Robust MM-Estimation and Inference in Mixed Linear Models

Mixed linear models are used to analyse data in many settings. These models generally rely on the normality assumption and are often fitted by means of the maximum likelihood estimator (MLE) or the restricted maximum likelihood estimator (REML). However, the sensitivity of these estimation techniques and related tests to this underlying assumption has been identified as a weakness that can even lead to wrong interpretations. Recently Copt and Victoria-Feser(2005) proposed a high breakdown estimator, namely an S-estimator, for general mixed linear models. It has the advantage of being easy to compute - even for highly structured variance matrices - and allow the computation of a robust score test. However this proposal cannot be used to define a likelihood ratio type test which is certainly the most direct route to robustify an F-test. As the latter is usually a key tool to test hypothesis in mixed linear models, we propose two new robust estimators that allow the desired extension. They also lead to resistant Wald-type tests useful for testing contrasts and covariate efects. We study their properties theoretically and by means of simulations. An analysis of a real data set illustrates the advantage of the new approach in the presence of outlying observations.

Efficacy and safety of atacicept for prevention of flares in patients with moderate-to-severe systemic lupus erythematosus (SLE): 52-week data (APRIL-SLE randomised trial)

OBJECTIVES: Despite advances in systemic lupus erythematosus (SLE) treatment, many patients suffer from the disease and side effects. Atacicept is a fusion protein that blocks B-lymphocyte stimulator and a proliferation-inducing ligand, which are increased in patients with SLE. METHODS: In this double-blind, placebo-controlled study, patients with moderate-to-severe SLE were randomised to atacicept 75 mg or atacicept 150 mg administered subcutaneously, or placebo twice-weekly for 4 weeks, then weekly for 48 weeks. Primary and secondary efficacy measures were the proportion of patients experiencing at least one flare of British Isles Lupus Assessment Group A or B, and time to first flare, respectively. RESULTS: Enrolment in the atacicept 150 mg arm was discontinued prematurely due to two deaths. In the intention-to-treat population (n=461), there was no difference in flare rates or time to first flare between atacicept 75 mg and placebo. Analysis of patients treated with atacicept 150 mg suggested beneficial effect versus placebo in flare rates (OR: 0.48, p=0.002) and time to first flare (HR: 0.56, p=0.009). Both atacicept doses were associated with reductions in total Ig levels and anti-dsDNA antibodies, and increases in C3 and C4 levels. Most treatment-emergent adverse events were mild or moderate. CONCLUSIONS: There was no difference between atacicept 75 mg and placebo for flare rate or time to first flare. Analysis of atacicept 150 mg suggested benefit. TRIAL REGISTRATION NUMBER: EudraCT: 2007-003698-13; NCT00624338

Biolimus-A9 polymer-free coated stent in high bleeding risk patients with acute coronary syndrome: a Leaders Free ACS sub-study.

Aims: Although a true clinical challenge, high bleeding risk patients with an acute coronary syndrome (ACS) undergoing percutaneous coronary intervention (PCI) have never been specifically studied. Leaders Free ACS, a pre-specified Leaders Free sub-study, determined efficacy, and safety of a combination of 1-month dual anti-platelet therapy (DAPT) with implantation of either a polymer-free Biolimus-A9-coated stent (BA9-DCS) or a bare-metal stent (BMS) in these patients. Methods and results: Leaders Free included 2466 patients undergoing PCI who had at least 1 of 13 pre-defined factors for an increased bleeding risk. Of these, 659 ACS patients were included in this analysis (BA9-DCS 330, BMS 329). At 12-month follow-up, treatment with the BA9-DCS was more effective (clinically driven target-lesion revascularization 3.9 vs. 9.0%, P = 0.009) and safer (cumulative incidence of cardiac death, myocardial infarction, or definite or probable stent thrombosis 9.3 vs. 18.5%, P = 0.001), driven by significantly lower rates of cardiac mortality (3.4 vs. 6.9%, P = 0.049) and myocardial infarction (6.9 vs. 13.8%, P = 0.005). Conclusion: We believe that the results of this sub-analysis from the Leaders Free trial are likely to significantly impact clinical practice for high bleeding risk patients presenting with an ACS: the use of a BMS can, in our view, no longer be recommended, and, given the paucity of available data for second-generation DES with shortened DAPT in these patients, the BA9-DCS should currently be considered as the device with the strongest evidence to support its use for this indication

2-Year Outcomes of High Bleeding Risk Patients After Polymer-Free Drug-Coated Stents.

BACKGROUND: A 1-year follow-up, polymer-free metallic stent coated with biolimus-A9 followed by 1-month dual antiplatelet therapy is safer and more effective than a bare-metal stent (BMS) for patients with high risk of bleeding. OBJECTIVES: This study analyzed 2-year outcomes to determine whether these benefits are maintained. METHODS: In a prospective, multicenter, double-blind trial, we randomized 2,466 high bleeding risk patients to receive a drug-coated stent (DCS) or a BMS followed by 1-month dual antiplatelet therapy. The primary safety endpoint was a composite of cardiac death, myocardial infarction, or stent thrombosis. The primary efficacy endpoint was clinically driven target lesion revascularization. RESULTS: At 2 years, the primary safety endpoint had occurred in 147 DCS and 180 BMS patients (15.3%) (hazard ratio: 0.80; 95% confidence interval: 0.64 to 0.99; p = 0.039). Clinically driven target lesion revascularization occurred for 77 DCS and 136 BMS patients (12.0%) (hazard ratio: 0.54; 95% confidence interval: 0.41 to 0.72; p 75 years, anemia, raised plasma creatinine, and planned long-term anticoagulation. Correlates of the primary safety endpoint were age, anemia, congestive heart failure, multivessel disease, number of stents implanted, and use of a BMS rather than a DCS. CONCLUSIONS: Safety and efficacy benefits of DCS over BMS were maintained for 2 years in high bleeding risk patients. Rates of major bleeding and coronary thrombotic events were no different and were associated with a substantial and comparable mortality risk. (A Prospective Randomized Comparison of the BioFreedom Biolimus A9 Drug Coated Stent Versus the Gazelle Bare Metal Stent in Patients With High Risk of Bleeding [LEADERS FREE]; NCT01623180)

High Breakdown Inference in the Mixed Linear Model

Mixed linear models are used to analyse data in many settings. These models have in most cases a multivariate normal formulation. The maximum likelihood estimator (MLE) or the residual MLE (REML) are usually chosen to estimate the parameters. However, the latter are based on the strong assumption of exact multivariate normality. Welsh and Richardson (1997) have shown that these estimators are not robust to small deviations from the multivariate normality. This means in practice for example that a small proportion of data (even only one) can drive the value of the estimates on their own. Since the model is multivariate, we propose in this paper a high breakdown robust estimator for very general mixed linear models, that inlcude for example covariates. This robust estimator belongs to the class of S-estimators (Rousseeuw and Yohai 1984) from which we can derive the asymptotic properties for the inference. We also use it as a diagnostic tool to detect outlying subjects. We discuss the advantages of this estimator compared to other robust estimators proposed previously and illustrate its performance with simulation studies and the analysis of four datasets