In a longitudinal clinical study to compare two groups, the primary end point is often the time to a specific event (eg, disease progression, death). The hazard ratio estimate is routinely used to ...empirically quantify the between-group difference under the assumption that the ratio of the two hazard functions is approximately constant over time. When this assumption is plausible, such a ratio estimate may capture the relative difference between two survival curves. However, the clinical meaning of such a ratio estimate is difficult, if not impossible, to interpret when the underlying proportional hazards assumption is violated (ie, the hazard ratio is not constant over time). Although this issue has been studied extensively and various alternatives to the hazard ratio estimator have been discussed in the statistical literature, such crucial information does not seem to have reached the broader community of health science researchers. In this article, we summarize several critical concerns regarding this conventional practice and discuss various well-known alternatives for quantifying the underlying differences between groups with respect to a time-to-event end point. The data from three recent cancer clinical trials, which reflect a variety of scenarios, are used throughout to illustrate our discussions. When there is not sufficient information about the profile of the between-group difference at the design stage of the study, we encourage practitioners to consider a prespecified, clinically meaningful, model-free measure for quantifying the difference and to use robust estimation procedures to draw primary inferences.
For a study with an event time as the endpoint, its survival function contains all the information regarding the temporal, stochastic profile of this outcome variable. The survival probability at a ...specific time point, say t, however, does not transparently capture the temporal profile of this endpoint up to t. An alternative is to use the restricted mean survival time (RMST) at time t to summarize the profile. The RMST is the mean survival time of all subjects in the study population followed up to t, and is simply the area under the survival curve up to t. The advantages of using such a quantification over the survival rate have been discussed in the setting of a fixed-time analysis. In this article, we generalize this approach by considering a curve based on the RMST over time as an alternative summary to the survival function. Inference, for instance, based on simultaneous confidence bands for a single RMST curve and also the difference between two RMST curves are proposed. The latter is informative for evaluating two groups under an equivalence or noninferiority setting, and quantifies the difference of two groups in a time scale. The proposal is illustrated with the data from two clinical trials, one from oncology and the other from cardiology.
Pulmonary congestion is a common and important finding in heart failure (HF). While clinical examination and chest radiography are insensitive, lung ultrasound (LUS) is a novel technique that may ...detect and quantify subclinical pulmonary congestion. We sought to independently relate LUS and clinical findings to 6-month HF hospitalizations and all-cause mortality (composite primary outcome).
We used LUS to examine 195 NYHA class II-IV HF patients (median age 66, 61% men, 74% white, ejection fraction 34%) during routine cardiology outpatient visits. Lung ultrasound was performed in eight chest zones with a pocket ultrasound device (median exam duration 2 min) and analysed offline.
In 185 patients with adequate LUS images in all zones, the sum of B-lines (vertical lines on LUS) ranged from 0 to 13. B-lines, analysed by tertiles, were associated with clinical and laboratory markers of congestion. Thirty-two per cent of patients demonstrated ≥3 B-lines on LUS, yet 81% of these patients had no findings on auscultation. During the follow-up period, 50 patients (27%) were hospitalized for HF or died. Patients in the third tertile (≥3 B-lines) had a four-fold higher risk of the primary outcome (adjusted HR 4.08, 95% confidence interval, CI 1.95, 8.54; P < 0.001) compared with those in the first tertile and spent a significantly lower number of days alive and out of the hospital (125 days vs. 165 days; adjusted P < 0.001).
Pulmonary congestion assessed by ultrasound is prevalent in ambulatory patients with chronic HF, is associated with other features of clinical congestion, and identifies those who have worse prognosis.
Objectives We sought to investigate the clinical prognostic value of longitudinal and circumferential strain (S) and strain rate (SR) in patients after high-risk myocardial infarction (MI). ...Background Left ventricular (LV) contractile performance after MI is an important predictor of long-term outcome. Tissue deformation imaging might more closely reflect myocardial contractility than traditional measures of systolic functions. Methods The VALIANT (Valsartan in Acute Myocardial Infarction Trial) Echo study enrolled 603 patients with LV dysfunction, heart failure, or both 5 days after MI. We measured global peak longitudinal S and systolic SR (SRs) from apical 4- and 2-chamber views and global circumferential S and SRs from parasternal short-axis view with speckle tracking software (Velocity Vector Imaging, Siemens, Inc., Mountain View, California). We related global S and SRs to LV remodeling at 20-month follow-up and to clinical outcomes. Results Both longitudinal (mean: −5.1 ± 1.6 100/ms) and circumferential SRs (mean: −8.0 ± 2.8 100/ms) were predictive of death or hospital stay for heart failure (hazard ratio: 2.4, 95% confidence interval CI: 2.0 to 3.1, p < 0.001; hazard ratio: 1.3, 95% CI: 1.2 to 1.4, p < 0.001, respectively) after adjustment for clinical covariates by Cox proportional hazards, and longitudinal SRs further improved in predicting 18-month survivor on a model based on clinical and standard echocardiographic measures (increase in area under the receiver-operator characteristic curve: 0.13, p = 0.009). With multivariable logistic regression, circumferential SRs, but not longitudinal SRs, was strongly predictive of remodeling (odds ratio: 1.3, 95% CI: 1.1 to 1.4, p < 0.001). Conclusions Both longitudinal and circumferential SRs were independent predictors of outcomes after MI, whereas only circumferential SRs was predictive of remodeling, suggesting that preserved circumferential function might serve to restrain ventricular enlargement after MI.
The t‐year mean survival or restricted mean survival time (RMST) has been used as an appealing summary of the survival distribution within a time window 0, t. RMST is the patient's life expectancy ...until time t and can be estimated nonparametrically by the area under the Kaplan‐Meier curve up to t. In a comparative study, the difference or ratio of two RMSTs has been utilized to quantify the between‐group‐difference as a clinically interpretable alternative summary to the hazard ratio. The choice of the time window 0, t may be prespecified at the design stage of the study based on clinical considerations. On the other hand, after the survival data have been collected, the choice of time point t could be data‐dependent. The standard inferential procedures for the corresponding RMST, which is also data‐dependent, ignore this subtle yet important issue. In this paper, we clarify how to make inference about a random “parameter.” Moreover, we demonstrate that under a rather mild condition on the censoring distribution, one can make inference about the RMST up to t, where t is less than or even equal to the largest follow‐up time (either observed or censored) in the study. This finding reduces the subjectivity of the choice of t empirically. The proposal is illustrated with the survival data from a primary biliary cirrhosis study, and its finite sample properties are investigated via an extensive simulation study.
In a comparative clinical study with progression-free survival (PFS) or overall survival (OS) as the end point, the hazard ratio (HR) is routinely used to design the study and to estimate the ...treatment effect at the end of the study. The clinical interpretation of the HR may not be straightforward, especially when the underlying model assumption is not valid. A robust procedure for study design and analysis that enables clinically meaningful interpretation of trial results is warranted.
To discuss issues of conventional trial design and analysis and to present alternatives to the HR using a recent immunotherapy study as an illustrative example.
By comparing 2 groups in a survival analysis, we discuss issues of using the HR and present the restricted mean survival time (RMST) as a summary measure of patients’ survival profile over time. We show how to use the difference or ratio in RMST between 2 groups as an alternative for designing and analyzing a clinical study with an immunotherapy study as an illustrative example.
Overall survival or PFS. Group contrast measures included HR, RMST difference or ratio, and the event rate difference.
For the illustrative example, the HR procedure indicates that nivolumab significantly prolonged patient OS and was numerically better than docetaxel for PFS. However, the median PFS time of docetaxel was significantly better than that of nivolumab. Therefore, it may be difficult to use median OS and/or PFS to interpret of the HR value clinically. On the other hand, using RMST difference, nivolumab was significantly better than docetaxel for both OS and PFS. We also provide details regarding design of a future study with RMST-based measures.
The design and analysis of a conventional cancer clinical trial can be improved by adopting a robust statistical procedure that enables clinically meaningful interpretations of the treatment effect. The RMST-based quantitative method may be used as a primary tool for future cancer trials or to help us to better understand the clinical interpretation of the HR even when its model assumption is plausible.
Purpose Current Lynch syndrome (LS) prediction models quantify the risk to an individual of carrying a pathogenic germline mutation in three mismatch repair (MMR) genes: MLH1, MSH2, and MSH6. We ...developed a new prediction model, PREMM5, that incorporates the genes PMS2 and EPCAM to provide comprehensive LS risk assessment. Patients and Methods PREMM5 was developed to predict the likelihood of a mutation in any of the LS genes by using polytomous logistic regression analysis of clinical and germline data from 18,734 individuals who were tested for all five genes. Predictors of mutation status included sex, age at genetic testing, and proband and family cancer histories. Discrimination was evaluated by the area under the receiver operating characteristic curve (AUC), and clinical impact was determined by decision curve analysis; comparisons were made to the existing PREMM1,2,6 model. External validation of PREMM5 was performed in a clinic-based cohort of 1,058 patients with colorectal cancer. Results Pathogenic mutations were detected in 1,000 (5%) of 18,734 patients in the development cohort; mutations included MLH1 (n = 306), MSH2 (n = 354), MSH6 (n = 177), PMS2 (n = 141), and EPCAM (n = 22). PREMM5 distinguished carriers from noncarriers with an AUC of 0.81 (95% CI, 0.79 to 0.82), and performance was similar in the validation cohort (AUC, 0.83; 95% CI, 0.75 to 0.92). Prediction was more difficult for PMS2 mutations (AUC, 0.64; 95% CI, 0.60 to 0.68) than for other genes. Performance characteristics of PREMM5 exceeded those of PREMM1,2,6. Decision curve analysis supported germline LS testing for PREMM5 scores ≥ 2.5%. Conclusion PREMM5 provides comprehensive risk estimation of all five LS genes and supports LS genetic testing for individuals with scores ≥ 2.5%. At this threshold, PREMM5 provides performance that is superior to the existing PREMM1,2,6 model in the identification of carriers of LS, including those with weaker phenotypes and individuals unaffected by cancer.
In comparing two treatments with the event time observations, the hazard ratio (HR) estimate is routinely used to quantify the treatment difference. However, this model dependent estimate may be ...difficult to interpret clinically especially when the proportional hazards (PH) assumption is violated. An alternative estimation procedure for treatment efficacy based on the restricted means survival time or t-year mean survival time (t-MST) has been discussed extensively in the statistical and clinical literature. On the other hand, a statistical test via the HR or its asymptotically equivalent counterpart, the logrank test, is asymptotically distribution-free. In this article, we assess the relative efficiency of the hazard ratio and t-MST tests with respect to the statistical power under various PH and non-PH models theoretically and empirically. When the PH assumption is valid, the t-MST test performs almost as well as the HR test. For non-PH models, the t-MST test can substantially outperform its HR counterpart. On the other hand, the HR test can be powerful when the true difference of two survival functions is quite large at end but not the beginning of the study. Unfortunately, for this case, the HR estimate may not have a simple clinical interpretation for the treatment effect due to the violation of the PH assumption.
We conducted a randomized controlled trial in older adults with hematologic malignancies to determine the impact of geriatrician consultation embedded in our oncology clinic alongside standard care. ...From February 2015 to May 2018, transplant-ineligible patients aged ≥75 years who presented for initial consultation for lymphoma, leukemia, or multiple myeloma at Dana-Farber Cancer Institute (Boston, MA, USA) were eligible. Pre-frail and frail patients, classified based on phenotypic and deficit-accumulation approaches, were randomized to receive either standard oncologic care with or without consultation with a geriatrician. The primary outcome was 1-year overall survival. Secondary outcomes included unplanned care utilization within 6 months of follow-up and documented end-of-life (EOL) goals-of-care discussions. Clinicians were surveyed as to their impressions of geriatric consultation. One hundred sixty patients were randomized to either geriatric consultation plus standard care (n=60) or standard care alone (n=100). The median age of the patients was 80.4 years (standard deviation = 4.2). Of those randomized to geriatric consultation, 48 (80%) completed at least one visit with a geriatrician. Consultation did not improve survival at 1 year compared to standard care (difference: 2.9%, 95% confidence interval: -9.5% to 15.2%, P=0.65), and did not significantly reduce the incidence of emergency department visits, hospital admissions, or days in hospital. Consultation did improve the odds of having EOL goals-of-care discussions (odds ratio = 3.12, 95% confidence interval: 1.03 to 9.41) and was valued by surveyed hematologic-oncology clinicians, with 62.9%-88.2% of them rating consultation as useful in the management of several geriatric domains.
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