# Using the Weibull Accelerated Failure Time Regression Model to Predict Time to Health Events
## 12 Discussion  
In this paper, we introduced how to use the Weibull AFT model to predict when an event will occur. We utilized mean survival time (mean time to failure time, mean time between failures), median survival time, and minimum prediction error survival time to make predictions about the time from the baseline to the event. We also assessed prediction accuracy using [PERSON]'s method. When we fixed \(k=2\), the accuracy was 55.6% for the median, 50% for the MTTF, and 51.1% for the MPET. However, by setting \(k=3\), as suggested by [PERSON] and [PERSON], the accuracy rate increased to 77.8%, 66.7%, and 67.8%, respectively. It is worth noting that our sample size was relatively small, and we only used two predictors. With a larger sample and more predictors, the accuracy rate could potentially be even higher. If there are many covariates that could be included in the model, various variable selection methods, such as backward elimination, forward selection, stepwise selection, and all possible subset selection can be employed. These methods may incorporate different stopping rules, such as p-values, Akaike information criterion (AIC), Bayesian information criterion (BIC), and Mallows's Cp statistic to construct clinical prediction models [14]. Additionally, in this sample, we did not observe that the MPET had a significantly better accuracy rate than the median survival time. Parametric survival models offer advantages in predicting survival time compared to the semiparametric Cox regression model. The Cox regression model, which can be specified as \(S_{i}(t|x_{i})=S_{0}(t)^{\exp(x_{i}^{\prime}\beta)}\), cannot directly predict time. Instead, it requires first  
\begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**ID** & **Stage** & **Age** & **Death** & **Time** & **Median (95\% CI)** & **MTTF** & **MPET** \\ \hline
59 & 3 & 74 & 1 & 1.8 & 3.76 (1.96, 5.56), 0 & 4.97, 0 & 4.75, 0 \\
60 & 3 & 72 & 1 & 1.9 & 3.9 (2.12, 5.68), 0  
specifying a certain period of time and then calculates the probability of an event within that period of time. The lognormal model is an alternative parametric model that can be employed to fit survival data. However, it comes with a drawback--parametric survival models, including the lognormal model, necessitate stronger assumptions compared to semiparametric models. Other models, like the logistic regression model or neural network models, are typically utilized to model binary events, regardless of when those events occurred. Poisson regression models can also be applied to model survival data with count data types (0, 1, 2, 3, and so forth). Nevertheless, similar to the Cox model, a prespecified period of time is required to calculate the probability of an event. The choice of which model to use should be guided by the specific questions we aim to address and the type of available data [15]. Currently, most clinical prediction models calculate a patient's probability of having or developing a specific disease or risk scores based on these probabilities [16]. However, providing a probability can be challenging to understand for the general population, and probability itself can be defined in various ways [17]. In practice, the time axis remains the most natural measure for both clinicians and patients. Predicting when an event will occur can offer a practical and concrete guide to clinicians and healthcare providers for managing their patients [18]. It can also assist families and patients in making suitable plans for the remaining lifespan. In this paper, our intention was not to utilize the publicly available larynx cancer dataset for the development of an actual prediction tool. Rather, we employed the dataset to illustrate the application of statistical methods and evaluate point accuracy. Developing a real prediction tool would require a much larger dataset and rigorous internal and external validations.