continuous covariate
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Background: Direct oral anticoagulants (DOACs) are preferred over warfarin for stroke prevention in atrial fibrillation (AF). Meta-analyses using individual patient data offer significant advantages over study-level data. Methods: We used individual patient data from the COMBINE AF database, which includes all patients randomized in the 4 pivotal trials of DOACs vs warfarin in AF (RE-LY, ROCKET AF, ARISTOTLE, ENGAGE AF-TIMI 48), to perform network meta-analyses using a stratified Cox model with random effects comparing standard-dose DOAC, lower-dose DOAC, and warfarin. Hazard ratios (95% CIs) were calculated for efficacy and safety outcomes. Covariate-by-treatment interaction was estimated for categorical covariates and for age as a continuous covariate, stratified by sex. Results: A total of 71,683 patients were included (29,362 on standard-dose DOAC, 13,049 on lower-dose DOAC, 29,272 on warfarin). Compared with warfarin, standard-dose DOACs were associated with a significantly lower hazard of stroke/systemic embolism (883/29312 [3.01%] vs 1080/29229 [3.69%]; HR 0.81, 95% CI 0.74-0.89), death (2276/29312 [7.76%] vs 2460/29229 [8.42%]; HR 0.92, 95% CI 0.87-0.97) and intracranial bleeding (184/29270 [0.63%] vs 409/29187 [1.40%]; HR 0.45, 95% CI 0.37-0.56), but no statistically different hazard of major bleeding (1479/29270 [5.05%] vs 1733/29187 [5.94%]; HR 0.86, 95% CI 0.74-1.01), whereas lower-dose DOACs were associated with no statistically different hazard of stroke/systemic embolism (531/13049 [3.96%] vs 1080/29229 [3.69%]; HR 1.06, 95% CI 0.95-1.19) but a lower hazard of intracranial bleeding (55/12985 [0.42%] vs 409/29187 [1.40%]; HR 0.28, 95% CI 0.21-0.37), death (1082/13049 [8.29%] vs 2460/29229 [8.42%]; HR 0.90, 95% CI 0.83-0.97), and major bleeding (564/12985 [4.34%] vs 1733/29187 [5.94%]; HR 0.63, 95% CI 0.45-0.88). Treatment effects for standard- and lower-dose DOACs versus warfarin were consistent across age and sex for stroke/systemic embolism and death, whereas standard-dose DOACs were favored in patients with no history of vitamin K antagonist use (p=0.01) and lower creatinine clearance (p=0.09). For major bleeding, standard-dose DOACs were favored in patients with lower body weight (p=0.02). In the continuous covariate analysis, younger patients derived greater benefits from standard-dose (interaction p=0.02) and lower-dose DOACs (interaction p=0.01) versus warfarin. Conclusions: Compared with warfarin, DOACs have more favorable efficacy and safety profiles among patients with AF.

Identification of a subset of patients who may be sensitive to a specific treatment is an important problem in clinical trials. In this paper, we consider the case where the treatment effect is measured by longitudinal outcomes, such as quality of life scores assessed over the duration of a clinical trial, and the subset is determined by a continuous baseline covariate, such as age and expression level of a biomarker. A threshold linear mixed model is introduced, and a smoothing maximum likelihood method is proposed to obtain the estimation of the parameters in the model. Broyden-Fletcher-Goldfarb-Shanno algorithm is employed to maximize the proposed smoothing likelihood function. The proposed procedure is evaluated through simulation studies and application to the analysis of data from a randomized clinical trial on patients with advanced colorectal cancer.

Parametric and non-parametric approaches are developed to test the adequacy of the polynomial model Y=β°+j=1pβjXj+ε  when there is no replication in the values of the independent variable. The proposed tests avoid partitioning of the sample space of the continuous covariate. This paper suggests three tests based on the following concept: if the model is appropriate for a selected application, then the error component ε1,ε2,…,εn is a random sample with zero mean and constant variance. Simulation results are provided to illustrate the power and size of the proposed tests. An example is used to illustrate the methodologies. These tests are also compared with the classical lack-of-fit test to demonstrate their advantage.

Identification of relevant biomarkers that are associated with a treatment effect is one requirement for adequate treatment stratification and consequently to improve health care by administering the best available treatment to an individual patient. Various statistical approaches were proposed that allow assessing the interaction between a continuous covariate and treatment. Nevertheless, categorization of a continuous covariate, e.g., by splitting the data at the observed median value, appears to be very prevalent in practice. In this article, we present a simulation study considering data as observed in a randomized clinical trial with a time-to-event outcome performed to compare properties of such approaches, namely, Cox regression with linear interaction, Multivariable Fractional Polynomials for Interaction (MFPI), Local Partial-Likelihood Bootstrap (LPLB), and the Subpopulation Treatment Effect Pattern Plot (STEPP) method, and of strategies based on categorization of continuous covariates (splitting the covariate at the median, splitting at quartiles, and using an “optimal” split by maximizing a corresponding test statistic). In different scenarios with no interactions, linear interactions or nonlinear interactions, type I error probability and the power for detection of a true covariate-treatment interaction were estimated. The Cox regression approach was more efficient than the other methods for scenarios with monotonous interactions, especially when the number of observed events was small to moderate. When patterns of the biomarker-treatment interaction effect were more complex, MFPI and LPLB performed well compared to the other approaches. Categorization of data generally led to a loss of power, but for very complex patterns, splitting the data into multiple categories might help to explore the nature of the interaction effect. Consequently, we recommend application of statistical methods developed for assessment of interactions between continuous biomarkers and treatment instead of arbitrary or data-driven categorization of continuous covariates.

5546 Background: A pre-operative predictive biomarker of CC0 interval debulking surgery (IDS) likelihood would be helpful. The modeled CA125 elimination rate constant KELIM predicts OS in 1st line setting (You et al. Clin Cancer Res 2019). The predictive/prognostic values of KELIM regarding CC scores at IDS, and survivals, during neo-adjuvant chemotherapy were assessed. Methods: The data of the CHIVA randomized phase II trial, comparing carboplatin-paclitaxel +/- nintedanib before IDS (NCT01583322), were used. A semi-mechanistic model was built to describe CA125 longitudinal kinetics during the first 100 treatment days. The relationships between KELIM and IDS CC scores, PFS & OS, were assessed with other major prognostic factors (grade, histology, GCIG CA125 response, FIGO stage, and arm) using multivariate logistic regression (logit), C-index & survival tests. Results: The longitudinal kinetics of 529 CA125 values, assessed every 3 weeks during neo-adj chemotherapy, were modeled in 133 patients (out of 188). KELIM (as a continuous covariate) was the only significant predictive factor of CC0 IDS likelihood using multivariate analyses (OR = 12.37, 95% CI [4.32-39.67]). CC0 IDS probability can be estimated with patient KELIM: ≥ 90 % if standardized KELIM ≥ 0.12. Non-parametric survival models confirmed the independent predictive values of KELIM categorized by terciles regarding PFS & OS (Table). The parametric model linking KELIM (as a continuous covariate) with OS allows to predict the patient survivals (months) based on their estimated KELIM (HR = 0.20, [0.10-0.39]). Conclusions: The prognostic & predictive values of the modeled CA125 KELIM are also confirmed regarding CC0 IDS likelihood, PFS and OS with neo-adjuvant chemotherapy. Patient KELIM is calculable online, based on observed CA125 values, on http://www.biomarker-kinetics.org/ . Clinical trial information: 2011-006288-23. [Table: see text]

AbstractA way to enhance our understanding of the development and progression of complex diseases is to investigate the influence of cellular environments on gene co-expression (i.e. gene-pair correlations). Often, changes in gene co-expression are investigated across two or more biological conditions defined by categorizing a continuous covariate. However, the selection of arbitrary cut-off points may have an influence on the results of an analysis. To address this issue, we use a general linear model (GLM) for correlated data to study the relationship between gene-module co-expression and a covariate like metabolite concentration. The GLM specifies the gene-pair correlations as a function of the continuous covariate. The use of the GLM allows for investigating different (linear and non-linear) patterns of co-expression. Furthermore, the modeling approach offers a formal framework for testing hypotheses about possible patterns of co-expression. In our paper, a simulation study is used to assess the performance of the GLM. The performance is compared with that of a previously proposed GLM that utilizes categorized covariates. The versatility of the model is illustrated by using a real-life example. We discuss the theoretical issues related to the construction of the test statistics and the computational challenges related to fitting of the proposed model.

353 Background: Recent RANGE results showed significant improvement in PFS, a non-significant positive trend in OS, increased ORR and acceptable safety with RAM+DOC vs P+DOC in UC pts (Petrylak et al. Lancet 2017; Petrylak et al. ESMO 2018, abstr 865PD). RAM ER-OS relationships in RANGE are reported here. Methods: Pts received RAM (10 mg/kg) + DOC or P + DOC (Day 1 of a 21 day cycle) until discontinuation criteria were met. Population pharmacokinetic analysis predicted RAM minimum concentrations after first dose (RAM Cmin, 1). Multivariate Cox regression & matched case control (MCC) analyses using exposure treated as a continuous covariate, or grouped as quartiles, evaluated the ER-OS relationship. Results: Several poor prognostic factors, including Bellmunt risk factors, appeared to be more frequent in the lower exposure quartiles, suggesting a possible disease-PK interaction. Increasing RAM exposure as a continuous covariate in an ER population of n=246 pts significantly ( p=0.01) associated with improvements in OS. Higher exposure quartiles trended toward longer survival & smaller HRs compared to P (Table, Q1=lowest). Conclusions: OS and ORR benefits favored Q4, a group which was associated with more favorable prognostic features and higher exposure. The observed disease-PK interaction may confound the interpretation of the ER results and warrants further exploration. Clinical trial information: NCT02426125. [Table: see text]

Lord's Paradox occurs when a continuous covariate is statistically controlled for and the relationship between a continuous outcome and group status indicator changes in both magnitude and direction. This phenomenon poses a challenge to the notion of evidence-based policy, where data are supposed to be self-evident. We examined 50 effect size estimates from 34 large-scale educational interventions, and found that impact estimates are affected in magnitude, with or without reversal in sign, when there is substantial baseline imbalance. We also demonstrated that multilevel modelling can ameliorate the divergence in sign and/or magnitude of effect estimation, which, together with project specific knowledge, promises to help those who are presented with conflicting or confusing evidence in decision making.