Power and sample size calculation for the additive hazard model

Effect of early administration of tetracosactide on mortality and host response in critically ill patients requiring rescue surgery: a sensitivity analysis of the STOPSHOCK phase 3 randomized controlled trial

BACKGROUND

Undifferentiated shock is recognized as a criticality state that is transitional in immune-mediated topology for casual risk of lethal microcirculatory dysfunction. This was a sensitivity analysis of a drug (tetracosactide; TCS10) targeting melanocortin receptors (MCRs) in a phase 3 randomized controlled trial to improve cardiovascular surgical rescue outcome by reversing mortality and hemostatic disorders.

METHODS

Sensitivity analysis was based on a randomized, two-arm, multicenter, double-blind, controlled trial. The Naïve Bayes classifier was performed by density-based sensitivity index for principal strata as proportional hazard model of 30-day surgical risk mortality according to European System for Cardiac Operative Risk Evaluation inputs-outputs in 100 consecutive cases (from August to September 2013 from Emilia Romagna region, Italy). Patients included an agent-based TCS10 group (10 mg, single intravenous bolus before surgery; n = 56) and control group (n = 44) and the association with cytokines, lactate, and bleeding-blood transfusion episodes with the prior-risk log-odds for mortality rate in time-to-event was analyzed.

RESULTS

Thirty-day mortality was significantly improved in the TCS10 group vs. control group (0 vs. 8 deaths, P < 0.0001). Baseline levels of interleukin (IL)-6, IL-10, and lactate were associated with bleeding episodes, independent of TCS10 treatment [odds ratio (OR) = 1.90, 95% confidence interval (CI) 1.39-2.79; OR = 1.53, 95%CI 1.17-2.12; and OR = 2.92, 95%CI 1.40-6.66, respectively], while baseline level of Fms-like tyrosine kinase 3 ligand (Flt3L) was associated with lower bleeding rates in TCS10-treated patients (OR = 0.31, 95%CI 0.11-0.90, P = 0.03). For every 8 TCS10-treated patients, 1 bleeding case was avoided. Blood transfusion episodes were significantly reduced in the TCS10 group compared to the control group (OR = 0.32, 95%CI 0.14-0.73, P = 0.01). For every 4 TCS10-treated patients, 1 transfusion case was avoided.

CONCLUSIONS

Sensitivity index underlines the quality target product profile of TCS10 in the runway of emergency casualty care. To introduce the technology readiness level in real-life critically ill patients, further large-scale studies are required.

TRIAL REGISTRATION

European Union Drug Regulating Authorities Clinical Trials Database (EudraCT Number: 2007-006445-41 ).

Design and analysis of cluster randomized trials with time-to-event outcomes under the additive hazards mixed model

A primary focus of current methods for cluster randomized trials (CRTs) has been for continuous, binary, and count outcomes, with relatively less attention given to right-censored, time-to-event outcomes. In this article, we detail considerations for sample size requirement and statistical inference in CRTs with time-to-event outcomes when the intervention effect parameter is specified through the additive hazards mixed model (AHMM), which includes a frailty term to explicitly account for the dependency between the failure times. First, we discuss improved inference for the treatment effect parameter via bias-corrected sandwich variance estimators and randomization-based test under AHMM, addressing potential small-sample biases in CRTs. Next, we derive a new sample size formula for AHMM analysis of CRTs accommodating both equal and unequal cluster sizes. When the cluster sizes vary, our sample size formula depends on the mean and coefficient of variation of cluster sizes, based on which we articulate the impact of cluster size variation in CRTs with time-to-event outcomes. Furthermore, we obtain the insight that the classical variance inflation factor for CRTs with a non-censored outcome can in fact apply to CRTs with a time-to-event outcome, providing that an appropriate definition of the intraclass correlation coefficient is considered under AHMM. Simulation studies are carried out to illustrate key design and analysis considerations in CRTs with a small to moderate number of clusters. The proposed sample size procedure and analytical methods are further illustrated using the context of the STrategies to Reduce Injuries and Develop Confidence in Elders CRT.

Violations of proportional hazard assumption in Cox regression model of transcriptomic data in TCGA pan-cancer cohorts

Background

Cox proportional hazard regression (CPH) model relies on the proportional hazard (PH) assumption: the hazard of variables is independent of time. CPH has been widely used to identify prognostic markers of the transcriptome. However, the comprehensive investigation on PH assumption in transcriptomic data has lacked.

Results

The whole transcriptomic data of the 9,056 patients from 32 cohorts of The Cancer Genome Atlas and the 3 lung cancer cohorts from Gene Expression Omnibus were collected to construct CPH model for each gene separately for fitting the overall survival. An average of 8.5% gene CPH models violated the PH assumption in TCGA pan-cancer cohorts. In the gene interaction networks, both hub and non-hub genes in CPH models were likely to have non-proportional hazards. Violations of PH assumption for the same gene models were not consistent in 5 non-small cell lung cancer datasets (all kappa coefficients < 0.2), indicating that the non-proportionality of gene CPH models depended on the datasets. Furthermore, the introduction of log(t) or sqrt(t) time-functions into CPH improved the performance of gene models on overall survival fitting in most tumors. The time-dependent CPH changed the significance of log hazard ratio of the 31.9% gene variables.

Conclusions

Our analysis resulted that non-proportional hazards should not be ignored in transcriptomic data. Introducing time interaction term ameliorated performance and interpretability of non-proportional hazards of transcriptome data in CPH.