Background:Quantitative differences in biomarker expression relative to age and molecular subtypes have not been well documented in invasive breast cancer (IBCA).Methods:Oestrogen receptor (ER), progesterone receptor (PR), HER2, ki67, p53 and DNA ploidy was performed by image analysis in 162 consecutive IBCAs in women (⩽40 years) and compared with women ⩾50 years (100 cases). Molecular subtypes were defined by immunohistochemistry (IHC).Results:Among young women, tumours were frequently ER negative (P=0.01) with lower ER (P<0.00), PR (P=0.03), higher ki67 index (KI) (P=0.01) and p53 (P=0.00) compared with older women. Triple negative was more frequent among young women with frequent lymph node involvement compared with older women. Luminal B among young vs old women showed lower ER (67% vs 88%), PR (32% vs 52%), higher KI (48% vs 34%) and p53 (19% vs 7%). Linear regression model showed increasing KI (P<0.0001) and p53 (P=0.0003) according to the molecular subtypes. Survival difference among subtypes was demonstrated by multivariate analysis (P=0.0092) after adjusting for age, race, tumour size, grade and stage.Conclusion:We demonstrated significant differences in biomarker expression relative to age and molecular subtypes. Molecular subtype defined by IHC was an independent prognostic factor.

In this paper we study sample size calculation methods for the asymptotic Wilcoxon-Mann-Whitney test for data with or without ties. The existing methods are applicable either to data with ties or to data without ties but not to both cases. While the existing methods developed for data without ties perform well, the methods developed for data with ties have limitations in that they are either applicable to proportional odds alternatives or have computational difficulties. We propose a new method which has a closed-form formula and therefore is very easy to calculate. In addition, the new method can be applied to both data with or without ties. Simulations have demonstrated that the new sample size formula performs very well as the corresponding actual powers are close to the nominal powers.

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In this article, we construct two likelihood‐based confidence intervals (CIs) for a binomial proportion parameter using a double‐sampling scheme with misclassified binary data. We utilize an easy‐to‐implement closed‐form algorithm to obtain maximum likelihood estimators of the model parameters by maximizing the full‐likelihood function. The two CIs are a naïve Wald interval and a modified Wald interval. Using simulations, we assess and compare the coverage probabilities and average widths of our two CIs. Finally, we conclude that the modified Wald interval, unlike the naïve Wald interval, produces close‐to‐nominal CIs under various simulations and, thus, is preferred in practice. Utilizing the expressions derived, we also illustrate our two CIs for a binomial proportion parameter using real‐data example.

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