Frailty Cox
Frailty Cox is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Education Sciences sample dataset — how the analysis is run, what the MerQur output looks like, and how the result is reported in APA 7 format.
🎯 What is it for?
Frailty Cox automatically performs all required assumption checks (normality, homogeneity of variance, etc.) for the relevant data type in the background and presents the results with a clear table + chart. Automatic interpretation to the APA 7 standard, effect sizes such as Cohen’s d/η²/R², and 95% confidence intervals are reported.
📌 When is it used?
- Statistical analysis of measurements in the Education Sciences domain
- To produce APA 7-compatible result tables for academic publications
- Hypothesis testing and decision-making processes
- Undergraduate / master’s / PhD theses after the appropriate method has been selected
📐 Assumptions
- Appropriate scale — Variables must be at the measurement level required by the analysis (nominal/ordinal/interval/ratio)
- Independent observations — Observations must come from individuals independent of one another
- Sufficient sample size — The minimum n requirement for the analysis must be met
- Outlier check — Outliers must be detected and evaluated
If assumptions are violated, MerQur automatically suggests a non-parametric or robust alternative.
🛠 How to do it in MerQur
Load the data. Select the sample file from File → Open. MerQur auto-detects column types.
Select the analysis. From the left side select Frailty Cox.
Panel assignments (form fields in the program):
- duration_col:
sure_donem - event_col:
terk - feature_cols:
['yas'] - cluster_col:
klinik_grup
Optional settings. Effect size ✓ · 95% confidence interval ✓ · Assumption checks (automatic).
▶ Run — click the button. Results are produced automatically as a table + chart.
📄 Export to Word. APA 7-formatted report with italic statistical symbols.
📊 Sample Dataset — Education Sciences
ℹ Note: The scenario, MerQur output and interpretation below were produced by actually running the real example dataset in MerQur. Numeric results on your own data will differ; the goal is to show how the analysis is set up and interpreted end-to-end.
🎬 Example File
This analysis is demonstrated on the following example dataset for Education Sciences:
Egitim_Bilimleri/93_frailty_cox_school.xlsx
🎬 Scenario
Suppose we are again modeling time to dropout, but this time our 120 students are nested within different schools, and we suspect that students from the same school share unobserved risk factors, such as school climate or local support. Ignoring this clustering would understate the uncertainty in our estimates. For each student we have the number of terms enrolled in duration_term, the dropout indicator, their age, and a clinical_group label (K1 to K4), plus the school_id that defines the cluster. We use a Frailty Cox Model, which adds a random school-level frailty term to the Cox model so we can estimate covariate effects while accounting for shared, school- specific risk.
⚙️ Variable Selection
- Time (duration): duration_term
- Event: dropout
- Frailty / cluster: school_id
- Predictors (covariates): age, clinical_group (K1/K2/K3/K4)
Data Preview (First 5 Rows)
| student_id | school_id | duration_term | dropout | age | clinical_group |
|---|---|---|---|---|---|
| 1 | 1 | 5.4 | 0 | 20 | K1 |
| 2 | 1 | 2.8 | 0 | 24 | K4 |
| 3 | 1 | 8.9 | 1 | 22 | K3 |
| 4 | 1 | 6.9 | 0 | 22 | K2 |
| 5 | 1 | 0.5 | 1 | 21 | K2 |
n = 120 · Columns: student_id, school_id, duration_term, dropout, age, clinical_group
📈 MerQur Output
💬 Interpretation
Students are clustered within schools; students in the same school share unmeasured common factors (school climate, teacher quality, resources) and carry similar dropout risk. Frailty Cox adds a shared “frailty” (random effect) for each school to model this clustering — the mixed-model version of survival analysis. Concordance 0.56. Accounting for school-level hidden differences gives both correct standard errors and information on “how much heterogeneity exists between schools”. It is the correct method for clustered educational survival data (schools, classes).
⚠ Common Mistakes
- Misidentifying the data type (e.g., loading a categorical variable as numeric)
- Skipping assumption checks and going straight to the p-value
- Failing to report effect size — APA 7 requires both p and effect size
- Failing to apply a Type I error correction (Bonferroni/Tukey) in multiple comparisons
- Not switching to a non-parametric alternative when n is insufficient
📹 Video Walkthrough
Watch the video below for an end-to-end walkthrough of this analysis on a Education Sciences file.
▶ Frailty Cox — video walkthrough
This analysis is demonstrated on a sample dataset from Anaesthesiology (the steps are identical across disciplines). The link jumps straight to 9:54. Narration is in Turkish.
🧪 Natural Sciences & Mathematics · 🏛 Architecture, Planning & Design · ⚙ Engineering · 🏥 Health Sciences · 📊 Social, Humanities & Admin Sciences · 🏃 Sport Sciences · 🌾 Agriculture, Forestry & Aquatic
📚 If You Used This Analysis, Cite MerQur
If you performed this analysis using MerQur in a scientific study, please use the citation below as part of your academic citation obligations (APA 7):
Örücü, Ö. K. (2026). MerQur: Integrated Academic Data Analysis & Reporting Platform [Computer software] (Version 1.0.0). https://doi.org/10.53463/merqur.2026001
For BibTeX, RIS, EndNote and the English citation form: all citation formats →
- American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.).
- Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). Sage.
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.