The analysis of multiple outcomes, multiple variables and variables selection in hematopoietic cell transplantation studies

Time-to-event data are common in cancer research such as hematopoietic cell transplantation (HCT) for leukemia. In time-to-event data, failure times are often unobserved, that is, “censored”. For example, if a leukemia patient who received HCT survived at the last followup, the event time of that patient is unknown. Because of censoring, traditional regression models including linear regression or generalized linear regression cannot be used for the analysis of time-to-event data. To appropriately account for censoring, many statistical techniques have been developed. The Kaplan-Meier estimator is commonly used to estimate survival probabilities given a time or graphically display the survival curve of the outcome. To evaluate covariate effects on the survival outcome, the Cox proportional hazards model [1] is widely used in practice. The Cox proportional hazards model requires the proportional hazard assumption which means that covariate effects are constant over time. When the proportional hazard assumption is invalid, one can use the stratified Cox model, the Cox model with time-varying effects, the additive hazards model [2], or the accelerated failure time model [3]. Most of these methods can be implemented using standard software such as R (survival [4], aftgee [5], and timereg [6]) and SAS (PROC PHREG, PROC LIFEREG, PROC LIFETEST).

All aforementioned methods consider the univariate survival outcome, that is, one event type. However, in practice a subject is often exposed to multiple types of outcomes. Competing risks outcomes are one of such outcomes, where a failure from one cause prevents a subject from experiencing the other causes. For HCT, either non-relapse mortality (NRM) or relapse may occur for patients, where NRM and relapse are competing risks to each other. A subject can experience up to one type of outcome under the competing risks setting. On the other hand, a patient may experience the same type of outcome repeatedly over time, which is called recurrent events. For example, a patient who received HCT may experience multiple infections over time. Another important outcome in HCT is a composite endpoint. One of the most common composite endpoint in HCT studies is progression-free survival (PFS), where the event of interest is defined as disease progression/relapse or death without disease progression/relapse. However, PFS ignores an important event, death after disease progression/relapse. Instead of PFS, clinicians may be interested in considering disease progression/relapse and death with/without disease progression/relapse in the data analysis. Recently statistical techniques have been developed to analyze all outcomes over time rather than the first composite event only. In this article, we review various types of right-censored data with multiple outcome types including competing risks data, recurrent event data, and composite endpoints.

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