Statistical Methods in Medical Research

Marginal structural models are causal models designed to adjust for time-dependent confounders in observational studies with dynamically adjusted treatments. They are robust tools to assess causality in complex longitudinal data. In this paper, a marginal structural model is proposed with an innovative dose-delay joint-exposure model for Inverse-Probability-of-Treatment Weighted estimation of the causal effect of alterations to the therapy intensity. The model is motivated by a precise clinical question concerning the possibility of reducing dosages in a regimen. It is applied to data from a randomised trial of chemotherapy in osteosarcoma, an aggressive primary bone-tumour. Chemotherapy data are complex because their longitudinal nature encompasses many clinical details like composition and organisation of multi-drug regimens, or dynamical therapy adjustments. This manuscript focuses on the clinical dynamical process of adjusting the therapy according to the patient’s toxicity history, and the causal effect on the outcome of interest of such therapy modifications. Depending on patients’ toxicity levels, variations to therapy intensity may be achieved by physicians through the allocation of either a reduction or a delay of the next planned dose. Thus, a negative feedback is present between exposure to cytotoxic agents and toxicity levels, which acts as time-dependent confounders. The construction of the model is illustrated highlighting the high complexity and entanglement of chemotherapy data. Built to address dosage reductions, the model also shows that delays in therapy administration should be avoided. The last aspect makes sense from the cytological point of view, but it is seldom addressed in the literature.

Hồi quy logistic nhị phân là một trong những phương pháp thống kê được áp dụng thường xuyên nhất để phát triển các mô hình dự đoán lâm sàng. Các nhà phát triển của những mô hình này thường dựa vào tiêu chí Sự Kiện Trên Biến (Events Per Variable - EPV), đặc biệt là EPV ≥10, để xác định kích thước mẫu tối thiểu cần thiết và số lượng biến dự đoán ứng viên tối đa có thể được kiểm tra. Chúng tôi trình bày một nghiên cứu mô phỏng rộng rãi trong đó chúng tôi đã nghiên cứu ảnh hưởng của EPV, tỷ lệ sự kiện, số lượng biến dự đoán ứng viên, tương quan và phân phối của các biến dự đoán ứng viên, diện tích dưới đường cong ROC và hiệu ứng của biến dự đoán đối với hiệu suất dự đoán ngoài mẫu của các mô hình dự đoán. Hiệu suất ngoài mẫu (chuẩn hóa, phân biệt và sai số dự đoán xác suất) của các mô hình dự đoán đã phát triển được nghiên cứu trước và sau khi thu nhỏ hồi quy và chọn biến. Kết quả cho thấy rằng EPV không có mối quan hệ mạnh với các chỉ số hiệu suất dự đoán và không phải là tiêu chí phù hợp cho các nghiên cứu phát triển mô hình dự đoán (nhị phân). Chúng tôi chỉ ra rằng hiệu suất dự đoán ngoài mẫu có thể được xấp xỉ tốt hơn bằng cách xem xét số lượng biến dự đoán, kích thước mẫu tổng thể và tỷ lệ sự kiện. Chúng tôi đề xuất rằng việc phát triển các tiêu chí kích thước mẫu mới cho các mô hình dự đoán nên dựa trên ba tham số này và cung cấp các gợi ý để cải thiện việc xác định kích thước mẫu.

Health economic evaluations have recently become an important part of the clinical and medical research process and have built upon more advanced statistical decision-theoretic foundations. In some contexts, it is officially required that uncertainty about both parameters and observable variables be properly taken into account, increasingly often by means of Bayesian methods. Among these, probabilistic sensitivity analysis has assumed a predominant role. The objective of this article is to review the problem of health economic assessment from the standpoint of Bayesian statistical decision theory with particular attention to the philosophy underlying the procedures for sensitivity analysis.

The assumption of positivity or experimental treatment assignment requires that observed treatment levels vary within confounder strata. This article discusses the positivity assumption in the context of assessing model and parameter-specific identifiability of causal effects. Positivity violations occur when certain subgroups in a sample rarely or never receive some treatments of interest. The resulting sparsity in the data may increase bias with or without an increase in variance and can threaten valid inference. The parametric bootstrap is presented as a tool to assess the severity of such threats and its utility as a diagnostic is explored using simulated and real data. Several approaches for improving the identifiability of parameters in the presence of positivity violations are reviewed. Potential responses to data sparsity include restriction of the covariate adjustment set, use of an alternative projection function to define the target parameter within a marginal structural working model, restriction of the sample, and modification of the target intervention. All of these approaches can be understood as trading off proximity to the initial target of inference for identifiability; we advocate approaching this tradeoff systematically.

Propensity score methods are a part of the standard toolkit for applied researchers who wish to ascertain causal effects from observational data. While they were originally developed for binary treatments, several researchers have proposed generalizations of the propensity score methodology for non-binary treatment regimes. Such extensions have widened the applicability of propensity score methods and are indeed becoming increasingly popular themselves. In this article, we closely examine two methods that generalize propensity scores in this direction, namely, the propensity function (PF), and the generalized propensity score (GPS), along with two extensions of the GPS that aim to improve its robustness. We compare the assumptions, theoretical properties, and empirical performance of these methods. On a theoretical level, the GPS and its extensions are advantageous in that they are designed to estimate the full dose response function rather than the average treatment effect that is estimated with the PF. We compare GPS with a new PF method, both of which estimate the dose response function. We illustrate our findings and proposals through simulation studies, including one based on an empirical study about the effect of smoking on healthcare costs. While our proposed PF-based estimator preforms well, we generally advise caution in that all available methods can be biased by model misspecification and extrapolation.

The time-dependent receiver operating characteristic curve is often used to study the diagnostic accuracy of a single continuous biomarker, measured at baseline, on the onset of a disease condition when the disease onset may occur at different times during the follow-up and hence may be right censored. Due to right censoring, the true disease onset status prior to the pre-specified time horizon may be unknown for some patients, which causes difficulty in calculating the time-dependent sensitivity and specificity. We propose to estimate the time-dependent sensitivity and specificity by weighting the censored data by the conditional probability of disease onset prior to the time horizon given the biomarker, the observed time to event, and the censoring indicator, with the weights calculated nonparametrically through a kernel regression on time to event. With this nonparametric weighting adjustment, we derive a novel, closed-form formula to calculate the area under the time-dependent receiver operating characteristic curve. We demonstrate through numerical study and theoretical arguments that the proposed method is insensitive to misspecification of the kernel bandwidth, produces unbiased and efficient estimators of time-dependent sensitivity and specificity, the area under the curve, and other estimands from the receiver operating characteristic curve, and outperforms several other published methods currently implemented in R packages.

In this paper, we propose a generalized functional linear regression model for a binary outcome indicating the presence/absence of a cardiac disease with multivariate functional data among the relevant predictors. In particular, the motivating aim is the analysis of electrocardiographic traces of patients whose pre-hospital electrocardiogram (ECG) has been sent to 118 Dispatch Center of Milan (the Italian free-toll number for emergencies) by life support personnel of the basic rescue units. The statistical analysis starts with a preprocessing of ECGs treated as multivariate functional data. The signals are reconstructed from noisy observations. The biological variability is then removed by a nonlinear registration procedure based on landmarks. Thus, in order to perform a data-driven dimensional reduction, a multivariate functional principal component analysis is carried out on the variance-covariance matrix of the reconstructed and registered ECGs and their first derivatives. We use the scores of the Principal Components decomposition as covariates in a generalized linear model to predict the presence of the disease in a new patient. Hence, a new semi-automatic diagnostic procedure is proposed to estimate the risk of infarction (in the case of interest, the probability of being affected by Left Bundle Brunch Block). The performance of this classification method is evaluated and compared with other methods proposed in literature. Finally, the robustness of the procedure is checked via leave- j-out techniques.