Discrete Conditional Phase-type model (DC_Ph) for patient waiting time with a logistic regression component to predict patient admission to hospital

Discrete Conditional Phase-type (DC-Ph) models are a family of models which represent skewed survival data conditioned on specific inter-related discrete variables. The survival data is modeled using a Coxian phase-type distribution which is associated with the inter-related variables using a range of possible data mining approaches such as Bayesian networks (BNs), the Naïve Bayes Classification method and classification regression trees. This paper utilizes the Discrete Conditional Phase-type model (DC-Ph) to explore the modeling of patient waiting times in an Accident and Emergency Department of a UK hospital. The resulting DC-Ph model takes on the form of the Coxian phase-type distribution conditioned on the outcome of a logistic regression model.

Relevance of breast cancer hormone receptors and other factors to the efficacy of adjuvant tamoxifen: patient-level meta-analysis of randomised trials

Background: As trials of 5 years of tamoxifen in early breast cancer mature, the relevance of hormone receptor measurements (and other patient characteristics) to long-term outcome can be assessed increasingly reliably. We report updated meta-analyses of the trials of 5 years of adjuvant tamoxifen.
Methods: We undertook a collaborative meta-analysis of individual patient data from 20 trials (n=21457) in early breast cancer of about 5 years of tamoxifen versus no adjuvant tamoxifen, with about 80% compliance. Recurrence and death rate ratios (RRs) were from log-rank analyses by allocated treatment.
Findings: In oestrogen receptor (ER)-positive disease (n=10 645), allocation to about 5 years of tamoxifen substantially reduced recurrence rates throughout the first 10 years (RR 0.53 [SE 0.03] during years 0-4 and RR 0.68 [0.06] during years 5-9 [both 2p<0.00001]; but RR 0.97 [0.10] during years 10-14, suggesting no further gain or loss after year 10). Even in marginally ER-positive disease (10-19 fmol/mg cytosol protein) the recurrence reduction was substantial (RR 0.67 [0.08]). In ER-positive disease, the RR was approximately independent of progesterone receptor status (or level), age, nodal status, or use of chemotherapy. Breast cancer mortality was reduced by about a third throughout the first 15 years (RR 0.71 [0.05] during years 0-4, 0.66 [0.05] during years 5-9, and 0.68 [0.08] during years 10-14; p<0.0001 for extra mortality reduction during each separate time period). Overall non-breast-cancer mortality was little affected, despite small absolute increases in thromboembolic and uterine cancer mortality (both only in women older than 55 years), so all-cause mortality was substantially reduced. In ER-negative disease, tamoxifen had little or no effect on breast cancer recurrence or mortality.
Interpretation: 5 years of adjuvant tamoxifen safely reduces 15-year risks of breast cancer recurrence and death. ER status was the only recorded factor importantly predictive of the proportional reductions. Hence, the absolute risk reductions produced by tamoxifen depend on the absolute breast cancer risks (after any chemotherapy) without tamoxifen.
Funding: Cancer Research UK, British Heart Foundation, and Medical Research Council.

Effect of radiotherapy after breast-conserving surgery on 10-year recurrence and 15-year breast cancer death: meta-analysis of individual patient data for 10,801 women in 17 randomised trials

Background: After breast-conserving surgery, radiotherapy reduces recurrence and breast cancer death, but it may do so more for some groups of women than for others. We describe the absolute magnitude of these reductions according to various prognostic and other patient characteristics, and relate the absolute reduction in 15-year risk of breast cancer death to the absolute reduction in 10-year recurrence risk.
Methods: We undertook a meta-analysis of individual patient data for 10?801 women in 17 randomised trials of radiotherapy versus no radiotherapy after breast-conserving surgery, 8337 of whom had pathologically confirmed node-negative (pN0) or node-positive (pN+) disease.
Findings: Overall, radiotherapy reduced the 10-year risk of any (ie, locoregional or distant) first recurrence from 35·0% to 19·3% (absolute reduction 15·7%, 95% CI 13·7–17·7, 2p<0·00001) and reduced the 15-year risk of breast cancer death from 25·2% to 21·4% (absolute reduction 3·8%, 1·6–6·0, 2p=0·00005). In women with pN0 disease (n=7287), radiotherapy reduced these risks from 31·0% to 15·6% (absolute recurrence reduction 15·4%, 13·2–17·6, 2p<0·00001) and from 20·5% to 17·2% (absolute mortality reduction 3·3%, 0·8–5·8, 2p=0·005), respectively. In these women with pN0 disease, the absolute recurrence reduction varied according to age, grade, oestrogen-receptor status, tamoxifen use, and extent of surgery, and these characteristics were used to predict large (=20%), intermediate (10–19%), or lower (<10%) absolute reductions in the 10-year recurrence risk. Absolute reductions in 15-year risk of breast cancer death in these three prediction categories were 7·8% (95% CI 3·1–12·5), 1·1% (–2·0 to 4·2), and 0·1% (–7·5 to 7·7) respectively (trend in absolute mortality reduction 2p=0·03). In the few women with pN+ disease (n=1050), radiotherapy reduced the 10-year recurrence risk from 63·7% to 42·5% (absolute reduction 21·2%, 95% CI 14·5–27·9, 2p<0·00001) and the 15-year risk of breast cancer death from 51·3% to 42·8% (absolute reduction 8·5%, 1·8–15·2, 2p=0·01). Overall, about one breast cancer death was avoided by year 15 for every four recurrences avoided by year 10, and the mortality reduction did not differ significantly from this overall relationship in any of the three prediction categories for pN0 disease or for pN+ disease.
Interpretation: After breast-conserving surgery, radiotherapy to the conserved breast halves the rate at which the disease recurs and reduces the breast cancer death rate by about a sixth. These proportional benefits vary little between different groups of women. By contrast, the absolute benefits from radiotherapy vary substantially according to the characteristics of the patient and they can be predicted at the time when treatment decisions need to be made.
Funding: Cancer Research UK, British Heart Foundation, and UK Medical Research Council.