David Faraggi

Survival of diffuse large cell lymphoma. A multivariate analysis including dose intensity variables

Ninety‐five newly diagnosed patients with diffuse large cell lymphoma (DLCL) treated by cyclophosphamide (CTX), doxorubicin (ADM), vincristine (VCR), and prednisone (CHOP regimen) chemotherapy were evaluated for survival factors including dose intensity (DI). DI calculations were done for the initial cycles needed to achieve maximal response. The medians of the relative DI for CTX, ADM, and VCR were 0.9, 0.86, and 0.79, respectively. The median of the average relative DI (ARDI) was 0.83 (range, 0.28 to 1.14). The univariate analysis of potential prognostic variables showed that the following significantly decreased the survival rate: age older than 60 years (P = 0.0005), Stage III to IV (P = 0.02), male sex (P = 0.03), and all four DI variables (CTX, ADM, VCR, and ARDI) less than the median (P = 0.01 to 0.0001). A multivariate analysis by the stepwise proportional hazards model of Cox indicated that the factors predicting a poor prognosis were ARDI less than the median (P = 0.0003) and age older than 60 years (P = 0.02). A multivariate survival analysis of those who achieved complete remission showed ARDI less than the median (P = 0.0003), CTX less than the median (P = 0.02), and Stage III to IV (P = 0.02) to be the most negative factors regarding survival. In conclusion, a high DI in the initial cycles of CHOP chemotherapy for DLCL has a significant positive impact on survival.

A SIMULATION STUDY OF CROSS‐VALIDATION FOR SELECTING AN OPTIMAL CUTPOINT IN UNIVARIATE SURVIVAL ANALYSIS

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.

Confidence intervals for the generalized ROC criterion.

Receiver operating characteristic (ROC) curves are frequently used to assess the usefulness of diagnostic markers. When several diagnostic markers are available, they can be combined by a best linear combination: that is, when the area under the ROC curve of this combination is maximized among all possible linear combinations. This maximal area is the generalized ROC criterion, which provides a measure of how effective the combination of the markers is. This criterion needs to be estimated from the data, and is usually evaluated against single markers. In the present paper, we provide confidence intervals for the generalized ROC criterion under the assumption of homogeneous covariance matrices, derive an approximation for the heterogeneous covariance matrices case, and evaluate the approximation via a simulation study. Finally, we present an illustrative example.

Adjusting receiver operating characteristic curves and related indices for covariates

Summary. Continuous markers are often used to discriminate between diseased and healthy populations. In this context, the receiver operating characteristic (ROC) curve is a popular graphical visualization of the discriminatory effectiveness of the marker. Several indices which summarize the discriminatory power of the marker are used, the most common being the area under the ROC curve and the Youden index. We examine covariate effects on these indices, assuming that the marker, possibly transformed, follows the normal distribution. The ROC curve adjusted for covariates is estimated and approximate adjusted confidence intervals for the area under the ROC curve are provided. Further, we investigate bootstrap confidence intervals for both the Youden index and the corresponding critical threshold value, both adjusted for covariates. We motivate this methodology with an example of fingerstick post-prandial blood glucose as a marker for diabetes patients where age is known to be an important covariate for this marker, and we examine how age influences the discriminatory power of the marker.

mROC: a computer program for combining tumour markers in predicting disease states

Receiver operating characteristic (ROC) curves are limited when several diagnostic tests are available, mainly due to the problems of multiplicity and inter-relationships between the different tests. The program presented in this paper uses the generalised ROC criteria, as well as its confidence interval, obtained from the non-central F distribution, as a possible solution to this problem. This criterion corresponds to the best linear combination of the test for which the area under the ROC curve is maximal. Quantified marker values are assumed to follow a multivariate normal distribution but not necessarily with equal variances for two populations. Other options include Box-Cox variable transformations, QQ-plots, interactive graphics associated with changes in sensitivity and specificity as a function of the cut-off. We provide an example to illustrate the usefulness of data transformation and of how linear combination of markers can significantly improve discriminative power. This finding highlights potential difficulties with methods that reject individual markers based on univariate analyses.

Methodological issues associated with tumor marker development Biostatistical aspects

The search for markers as potential prognostic factors for different stages of disease is becoming a major task in clinical research. Enormous amounts of information on the effectiveness of tumor markers are being published, and many of these results are conflicting and thus adding confusion to the area. In this paper we discuss the problem of multiplicity that we believe is one of the major statistical reasons for the conflicting results. We further review the ROC curve and the area under it as a popular statistical tool for evaluating the ability of a marker to distinguish between two populations. Finally we provide an extension to the ROC analysis when several markers are available.

TBARS and cardiovascular disease in a population-based sample.

Background Oxygen radicals might play a crucial role in the pathogenesis of various diseases, including atherosclerosis. Thiobarbituric acid reaction substances (TBARS), a biomarker of oxidative stress, have been proposed as a summary measure of total circulating oxidation. However, there is no strong indication that circulating levels of TBARS are increased in patients with atherosclerosis. Design We evaluated the relation between TBARS and cardiovascular disease (CVD) in a cross-sectional random sample of white men and women from Buffalo, New York. Methods Logistic regression was used to estimate the risk associated with high levels of TBARS. The area under the ROC curve was used to evaluate the discriminating power of TBARS. Results After adjusting for age and gender, TBARS levels were significantly higher in those with prevalent CVD (OR=1.73, 95% CI=1.32–2.38), compared to those without a CVD diagnosis. These OR were almost 50% higher after correcting for measurement error (ME) (OR=1.93, 95% CI=1.07–3.40). The area under the ROC curve was 0.69 (95% CI=0.62–0.77) and when corrected for ME reached 0.80 (95% CI=0.65–0.89). Conclusions Our results indicate that elevated levels of TBARS were associated with increase risk of the prevalence of CVD, but this effect was no longer significant after adjusting for glucose.

Bayesian variable selection method for censored survival data.

A Bayesian variable selection method for censored data is proposed in this paper. Based on the sufficiency and asymptotic normality of the maximum partial likelihood estimator, we approximate the posterior distribution of the parameters in a proportional hazards model. We consider a parsimonious model as the full model with some covariates unobserved and replaced by their conditional expected values. A loss function based on the posterior expected estimation error of the log-risk for the proportional hazards model is used to select a parsimonious model. We derive computational expressions for this loss function for both continuous and binary covariates. This approach provides an extension of Lindleys (1968, Journal of the Royal Statistical Society, Series B 30, 31-66) variable selection criterion for the linear case. Data from a randomized clinical trial of patients with primary biliary cirrhosis of the liver (PBC) (Fleming and Harrington, 1991, Counting Processes and Survival Analysis) is used to illustrate the proposed method and a simulation study compares it with the backward elimination procedure.

A Randomised Trial to Evaluate the Effects of Low‐dose Aspirin in Gestation and Reproduction: Design and Baseline Characteristics

BACKGROUND Low-dose aspirin (LDA) has been proposed to improve pregnancy outcomes in couples experiencing recurrent pregnancy loss. However, results from studies of LDA on pregnancy outcomes have been inconsistent, perhaps because most studies evaluated LDA-initiated post-conception. The purpose of the Effects of Aspirin in Gestation and Reproduction (EAGeR) trial was to determine whether preconception-initiated LDA improves livebirth rates in women with one to two prior losses. METHODS We performed a multicentre, block randomised, double-blind, placebo-controlled trial. Study participants were recruited using community-based advertisements and physician referral to four university medical centres in the US (2006-12). Eligible women were aged 18-40 years actively trying to conceive, with one to two prior losses. Participants were randomised to receive daily LDA (81 mg/day) or a matching placebo, and all were provided with daily 400-mcg folic acid. Follow-up continued for ≤6 menstrual cycles while attempting to conceive. For those who conceived, treatment was continued until 36 weeks gestation. The primary outcome was the cumulative livebirth rate over the trial period. RESULTS There were 1228 women randomised (615 LDA, 613 placebo). Participants had a mean age of 28.7, were mostly white (95%), well educated (86% more than high school education), and employed (75%) with a household income >

Confidence Intervals for the Overlapping Coefficient: the Normal Equal Variance Case

100 000 annually (40%). The characteristics of those in the treatment and placebo arms were well balanced. CONCLUSIONS We describe the study design, recruitment, data collection, and baseline characteristics of participants enrolled in EAGeR, which aimed to determine the effect of LDA on livebirth and other pregnancy outcomes in these women.