Clinician's Approach to Advanced Statistical Methods: Win Ratios, Restricted Mean Survival Time, Responder Analyses, and Standardized Mean Differences

Novel statistical methods have emerged in recent medical literature, which clinicians must understand to properly appraise and integrate evidence into their practice. Some of these key concepts include win ratios, restricted mean survival time, responder analyses, and standardized mean difference. This article offers guidance to busy clinicians on the comprehension and practical applicability of the results to patients. Win ratios provide an alternative method to analyze composite outcomes by prioritizing individual components of the composite; prioritization of the outcomes should be evidence-based, pre-specified, and patient-centered. Restricted mean survival time presents a method to analyze Kaplan-Meier curves when assumptions required for Cox proportional hazards analysis are not met. As it only considers outcomes that occur within a specific timeframe, the duration of follow-up must be appropriately defined and based on prior epidemiologic and mechanistic evidence. Researchers can analyze continuous outcomes with responder analyses, in which participants are dichotomized into "responders" or "non-responders." While clinicians and patients may more easily grasp outcomes analyzed in this way, they should be aware of the loss of information and resulting imprecision, as well as potential to manipulate data presentation. When meta-analyzing continuous outcomes, point estimates can be converted to standardized mean differences to facilitate the combination of data utilizing various outcome measures. However, clinicians may find it challenging to grasp the clinical meaningfulness of a standardized mean difference, and may benefit from converting it to well-known outcomes. By providing the background knowledge of these statistical methods, along with practical applicability, benefits, and inevitable limitations, this article aims to provide clinicians with an approach to appraise the literature and apply the results in clinical practice.

Years of life lost to cancer among the United States HIV population, 2006-2015

OBJECTIVES

We estimated years of life lost (YLLs) to all causes of death and YLL lost to cancer among persons with HIV (PWH) in the United States.

DESIGN

Linked HIV and cancer registry data from the HIV/AIDS Cancer Match Study were used to identify incident cancers and deaths among PWH in 11 regions of the United States during 2006-2015.

METHODS

Mean YLL (MYLL) to all causes of death and MYLL to cancer during 2006-2015 were derived from the restricted mean survival estimated from Cox proportional hazards regression models. MYLLs were then upweighted to the national population of PWH to obtain all-cause total YLL (TYLL) and cancer-related TYLL in the United Staets during 2006-2015.

RESULTS

Among 466 234 PWH in the study population, 25 772 (5.5%) developed cancer during 2006-2015. Nationally, an estimated 134 986 years of life were lost to cancer of all types during 2006-2015 among PWH, representing 9.6% of TYLL to all causes. Non-Hodgkin lymphoma (NHL), Kaposi sarcoma, anal cancer, and lung cancer were the four largest cancer contributors (45% of TYLL to cancer). The largest fraction of TYLL occurred among back PWH, MSM, and PWH aged 40-59 years old.

CONCLUSION

PWH have higher mortality rates after developing cancer. NHL, Kaposi sarcoma and anal and lung cancers were large contributors to YLL to cancer in the United States population of PWH, highlighting opportunities to reduce cancer mortality through improved access to antiretroviral treatment, prevention, and screening.

Robust Adaptive Incorporation of Historical Control Data in a Randomized Trial of External Cooling to Treat Septic Shock

This paper proposes randomized controlled clinical trial design to evaluate external cooling as a means to control fever and thereby reduce mortality in patients with septic shock. The trial will include concurrent external cooling and control arms while adaptively incorporating historical control arm data. Bayesian group sequential monitoring will be done using a posterior comparative test based on the 60-day survival distribution in each concurrent arm. Posterior inference will follow from a Bayesian discrete time survival model that facilitates adaptive incorporation of the historical control data through an innovative regression framework with a multivariate spike-and-slab prior distribution on the historical bias parameters. For each interim test, the amount of information borrowed from the historical control data will be determined adaptively in a manner that reflects the degree of agreement between historical and concurrent control arm data. Guidance is provided for selecting Bayesian posterior probability group-sequential monitoring boundaries. Simulation results elucidating how the proposed method borrows strength from the historical control data are reported. In the absence of historical control arm bias, the proposed design controls the type I error rate and provides substantially larger power than reasonable comparators, whereas in the presence bias of varying magnitude, type I error rate inflation is curbed.

Estimation and modeling of the restricted mean time lost in the presence of competing risks

Survival data with competing or semi-competing risks are common in observational studies. As an alternative to cause-specific and subdistribution hazard ratios, the between-group difference in cause-specific restricted mean times lost (RMTL) gives the mean difference in life expectancy lost to a specific cause of death or in disease-free time lost, in the case of a nonfatal outcome, over a prespecified period. To adjust for covariates, we introduce an inverse probability weighted estimator and its variance for the marginal difference in RMTL. We also introduce an inverse probability of censoring weighted regression model for the RMTL. In simulation studies, we examined the finite sample performance of the proposed methods under proportional and nonproportional subdistribution hazards scenarios. We illustrated both methods with competing risks data from the Framingham Heart Study. We estimated sex differences in atrial fibrillation (AF)-free times lost over 40 years. We also estimated sex differences in mean lifetime lost to cardiovascular disease (CVD) and non-CVD death over 10 years among individuals with AF.

Deep learning for survival outcomes

Deep learning is a class of machine learning algorithms that are popular for building risk prediction models. When observations are censored, the outcomes are only partially observed and standard deep learning algorithms cannot be directly applied. We develop a new class of deep learning algorithms for outcomes that are potentially censored. To account for censoring, the unobservable loss function used in the absence of censoring is replaced by a censoring unbiased transformation. The resulting class of algorithms can be used to estimate both survival probabilities and restricted mean survival. We show how the deep learning algorithms can be implemented by adapting software for uncensored data by using a form of response transformation. We provide comparisons of the proposed deep learning algorithms to existing risk prediction algorithms for predicting survival probabilities and restricted mean survival through both simulated datasets and analysis of data from breast cancer patients.

RNA processing genes characterize RNA splicing and further stratify colorectal cancer

Objectives

Due to the limited evaluation of the prognostic value of RNA processing genes (RPGs), which are regulators of alternative splicing events (ASEs) that have been shown to be associated with tumour progression, this study sought to determine whether colorectal cancer (CRC) could be further stratified based on the expression pattern of RPGs.

Materials and Methods

The gene expression profiles of CRCs were collected from TCGA (training set) and three external validation cohorts, representing 1060 cases totally. Cox regression with least absolute shrinkage and selection operator (LASSO) penalty was used to develop an RNA processing gene index (RPGI) risk score. Kaplan‐Meier curves, multivariate Cox regression and restricted mean survival (RMS) analyses were harnessed to evaluate the prognostic value of the RPGI.

Results

A 22‐gene RPGI signature was developed, and its risk score served as a strong independent prognostic factor across all data sets when adjusted for major clinical variables. Moreover, ASEs for certain genes, such as FGFR1 and the RAS oncogene family, were significantly correlated with RPGI. Expression levels of genes involved in splicing‐ and tumour‐associated pathways were significantly correlated with RPGI score. Furthermore, a combination of RPGI with age and tumour stage resulted in significantly improved prognostic accuracy.

Conclusions

Our findings highlighted the prognostic value of RPGs for risk stratification of CRC patients and provide insights into specific ASEs associated with the development of CRC.

Improving testing and description of treatment effect in clinical trials with survival outcomes

Cox model inference and the log-rank test have been the cornerstones for design and analysis of clinical trials with survival outcomes. In this article, we summarize some recently developed methods for analyzing survival data when the hazards may possibly be nonproportional and also propose some new estimators for summary measures of the treatment effect. These methods utilize the short-term and long-term hazard ratio model proposed in Yang and Prentice (2005), which contains the Cox model and also accommodates various nonproportional hazards scenarios. Without the proportional hazards assumption, these methods often improve the log-rank test and inference procedures based on the Cox model, as well as nonparametric procedures currently available in the literature. The proposed methods have sound theoretical justifications and can be computed quickly. R codes for implementing them are available. Detailed illustrations with 3 clinical trials are provided.

On representing the prognostic value of continuous gene expression biomarkers with the restricted mean survival curve

Motivation

Researchers developing biomarkers for cancer prognosis from quantitative gene expression data are often faced with an odd methodological discrepancy: while Cox's proportional hazards model, the appropriate and popular technique, produces a continuous and relative risk score, it is hard to cast the estimate in clear clinical terms like median months of survival and percent of patients affected. To produce a familiar Kaplan-Meier plot, researchers commonly make the decision to dichotomize a continuous (often unimodal and symmetric) score. It is well known in the statistical literature that this procedure induces significant bias.

Results

We illustrate the liabilities of common techniques for categorizing a risk score and discuss alternative approaches. We promote the use of the restricted mean survival (RMS) and the corresponding RMS curve that may be thought of as an analog to the best fit line from simple linear regression.

Conclusions

Continuous biomarker workflows should be modified to include the more rigorous statistical techniques and descriptive plots described in this article. All statistics discussed can be computed via standard functions in the Survival package of the R statistical programming language. Example R language code for the RMS curve is presented in the appendix.

SAS and R functions to compute pseudo-values for censored data regression

Recently, in a series of papers, a method based on pseudo-values has been proposed for direct regression modeling of the survival function, the restricted mean and cumulative incidence function with right censored data. The models, once the pseudo-values have been computed, can be fit using standard generalized estimating equation software. Here we present SAS macros and R functions to compute these pseudo-values. We illustrate the use of these routines and show how to obtain regression estimates for a study of bone marrow transplant patients.