| Survival analysis is a commonly used tool in many fields but has seen little use in education research despite a common number of research questions for which it is well suited. Researchers often use logistic regression instead; however, this omits useful information. In research on retention and graduation for example, the timing of the event is an important piece of information omitted when using logistic regression. A simulation study was conducted to evaluate four methods of analyzing competing risks survival data, Cox proportional hazards regression, Weibull regression, Fine and Gray's Method, and Cox proportional hazards regression with frailty. College student retention and graduation is presented as an example. The results indicate that there is no one best model for all simulated scenarios. Instead, it appears the selection of the method of analysis should be based on the characteristics of the data. Both Cox proportional hazards and the Weibull regression are accurate with the base combination (sample size of 500 per group, continuous event time format, no correlation between event times, homogeneous shape parameter for both events for both groups, homogeneous failure rates for both events for both groups, and no frailty) as well as when one parameter is changed from the base combination. In addition, for data where the event time distribution shape does not differ by event, the accuracy of the models is quite similar. However, differences begin to emerge with some combinations of conditions. Cox performs especially poorly with data sets containing both differing event time distribution shapes by event and differing failure rates by group or event while Weibull is least accurate with the combination of homogeneous event time distribution shape, heterogeneous failure rate by group and/or event, and discrete format time. Fine and Gray's method was often ranked last by accuracy, but there are some situations where its accuracy is quite good including retention and graduation data. Cox proportional hazards regression with frailty performed very similarly to the Cox regression without frailty with no clear benefits. |
