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The number needed to treat (NNT) is an efficacy index commonly used in randomized clinical trials. The NNT is the average number of treated patients for each undesirable patient outcome, for example, death, prevented by the treatment. We introduce a systematic theoretically-based framework to model and estimate the conditional and the harmonic mean NNT in the presence of explanatory variables, in various models with dichotomous and nondichotomous outcomes. The conditional NNT is illustrated in a series of four primary examples; logistic regression, linear regression, Kaplan-Meier estimation, and Cox regression models. Also, we establish and prove mathematically the exact relationship between the conditional and the harmonic mean NNT in the presence of explanatory variables. We introduce four different methods to calculate asymptotically-correct confidence intervals for both indices. Finally, we implemented a simulation study to provide numerical demonstrations of the aforementioned theoretical results and the four examples. Numerical analysis showed that the parametric estimators of the NNT with nonparametric bootstrap-based confidence intervals outperformed other examined combinations in most settings. An R package and a web application have been developed and made available online to calculate the conditional and the harmonic mean NNTs with their corresponding confidence intervals.

Dynamic treatment regimes operationalize precision medicine as a sequence of decision rules, one per stage of clinical intervention, that map up-to-date patient information to a recommended intervention. An optimal treatment regime maximizes the mean utility when applied to the population of interest. Methods for estimating an optimal treatment regime assume the data to be fully observed, which rarely occurs in practice. A common approach is to first use multiple imputation and then pool the estimators across imputed datasets. However, this approach requires estimating the joint distribution of patient trajectories, which can be high-dimensional, especially when there are multiple stages of intervention. We examine the application of inverse probability weighted estimating equations as an alternative to multiple imputation in the context of monotonic missingness. This approach applies to a broad class of estimators of an optimal treatment regime including both Q-learning and a generalization of outcome weighted learning. We establish consistency under mild regularity conditions and demonstrate its advantages in finite samples using a series of simulation experiments and an application to a schizophrenia study.

Individualized treatment regimes (ITRs) aim to recommend treatments based on patient-specific characteristics in order to maximize the expected clinical outcome. Outcome weighted learning approaches have been proposed for this optimization problem with primary focus on the binary treatment case. Many require assumptions of the outcome value or the randomization mechanism. In this paper, we propose a general framework for multicategory ITRs using generic surrogate risk. The proposed method accommodates the situations when the outcome takes negative value and/or when the propensity score is unknown. Theoretical results about Fisher consistency, excess risk, and risk consistency are established. In practice, we recommend using differentiable convex loss for computational optimization. We demonstrate the superiority of the proposed method under multinomial deviance risk to some existing methods by simulation and application on data from a clinical trial.

Objective The role of baseline severity as effect modifier in various psychiatric disorders is a topic of controversy and of clinical import. This study aims to examine whether baseline severity modifies the efficacy of various antidepressants for major depression through individual participant data (IPD) meta‐analysis. Method We identified all placebo‐controlled, double‐blind randomised trials of new generation antidepressants in the acute phase treatment of major depression conducted in Japan and requested their IPD through the public–private partnerships (PPPs) between the relevant academic societies and the pharmaceutical companies. The effect modification by baseline depression severity was examined through six increasingly complex competing mixed‐effects models for repeated measures. Results We identified eleven eligible trials and obtained IPD from six, which compared duloxetine, escitalopram, mirtazapine, paroxetine or bupropion against placebo (total n = 2464). The best‐fitting model revealed that the interaction between baseline severity and treatment was not statistically significant (coefficient = −0.04, 95% confidence interval: −0.16 to 0.08, P = 0.49). Several sensitivity analyses confirmed the robustness of the findings. Conclusion We may expect as much benefit from antidepressant treatments for mild, moderate or severe major depression. Clinical practice guidelines will need to take these findings into consideration.

AIMS Semaphorin 4D (Sema4D) is expressed on platelets and T-cells and known to be involved in inflammation. The aims of this study include comparing Sema4D and N terminal pro brain natriuretic peptide (NT-proBNP) serum levels in heart failure (HF) patients to a control group, evaluating the correlation between Sema4D and NT-proBNP levels, and assessing Sema4D serum levels in HF patients during acute exacerbation and remission. METHODS AND RESULTS Forty-five patients diagnosed with HF (based on echocardiographic findings, positive NT-proBNP levels, and normal C-reactive protein) and 11 healthy controls (declaring no chronic diseases or medications) comprised the study population. Demographic, clinical, laboratory, and echocardiographic data were used to create the study database. NT-proBNP and Sema4D serum samples were taken on admission and discharge. NT-proBNP levels were significantly higher in the HF group than in controls (P

In many classical estimation problems, the parameter space has a boundary. In most cases, the standard asymptotic properties of the estimator do not hold when some of the underlying true parameters lie on the boundary. However, without knowledge of the true parameter values, confidence intervals constructed assuming that the parameters lie in the interior are generally over-conservative. A penalized estimation method is proposed in this article to address this issue. An adaptive lasso procedure is employed to shrink the parameters to the boundary, yielding oracle inference which adapt to whether or not the true parameters are on the boundary. When the true parameters are on the boundary, the inference is equivalent to that which would be achieved with a priori knowledge of the boundary, while if the converse is true, the inference is equivalent to that which is obtained in the interior of the parameter space. The method is demonstrated under two practical scenarios, namely the frailty survival model and linear regression with order-restricted parameters. Simulation studies and real data analyses show that the method performs well with realistic sample sizes and exhibits certain advantages over standard methods.