Originally published as JCO Early Release 10.1200/JCO.2004.03.091 on September 20 2004

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Preoperative Sensitivity and Specificity for Early-Stage Ovarian Cancer When Combining Cancer Antigen CA-125II, CA 15-3, CA 72-4, and Macrophage Colony-Stimulating Factor Using Mixtures of Multivariate Normal Distributions

From the Massachusetts General Hospital and Harvard Medical School, Boston, MA; The University of Texas M.D. Anderson Cancer Center, Houston, TX; Duke University Medical Center, Durham, NC; Johns Hopkins Medical Institutions, Baltimore, MD; Groningen University Hospital, Groningen, the Netherlands; and St Bartholomew’s Hospital, London, United Kingdom

Address reprint requests to Steven J. Skates, PhD, Massachusetts General Hospital, 50 Stanford St, Suite 560, Boston, MA 02114, e-mail: sskates{at}partners.org

	ABSTRACT

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PURPOSE: In CA-125–based ovarian cancer screening trials, overall specificity and screening sensitivity of ultrasound after an elevated CA-125 exceeded 99.6% and 70%, respectively, thereby yielding a positive predictive value (PPV) exceeding 10%. However, sensitivity for early-stage disease was only 40%. This study aims to increase preoperative sensitivity for early-stage ovarian cancer while maintaining the annual referral rate to ultrasound at 2% by combining information across CA-125II, CA 15-3, CA 72-4, and macrophage colony-stimulating factor (M-CSF). For direct comparisons between marker panels, all sensitivity results correspond to a 98% fixed first-line specificity (referral rate 2%).

PATIENTS AND METHODS: Logistic regression, classification tree, and mixture discriminant analysis (MDA) models were fit to a training data set of preoperative serum measurements (63 patients, 126 healthy controls) from one center. Estimates from the training set applied to an independent validation set (60 stage I to II patients, 98 healthy controls) from two other centers provided unbiased estimates of sensitivity.

RESULTS: Preoperative sensitivities for early-stage disease of the optimal panels were 45% for CA-125II; 67% for CA-125II and CA 72-4; 70% for CA-125II, CA 72-4, and M-CSF; and 68% for all four markers (latter two results using MDA).

CONCLUSION: Efficiently combining information on CA-125II, CA 72-4, and M-CSF significantly increased preoperative early-stage sensitivity from 45% with CA-125II alone to 70%, while maintaining 98% first-line specificity. Screening trials with these markers using MDA followed by referral to ultrasound may maintain previously high levels of specificity and PPV, while significantly increasing early-stage screening sensitivity. MDA is a useful, biologically justified method for combining biomarkers.

	INTRODUCTION

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Screening for ovarian cancer is an appealing approach to reducing mortality—there is a substantial contrast in survival rates between early- and late-stage ovarian cancer cases, with most ovarian cancers (> 75%) clinically detected in late stages.¹ Ovarian cancer mortality has been relatively constant for more than 30 years,² so investigating alternatives such as early detection is warranted. The low annual incidence of ovarian cancer (40 to 50 per 100,000) for women older than 50 years, creates a significant hurdle for early detection.³ Because of the morbidity of surgical exploration for possible ovarian cancer, an ovarian cancer screening program should refer to surgery at most 10 women for each woman with screen-detected ovarian cancer (a positive predictive value [PPV] > 10%),⁴ which requires a highly sensitive test (> 75%) and an extremely high overall screening specificity (> 99.6%).⁵

Screening trials based on serum cancer antigen (CA) -125 followed by transvaginal ultrasound for an elevated CA-125 have demonstrated a PPV in excess of 20%.^6-8 Approximately 2% of patients per year are referred to ultrasound, so that first-line CA-125 specificity is 98%. In the larger trial, the screening sensitivity of this approach is 71%, with a early-stage screening sensitivity of 40%.⁷ Longitudinal CA-125 evaluation may improve screening sensitivity^5,9,10 and prospective trials are underway to test such an approach. Another approach to increasing sensitivity is to measure additional biomarkers. Many studies have reported putative biomarkers,¹¹ with some reporting increased sensitivity at the cost of decreased specificity,^12,13 or vice versa.¹⁴ Specificity decreases because a result is naively positive if any individual marker exceeds its cut point. Similarly, sensitivity decreases because a result is naively positive if multiple markers need to be positive. Such methods of combining multiple markers are inefficient. Other studies have used artificial neural networks to combine information across multiple markers,¹⁵ or genetic algorithms for unknown markers,¹⁶ to improve specificity while sensitivity was kept constant. The addition of information, whether from new markers or longitudinal values, when efficiently used, should always yield a test better able to distinguish between patients and controls; that is, increase sensitivity while maintaining specificity, or vice versa, or simultaneously increase both operating characteristics.

This article evaluates the performance of several more efficient approaches to combining information in known multiple markers: logistic regression, classification trees, and mixture discriminant analysis (MDA) based on a biologic motivation.¹⁷ The multiple markers are CA-125, CA 15-3, CA 72-4, and macrophage colony-stimulating factor (M-CSF), and the information is measured as the sensitivity at a fixed specificity. CA 15-3 is a marker developed for breast cancer, CA 72-4 was developed for pancreatic cancer, and M-CSF is a cytokine that stimulates proliferation and differentiation of monocytes, but that can also act as an autocrine or paracrine growth factor for some epithelial cancers.

These markers are measured in preoperative serum and serum from healthy controls in a training set from early- and late-stage patients from St Bartholomew’s Hospital (London, United Kingdom) and a validation set from only early-stage patients from Duke University Medical Center (Durham, NC) and Groningen University Hospital (Groningen, the Netherlands). Developing methods for combining information across markers in the training set with patients from all stages, and applying methods in an independent validation set where patients are only in early stage and samples are from institutions distinct from the training set, yields unbiased estimates of preoperative sensitivity and specificity, with greater robustness to institutional source and stage distribution than when training and validation data sets are created by randomly selecting data from one source data set. The resulting homogeneity will likely yield an overly optimistic estimate when applied to samples from new institutions, whereas the results given by our approach are likely more generalizable.

	PATIENTS AND METHODS

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Subjects
The training set consisted of 63 patient cases and 126 healthy controls from St Bartholomew’s Hospital, and the validation set consisted of 30 patient cases and 50 controls from Duke University Medical Center, combined with 30 patient cases and 48 controls from Groningen University Hospital, for a total of 347 samples. The local institutional review boards approved the protocol for the study. The distributions of stage and histology in the training and validation data sets are given in Table 1. In the training set, 27 were early-stage invasive epithelial ovarian cancers and 36 were late-stage invasive epithelial ovarian cancers. In the validation set, which were all early stage, 45 were invasive (38 stage I, four stage II, and three stage IIIA), 12 were borderline (10 stage I, two stage II), and three were nonepithelial (stage I granulosa cell, stage I malignant mixed Müllerian, one stage I endodermal sinus). Mucinous tumors were more common in the validation set (40%) than in the training set (15%); however, the training and validation sets were chosen without regard to histology. Reports of early-stage ovarian cancer trials indicate a higher proportion of mucinous tumors (25%)¹⁸ compared with trials of late-stage ovarian cancer (5%),^19,20 and in screening trials (10%).⁶ Results for the validation data may reflect more favorably on markers sensitive to mucinous ovarian tumors²¹ than may be expected in a screening trial. The approach to obtaining unbiased estimates of preoperative sensitivity is to estimate the parameters of the statistical models in the training set, and independently determine the models’ performance for early-stage patients in the validation set. Data from control subjects determine the marker combinations corresponding to a fixed specificity of 98%.

View larger version (24K): [in this window] [in a new window]   Fig 1. Histograms of (A) monocyte colony-stimulating factor (M-CSF), (B) cancer antigen (CA) 15-3, (C) CA 72-4, and (D) CA-125 for the patients in the training set.

Classification Trees
Using classification trees,^26,27 the data were recursively split into two on the basis of a cut point for a marker, beginning with the marker for which a single cut point yields the highest classification accuracy. The two parts of the data then form the basis for a tree, and each part is split independently of the other by identifying the marker for which a subsequent split distinguishes patient cases from controls most accurately. The tree continues to be generated until no significant improvement in accuracy occurs. At each terminus is a probability of having ovarian cancer. Screening decisions are made by passing marker results through the decision tree until a terminal node is reached. A positive result corresponds to arriving at a terminus associated with a probability of cancer that exceeds a cutoff chosen to set specificity in the validation set at 98%. This approach complements logistic regression, given that interactions between the markers are well captured by classification trees because of the independent searches for subsequent markers on both sides of a split. However, because of small sample sizes after a few splits, accuracy may diminish. Although apparent high sensitivity and specificity can be obtained in the training set, operating characteristics in the validation set can be substantially reduced.

MDA
The histograms in Figure 1 give a one-dimensional estimate of the density for each marker, and with a sufficient number of subjects the histogram would become a smooth curve. MDA approximates the density for patient cases and density for controls using a mixture of multivariate normal distributions. The patient cases are distinguished optimally from the controls through the ratio of the density for patient cases with the density for controls using Bayes’ theorem,²⁸ which gives the predicted probability of having ovarian cancer (similar to logistic regression). Screening decisions for new subjects, such as referral to ultrasound, are then made on the basis of the predicted probability.

The motivation for MDA¹⁷ in this application arises from the biologic observation of ovarian cancer heterogeneity.²⁴ Ovarian cancers are a mixture of histologic subtypes (serous, endometrioid, mucinous, clear-cell, and others), and biomarkers may behave differently for each component of the mixture (subtype). MDA emulates this mixture by estimating the proportion of cancers in each component, and estimates a separate multivariate normal biomarker distribution for each component. Histology may not be the defining factor for biomarker distribution, and additional refinement may derive from microarray analysis. Given that the best division into components is unknown, MDA estimates which patients belong to each component directly based on the distribution of the biomarkers. The estimated density is then the mixture of the component densities. This procedure is performed for both the patient cases and for the control subjects, and aims to capture the biologic heterogeneity of disease and the heterogeneity of biomarkers among patient cases and control subjects. Theoretically, this approach provides the optimal result, similar to methods based on other motivations.²⁹ Such approaches efficiently use the information in the joint distribution of the multiple markers.

In practice, the difficulty with MDA is estimating the large number of parameters from a limited number of subjects. Exploratory analyses indicated that three-mixture components for patient cases and one component for controls provide a reasonable trade-off between accuracy and flexibility as indicated by the number of parameters. For one to four markers, the number of parameters required for linear logistic regression is two, three, four, and five, whereas for MDA, the number of parameters is much larger: seven, 13, 20, and 28. The MDA approach is available in the R language environment freely available at www.r-project.org, and in this implementation, readily provides the best two-dimensional representation of multiple markers for distinguishing between the patients and controls, graphically displaying the increased separation provided by additional markers.

Panels of Markers
For each panel size from one to four, this study gives the sensitivity using the three types of models (logistic, tree, MDA) at fixed specificities of 98% and 95%. The additional information in a marker, beyond the markers already in a panel, is summarized by the increase in sensitivity at a fixed specificity.

	RESULTS

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Table 2 summarizes the operating characteristics of each of the three modeling approaches based on all four markers when the model is developed on the training set and reapplied to the training set at two fixed specificities: 98% and 95%. The first choice of specificity corresponds to a first-line specificity of 98%,^6,8 resulting in an overall specificity of 99.9% and screening sensitivity of 71%. Maintaining a first-line specificity of 98% with multiple markers is likely to maintain the high level of overall screening specificity and simultaneously increase screening sensitivity. The second choice is a fixed specificity of 95%. This choice will allow greater improvements in sensitivity at the cost of an increase from 2% to 5% of patients referred to ultrasound per year, and a decrease in overall specificity. However, given that the overall specificity currently is at 99.9%, and a specificity of 99.6% is required to achieve a 10% PPV, there is some leeway to decrease the first-line specificity, so results for both specificities are provided.

View larger version (14K): [in this window] [in a new window]   Fig 2. Receiver operator characteristic curves for combining two markers (cancer antigen [CA] 15-3 and macrophage colony-stimulating factor) using mixture discriminant analysis (MDA) and logistic regression.

View larger version (21K): [in this window] [in a new window]   Fig 3. Best two-dimensional representation of separation provided by (A) cancer antigen (CA) -125II and CA 72-4; (B) CA-125II, CA 72-4, and macrophage colony-stimulating factor (M-CSF); and (C) CA-125II, CA 72-4, M-CSF, and CA 15-3. , control subjects; , early-stage patients.

	DISCUSSION

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Having independent training and validation data sets from separate institutions to estimate model parameters and then independently evaluate the model’s performance ensures the sensitivity estimates are unbiased and more applicable to other sets of subjects outside this study. On a similar conservative note, the inclusion of 12 borderline tumors among 60 patient cases in the validation set may, in fact, lower the sensitivity estimates compared with a set with only invasive tumors, given that borderline tumors generally have lower marker levels than invasive tumors. Conversely, the over-representation of mucinous tumors in the validation data likely provides a greater contribution for CA 72-4 than would be expected in a screening trial.

For the patient cases, markers are measured in preoperative serum. The sensitivity based on serum from clinically diagnosed patients, who are often symptomatic by time of diagnosis, is likely to be an upwardly biased estimate of the ultimate goal of maximizing early-stage sensitivity in a screening program. Nevertheless, it provides a useful surrogate measure of which additional markers are likely to contribute to increased screening sensitivity. Preoperative serum specimens are more easily obtained than are sera from patients identified in a screening trial, given that even in the postmenopausal group (which has the highest incidence), at least 2,500 women need to be screened to obtain preclinical serum from the one patient case expected. Given that preoperative serum is more readily obtained, it is usually available from many more patients than is screening serum from patients in screening programs before detection. The substantially increased sample size results in greater accuracy of the sensitivity estimate and firmer conclusions concerning which markers should be included in subsequent studies. After the best panel of markers has been identified on the basis of preoperative patient sera, the next step would be to examine the panel on the sera obtained before clinical diagnosis (such sera are much more difficult to obtain) and stored in biorepositories developed as a valuable by-product of screening trials.

In general, the accuracy of the classification trees in the validation data is much lower than in the logistic regression and mixture models, which yield fairly similar results. It is likely that the classification-tree approach would perform better where discrete variables are involved in prediction, such as menopausal status or BRCA carrier status, as distinct from markers that are continuous variables. The logistic regression model provides a commonly available approach to combining information in multiple markers, whereas MDA does provide a slight increase in performance at times. In one logistic regression, a squared term for M-CSF was significant and improved the sensitivity substantially from 40% to 50%. Although squared terms were not significant for any other combination of markers, it is possible for a substantial improvement in sensitivity to have been missed by not incorporating nonsignificant squared terms.

Another issue is that logistic regression requires many fewer parameters than MDA, and thus the statistical accuracy with which the MDA parameters are estimated is likely to be less than that for logistic regression. Hence the estimate for sensitivity based on the MDA model may be adversely affected, and only improved with a substantial increase in number of subjects. Another possibility is that the available software for implementing MDA does not allow for separate variances and covariances in patients and controls. It is likely that there is significantly greater variation in the joint distribution of markers among ovarian cancer patients than in controls, which is accounted for in this study by the greater number of subclasses in the patient cases. However, more flexibility would result if patient cases and controls, and their subclasses, had separate variance and covariance matrices. This expansion of the model is the subject of additional work that will provide greater accuracy in approximating the true multivariate marker distributions, and consequently achieve improved operating characteristics. However, in any given situation, it may not be clear whether MDA is preferable to logistic regression, and the two methods should be viewed as giving alternative approaches for combining the information in multiple biomarkers.

These results show the promise of combining the information on multiple markers in a systematic approach for the early detection of ovarian cancer. The preoperative sensitivity estimate of 70% will likely be an overestimate of the early-stage screening sensitivity, thus adding further impetus for addition of new markers to the panel. Additional estimates of screening sensitivity could be determined by measuring markers in sera collected in a prospective screening program. The stage at the time of screen detection is not known in a retrospective study on sera from a biorepository. Therefore, stage-specific screening sensitivity cannot be measured. Only a prospective clinical trial can evaluate the sensitivity for early-stage preclinical disease, while simultaneously estimating positive predictive value. Furthermore, a prospective randomized clinical trial will provide the ultimate measure of a screening program; namely, the disease-specific reduction in mortality of the target disease. Until this criterion can be significantly reduced, measurement of potential biomarkers for the early detection of ovarian cancer should remain in the context of clinical research studies and cannot be advocated for clinical care in the general population. However, for high-risk individuals from families with genetic mutations or multiple ovarian and/or breast cancers, for whom screening with CA-125 may already be ongoing,³⁰ definitive evaluation of the addition of other markers would require a prospective screening trial of multiple markers.

	Authors’ Disclosures of Potential Conflicts of Interest

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The following authors or their immediate family members have indicated a financial interest. No conflict exists for drugs or devices used in a study if they are not being evaluated as part of the investigation. Received more than $2,000 a year from a company for either of the last 2 years: Robert C. Bast Jr, Fujirebio.

	NOTES

 
Supported by a SPORE Grant in Ovarian Cancer 1P50 CA83639 from the National Cancer Institute, Department of Health and Human Services.

A poster presentation of preliminary results from this study was given at the 38th Annual Meeting of the American Society of Clinical Oncology, Orlando, FL, May 18-21, 2002.

Authors’ disclosures of potential conflicts of interest are found at the end of this article.

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Submitted March 14, 2003; accepted April 29, 2004.

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