A non-parametric framework for estimating threshold limit values

Evaluation of CD3 and CD8 T-Cell Immunohistochemistry for Prognostication and Prediction of Benefit From Adjuvant Chemotherapy in Early-Stage Colorectal Cancer Within the QUASAR Trial

PURPOSE

High densities of tumor infiltrating CD3 and CD8 T-cells are associated with superior prognosis in colorectal cancer (CRC). Their value as predictors of benefit from adjuvant chemotherapy is uncertain.

PATIENTS AND METHODS

Tumor tissue from 868 patients in the QUASAR trial (adjuvant fluorouracil/folinic acid v observation in stage II/III CRC) was analyzed by CD3 and CD8 immunohistochemistry. Pathologists, assisted by artificial intelligence, calculated CD3 and CD8 cell densities (cells/mm2) in the core tumor (CT) and invasive margin (IM). Participants were randomly partitioned into training and validation sets. The primary outcome was recurrence-free interval (RFI), 2-year RFI for assessment of biomarker-treatment interactions. Maximum-likelihood methods identified optimal high-risk/low-risk group cutpoints in the training set. Prognostic analyses were repeated in the validation set.

RESULTS

In the training set, the recurrence rate in the high-risk group was twice that in the low-risk group for all measures (CD3-CT: rate ratio [RR], 2.00, P = .0008; CD3-IM: 2.38, P < .00001; CD8-CT: 2.17, P = .0001; CD8-IM: 2.13, P = .0001). This was closely replicated in the validation set (RR, 1.96, 1.79, 1.72, 1.72, respectively). In multivariate analyses, prognostic effects were similar in colon and rectal cancers, and in stage II and III disease. Proportional reductions in recurrence with adjuvant chemotherapy were of similar magnitude in the high- and low-recurrence risk groups. Combining information from CD3-IM and CD3-CT (CD3 Score) generated high-, intermediate-, and low-risk groups with numbers needed to treat (NNTs) to prevent one disease recurrence being 11, 21, and 36, respectively.

CONCLUSION

Recurrence rates in the high-risk CD3/CD8 groups are twice those in the low-risk groups. Proportional reductions with chemotherapy are similar, allowing NNTs derived in QUASAR to be updated using contemporary, nonrandomized data sets.

Intratumoral stromal morphometry predicts disease recurrence but not response to 5-fluorouracil-results from the QUASAR trial of colorectal cancer

AIMS

The biological importance of tumour-associated stroma is becoming increasingly apparent, but its clinical utility remains ill-defined. For stage II/Dukes B colorectal cancer (CRC), clinical biomarkers are urgently required to direct therapeutic options. We report here prognostic/predictive analyses, and molecular associations, of stromal morphometric quantification in the Quick and Simple and Reliable (QUASAR) trial of CRC.

METHODS AND RESULTS

Relative proportions of tumour epithelium (PoT) or stroma (PoS) were morphometrically quantified on digitised haematoxylin and eosin (H&E) sections derived from 1800 patients enrolled in QUASAR, which randomised 3239 (91% stage II) CRC patients between adjuvant fluorouracil/folinic acid (FUFA) chemotherapy and observation. The prognostic and predictive values of PoT/PoS measurements were determined by the use of stratified log-rank analyses. A high proportion of tumour stroma (≥50%) was associated with an increased recurrence risk: 31.3% (143/457) recurrence for ≥50% versus 21.9% (294/1343) for <50% [rate ratio (RR) 1.62; 95% confidence interval (CI) 1.30-2.02; P < 0.0001]. Of patients with stromal proportions of ≥65%, 40% (46/115) had recurrent disease within 10 years. The adverse prognostic effect of a high stromal proportion was independent of established prognostic variables, and was maintained in stage II/Dukes B patients (RR 1.62; 95% CI 1.26-2.08; P = 0.0002). KRAS mutation in the presence of a high stromal proportion augmented recurrence risk (RR 2.93; 95% CI 1.87-4.59; P = 0.0005). Stromal morphometry did not predict response to FUFA chemotherapy.

CONCLUSIONS

Simple digital morphometry applied to a single representative H&E section identifies CRC patients with a >50% higher risk of disease recurrence. This technique can reliably partition patients into subpopulations with different risks of tumour recurrence in a simple and cost-effective manner. Further prospective validation is warranted.

Calcium intake and bone mineral density as an example of non-linearity and threshold analysis

Non-linearity is a likely phenomenon in bone metabolism, but is often ignored in pertinent epidemiological studies. Using NHANES III data on calcium intake and bone mineral density, the most important non-linear methods are introduced and discussed. The results should motivate researchers to consider non-linearity in this field more frequently.

INTRODUCTION

Many relationships in bone metabolism and homeostasis are likely to follow non-linear patterns. Detailed dose-response analyses allowing for non-linear associations nonetheless remain scarce in this field.

METHODS

A detailed analysis of NHANES III data on dietary calcium intake and bone mineral density was used to demonstrate the application and some of the challenges of the most important dose-response methods, including LOESS, categorical analysis, fractional polynomials, restricted cubic splines, and segmented regression.

RESULTS

The spline estimate suggested increasing bone mineral density up to a calcium intake of about 1 g/day and a plateau thereafter. In segmented regression, the break-point marking the beginning of the plateau was placed at an intake of 0.58 (95 % confidence interval, 0.33 to 0.82) g/day. Sensitivity analyses suggested a less curved dose-response in women.

CONCLUSIONS

Knowing about the possibilities and limitations of non-linear dose-response approaches should encourage researchers to consider these methods more frequently in studies on bone health and disease. The example analysis suggested bone mineral density to reach a plateau slightly below current calcium intake recommendations, with fairly pronounced differences of the dose-response shape by sex and menopausal status.

Identifying change points in a covariate effect on time-to-event analysis with reduced isotonic regression

Isotonic regression is a useful tool to investigate the relationship between a quantitative covariate and a time-to-event outcome. The resulting non-parametric model is a monotonic step function of a covariate X and the steps can be viewed as change points in the underlying hazard function. However, when there are too many steps, over-fitting can occur and further reduction is desirable. We propose a reduced isotonic regression approach to allow combination of small neighboring steps that are not statistically significantly different. In this approach, a second stage, the reduction stage, is integrated into the usual monotonic step building algorithm by comparing the adjacent steps using appropriate statistical testing. This is achieved through a modified dynamic programming algorithm. We implemented the approach with the simple exponential distribution and then its extension, the Weibull distribution. Simulation studies are used to investigate the properties of the resulting isotonic functions. We apply this methodology to the Diabetes Control and Complication Trial (DCCT) data set to identify potential change points in the association between HbA1c and the risk of severe hypoglycemia.