conclusions: Microarray studies are closely related to classical study designs and therefore have to obey the same principles of comparability as these. Their validity should not be compromised by selection, confounding or information bias. The so-called study-base principle, calling for comparability and thorough definition of the compared cell populations, is the key principle for the choice of biomedical samples and controls in microarray studies.

Practical Considerations on the Use of Extreme Sib-pairs for Obesity

Objectives: The extreme sib-pair approach has been shown to be a powerful strategy to identify susceptibility loci linked to quantitative traits. The body mass index is the usually assessed trait in genetic studies on human obesity. Environmental factors clearly play an important role for this trait. We hypothesized that the low weight of most sibs who were seemingly discordant to the obese index proband was influenced by other environmental and/or genetic factors like restrained eating or psychiatric disorders.

Methods: A screening questionnaire was sent to parents of all consecutively admitted patients three weeks prior to referral of index probands for inpatient treatment of obesity. The first 320 families were further investigated. Twenty-seven seemingly extremely discordant sib-pairs (ED) were identified and examined in detail.

Results: The low weight of most sibs who were seemingly discordant to the obese index proband was influenced by factors like restrained eating or psychiatric disorders. Only 20% of the interviewed ED could be considered as genuine ED.

Conclusion: We conclude that extensive medical evaluation is necessary if the aim is to guarantee genuine ED in family studies for human obesity. Non-paternity deserves specific attention in ED studies.

Sample Size Calculations for Controlled Clinical Trials Using Generalized Estimating Equations (GEE)

Objectives: Clinical trials with correlated response data based on generalized estimating equations (GEE) have become increasingly popular as they require smaller samples than classical methods that ignore the clustered nature of the data. We have recently derived the recommendation to use the independence estimating equations (IEE) as primary analysis in most controlled clinical trials instead of GEE with estimated correlations [1]. Although several approaches for sample size and power calculation have been proposed, we have shown that most of these procedures are very specific and not as general as required for designing clinical trials.

Methods: We extended the previously developed SAS macro GEESIZE to overcome this restriction. Specifically, we have added the option of an independence working correlation matrix required for the IEE. Additionally, we have reformulated the hypotheses to allow for coding that includes an intercept term instead of the previously used analysis of variance coding.

Results: To demonstrate the validity of GEESIZE we investigate the calculated sample sizes for specific models where closed formulae are available. For illustration, we utilize GEESIZE for planning a new trial on the treatment of hypertension and thereby exemplify its flexibility.

Conclusions: We show that our freely available macro is a very general and useful tool for sample size calculation purposes in clinical trials with correlated data.

Discussion of “The Evolution of Boosting Algorithms” and “Extending Statistical Boosting”

This article is part of a For-Discussion-Section of Methods of Information in Medicine about the papers “The Evolution of Boosting Algorithms – From Machine Learning to Statistical Modelling” [1] and “Extending Statistical Boosting – An Overview of Recent Methodological Developments” [2], written by Andreas Mayr and co-authors. It is introduced by an editorial. This article contains the combined commentaries invited to independently comment on the Mayr et al. papers. In sub-sequent issues the discussion can continue through letters to the editor.

Location Tests for Biomarker Studies: A Comparison Using Simulations for the Two-sample Case

Background: Gene, protein, or metabolite expression levels are often non-normally distributed, heavy tailed and contain outliers. Standard statistical approaches may fail as location tests in this situation.

Objectives: In three Monte-Carlo simulation studies, we aimed at comparing the type I error levels and empirical power of standard location tests and three adaptive tests [O’Gorman, Can J Stat 1997; 25: 269 –279; Keselman et al., Brit J Math Stat Psychol 2007; 60: 267– 293; Szymczak et al., Stat Med 2013; 32: 524 – 537] for a wide range of distributions.

Methods: We simulated two-sample scena -rios using the g-and-k-distribution family to systematically vary tail length and skewness with identical and varying variability between groups.

Results: All tests kept the type I error level when groups did not vary in their variability. The standard non-parametric U-test per -formed well in all simulated scenarios. It was outperformed by the two non-parametric adaptive methods in case of heavy tails or large skewness. Most tests did not keep the type I error level for skewed data in the case of heterogeneous variances.

Conclusions: The standard U-test was a powerful and robust location test for most of the simulated scenarios except for very heavy tailed or heavy skewed data, and it is thus to be recommended except for these cases. The non-parametric adaptive tests were powerful for both normal and non-normal distributions under sample variance homogeneity. But when sample variances differed, they did not keep the type I error level. The parametric adaptive test lacks power for skewed and heavy tailed distributions.

Generalized Estimating Equations

Background: Generalized estimating equations (GEE) are an extension of generalized linear models (GLM) in that they allow adjusting for correlations between observations. A major strength of GEE is that they do not require the correct specification of the multivariate distribution but only of the mean structure.

Objectives: Several concerns have been raised about the validity of GEE when applied to dichotomous dependent variables. In this contribution, we summarize the theoretical findings concerning efficiency and validity of GEE.

Methods: We introduce the GEE in a formal way, summarize general findings on the choice of the working correlation matrix, and show the existence of a dilemma for the optimal choice of the working correlation matrix for dichotomous dependent variables.

Results: Biological and statistical arguments for choosing a specific working correlation matrix are given. Three approaches are described for overcoming the range restriction of the correlation coefficient.

Conclusions: The three approaches described in this article for overcoming the range restrictions for dichotomous dependent variables in GEE models provide a simple and practical way for use in applications.

In vitro effects of the toll-like receptor agonists monophosphoryl lipid A and CpG-rich oligonucleotides on cytokine production by equine cells

Insect bite hypersensitivity (IBH) is an equine allergic dermatitis to Culicoides spp. antigens. Attempts at using allergen-specific immunotherapy (AIT) as a treatment for IBH have so far proven unsuccessful. Toll-like receptor (TLR) agonists can promote a shift in the immune response from the allergy-promoting T helper cell 2 (Th2) response towards a Th1 and/or regulatory response. The aim of this study was to evaluate two immunomodulatory TLR agonists in vitro as potential vaccine adjuvants for a more efficacious AIT in IBH. Peripheral blood mononuclear cells (PBMCs) from healthy and IBH-affected horses were stimulated with the TLR-agonists monophosphoryl lipid A (MPLA) or CpG-rich oligodeoxynucleotides (CpG-ODN) in the presence or absence of Culicoides spp. allergens. Cytokine concentrations of interferon (IFN)-α, IFN-γ, interleukin (IL)-4, IL-10 and IL-17 were quantified in the supernatants of stimulated PBMCs. MPLA induced IL-10 secretion in all horses, regardless of presence and nature of antigens, while suppressing antigen-induced production of IFN-γ, IL-4 and IL-17. CpG-ODN significantly increased IFN-α, IFN-γ and IL-4 production, but had little effect on IL-10 production. In conclusion, MPLA promotes a regulatory immune response and is therefore a promising adjuvant candidate for allergy vaccines in horses. While C-class CpG-ODN is an unsuitable adjuvant for AIT, it induces IFN-γ and IFN-α, and thus may be a useful adjuvant in combination with vaccines for equine infectious or neoplastic diseases.

H.E.S.S. Limits on Linelike Dark Matter Signatures in the 100 GeV to 2 TeV Energy Range Close to the Galactic Center

A search for dark matter linelike signals iss performed in the vicinity of the Galactic Center by the H.E.S.S. experiment on observational data taken in 2014. An unbinned likelihood analysis iss developed to improve the sensitivity to linelike signals. The upgraded analysis along with newer data extend the energy coverage of the previous measurement down to 100 GeV. The 18 h of data collected with the H.E.S.S. array allow one to rule out at 95% C.L. the presence of a 130 GeV line (at l=-1.5°, b=0° and for a dark matter profile centered at this location) previously reported in Fermi-LAT data. This new analysis overlaps significantly in energy with previous Fermi-LAT and H.E.S.S.

RESULTS

No significant excess associated with dark matter annihilations was found in the energy range of 100 GeV to 2 TeV and upper limits on the gamma-ray flux and the velocity weighted annihilation cross section are derived adopting an Einasto dark matter halo profile. Expected limits for present and future large statistics H.E.S.S. observations are also given.

Search for Dark Matter Annihilations towards the Inner Galactic Halo from 10 Years of Observations with H.E.S.S

The inner region of the Milky Way halo harbors a large amount of dark matter (DM). Given its proximity, it is one of the most promising targets to look for DM. We report on a search for the annihilations of DM particles using γ-ray observations towards the inner 300 pc of the Milky Way, with the H.E.S.S. array of ground-based Cherenkov telescopes. The analysis is based on a 2D maximum likelihood method using Galactic Center (GC) data accumulated by H.E.S.S. over the last 10 years (2004-2014), and does not show any significant γ-ray signal above background. Assuming Einasto and Navarro-Frenk-White DM density profiles at the GC, we derive upper limits on the annihilation cross section ⟨σv⟩. These constraints are the strongest obtained so far in the TeV DM mass range and improve upon previous limits by a factor 5. For the Einasto profile, the constraints reach ⟨σv⟩ values of 6×10^{-26}  cm^{3} s^{-1} in the W^{+}W^{-} channel for a DM particle mass of 1.5 TeV, and 2×10^{-26}  cm^{3} s^{-1} in the τ^{+}τ^{-} channel for a 1 TeV mass. For the first time, ground-based γ-ray observations have reached sufficient sensitivity to probe ⟨σv⟩ values expected from the thermal relic density for TeV DM particles.

[Job stress of nursing aides in Swiss nursing homes : Nonlinear canonical analysis]

BACKGROUND

Due to demographic changes, the demand for care in nursing homes for the elderly and infirmed is growing. At the same time nursing staff shortages are also increasing. Nursing aides are the primary care providers and comprise the largest staff group in Swiss nursing homes. They are exposed to various forms of job stress, which threaten job retention.

OBJECTIVE

The aim of this study was to discover which features of the work situation and which personal characteristics of the nursing aides were related to the workload.

MATERIAL AND METHODS

Data from nursing aides in Swiss nursing homes were investigated through a secondary analysis of a national quantitative cross-sectional study, using descriptive statistics and a nonlinear canonical correlation analysis.

RESULTS

A total of 1054 nursing aides were included in the secondary analysis, 94.6 % of whom were women between the ages of 42 and 61 years. The job stress most frequently mentioned in the descriptive analysis, almost 60 % of the participants referred to it, was staff shortage. The nonlinear canonical correlation analysis revealed that many job strains are caused by social and organizational issues. In particular, a lack of support from supervisors was associated with staff not feeling appreciated. These job strains correlated with a high level of responsibility, the feeling of being unable to work independently and a feeling of being exploited. These strains were predominant in the nursing aides between 32 and 51 years old who had part time jobs but workloads of 80-90 %.

CONCLUSION

Middle-aged nursing aides who worked to 80-90 % are particularly at risk to resign from the position prematurely. Measures need to be mainly implemented in the social and organizational areas. It can be assumed that a targeted individual support, recognition and promotion of nursing aides may decrease the level of job strain.

Development of a simple tool to predict the risk of postpartum diabetes in women with gestational diabetes mellitus

AIMS

Women with gestational diabetes mellitus (GDM) have an increased risk of diabetes postpartum. We developed a score to predict the long-term risk of postpartum diabetes using clinical and anamnestic variables recorded during or shortly after delivery.

METHODS

Data from 257 GDM women who were prospectively followed for diabetes outcome over 20 years of follow-up were used to develop and validate the risk score. Participants were divided into training and test sets. The risk score was calculated using Lasso Cox regression and divided into four risk categories, and its prediction performance was assessed in the test set.

RESULTS

Postpartum diabetes developed in 110 women. The computed training set risk score of 5 × body mass index in early pregnancy (per kg/m(2)) + 132 if GDM was treated with insulin (otherwise 0) + 44 if the woman had a family history of diabetes (otherwise 0) - 35 if the woman lactated (otherwise 0) had R (2) values of 0.23, 0.25, and 0.33 at 5, 10, and 15 years postpartum, respectively, and a C-Index of 0.75. Application of the risk score in the test set resulted in observed risk of postpartum diabetes at 5 years of 11 % for low risk scores ≤140, 29 % for scores 141-220, 64 % for scores 221-300, and 80 % for scores >300.

CONCLUSIONS

The derived risk score is easy to calculate, allows accurate prediction of GDM-related postpartum diabetes, and may thus be a useful prediction tool for clinicians and general practitioners.