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Survival Analysis
Published in Marcello Pagano, Kimberlee Gauvreau, Heather Mattie, Principles of Biostatistics, 2022
Marcello Pagano, Kimberlee Gauvreau, Heather Mattie
As with other regression models, explanatory variables can be categorical or continuous. Coefficients can be interpreted in a manner analogous to the logistic regression model. If the explanatory variable is dichotomous, we can exponentiate the estimated coefficient to obtain a hazard ratio. The hazard ratio is the ratio of the hazards for two study subjects, one of whom has the risk factor of interest while the other does not. The hazard ratio can be interpreted as the instantaneous relative risk of failure at time t, given that both individuals have survived up until time t. For a continuous explanatory variable, the estimated hazard ratio is the relative risk of failure associated with a one unit increase in X.
Challenges in Cancer Clinical Trials
Published in Wei Zhang, Fangrong Yan, Feng Chen, Shein-Chung Chow, Advanced Statistics in Regulatory Critical Clinical Initiatives, 2022
where j =1, …, J is the jth event time; , and Rj are the patients at risk at the time j for the treatment, control arms and at the study level, respectively; and Dj are the patients having had events at the time j for treatment arm and at the study level, respectively. Under the null hypothesis of identical survival function between arms, the Log-rank test statistic follows normal distribution approximately. In terms of treatment effect estimation, hazard ratio, which describes the relative risk based on comparison of hazard rates, is usually used to quantify the treatment effect and is produced by Cox method based on proportional hazard assumption. Proportional hazard assumption indicates that the hazard ratio for any two individuals is constant over time.
Clinical Trial Designs
Published in Gary L. Rosner, Purushottam W. Laud, Wesley O. Johnson, Bayesian Thinking in Biostatistics, 2021
Gary L. Rosner, Purushottam W. Laud, Wesley O. Johnson
One might calculate key posterior probabilities for the skeptic and enthusiast. Here, smaller hazard ratios indicate improvement by the treatment over the control. The skeptic would now assign probabilities to regions of θ, such as , , and . The enthusiast's corresponding posterior probabilities are , and .
Interventional oncological treatment of breast cancer liver metastasis (BCLM): single center long-term evaluation over 26 years using thermoablation techniques like LITT, MWA and TACE in a multimodal application
Published in International Journal of Hyperthermia, 2023
Thomas J. Vogl, Jason Freichel, Tatjana Gruber-Rouh, Nour Eldin Nour Eldin, Sven Becker, Christine Solbach, Ulrich Stefenelli, Nagy N. N. Naguib
Hazard ratios again relate to the risk of death, i.e. the non-survival of patients in this study. For example, the hazard ratio for LITT (first column of Table 6) with a value of HR = 0.314 indicates a death risk factor of 68.6% (1–0.314 = 0.686, 95%-CI value between 0.26 and 0.381). This means that the risk of death in the case of treatment with LITT is 68.6% lower compared to all other factors included in the model. Another example MWA shows a hazard ratio of HR = 0.16. Thus, it can be stated that MWA has a risk-of-death which is 84% better compared to all other factors (1-0.16 = 0.84). Based on this statistical test, amongst the compared methods MWA ranks best (HR = 0.16), followed by LITT (HR = 0.314) closely followed by MWA + TACE (HR = 0.319), LITT + TACE (HR = 0.387). Regarding the age of patients, HR = 1.006 indicates that for each +1year-step along the timeline, the risk-of-death increases by the factor of 0.6 (95% CI between HR-levels of 0.999 and 1.013)
Quantifying treatment differences in confirmatory trials under non-proportional hazards
Published in Journal of Applied Statistics, 2022
When the proportional hazards assumption holds, the hazard ratio captures the relative difference between the randomized treatment groups, which has clinical interpretation. However, when the underlying proportional hazards assumption is violated, the log-rank test loses power and the hazard ratio does not has a straightforward clinical interpretation as its value depends on the accrual distribution, dropout pattern and the study follow-up time, which may lead to different trial results and parameter estimates in different trials even if patients come from the same population and survival curves are identical (see [23]). Alternative approaches to deal with non-proportional hazards patterns include the weighted log-rank test and the test based on the restricted mean survival time (RMST).
Efficacy of Adalimumab in Non-Infectious Uveitis Across Different Etiologies: A Post Hoc Analysis of the VISUAL I and VISUAL II Trials
Published in Ocular Immunology and Inflammation, 2021
Pauline T. Merrill, Albert Vitale, Manfred Zierhut, Hiroshi Goto, Martina Kron, Alexandra P. Song, Sophia Pathai, Eric Fortin
For this post hoc analysis, patients were categorized into different uveitis etiologies, which they presented at study entry, as predefined in the VISUAL studies. Patients with idiopathic uveitis diagnoses were further stratified by location of uveitis at study entry (intermediate, posterior, or panuveitis). Efficacy was assessed by time to treatment failure, defined as the time from randomization to occurrence of one or more of the following four criteria affecting at least one eye: (1) new, active, inflammatory chorioretinal or vascular lesions; (2) inability to achieve ≤0.5+ anterior chamber (AC) cell at week 6 or a 2-step increase in AC cell grade relative to best state achieved after week 6 (VISUAL I), or a 2-step increase in AC cell grade relative to baseline at or after week 2 (VISUAL II); (3) inability to achieve ≤0.5+ vitreous haze (VH) grade at week 6 or a 2-step increase relative to best state achieved after week 6 (VISUAL I), or a 2-step increase in VH grade relative to baseline at or after week 2 (VISUAL II); and (4) worsening of best corrected visual acuity by ≥15 letters relative to best state achieved at any other visit (VISUAL I) or relative to baseline at or after week 2 (VISUAL II; Table 1). Time to treatment failure was analyzed using time to event analysis, in which the probability of an event was calculated over time. The hazard ratio was calculated to compare the risk of an event between treatment groups. Safety was monitored by frequency and severity of adverse events (AEs) and reported for patients who received at least 1 dose of study drug.