Finite sample pointwise confidence intervals for a survival distribution with right-censored data

An evaluation of confidence intervals for a cumulative proportion to enable decisions at interim reviews of single-arm trials

BACKGROUND

Clinical trials often include interim analyses of the proportion of participants experiencing an event by a fixed time-point. A pre-specified proportion excluded from a corresponding confidence interval (CI) may lead an independent monitoring committee to recommend stopping the trial. Frequently this cumulative proportion is estimated by the Kaplan-Meier estimator with a Wald approximate CI, which may have coverage issues with small samples.

METHODS

We reviewed four alternative CI methods for cumulative proportions (Beta Product Confidence Procedure (BPCP), BPCP Mid P, Rothman-Wilson, Thomas-Grunkemeier) and two CI methods for simple proportions (Clopper-Pearson, Wilson). We conducted a simulation study comparing CI methods across true event proportions for 12 scenarios differentiated by sample sizes and censoring patterns. We re-analyzed interim data from A5340, a HIV cure trial considering the proportion of participants experiencing virologic failure.

RESULTS

Our simulation study highlights the lower and upper tail error probabilities for each CI method. Across scenarios, we found differences in the performance of lower versus upper bounds. No single method is always preferred. The upper bound of a Wald approximate CI performed reasonably with some error inflation, whereas the lower bound of the BPCP Mid P method performed well. For a trial design similar to A5340, we recommend BPCP Mid P.

CONCLUSIONS

The design of future single-arm interim analyses of event proportions should consider the most appropriate CI method based on the relevant bound, anticipated sample size and event proportion. Our paper summarizes available methods, demonstrates performance in a simulation study, and includes code for implementation.

Conservative treatment using laser diode and systemic chemotherapy for early-stage bilateral retinoblastoma: A 14-year prospective cohort study

BACKGROUND

Solid evidence of the safety and effectiveness of retinoblastoma (RB) conservative treatment using thermotherapy and systemic chemotherapy with long-term follow-up is scarce, especially in low-resource countries.

AIMS

This study examined the outcomes of this treatment and associated predictors in Vietnam to strengthen the current RB treatment protocol focusing on preserving eye and vision in low-resource settings.

METHODS AND RESULTS

A prospective cohort study was conducted at Ho Chi Minh City Eye Hospital in Vietnam from 2005 to 2019. All eligible patients with bilateral RB (one eye already removed and another eye classified as group A or B) and without previous treatment were recruited. All patients received thermotherapy and six cycles of systemic three-agent chemotherapy repeated every 4 weeks. A standardized questionnaire was used to collect information on study participants' age, symptoms, tumor characteristics, treatment, and outcomes. Among 50 eyes of all 50 patients with a median age of 9 (4-20) months, 34 eyes were in group B (68%). The median follow-up time was 60 (60-84) months. All 139 preserved tumors regressed mostly to type 4 (70.4%) and type 3 (23.7%) scars. Kaplan-Meier analysis found the overall globe-salvage rate at 5 years of 91.9% (95% CI: 80.1%-97.7%). Most eyes (41/50, 82%, 95% CI: 69.2%-90.2%) had a final visual acuity ≥0.1. The visual acuity is higher when tumors regressed to a type 4 scar (p = .007, AOR = 8.098, 95% CI: 1.79-36.53) which also shows less enucleation than a type 3 scar (p = .002, AOR = 0.06, 95% CI: 0.01-0.37%). Gender effect on visual acuity after treatment was significant and may be due to discrimination. No major complications were recorded.

CONCLUSION

Conservative treatment of early-stage RB is safe and effective. Long-term, thorough follow-ups of patients post-treatment are needed. The regression patterns of scars could be a useful indicator of treatment failure.

Long-Term Survival Following Minimally Invasive Lung Cancer Surgery: Comparing Robotic-Assisted and Video-Assisted Surgery

Simple Summary

Video-assisted thoracoscopic surgery (VATS) and robotic-assisted thoracoscopic surgery (RATS) are known to be safe and efficient surgical procedures to treat lung cancer. Both VATS and RATS allow anatomical resection associated with radical lymph node dissection. However, RATS, unlike VATS, allows the thoracic surgeon to mimic an open approach and to perform lung resection. We hypothesized that the technical advantages of RATS, compared with VATS, would allow more precise resection, with “better lymph node dissection” which could increase survival compared to VATS. Nevertheless, VATS, and RATS nodal up-staging are still debated, with conflicting results and in our study, as well as in the medical literature, RATS failed to show its superiority over VATS in resectable non-small cell lung cancer.

Abstract

Background: Nowadays, video-assisted thoracoscopic surgery (VATS) and robotic-assisted thoracoscopic surgery (RATS) are known to be safe and efficient surgical procedures to treat early-stage non-small cell lung cancer (NSCLC). We assessed whether RATS increased disease-free survival (DFS) compared with VATS for lobectomy and segmentectomy. Methods: This retrospective cohort study included patients treated for resectable NSCLC performed by RATS or VATS, in our tertiary care center from 2012 to 2019. Patients’ data were prospectively recorded and reviewed in the French EPITHOR database. Primary outcomes were 5-year DFS for lobectomy and 3-year DFS for segmentectomy, compared by propensity-score adjusted difference of Kaplan–Meier estimates. Results: Among 844 lung resections, 436 VATS and 234 RATS lobectomies and 46 VATS and 128 RATS segmentectomies were performed. For lobectomy, the adjusted 5-year DFS was 60.9% (95% confidence interval (CI) 52.9–68.8%) for VATS and 52.7% (95%CI 41.7–63.7%) for RATS, with a difference estimated at −8.3% (−22.2–+4.9%, p = 0.24). For segmentectomy, the adjusted 3-year DFS was 84.6% (95%CI 69.8–99.0%) for VATS and 72.9% (95%CI 50.6–92.4%) for RATS, with a difference estimated at −11.7% (−38.7–+7.8%, p = 0.21). Conclusions: RATS failed to show its superiority over VATS for resectable NSCLC.

Outcome after resection for perihilar cholangiocarcinoma in patients with primary sclerosing cholangitis: an international multicentre study

BACKGROUND

Resection for perihilar cholangiocarcinoma (pCCA) in primary sclerosing cholangitis (PSC) has been reported to lead to worse outcomes than resection for non-PSC pCCA. The aim of this study was to compare prognostic factors and outcomes after resection in patients with PSC-associated pCCA and non-PSC pCCA.

METHODS

The international retrospective cohort comprised patients resected for pCCA from 21 centres (2000-2020). Patients operated with hepatobiliary resection, with pCCA verified by histology and with data on PSC status, were included. The primary outcome was overall survival. Secondary outcomes were disease-free survival and postoperative complications.

RESULTS

Of 1128 pCCA patients, 34 (3.0%) had underlying PSC. Median overall survival after resection was 33 months for PSC patients and 29 months for non-PSC patients (p = .630). Complications (Clavien-Dindo grade ≥ 3) were more frequent in PSC pCCA (71% versus 44%, p = .003). The rate of posthepatectomy liver failure (21% versus 17%, p = .530) and 90-day mortality (12% versus 13%, p = 1.000) was similar for PSC and non-PSC patients.

CONCLUSION

Median overall survival after resection for pCCA was similar in patients with underlying PSC and non-PSC patients. Complications were more frequent after resection for PSC-associated pCCA, with no difference in postoperative mortality.

Natural history of disease in cynomolgus monkeys exposed to Ebola virus Kikwit strain demonstrates the reliability of this non-human primate model for Ebola virus disease

Filoviruses (Family Filoviridae genera Ebolavirus and Marburgvirus) are negative-stranded RNA viruses that cause severe health effects in humans and non-human primates, including death. Except in outbreak settings, vaccines and other medical countermeasures against Ebola virus (EBOV) will require testing under the FDA Animal Rule. Multiple vaccine candidates have been evaluated using cynomolgus monkeys (CM) exposed to EBOV Kikwit strain. To the best of our knowledge, however, animal model development data supporting the use of CM in vaccine research have not been submitted to the FDA. This study describes a large CM database (122 CM, 62 female and 60 male, age 2 to 9 years) and demonstrates the consistency of the CM model through time to death models and descriptive statistics. CMs were exposed to EBOV doses of 0.1 to 100,000 PFU in 33 studies conducted at three Animal Biosafety Level 4 facilities, by three exposure routes. Time to death was modeled using Cox proportional hazards models with a frailty term that incorporated study-to-study variability. Despite significant differences attributed to exposure variables, all CMs exposed to the 100 to 1,000 pfu doses commonly used in vaccine studies died or met euthanasia criteria within 21 days of exposure, median 7 days, 93% between 5 and 12 days of exposure. Moderate clinical signs were observed 4 to 5 days after exposure and preceded death or euthanasia by approximately one day. Viremia was detected within a few days of infection. Hematology indices were indicative of viremia and the propensity for hemorrhage with progression of Ebola viremia. Changes associated with coagulation parameters and platelets were consistent with coagulation disruption. Changes in leukocyte profiles were indicative of an acute inflammatory response. Increased liver enzymes were observed shortly after exposure. Taken together, these factors suggest that the cynomolgus monkey is a reliable animal model for human disease.

Efficacy of the bivalent HPV vaccine against HPV 16/18-associated precancer: long-term follow-up results from the Costa Rica Vaccine Trial

BACKGROUND

Oncogenic human papillomavirus (HPV) infections cause most cases of cervical cancer. Here, we report long-term follow-up results for the Costa Rica Vaccine Trial (publicly funded and initiated before licensure of the HPV vaccines), with the aim of assessing the efficacy of the bivalent HPV vaccine for preventing HPV 16/18-associated cervical intraepithelial neoplasia grade 2 or worse (CIN2+).

METHODS

Women aged 18-25 years were enrolled in a randomised, double-blind, controlled trial in Costa Rica, between June 28, 2004, and Dec 21, 2005, designed to assess the efficacy of a bivalent vaccine for the prevention of infection with HPV 16/18 and associated precancerous lesions at the cervix. Participants were randomly assigned (1:1) to receive an HPV 16/18 AS04-adjuvanted vaccine or control hepatitis A vaccine. Vaccines were administered intramuscularly in three 0·5 mL doses at 0, 1, and 6 months and participants were followed up annually for 4 years. After the blinded phase, women in the HPV vaccine group were invited to enrol in the long-term follow-up study, which extended follow-up for 7 additional years. The control group received HPV vaccine and was replaced with a new unvaccinated control group. Women were followed up every 2 years until year 11. Investigators and patients were aware of treatment allocation for the follow-up phase. At each visit, clinicians collected cervical cells from sexually active women for cytology and HPV testing. Women with abnormal cytology were referred to colposcopy, biopsy, and treatment as needed. Women with negative results at the last screening visit (year 11) exited the long-term follow-up study. The analytical cohort for vaccine efficacy included women who were HPV 16/18 DNA-negative at vaccination. The primary outcome of this analysis was defined as histopathologically confirmed CIN2+ or cervical intraepithelial neoplasia grade 3 or worse associated with HPV 16/18 cervical infection detected at colposcopy referral. We calculated vaccine efficacy by year and cumulatively. This long-term follow-up study is registered with ClinicalTrials.gov, NCT00867464.

FINDINGS

7466 women were enrolled in the Costa Rica Vaccine Trial; 3727 received the HPV vaccine and 3739 received the control vaccine. Between March 30, 2009, and July 5, 2012, 2635 women in the HPV vaccine group and 2836 women in the new unvaccinated control group were enrolled in the long-term follow-up study. 2635 women in the HPV vaccine group and 2677 women in the control group were included in the analysis cohort for years 0-4, and 2073 women from the HPV vaccine group and 2530 women from the new unvaccinated control group were included in the analysis cohort for years 7-11. Median follow-up time for the HPV group was 11·1 years (IQR 9·1-11·7), 4·6 years (4·3-5·3) for the original control group, and 6·2 years (5·5-6·9) for the new unvaccinated control group. At year 11, vaccine efficacy against incident HPV 16/18-associated CIN2+ was 100% (95% CI 89·2-100·0); 34 (1·5%) of 2233 unvaccinated women had a CIN2+ outcome compared with none of 1913 women in the HPV group. Cumulative vaccine efficacy against HPV 16/18-associated CIN2+ over the 11-year period was 97·4% (95% CI 88·0-99·6). Similar protection was observed against HPV 16/18-associated CIN3-specifically at year 11, vaccine efficacy was 100% (95% CI 78·8-100·0) and cumulative vaccine efficacy was 94·9% (73·7-99·4). During the long-term follow-up, no serious adverse events occurred that were deemed related to the HPV vaccine. The most common grade 3 or worse serious adverse events were pregnancy, puerperium, and perinatal conditions (in 255 [10%] of 2530 women in the unvaccinated control group and 201 [10%] of 2073 women in the HPV vaccine group). Four women in the unvaccinated control group and three in the HPV vaccine group died; no deaths were deemed to be related to the HPV vaccine.

INTERPRETATION

The bivalent HPV vaccine has high efficacy against HPV 16/18-associated precancer for more than a decade after initial vaccination, supporting the notion that invasive cervical cancer is preventable.

FUNDING

US National Cancer Institute.

Nonparametric generalized fiducial inference for survival functions under censoring

Since the introduction of fiducial inference by Fisher in the 1930s, its application has been largely confined to relatively simple, parametric problems. In this paper, we present what might be the first time fiducial inference is systematically applied to estimation of a nonparametric survival function under right censoring. We find that the resulting fiducial distribution gives rise to surprisingly good statistical procedures applicable to both one-sample and two-sample problems. In particular, we use the fiducial distribution of a survival function to construct pointwise and curvewise confidence intervals for the survival function, and propose tests based on the curvewise confidence interval. We establish a functional Bernstein–von Mises theorem, and perform thorough simulation studies in scenarios with different levels of censoring. The proposed fiducial-based confidence intervals maintain coverage in situations where asymptotic methods often have substantial coverage problems. Furthermore, the average length of the proposed confidence intervals is often shorter than the length of confidence intervals for competing methods that maintain coverage. Finally, the proposed fiducial test is more powerful than various types of log-rank tests and sup log-rank tests in some scenarios. We illustrate the proposed fiducial test by comparing chemotherapy against chemotherapy combined with radiotherapy, using data from the treatment of locally unresectable gastric cancer.

Data maturity and follow-up in time-to-event analyses

We propose methods to determine the minimum number of subjects remaining at risk after which Kaplan-Meier survival plots for time-to-event outcomes should be curtailed, as, once the number remaining at risk drops below this minimum, the survival estimates are no longer meaningful in the context of the investigation. The size of the decrease of the Kaplan-Meier survival estimate S(t) at time t if one extra event should occur is considered in two ways. In the first approach, the investigator sets a maximum acceptable absolute decrease in S(t) should one extra event occur. In the second, a minimum acceptable number of subjects still at risk is calculated by comparing the size of the decrease in S(t) if an extra event should occur with the variability of the survival estimate had all subjects been followed to that time (confidence interval approach). We recommend calculating both limits for the number still at risk and then making an informed choice in the context of the particular investigation. We explore further how the amount of information actually available can assist in considering issues of data maturity for studies whose outcome of interest is a survival percentage at a particular time point. We illustrate the approaches with a number of published studies having differing sample sizes and censoring issues. In particular, one study was the subject of some controversy regarding how far in time the Kaplan-Meier plot should be extended. The proposed methods allow for limits to be calculated simply using the output provided by most statistical packages.

Confidence intervals for directly standardized rates using mid-p gamma intervals

Directly standardized rates continue to be an integral tool for presenting rates for diseases that are highly dependent on age, such as cancer. Statistically, these rates are modeled as a weighted sum of Poisson random variables. This is a difficult statistical problem, because there are k observed Poisson variables and k unknown means. The gamma confidence interval has been shown through simulations to have at least nominal coverage in all simulated scenarios, but it can be overly conservative. Previous modifications to that method have closer to nominal coverage on average, but they do not achieve the nominal coverage bound in all situations. Further, those modifications are not central intervals, and the upper coverage error rate can be substantially more than half the nominal error. Here we apply a mid-p modification to the gamma confidence interval. Typical mid-p methods forsake guaranteed coverage to get coverage that is sometimes higher and sometimes lower than the nominal coverage rate, depending on the values of the parameters. The mid-p gamma interval does not have guaranteed coverage in all situations; however, in the (not rare) situations where the gamma method is overly conservative, the mid-p gamma interval often has at least nominal coverage. The mid-p gamma interval is especially appropriate when one wants a central interval, since simulations show that in many situations both the upper and lower coverage error rates are on average less than or equal to half the nominal error rate.

Statistical description for survival data

Statistical description is always the first step in data analysis. It gives investigator a general impression of the data at hand. Traditionally, data are described as central tendency and deviation. However, this framework does not fit to the survival data (also termed time-to-event data). Such data type contains two components. One is the survival time and the other is the status. Researchers are usually interested in the probability of event at a given survival time point. Hazard function, cumulative hazard function and survival function are commonly used to describe survival data. Survival function can be estimated using Kaplan-Meier estimator, which is also the default method in most statistical packages. Alternatively, Nelson-Aalen estimator is available to estimate survival function. Survival functions of subgroups can be compared using log-rank test. Furthermore, the article also introduces how to describe time-to-event data with parametric modeling.