An approach to trial design and analysis in the era of non-proportional hazards of the treatment effect

Background: Most randomized controlled trials with a time-to-event outcome are designed and analysed under the proportional hazards assumption, with a target hazard ratio for the treatment effect in mind. However, the hazards may be non-proportional. We address how to design a trial under such conditions, and how to analyse the results. Methods: We propose to extend the usual approach, a logrank test, to also include the Grambsch-Therneau test of proportional hazards. We test the resulting composite null hypothesis using a joint test for the hazard ratio and for time-dependent behaviour of the hazard ratio. We compute the power and sample size for the logrank test under proportional hazards, and from that we compute the power of the joint test. For the estimation of relevant quantities from the trial data, various models could be used; we advocate adopting a pre-specified flexible parametric survival model that supports time-dependent behaviour of the hazard ratio. Results: We present the mathematics for calculating the power and sample size for the joint test. We illustrate the methodology in real data from two randomized trials, one in ovarian cancer and the other in treating cellulitis. We show selected estimates and their uncertainty derived from the advocated flexible parametric model. We demonstrate in a small simulation study that when a treatment effect either increases or decreases over time, the joint test can outperform the logrank test in the presence of both patterns of non-proportional hazards. Conclusions: Those designing and analysing trials in the era of non-proportional hazards need to acknowledge that a more complex type of treatment effect is becoming more common. Our method for the design of the trial retains the tools familiar in the standard methodology based on the logrank test, and extends it to incorporate a joint test of the null hypothesis with power against non-proportional hazards. For the analysis of trial data, we propose the use of a pre-specified flexible parametric model that can represent a time-dependent hazard ratio if one is present

Prevalent cases in observational studies of cancer survival: do they bias hazard ratio estimates?

Observational epidemiological studies often include prevalent cases recruited at various times past diagnosis. This left truncation can be dealt with in non-parametric (Kaplan–Meier) and semi-parametric (Cox) time-to-event analyses, theoretically generating an unbiased hazard ratio (HR) when the proportional hazards (PH) assumption holds. However, concern remains that inclusion of prevalent cases in survival analysis results inevitably in HR bias. We used data on three well-established breast cancer prognosticators – clinical stage, histopathological grade and oestrogen receptor (ER) status – from the SEARCH study, a population-based study including 4470 invasive breast cancer cases (incident and prevalent), to evaluate empirically the effectiveness of allowing for left truncation in limiting HR bias. We found that HRs of prognostic factors changed over time and used extended Cox models incorporating time-dependent covariates. When comparing Cox models restricted to subjects ascertained within six months of diagnosis (incident cases) to models based on the full data set allowing for left truncation, we found no difference in parameter estimates (P=0.90, 0.32 and 0.95, for stage, grade and ER status respectively). Our results show that use of prevalent cases in an observational epidemiological study of breast cancer does not bias the HR in a left truncation Cox survival analysis, provided the PH assumption holds true

Prognostic significance of osteopontin expression in early-stage non-small-cell lung cancer

Osteopontin (OPN) is a multifunctional protein, which has recently been shown to be linked to tumorigenesis, progression and metastasis in different malignancies. Since non-small-cell lung cancer (NSCLC)'s prognosis remains bad, with few predictors of outcome, the purpose of this study was to evaluate if OPN might be involved in NSCLC's biology and therefore represent a prognostic marker and a target for new therapeutic trials. Immunohistochemistry was used to detect OPN expression, evaluated as percentage of neoplastic cells with cytoplasmic immunoreactivity, in a wide cohort of patients with stage I NSCLC (136 cases). The median value of this series (20% of positive cells) was used as the cutoff value to distinguish tumours with low (<20%) from tumours with high (⩾20%) OPN expression. A statistically significant correlation between high levels of OPN and shorter overall (P=0.034) and disease-free (P=0.011) survival in our patients was shown. Our results support the hypothesis that high OPN expression is a significantly unfavourable prognostic factor for the survival of patients with stage I NSCLC. This conclusion has notable importance in terms of the biological characterization of early-stage tumours and therapeutic opportunities

Vascular endothelial growth factor in node-positive breast cancer patients treated with adjuvant tamoxifen

In 212 postmenopausal women with node-positive oestrogen receptor-positive (ER(LBA)) breast cancer subjected to radical surgery and adjuvant tamoxifen, the risk of 6-year relapse increased with increasing values of intratumoral vascular endothelial growth factor (VEGF) in patients whose tumours had a low/intermediate ER(LBA) content compared to patients with high-ER(LBA) tumours. These findings indicate that tumour progression, activated or sustained by high VEGF levels, may be counteracted in high-ER(LBA) cancers by tamoxifen, which in contrast fails to contrast the metastatic potential in low-ER(LBA) tumours

Delays in Leniency Application: Is There Really a Race to the Enforcer's Door?

This paper studies cartels’ strategic behavior in delaying leniency applications, a take-up decision that has been ignored in the previous literature. Using European Commission decisions issued over a 16-year span, we show, contrary to common beliefs and the existing literature, that conspirators often apply for leniency long after a cartel collapses. We estimate hazard and probit models to study the determinants of leniency-application delays. Statistical tests find that delays are symmetrically affected by antitrust policies and macroeconomic fluctuations. Our results shed light on the design of enforcement programs against cartels and other forms of conspiracy

Treatment outcomes of new tuberculosis patients hospitalized in Kampala, Uganda: a prospective cohort study.

BACKGROUND: In most resource limited settings, new tuberculosis (TB) patients are usually treated as outpatients. We sought to investigate the reasons for hospitalisation and the predictors of poor treatment outcomes and mortality in a cohort of hospitalized new TB patients in Kampala, Uganda. METHODS AND FINDINGS: Ninety-six new TB patients hospitalised between 2003 and 2006 were enrolled and followed for two years. Thirty two were HIV-uninfected and 64 were HIV-infected. Among the HIV-uninfected, the commonest reasons for hospitalization were low Karnofsky score (47%) and need for diagnostic evaluation (25%). HIV-infected patients were commonly hospitalized due to low Karnofsky score (72%), concurrent illness (16%) and diagnostic evaluation (14%). Eleven HIV uninfected patients died (mortality rate 19.7 per 100 person-years) while 41 deaths occurred among the HIV-infected patients (mortality rate 46.9 per 100 person years). In all patients an unsuccessful treatment outcome (treatment failure, death during the treatment period or an unknown outcome) was associated with duration of TB symptoms, with the odds of an unsuccessful outcome decreasing with increasing duration. Among HIV-infected patients, an unsuccessful treatment outcome was also associated with male sex (P = 0.004) and age (P = 0.034). Low Karnofsky score (aHR = 8.93, 95% CI 1.88 - 42.40, P = 0.001) was the only factor significantly associated with mortality among the HIV-uninfected. Mortality among the HIV-infected was associated with the composite variable of CD4 and ART use, with patients with baseline CD4 below 200 cells/µL who were not on ART at a greater risk of death than those who were on ART, and low Karnofsky score (aHR = 2.02, 95% CI 1.02 - 4.01, P = 0.045). CONCLUSION: Poor health status is a common cause of hospitalisation for new TB patients. Mortality in this study was very high and associated with advanced HIV Disease and no use of ART

Cyclophosphamide- metabolizing enzyme polymorphisms and survival outcomes after adjuvant chemotherapy for node-positive breast cancer: a retrospective cohort study

Abstract Introduction Cyclophosphamide-based adjuvant chemotherapy is a mainstay of treatment for women with node-positive breast cancer, but is not universally effective in preventing recurrence. Pharmacogenetic variability in drug metabolism is one possible mechanism of treatment failure. We hypothesize that functional single nucleotide polymorphisms (SNPs) in drug metabolizing enzymes (DMEs) that activate (CYPs) or metabolize (GSTs) cyclophosphamide account for some of the observed variability in disease outcomes. Methods We performed a retrospective cohort study of 350 women enrolled in a multicenter, randomized, adjuvant breast cancer chemotherapy trial (ECOG-2190/INT-0121). Subjects in this trial received standard-dose cyclophosphamide, doxorubicin and fluorouracil (CAF), followed by either observation or high-dose cyclophosphamide and thiotepa with stem cell rescue. We used bone marrow stem cell-derived genomic DNA from archival specimens to genotype CYP2B6, CYP2C9, CYP2D6, CYP3A4, CYP3A5, GSTM1, GSTT1, and GSTP1. Cox regression models were computed to determine associations between genotypes (individually or in combination) and disease-free survival (DFS) or overall survival (OS), adjusting for confounding clinical variables. Results In the full multivariable analysis, women with at least one CYP3A4 *1B variant allele had significantly worse DFS than those who were wild-type *1A/*1A (multivariate hazard ratio 2.79; 95% CI 1.52, 5.14). CYP2D6 genotype did not impact this association among patients with estrogen receptor (ER) -positive tumors scheduled to receive tamoxifen. Conclusions These data support the hypothesis that genetic variability in cyclophosphamide metabolism independently impacts outcome from adjuvant chemotherapy for breast cancer

Lower age at menarche affects survival in older Australian women: results from the Australian Longitudinal Study of Ageing

Extent: 10p.Background: While menarche indicates the beginning of a woman's reproductive life, relatively little is known about the association between age at menarche and subsequent morbidity and mortality. We aimed to examine the effect of lower age at menarche on all-cause mortality in older Australian women over 15 years of follow-up. Methods: Data were drawn from the Australian Longitudinal Study of Ageing (n = 1,031 women aged 65-103 years). We estimated the hazard ratio (HR) associated with lower age at menarche using Cox proportional hazards models, and adjusted for a broad range of reproductive, demographic, health and lifestyle covariates. Results: During the follow-up period, 673 women (65%) died (average 7.3 years (SD 4.1) of follow-up for decedents). Women with menses onset < 12 years of age (10.7%; n = 106) had an increased hazard of death over the follow-up period (adjusted HR 1.28; 95%CI 0.99-1.65) compared with women who began menstruating aged ≥ 12 years (89.3%; n = 883). However, when age at menarche was considered as a continuous variable, the adjusted HRs associated with the linear and quadratic terms for age at menarche were not statistically significant at a 5% level of significance (linear HR 0.76; 95%CI 0.56 - 1.04; quadratic HR 1.01; 95%CI 1.00-1.02). Conclusion: Women with lower age at menarche may have reduced survival into old age. These results lend support to the known associations between earlier menarche and risk of metabolic disease in early adulthood. Strategies to minimise earlier menarche, such as promoting healthy weights and minimising family dysfunction during childhood, may also have positive longer-term effects on survival in later life.Lynne C Giles, Gary FV Glonek, Vivienne M Moore, Michael J Davies and Mary A Luszc