Quick Answer: Accelerated Failure Time Model Result

The worked analysis used 649 rows from the student-performance dataset. Because the dataset does not contain a native survival duration variable, the teaching workflow created aft_time = absences + 1. The event variable was coded as aft_event = 1 when G3 < 10 or failures > 0; otherwise the observation was treated as right censored. The model therefore demonstrates the mechanics of AFT modeling, censoring and acceleration-factor interpretation on a prepared educational dataset.

Exact variables used in the model: the outcome/time field is aft_time; the event/status field is aft_event; the academic predictors are G1 and G2; the student-background predictors are studytime, age, Medu and Fedu; and the 0/1 coded categorical predictors are school_MS, sex_M and address_U. In plain language, the model asks whether grades, study time, age, parent education, school code, sex code and address code stretch or compress the prepared time-to-event variable.

The final fitted comparison showed 151 events and 498 right-censored cases, giving an event rate of approximately 23.27%. The Weibull AFT model had the better fit by AIC, with AIC = 1000.245, BIC = 1049.475, log likelihood = -489.123 and shape = 1.384. The Log-Normal AFT model had AIC = 1018.302, BIC = 1067.532, log likelihood = -498.151 and sigma = 1.081.

What Is an Accelerated Failure Time Model?

An Accelerated Failure Time Model is a parametric survival-regression model for time-to-event data. Instead of describing covariate effects as hazard ratios, the AFT model describes covariate effects as time ratios or acceleration factors. This makes the interpretation direct: a coefficient can be transformed into exp(coefficient), which tells whether a predictor is associated with longer or shorter predicted survival time.

In an AFT model, a value above 1 for the acceleration factor means the expected event time is multiplied upward. A value below 1 means the expected event time is multiplied downward. For example, an acceleration factor of 1.20 suggests a 20% longer predicted time to event, while an acceleration factor of 0.80 suggests a 20% shorter predicted time to event, assuming the model and distribution are appropriate.

AFT models are commonly used in survival analysis, reliability engineering, health studies, insurance time-to-claim modeling, customer churn timing, employee retention, time-to-graduation and other situations where the outcome is a duration and some observations may be censored.

When to Use an Accelerated Failure Time Model

Use an AFT model when the outcome is a time until an event and a parametric survival distribution is acceptable. AFT models are especially useful when the researcher wants to describe how predictors stretch or compress survival time instead of only reporting hazard ratios.

Before using AFT, check whether you have a meaningful duration variable, a valid event indicator, independent censoring, enough events, and a reasonable distributional choice. For supporting diagnostic concepts, see outlier detection, log transformation, Box-Cox transformation, p-value and confidence interval.

AFT Model Formula and Acceleration Factor

The basic AFT model writes the log survival time as a linear predictor plus an error term:

Here, T is the survival time, X variables are predictors, β values are coefficients, σ is the scale parameter and ε follows a distribution such as normal, logistic or extreme value depending on the chosen AFT family.

The most useful applied transformation is:

In the worked results, school_MS had an acceleration factor of 0.602 in the Weibull model. As a time ratio, that is interpreted as shorter predicted time to event for the coded group, but the large confidence interval and nonsignificant p-value mean this should not be treated as a confirmed population effect.

Null and Alternative Hypotheses for an AFT Model

The hypothesis for each coefficient asks whether that predictor changes log survival time after other model terms are controlled.

Dataset and Variables Used

The workbook uses the student-performance dataset and prepares a time-to-event demonstration. The most important point is that the reader must know exactly what each variable name means before interpreting the AFT coefficients. In this post, aft_time is the model time variable, aft_event is the event/censoring indicator, and the predictors are G1, G2, studytime, age, Medu, Fedu, school_MS, sex_M and address_U.

Plain-English Variable Dictionary for This AFT Model

How the Created Outcome Should Be Understood

The created time variable is aft_time = absences + 1. Adding 1 avoids zero time values because survival models require positive time. The event variable is aft_event, where 1 means the prepared event occurred and 0 means the case is right censored. The event rule is based on low final grade and past failure: aft_event = 1 when G3 < 10 or failures > 0. This makes the example useful for teaching AFT mechanics, but it must be described as a prepared educational survival outcome rather than a naturally observed medical or engineering failure time.

Variables Used in Each Output

The key sample counts were N = 649, 151 events and 498 censored observations. For background on distribution and scale, see standard deviation, standard error, normal distribution and standard normal distribution.

Model Fit: Log-Normal AFT vs Weibull AFT

The workbook fits and compares two parametric AFT models: Log-Normal AFT and Weibull AFT. Both models use the same time/status structure: aft_time is the survival-time variable and aft_event is the event indicator. Both models also use the same predictors: G1, G2, studytime, age, Medu, Fedu, school_MS, sex_M and address_U. AIC and BIC are used as the main model-comparison statistics. Smaller values generally indicate the preferred model among the fitted candidates.

The Weibull AFT model improved the AIC by about 18.06 points compared with the Log-Normal AFT model. The Weibull model also had the lower BIC and a better log likelihood. Therefore, the fitted results support the Weibull AFT model as the better parametric choice for this prepared outcome.

Coefficient and Acceleration-Factor Interpretation

The coefficient table shows each model term, its estimated coefficient, standard error, z value, p value, confidence interval and acceleration factor. These terms are not abstract labels: G1 means first-period grade, G2 means second-period grade, studytime means study-time category, age is student age, Medu and Fedu are parent education levels, and school_MS, sex_M and address_U are 0/1 coded categorical variables. In an AFT model, the acceleration factor is often easier to explain than the raw coefficient.

Selected Weibull AFT Coefficients

SPSS Output Interpretation for Accelerated Failure Time Model

The SPSS output PDF provides the formal parametric survival-model output for the same AFT topic. It should be read together with the Python and R reports because the full article compares output formats across software. The most important SPSS interpretation points are the event definition, censoring status, fitted distribution, coefficient signs, p-values, confidence intervals and model-fit statistics.

Open the SPSS Accelerated Failure Time Model output PDF

The SPSS report should not be interpreted as a simple linear regression output. The dependent variable is not a raw numeric score; it is a survival duration with censoring. Therefore, the correct wording is about predicted time to event and event acceleration, not ordinary mean differences.

Python Chart-by-Chart Interpretation with Real Data

The Python report contains eight charts based on 649 observations. The survival duration is aft_time = absences + 1, while aft_event = 1 identifies a prepared event when G3 < 10 or failures > 0. There are 151 observed events and 498 right-censored observations. The discussion below integrates the numerical results directly into the explanation instead of placing a separate table under every figure.

Python Chart 1: Time-to-Event Distribution

The histogram describes the actual distribution of aft_time, not a generic survival variable. The duration was created by adding 1 to absences, which prevents zero values from entering the logarithmic AFT likelihood. The data are strongly concentrated at the beginning of the scale: 244 students have aft_time = 1, 110 have aft_time = 3, 93 have aft_time = 5, 49 have aft_time = 7, and 42 have aft_time = 9. The remaining records become progressively less frequent, while the right tail extends to aft_time = 31.

This is a highly right-skewed time distribution. Most students have very low constructed event/censoring times because their absence counts are small, while a limited number have much larger values. The long tail explains why modelling raw time with ordinary least squares would be awkward and why the AFT models work with a parametric survival distribution and a log-time interpretation. The chart also warns readers that a small group of high-absence observations can strongly influence fitted median-time predictions.

Python Chart 2: Event and Censoring Counts

The two bars show the complete status structure used by the likelihood. The event bar contains 151 cases, representing 23.27% of the 649 observations. The right-censored bar contains 498 cases, representing 76.73%. An event means the prepared rule G3 < 10 or failures > 0 was met; censoring means that event was not observed under the prepared rule at the available aft_time.

The difference between 151 and 498 is statistically important. AFT analysis does not discard the 498 censored students; each one contributes information that the event had not occurred up to its recorded time. However, the relatively small event group means the coefficient estimates depend heavily on only 151 observed events. This imbalance helps explain why the Python Log-Normal coefficient confidence intervals are extremely wide even when some point estimates appear above or below an acceleration factor of 1.

Python Chart 3: Kaplan-Meier Survival Curve

The Kaplan-Meier curve is the observed nonparametric survival pattern for aft_time and aft_event. At time 1, 649 cases are initially at risk, with 48 events at that time, and the estimated survival probability falls to 0.9260. Survival then declines to 0.8720 at time 3, 0.8034 at time 5, 0.7353 at time 7, and 0.6217 at time 10.

The curve reaches approximately one-half at aft_time = 13, where the Kaplan-Meier survival estimate is 0.5004. It continues downward to 0.4035 at time 15, 0.3267 at time 17, 0.1624 at time 25, and 0.0541 at time 31. These steps are the real benchmark that the Log-Normal and Weibull curves should approximate. The gradual decline followed by a thin late tail indicates that the fitted distribution must represent both the dense early times and the small number of long-duration observations.

Python Chart 4: Log-Normal Observed vs Predicted Median Time

Each point compares the recorded aft_time on the vertical axis with a Log-Normal predicted median time on the horizontal axis. The recorded times occupy a narrow range from about 1 to 33, but the fitted medians spread much farther, with several predictions extending beyond 200 and the largest visible predictions approaching roughly 270. The diagonal reference line represents exact agreement; points on that line would have a predicted median equal to the recorded time.

Most points do not follow the diagonal closely. Many cases have observed or censored times of 1, 3, 5, 7, or 9 while the model predicts substantially longer medians. This wide horizontal spread is consistent with the unstable Python Log-Normal coefficients and their large standard errors. The fitted model has log-likelihood = -498.1509, AIC = 1018.3019, BIC = 1067.5316, and sigma = 1.0813. Therefore, the chart suggests weak row-level agreement, especially for cases receiving very long fitted median times.

Python Chart 5: Weibull Observed vs Predicted Median Time

The Weibull scatterplot uses the same 649 recorded times, so the vertical axis again ranges from about 1 to 33. Predicted median times remain much wider than the observed scale, and some fitted values extend beyond 200. Many low observed times are paired with moderate or high predictions, so the point cloud still shows substantial deviation from the agreement line.

Although the visual dispersion remains large, the Weibull distribution fits the overall likelihood better than the Log-Normal distribution. Its log-likelihood is -489.1226, compared with -498.1509 for Log-Normal. Its AIC is 1000.2453 and BIC is 1049.4751, both 18.0566 points lower than the corresponding Log-Normal values. Consequently, Chart 5 should not be described as a perfect predictive fit; it shows that Weibull is the better of the two tested parametric forms, not that every individual time is predicted accurately.

Python Chart 6: Log-Normal Acceleration Factors

The vertical reference at an acceleration factor of 1 marks no change in expected time. The Python point estimates are G1 = 1.1447, G2 = 1.2137, studytime = 1.0454, age = 0.9460, Medu = 1.0674, Fedu = 1.0646, school_MS = 0.6314, sex_M = 0.8306, and address_U = 1.2219. Values above 1 point toward longer time to the prepared event; values below 1 point toward shorter time.

The confidence intervals reveal why the estimates cannot be interpreted as reliable predictor effects in the Python Log-Normal fit. For example, G1 has a 95% acceleration-factor interval from 0.2602 to 5.0356, G2 from 0.0279 to 52.8367, school_MS from 0.0998 to 3.9943, and address_U from 0.0183 to 81.7053. The most extreme interval is for Medu, extending from approximately zero to 84,279.6684, which forces the x-axis to become extremely wide and visually compresses most points near 1. Every displayed p-value is above .05, including G1 (.8581), G2 (.9199), school_MS (.6251), and address_U (.9255). The correct conclusion is instability and uncertainty, not evidence that these variables strongly change survival time.

Python Chart 7: Model Fit Comparison

The two bars compare the model-selection criterion directly. The Weibull AFT AIC is 1000.2453, while the Log-Normal AFT AIC is 1018.3019. Because smaller AIC is preferred, Weibull improves the criterion by 18.0566 points. The BIC results tell the same story: 1049.4751 for Weibull versus 1067.5316 for Log-Normal.

This is the clearest model-selection result in the Python output. Both models use the same 649 rows, 151 events, 498 censored observations, and 11 fitted parameters, so the lower information criteria are not caused by different sample sizes or parameter counts. They reflect the higher Weibull log-likelihood. The decision is therefore to prefer the Weibull AFT distribution among these two candidates, while still acknowledging the imperfect individual prediction pattern visible in Chart 5.

Python Chart 8: Predicted Survival Curves

The three curves translate fitted median times into survival probabilities. The low fitted-time profile declines fastest, the median profile declines at an intermediate rate, and the high fitted-time profile remains highest. Reading the plotted curves approximately, at time 10 the low, median, and high profiles are near 0.49, 0.78, and 0.93. At time 20 they are about 0.25, 0.55, and 0.79, and at time 30 they are roughly 0.15, 0.40, and 0.67.

The separation demonstrates the time-ratio meaning of the AFT model: a higher fitted median shifts the entire survival curve to the right, leaving a larger probability of remaining event-free at the same time. However, these are conditional model curves rather than the observed Kaplan-Meier curve. The observed Kaplan-Meier estimate is already about 0.5004 at time 13 and 0.0541 at time 31. Readers should therefore use Chart 8 to understand fitted profiles, while using Chart 3 and the AIC comparison to judge how the parametric model relates to the actual data.

R Charts, Tables and Independent Validation

The R workflow uses survival::Surv(aft_time, aft_event) and fits Weibull and Log-Normal models with G1, G2, studytime, age, Medu, Fedu, school, sex, and address. Unlike the unstable Python Log-Normal coefficient output, the R survreg results provide interpretable standard errors for the preferred Weibull model and identify four statistically significant terms. The supplied R report contains the same eight chart topics, and they are restored below with detailed discussion.

Open the complete R Accelerated Failure Time Model report PDF

R Model-Fit Results Table

The R table independently confirms the Python model-ranking result. With the same sample and censoring structure, Weibull has a less negative log likelihood and information criteria that are about 18.06 points lower. The R scale of 0.7223 is the survreg Weibull scale parameter; its reciprocal is approximately 1.3844, which corresponds to the shape-style value shown in the Python output.

R Chart 1: Time-to-Event Distribution

The R histogram validates the same concentration of small aft_time values. The largest single frequency occurs at aft_time = 1, where 244 observations are recorded. Frequencies remain high at time 3 (110 observations) and time 5 (93 observations), then fall sharply. Only a few records occupy the far tail between about 20 and 31. This pattern is consistent with a duration variable constructed from absences + 1, because most students report few absences.

In R, the skewness matters because survreg models the transformed time distribution rather than assuming normally distributed raw durations. The chart supports a parametric AFT approach, but it also signals that the fitted model must work hard to accommodate a very large early-time mass and a thin long-duration tail.

R Chart 2: Event and Censoring Counts

The R model uses exactly 151 events and 498 right-censored cases. The event group accounts for 23.27% of the sample, whereas the censored group accounts for 76.73%. Because Surv(aft_time, aft_event) distinguishes these two statuses, the R likelihood uses the density contribution for event observations and the survivor-function contribution for censored observations.

This chart is essential for interpreting the later coefficient results. The significant R effects are estimated after correctly retaining the 498 censored cases, not by treating censoring as missing data. The large censored group also explains why the Kaplan-Meier confidence limits become wider near the end of the curve, where very few cases remain at risk.

R Chart 3: Kaplan-Meier Survival Curve with Confidence Limits

The R Kaplan-Meier estimate follows the observed steps from survival 1.00 before the first event to 0.9260 at time 1, 0.8034 at time 5, 0.6217 at time 10, and 0.5004 at time 13. By time 25 survival is 0.1624, and at time 31 it is 0.0541. The confidence limits are tight early, when hundreds of cases remain at risk, and spread apart in the tail, when only a few observations remain.

This widening is visible around times 20 to 31 and should prevent overconfident interpretation of late survival probabilities. The R parametric curves are fitted to the full likelihood, but the Kaplan-Meier curve remains the clearest display of the raw event-time pattern and uncertainty.

R Chart 4: Log-Normal Observed vs Predicted Time

The R Log-Normal scatterplot shows the same basic mismatch between the narrow recorded-time scale and the much wider predicted-time scale. Recorded or censored aft_time values lie mainly between 1 and 17, with a small number reaching 33, while predicted medians extend past 250. The dense horizontal bands occur because aft_time is an integer transformation of absence counts, so many students share exactly the same time value.

The R fit statistics quantify this visual pattern: log likelihood = -498.1509, AIC = 1018.302, and BIC = 1067.532. The broad spread around the agreement line indicates that the Log-Normal model can generate very long medians for observations whose recorded time is short. This does not invalidate survival modelling, but it makes Log-Normal less convincing than Weibull for these data.

R Chart 5: Weibull Observed vs Predicted Time

The Weibull chart still contains many points far from the agreement line, especially observations with aft_time = 1 but fitted medians between roughly 20 and 250. Nevertheless, the overall survival likelihood improves. The R Weibull log likelihood is -489.1226, compared with -498.1509 for Log-Normal, and the AIC decreases to 1000.245.

Therefore, the R evidence supports a careful conclusion: Weibull is the preferred distribution among the two fitted models, but it is not a perfect row-by-row predictor. The scatterplot should be discussed together with the coefficient table and the nonparametric curve rather than used as a stand-alone claim of accuracy.

R Weibull Acceleration-Factor Table

R Chart 6: Acceleration-Factor Plot

The R coefficient plot gives a much clearer inferential pattern than the Python Log-Normal plot. Four confidence intervals do not cross 1. G1 has AF = 1.0984 with a 95% interval of 1.0111 to 1.1932; G2 has AF = 1.2336 with an interval of 1.1643 to 1.3070; schoolMS has AF = 0.6025 with an interval of 0.4551 to 0.7975; and addressU has AF = 1.3628 with an interval of 1.0652 to 1.7436.

The direction is straightforward. Higher G1 and G2 scores and an urban address are associated with longer expected aft_time, while the MS school category is associated with shorter expected time relative to GP. Studytime, age, Medu, Fedu, and sexM all have intervals crossing 1, so their plotted directions should not be presented as established effects. This chart and the consolidated coefficient table provide the main substantive R results.

R Chart 7: AIC Model Comparison

The R bars reproduce the exact comparison shown in the model-fit table: Weibull AIC = 1000.245 and Log-Normal AIC = 1018.302. The gap of about 18.06 is large enough to give clear relative support to Weibull among the two candidate distributions. BIC also favours Weibull by the same approximate amount, 1049.475 versus 1067.532.

This chart should be treated as a relative selection result, not proof that Weibull is universally correct. It states that, for these variables, event definitions, and 649 observations, Weibull balances fit and model complexity better than Log-Normal.

R Chart 8: Predicted Survival Curves

The R curves separate clearly across the full time range. At approximately time 10, the low fitted-time profile has survival near 0.49, the median profile near 0.78, and the high profile near 0.93. At time 20, the corresponding probabilities are roughly 0.25, 0.55, and 0.79. By time 30, they are about 0.15, 0.40, and 0.67.

The chart demonstrates the practical meaning of acceleration factors. Predictors that raise the fitted time shift a profile toward the upper curve; predictors that reduce fitted time shift it toward the lower curve. In this R model, higher G1, higher G2, and addressU contribute toward longer fitted time, while schoolMS contributes toward shorter fitted time. These curves are illustrative fitted profiles, so they complement rather than replace the observed Kaplan-Meier estimate.

Excel Worked Results Explained

The uploaded Excel workbook contains a dashboard, fitted statistics, coefficient tables, a data sample, a Kaplan-Meier table and an Excel AFT likelihood calculator. It names the variables directly: aft_time is the duration field, aft_event is the event/status field, and the main calculator columns include G1, G2, studytime and age plus the fitted coefficient terms. This makes the post useful for students who want to understand not only the output but also the formulas behind a parametric AFT model.

Excel Dashboard Summary

Excel AFT Calculator

The Excel calculator sheet demonstrates a Log-Normal likelihood setup. The row-level calculator uses aft_time, aft_event, G1, G2, studytime and age in the visible calculation area, while the coefficient block includes Intercept, G1, G2, studytime, age, Medu, Fedu, school_MS, sex_M, address_U and log_sigma. The sheet calculates linear predictors, sigma, standardized z values, log likelihood contributions and negative log-likelihood values. A Solver workflow can refit the model by minimizing total negative log likelihood over coefficient cells.

Kaplan-Meier Table in Excel

The Kaplan-Meier table shows the nonparametric survival estimate using aft_time and aft_event. It starts with 649 at risk at time 1. Survival is approximately 0.926 at time 1, 0.804 at time 5, 0.622 at time 10, 0.500 at time 13 and 0.054 at time 31. These values help readers compare the observed survival pattern against fitted parametric curves.

SPSS, R, Python and Excel Workflows for AFT Models

The same AFT idea can be reproduced in all four tools, but each tool has a different role. SPSS is useful for formal output, Python is useful for automated charts and reports, R is useful for survival modeling validation, and Excel is useful for formula teaching.

Code Blocks for Accelerated Failure Time Model

SPSS Syntax Pattern for AFT Model

* Accelerated Failure Time Model in SPSS.
* Time variable: aft_time.
* Event variable: aft_event, with 1 = event and 0 = right censored.

SET PRINTBACK=OFF MPRINT=OFF RESULTS=ON DECIMAL=DOT.
OUTPUT CLOSE ALL.
OUTPUT NEW NAME=AFT_Output.
OUTPUT ACTIVATE AFT_Output.

* Example assumes the prepared data file is already open.
FREQUENCIES VARIABLES=aft_event.
DESCRIPTIVES VARIABLES=aft_time G1 G2 studytime age Medu Fedu.

* Use the SPSS Parametric Accelerated Failure Time Models procedure
* or the equivalent menu command available in your SPSS version.
* Select aft_time as survival time, aft_event as event indicator,
* and choose Log-Normal / Weibull distributions for comparison.

OUTPUT SAVE OUTFILE='D:\DATA ANALYSIS\H Regression Tests and Models\Accelerated Failure Time Model\SPSS_Output\spv\Accelerated-Failure-Time-Model-SPSS-Output-Corrected.spv'.
OUTPUT EXPORT
  /CONTENTS EXPORT=ALL LAYERS=PRINTSETTING MODELVIEWS=PRINTSETTING
  /PDF DOCUMENTFILE='D:\DATA ANALYSIS\H Regression Tests and Models\Accelerated Failure Time Model\SPSS_Output\pdf\Accelerated-Failure-Time-Model-SPSS-Output-Corrected.pdf'.

Python Code Pattern for AFT Interpretation

import numpy as np
import pandas as pd

# Load data
df = pd.read_csv("dataset.csv")

# Prepared educational AFT variables
df["aft_time"] = df["absences"].abs() + 1
df["aft_event"] = ((df["G3"] < 10) | (df["failures"] > 0)).astype(int)

# Dummy variables used in the report
df["school_MS"] = (df["school"] == "MS").astype(int)
df["sex_M"] = (df["sex"] == "M").astype(int)
df["address_U"] = (df["address"] == "U").astype(int)

# AFT interpretation rule for fitted coefficients
coef = -0.507052
acceleration_factor = np.exp(coef)
print("Acceleration factor:", acceleration_factor)

# Plain interpretation
if acceleration_factor > 1:
    print("Predicted time to event is longer.")
elif acceleration_factor < 1:
    print("Predicted time to event is shorter.")
else:
    print("No time-ratio change.")

R Code Pattern for AFT Model

library(survival)

df <- read.csv("dataset.csv")
df$aft_time <- abs(df$absences) + 1
df$aft_event <- ifelse(df$G3 < 10 | df$failures > 0, 1, 0)
df$school_MS <- ifelse(df$school == "MS", 1, 0)
df$sex_M <- ifelse(df$sex == "M", 1, 0)
df$address_U <- ifelse(df$address == "U", 1, 0)

surv_obj <- Surv(time = df$aft_time, event = df$aft_event)

lognormal_fit <- survreg(
  surv_obj ~ G1 + G2 + studytime + age + Medu + Fedu + school_MS + sex_M + address_U,
  data = df,
  dist = "lognormal"
)

weibull_fit <- survreg(
  surv_obj ~ G1 + G2 + studytime + age + Medu + Fedu + school_MS + sex_M + address_U,
  data = df,
  dist = "weibull"
)

summary(lognormal_fit)
summary(weibull_fit)
AIC(lognormal_fit, weibull_fit)
exp(coef(weibull_fit))

Excel Formula Pattern for AFT Calculator

Prepared variables:
aft_time = ABS(absences) + 1
aft_event = IF(OR(G3 < 10, failures > 0), 1, 0)

Linear predictor:
eta = Intercept + b_G1*G1 + b_G2*G2 + b_studytime*studytime + ...

Scale:
sigma = EXP(log_sigma)

Standardized log-time residual:
z = (LN(aft_time) - eta) / sigma

Acceleration factor for a coefficient:
=EXP(coefficient)

Event likelihood idea:
Use the density contribution for rows where aft_event = 1.

Censored likelihood idea:
Use the survival contribution for rows where aft_event = 0.

Solver objective:
Minimize Total Negative Log-Likelihood by changing coefficient cells.

APA Reporting Wording for Accelerated Failure Time Model

When reporting an Accelerated Failure Time Model, state the time variable, event definition, censoring count, model distribution, predictor names and acceleration-factor interpretation. In this example, the required variable names are aft_time, aft_event, G1, G2, studytime, age, Medu, Fedu, school_MS, sex_M and address_U. Do not report the result as if it were ordinary least squares regression.

APA-Style Full Report

Short APA-Style Version

Plain-Language Reporting Version

Common Mistakes in Accelerated Failure Time Model Interpretation

Downloads and Resources

Use the files below to review the full AFT workflow across Python, R, SPSS and Excel. The duplicate chart URLs from the media upload list were not repeated in this post; only unique visual outputs are embedded.

Related Guides

The following Salar Cafe guides help explain assumptions, model diagnostics, statistical interpretation and reporting concepts used alongside survival modeling.