Variables with time-varying effects and the Cox model: some statistical concepts illustrated with a prognostic factor study in breast cancer.

BACKGROUND: The Cox model relies on the proportional hazards (PH) assumption, implying that the factors investigated have a constant impact on the hazard - or risk - over time. We emphasize the importance of this assumption and the misleading conclusions that can be inferred if it is violated; this is particularly essential in the presence of long follow-ups. METHODS: We illustrate our discussion by analyzing prognostic factors of metastases in 979 women treated for breast cancer with surgery. Age, tumour size and grade, lymph node involvement, peritumoral vascular invasion (PVI), status of hormone receptors (HRec), Her2, and Mib1 were considered. RESULTS: Median follow-up was 14 years; 264 women developed metastases. The conventional Cox model suggested that all factors but HRec, Her2, and Mib1 status were strong prognostic factors of metastases. Additional tests indicated that the PH assumption was not satisfied for some variables of the model. Tumour grade had a significant time-varying effect, but although its effect diminished over time, it remained strong. Interestingly, while the conventional Cox model did not show any significant effect of the HRec status, tests provided strong evidence that this variable had a non-constant effect over time. Negative HRec status increased the risk of metastases early but became protective thereafter. This reversal of effect may explain non-significant hazard ratios provided by previous conventional Cox analyses in studies with long follow-ups. CONCLUSIONS: Investigating time-varying effects should be an integral part of Cox survival analyses. Detecting and accounting for time-varying effects provide insights on some specific time patterns, and on valuable biological information that could be missed otherwise.

Activity and Safety of Palbociclib in Patients with Advanced Gastrointestinal Stromal Tumors Refractory to Imatinib and Sunitinib: A Biomarker-driven Phase II Study.

PURPOSE: CDKN2A loss is frequent in gastrointestinal stromal tumors (GISTs) and associated with aggressive outcome. Palbociclib is a CDK4 inhibitor with preclinical antitumor efficacy in tumors with P16/CDKN2A loss. PATIENTS AND METHODS: This is a multicenter single-arm phase II clinical trial assessing safety and efficacy of palbociclib in patients with advanced GIST bearing CDKN2A gene loss. Adults with unresectable locally advanced or metastatic, refractory to at least imatinib and sunitinib, measurable and documented progressive disease (PD) as per RECIST 1.1, and CDKN2A deletion centrally assessed were eligible. Patients received palbociclib 125 mg orally daily on a 21 days on/7 days off dosing schedule, until PD or unacceptable toxicity. The primary endpoint was 4-month non-PD rate according to RECIST 1.1. RESULTS: As of May 2017, 71 patients had been included in the study, and 29 patients (40.3%) met the molecular eligibility requirement. Twenty-five patients (86.2%) had grade 1-2 adverse events (AEs) and 12 patients (41.4%) grade 3-4 AEs possibly related to the drug. The planned interim statistical analysis performed after central histologic and radiological review showed that 19 (86.4%) out of the first 22 evaluable patients had PD at 4 months. CDKN2A status had no impact either on overall survival or outcome on previous standard lines of treatment. Translational analysis suggested upregulation of CCNE1 or downregulation of CDKN1A/P21 or LRRC3B as potential mechanisms of resistance. CONCLUSIONS: Palbociclib has no significant clinical activity as a single agent in P16/CDKN2A -deleted GIST refractory to imatinib and sunitinib.

Detecting trends in noisy data series: application to biomarker series.

It is common to define a change in health status or in a disease state on the basis of a sustained rise (or decline) in a biomarker over time. However, such observations are often subject to important variability unrelated to the underlying biologic process. The authors propose a method to evaluate rules that define an event on the basis of consecutive increases (or decreases) in the observations, given the presence of random variation. They examine how well these rules correctly identify a truly rising biomarker trajectory and, conversely, how often they can recognize a truly stable series or a slowly rising series. The method relies on simulation of realistic, sophisticated data sets that accurately reflect the systematic and random variations observed in marker series. These flexible, empirically based simulations enable estimation of the sensitivity and specificity of rules of consecutive rises as a function of the underlying trend, amount of random variation, and schedule of measurements (frequency and duration of follow-up). The authors illustrate the approach with postradiotherapy series of prostate-specific antigen, where three consecutive rises in prostate-specific antigen indicate treatment failure; the data are described by using a Bayesian hierarchical changepoint model. The method is particularly flexible and could be applied to evaluate other rules that purport to accurately detect upturns (downturns) in other noisy data series, including other medical data or other application areas.

Hierarchical changepoint models for biochemical markers illustrated by tracking postradiotherapy prostate-specific antigen series in men with prostate cancer.

PURPOSE: Biomarkers provide valuable information when detecting disease onset or monitoring disease progression; examples include bone mineral density (for osteoporosis), cholesterol (for coronary artery diseases), or prostate-specific antigens (PSA, for prostate cancer). Characteristics of markers series can then be used as prognostic factors of disease progression, such as the postradiotherapy PSA doubling time in men treated for prostate cancer. The statistical analysis of such data has to incorporate the within and between-series variabilities, the complex patterns of the series over time, the unbalanced format of the data, and the possibly nonconstant precision of the measurements. METHODS: We base our analysis on a population-based cohort of 470 men treated with radiotherapy for prostate cancer; after treatment, the log(2)PSA concentrations follow a piecewise-linear pattern. We illustrate the flexibility of Bayesian hierarchical changepoint models by estimating the individual and population postradiotherapy log(2)PSA profiles; parameters such as the PSA nadir and the PSA doubling time were estimated, and their associations with baseline patient characteristics were investigated. The residual PSA variability was modeled as a function of the PSA concentration. For comparison purposes, two alternative models were briefly considered. RESULTS: Precise estimates of all parameters of the PSA trajectory are provided at both the individual and population levels. Estimates suggest greater PSA variability at lower PSA concentrations, as well as an association between shorter PSAdts and greater baseline PSA levels, higher Gleason scores, and older age. CONCLUSIONS: The use of Bayesian hierarchical changepoint models accommodates multiple complex features of longitudinal data, permits realistic modeling of the variability as a function of the marker concentration, and provides precise estimates of all clinically important parameters. This type of model should be applicable to the study of marker series in other diseases.

A method is presented to plan the required sample size when estimating regression-based reference limits.

BACKGROUND AND OBJECTIVE: Reference limits are widely used in anthropometry, the behavioral sciences, medicine, and clinical chemistry. They describe the distribution of a quantitative variable in a healthy population, and are often a smooth function of age or another determinant. Thus, instead of estimating reference limits separately for several age groups, it is more economical and parsimonious to use regression methods to estimate reference limits as a function of age. Although the variability of regression-based reference limits has been addressed previously, the available methods to determine the sample sizes needed to estimate them are neither transparent nor user-friendly. METHODS: We propose a simple and intuitive formula using margins of error, to project the sample sizes required to achieve a given degree of precision, for different sampling strategies. RESULTS: We present two examples for the calculation of the sample size required to estimate a specific reference limit using various age distributions. CONCLUSION: We provide a simple formula to calculate the sample size needed to estimate a specific reference limit to a specified degree of precision. The structure of the formula can easily accommodate different age-sampling strategies.

Detection of frailty in elderly cancer patients: Improvement of the G8 screening test.

OBJECTIVE: The G8 is a screening test to identify frail elderly patients with cancer. Objectives were to design and evaluate the performance of alternative tests taking into account other predictive domains for frailty. METHODS: We conducted a literature review to identify predictive factors of frailty. Using a Delphi consensus, we collected 24 European experts' opinions to validate the most relevant items to improve the G8. Alternative tests were created and performance assessed on a development population (ONCODAGE cohort). The highest performing test was compared to the G8, and validated through both an internal and an external population validation (Aquitaine Geriatric Oncology cohort). RESULTS: The study population consisted of 1435 patients (ONCODAGE cohort) and 364 patients (Aquitaine Geriatric Oncology cohort). Twenty-three experts validated two items with a strong consensus (>75%): modification of the threshold for the G8 polypharmacy item to six drugs per day and replacement of the G8 item on neuropsychological problems by four Instrumental Activities of Daily Living (IADL) items predictive of incident dementia, creating three modified G8 tests (addition of either item, or both). Only the G8 IADL-modified test had better performance than the G8 when tested on the ONCODAGE cohort: sensitivity=77%, specificity=67%. This test was validated on the internal (sensitivity=78%, specificity=71%) and external (sensitivity=88%, specificity=69%) validation populations. CONCLUSION: Adding the four IADL items improves the performance of the G8. We have developed and validated a G8-modified test that is more specific than the G8 to detect frail elderly, while still sensitive and feasible in less than 10 min.

Protocol of the Definition for the Assessment of Time-to-event Endpoints in CANcer trials (DATECAN) project: formal consensus method for the development of guidelines for standardised time-to-event endpoints' definitions in cancer clinical trials.

INTRODUCTION: In randomised phase III cancer clinical trials, the most objectively defined and only validated time-to-event endpoint is overall survival (OS). The appearance of new types of treatments and the multiplication of lines of treatment have resulted in the use of surrogate endpoints for overall survival such as progression-free survival (PFS), or time-to-treatment failure. Their development is strongly influenced by the necessity of reducing clinical trial duration, cost and number of patients. However, while these endpoints are frequently used, they are often poorly defined and definitions can differ between trials which may limit their use as primary endpoints. Moreover, this variability of definitions can impact on the trial's results by affecting estimation of treatments' effects. The aim of the Definition for the Assessment of Time-to-event Endpoints in CANcer trials (DATECAN) project is to provide recommendations for standardised definitions of time-to-event endpoints in randomised cancer clinical trials. METHODS: We will use a formal consensus methodology based on experts' opinions which will be obtained in a systematic manner. RESULTS: Definitions will be independently developed for several cancer sites, including pancreatic, breast, head and neck and colon cancer, as well as sarcomas and gastrointestinal stromal tumours (GISTs). DISCUSSION: The DATECAN project should lead to the elaboration of recommendations that can then be used as guidelines by researchers participating in clinical trials. This process should lead to a standardisation of the definitions of commonly used time-to-event endpoints, enabling appropriate comparisons of future trials' results.

Functional decline in older patients with cancer receiving first-line chemotherapy.

PURPOSE: To determine factors associated with early functional decline during first-line chemotherapy in older patients. PATIENTS AND METHODS: Patients age ≥ 70 years receiving first-line chemotherapy for cancer were prospectively considered for inclusion across 12 centers in France. Functional decline was defined as a decrease of ≥ 0.5 points on the Activities of Daily Living (ADL) scale between the beginning of chemotherapy and the second cycle. Factors associated with functional decline were sought from pretreatment abbreviated comprehensive geriatric assessment, including ADL, Instrumental ADL (IADL), Mini-Nutritional Assessment (MNA), Mini-Mental State Examination (MMSE), Geriatric Depression Scale (GDS15), and Timed Get Up and Go (GUG) test, and from comorbidities (Cumulative Illness Rating Scale-Geriatrics), MAX2 index, and baseline biologic and clinical information. RESULTS: Of 364 included patients, 50 experienced functional decline (16.7%; median, 0.5 points). Abnormal preadmission performance status, IADL, GDS15, MMSE, GUG, and MNA were associated with increased likelihood of functional decline (univariate analysis). In the multivariate model adjusted for baseline ADL and MAX2 index, high baseline GDS (odds ratio [OR], 2.16; 95% CI, 1.09 to 4.30; P = .03) and low IADL scores (OR, 2.87; 95% CI, 1.06 to 7.79; P = .04) were independently associated with increased risk of functional decline. CONCLUSION: Our results outline associations between baseline depression, instrumental dependencies, and early functional decline during chemotherapy for older patients. ADL should be sequentially evaluated early during treatment. Baseline evaluation of GDS15 and IADL may be proposed to anticipate this event.

A statistical evaluation of rules for biochemical failure after radiotherapy in men treated for prostate cancer.

PURPOSE: The "PSA nadir + 2 rule," defined as any rise of 2 ng/ml above the current prostate-specific antigen (PSA) nadir, has replaced the American Society for Therapeutic Radiology and Oncology (ASTRO) rule, defined as three consecutive PSA rises, to indicate biochemical failure (BF) after radiotherapy in patients treated for prostate cancer. We propose an original approach to evaluate BF rules based on the PSAdt as the gold standard rule and on a simulation process allowing us to evaluate the BF rules under multiple settings (different frequency, duration of follow-up, PSA doubling time [PSAdt]). METHODS AND MATERIALS: We relied on a retrospective, population-based cohort of individuals identified by the Connecticut Tumor Registry and treated for localized prostate cancer with radiotherapy. We estimated the 470 underlying true PSA trajectories, including the PSAdt, using a Bayesian hierarchical changepoint model. Next, we simulated realistic, sophisticated data sets that accurately reflect the systematic and random variations observed in PSA series. We estimated the sensitivity and specificity by comparing the simulated PSA series to the underlying true PSAdt. RESULTS: For follow-up of more than 3 years, the specificity of the PSA nadir + 2 rule was systematically greater than that of the ASTRO criterion. In few settings, the nadir + 2 rule had a lower sensitivity than the ASTRO. The PSA nadir + 2 rule appeared less dependent on the frequency and duration of follow-up than the ASTRO. CONCLUSIONS: Our results provide some refinements to earlier findings as the BF rules were evaluated according to various parameters. In most settings, the PSA nadir + 2 rule outperforms the ASTRO criterion.