In this article, we propose an efficient control chart for monitoring small shifts in a process mean for scenarios where the process variable is observed with a correlated auxiliary variable. The proposed chart, called an AHWMA chart, is an homogeneously weighted moving average type control chart that uses both the process and auxiliary variables in the form of a regression estimator to provide an efficient and unbiased estimate of the mean of the process variable. We provide the design structure of the chart and examine its performance in terms of its run length properties. Using a simulation study, we compare its run length performance with several existing methods for detecting a small shift in the process mean. Our simulation results show that the proposed chart is more efficient in detecting a small shift in the process mean than its competitors. We provide a detailed study of the chart’s robustness to non-normal distributions and shown that the chart may also be designed to be less sensitive to non-normality. We give some recommendations on the application of the chart when the process parameters are unknown, and provide an example to show the implementation of the proposed new technique.

This paper presents a multivariate homogeneously weighted moving average (MHWMA) control chart for monitoring a process mean vector. The MHWMA control chart statistic gives a specific weight to the current observation, and the remaining weight is evenly distributed among the previous observations. We present the design procedure and compare the average run length (ARL) performance of the proposed chart with multivariate Chi-square, multivariate EWMA, and multivariate CUSUM control charts. The ARL comparison indicates superior performance of the MHWMA chart over its competitors, particularly for the detection of small shifts in the process mean vector. Examples are also provided to show the application of the proposed chart.

Background Tumor microenvironment (TME) characteristics are potential biomarkers of response to immune checkpoint inhibitors in metastatic melanoma. This study developed a method to perform unsupervised classification of TME of metastatic melanoma. Methods We used multiplex immunohistochemical and quantitative pathology-derived assessment of immune cell compositions of intratumoral and peritumoral regions of metastatic melanoma baseline biopsies to classify TME in relation to response to anti-programmed cell death protein 1 (PD-1) monotherapy or in combination with anti-cytotoxic T-cell lymphocyte-4 (ipilimumab (IPI)+PD-1). Results Spatial profiling of CD8+T cells, macrophages, and melanoma cells, as well as phenotypic PD-1 receptor ligand (PD-L1) and CD16 proportions, were used to identify and classify patients into one of three mutually exclusive TME classes: immune-scarce, immune-intermediate, and immune-rich tumors. Patients with immune-rich tumors were characterized by a lower proportion of melanoma cells and higher proportions of immune cells, including higher PD-L1 expression. These patients had higher response rates and longer progression-free survival (PFS) than those with immune-intermediate and immune-scarce tumors. At a median follow-up of 18 months (95% CI: 6.7 to 49 months), the 1-year PFS was 76% (95% CI: 64% to 90%) for patients with an immune-rich tumor, 56% (95% CI: 44% to 72%) for those with an immune-intermediate tumor, and 33% (95% CI: 23% to 47%) for patients with an immune-scarce tumor. A higher response rate was observed in patients with an immune-scarce or immune-intermediate tumor when treated with IPI+PD-1 compared with those treated with PD-1 alone. Conclusions Our study provides an automatic TME classification method that may predict the clinical efficacy of immunotherapy for patients with metastatic melanoma.