The role of the adaptive immune response in controlling the growth and recurrence of human tumors has been controversial. We characterized the tumor-infiltrating immune cells in large cohorts of human colorectal cancers by gene expression profiling and in situ immunohistochemical staining. Collectively, the immunological data (the type, density, and location of immune cells within the tumor samples) were found to be a better predictor of patient survival than the histopathological methods currently used to stage colorectal cancer. The results were validated in two additional patient populations. These data support the hypothesis that the adaptive immune response influences the behavior of human tumors. In situ analysis of tumor-infiltrating immune cells may therefore be a valuable prognostic tool in the treatment of colorectal cancer and possibly other malignancies.

https://science.sciencemag.org/content/sci/313/5795/1960.full.pdf

Type, Density, and Location of Immune Cells Within Human Colorectal Tumors Predict Clinical Outcome

Regression models are frequently used to develop diagnostic, prognostic, and health resource utilization models in clinical, health services, outcomes, pharmacoeconomic, and epidemiologic research, and in a multitude of non-health-related areas. Regression models are also used to adjust for patient heterogeneity in randomized clinical trials, to obtain tests that are more powerful and valid than unadjusted treatment comparisons.

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Regression Modeling Strategies

Statistical Analysis with Missing Data

Despite years of research and hundreds of reports on tumor markers in oncology, the number of markers that have emerged as clinically useful is pitifully small. Often, initially reported studies of a marker show great promise, but subsequent studies on the same or related markers yield inconsistent conclusions or stand in direct contradiction to the promising results. It is imperative that we attempt to understand the reasons that multiple studies of the same marker lead to differing conclusions. A variety of methodologic problems have been cited to explain these discrepancies. Unfortunately, many tumor marker studies have not been reported in a rigorous fashion, and published articles often lack sufficient information to allow adequate assessment of the quality of the study or the generalizability of study results. The development of guidelines for the reporting of tumor marker studies was a major recommendation of the National Cancer Institute-European Organisation for Research and Treatment of Cancer (NCI-EORTC) First International Meeting on Cancer Diagnostics in 2000. As for the successful CONSORT initiative for randomized trials and for the STARD statement for diagnostic studies, we suggest guidelines to provide relevant information about the study design, preplanned hypotheses, patient and specimen characteristics, assay methods, and statistical analysis methods. In addition, the guidelines suggest helpful presentations of data and important elements to include in discussions. The goal of these guidelines is to encourage transparent and complete reporting so that the relevant information will be available to others to help them to judge the usefulness of the data and understand the context in which the conclusions apply.

Reporting Recommendations for Tumor Marker Prognostic Studies (REMARK)

In medical research, continuous variables are often converted into categorical variables by grouping values into two or more categories. We consider in detail issues pertaining to creating just two groups, a common approach in clinical research. We argue that the simplicity achieved is gained at a cost; dichotomization may create rather than avoid problems, notably a considerable loss of power and residual confounding. In addition, the use of a data-derived 'optimal' cutpoint leads to serious bias. We illustrate the impact of dichotomization of continuous predictor variables using as a detailed case study a randomized trial in primary biliary cirrhosis. Dichotomization of continuous data is unnecessary for statistical analysis and in particular should not be applied to explanatory variables in regression models.

Dichotomizing continuous predictors in multiple regression: a bad idea.

The Youden Index is a frequently used summary measure of the ROC (Receiver Operating Characteristic) curve. It both, measures the effectiveness of a diagnostic marker and enables the selection of an optimal threshold value (cutoff point) for the marker. In this paper we compare several estimation procedures for the Youden Index and its associated cutoff point. These are based on (1) normal assumptions; (2) transformations to normality; (3) the empirical distribution function; (4) kernel smoothing. These are compared in terms of bias and root mean square error in a large variety of scenarios by means of an extensive simulation study. We find that the empirical method which is the most commonly used has the overall worst performance. In the estimation of the Youden Index the kernel is generally the best unless the data can be well transformed to achieve normality whereas in estimation of the optimal threshold value results are more variable.

/pdf/estimation-of-the-youden-index-and-its-associated-cutoff-2ymhs4o9au.pdf

Estimation of the Youden Index and its associated cutoff point.

The area under the receiver operating characteristic curve is frequently used as a measure for the effectiveness of diagnostic markers. In this paper we discuss and compare estimation procedures for this area. These are based on (i) the Mann-Whitney statistic; (ii) kernel smoothing; (iii) normal assumptions; (iv) empirical transformations to normality. These are compared in terms of bias and root mean square error in a large variety of situations by means of an extensive simulation study. Overall we find that transforming to normality usually is to be preferred except for bimodal cases where kernel methods can be effective.

Estimation of the area under the ROC curve.

Neural networks have received considerable attention recently, mostly by non-statisticians. They are considered by many to be very promising tools for classification and prediction. In this paper we present an approach to modelling censored survival data using the input-output relationship associated with a simple feed-forward neural network as the basis for a non-linear proportional hazards model. This approach can be extended to other models used with censored survival data. The proportional hazards neural network parameters are estimated using the method of maximum likelihood. These maximum likelihood based models can be compared, using readily available techniques such as the likelihood ratio test and the Akaike criterion. The neural network models are illustrated using data on the survival of men with prostatic carcinoma. A method of interpreting the neural network predictions based on the factorial contrasts is presented.

A neural network model for survival data.

https://www.thelancet.com/pdfs/journals/lancet/PIIS0140-6736(14)60157-4.pdf

Preconception low-dose aspirin and pregnancy outcomes: Results from the EAGeR randomised trial

Continuous measurements are often dichotomized for classification of subjects. This paper evaluates two procedures for determining a best cutpoint for a continuous prognostic factor with right censored outcome data. One procedure selects the cutpoint that minimizes the significance level of a logrank test with comparison of the two groups defined by the cutpoint. This procedure adjusts the significance level for maximal selection. The other procedure uses a cross-validation approach. The latter easily extends to accommodate multiple other prognostic factors. We compare the methods in terms of statistical power and bias in estimation of the true relative risk associated with the prognostic factor. Both procedures produce approximately the correct type I error rate. Use of a maximally selected cutpoint without adjustment of the significance level, however, results in a substantially elevated type I error rate. The cross-validation procedure unbiasedly estimated the relative risk under the null hypothesis while the procedure based on the maximally selected test resulted in an upward bias. When the relative risk for the two groups defined by the covariate and true changepoint was small, the cross-validation procedure provided greater power than the maximally selected test. The cross-validation based estimate of relative risk was unbiased while the procedure based on the maximally selected test produced a biased estimate. As the true relative risk increased, the power of the maximally selected test was about 10 per cent greater than the power obtained using cross-validation. The maximally selected test overestimated the relative risk by about 10 per cent. The cross-validation procedure produced at most 5 per cent underestimation of the true relative risk. Finally, we report the effect of dichotomizing a continuous non-linear relationship between covariate and risk. We compare using a linear proportional hazard model to using models based on optimally selected cutpoints. Our simulation study indicates that we can have a substantial loss of statistical power when we use cutpoint models in cases where there is a continuous relationship between covariate and risk.

https://rmgsc.cr.usgs.gov/outgoing/threshold_articles/Faraggi_Simon1996.pdf

David Faraggi

Papers

Estimation of the Youden Index and its associated cutoff point.

Estimation of the area under the ROC curve.

A neural network model for survival data.

Preconception low-dose aspirin and pregnancy outcomes: Results from the EAGeR randomised trial

A simulation study of cross-validation for selecting an optimal cutpoint in univariate survival analysis.