ܦܘܫܩܐ ܕܩܘܝܡܐ ܒܚܝ̈ܐ

ܛܥܢܐ ܕܝܗܝ̈ܒܬܐ (loading the data)

ܟܡܕܒܩܚ ܥܡܘ̈ܕܐ ܬܪܝܨܐܝܬ ܡܢ ܓܠܝܘܢܐ (worksheet)، ܥܡ ܣܕܪܐ ܕܪ̈ܫܐ (header row) – ܟܪܫܡܚ ܓܘ ܐܩܣܠ، ܟܢܣܚܚ، ܘܟܡܕܒܩܚ ܠܐܟܐ:

ܡܫܬܚܠܦ̈ܢܐ ܘܬܘܩ̈ܢܐ (Variables and settings)

ܐܝܡܢ ܡܦܠܚܝܚ (When to use)؟

ܐܡܢ ܕܡܫܬܚܠܦܢܐ ܬܠܝܐ (dependent variable) ܝܠܗ ܙܒܢܐ ܗܠ ܓܕܫܐ: ܐܝܬ ܢܘܩܙܐ ܕܫܘܪܝܐ (ܚܪܬܐ ܕܐܣܝܘܬܐ، ܫܘܪܝܐ ܕܝܘܠܦܢܐ، ܫܪܝܐ ܡܢ ܒܝܬ ܐܣܝܪ̈ܐ) ܘܓܕܫܐ ܕܠܡܐ ܗܘܐ (ܕܥܪܬܐ ܠܡܦܠܚܢܘܬܐ، ܦܠܛܬܐ، ܐܚܝܕܘܬܐ ܡܢ ܪܝܫ)، ܘܟܫܐܠܚ ܟܡܐ ܙܒܢܐ ܟܥܒܪ ܒܝܢܬܘܗܝ، ܘܡܘܢܐ ܟܡܥܒܕ ܥܠܗ (Jesussek & Volk-Jesussek, 2025, pp. 396-397). ܓܕܫܐ ܟܡܬܩܪܐ "ܠܐ ܡܨܠܚܢܘܬܐ" ܐܦ ܐܡܢ ܕܛܒܐ ܝܠܗ – ܕܥܪܬܐ ܠܦܠܚܐ، ܡܬܠܐ (Kleinbaum & Klein, 2012, p. 4). ܫܡܐ ܟܐܬܐ ܡܢ ܐܣܝܘܬܐ، ܐܠܐ "ܙܒܢܐ ܕܡܬܒܚܪ ܠܐ ܓܪܓ ܕܗܘܐ ܐܣܝܪܐ ܥܡ ܩܘܝܡܐ ܒܚܝ̈ܐ ܫܪܝܪܐ" (Jesussek & Volk-Jesussek, 2025, p. 398)، ܘܐܘܪ̈ܚܬܐ ܡܬܦܠܚ̈ܢ ܐܦ ܓܘ ܐܝܩܘܢܘܡܝܐ، ܓܘ ܙܒܢܬܐ ܘܓܘ ܝܕ̈ܥܬܐ ܕܟܢܫܐ ܘܕܗܘܦܟܐ (Nag, 2022, p. 1) – ܫܒܩܬܐ ܕܦܠܚ̈ܐ ܠܫܘܬܐܣܐ، ܫܪܝܐ ܕܓܘܪܐ (ܬܡܢ، ܦܐ̈ܬܐ 2-3)، ܙܒܢܐ ܗܠ ܕܥܪܬܐ ܠܦܠܚܐ ܒܬܪ ܡܠܝܘܬܐ (burnout). Cohen ܘܚܒܪ̈ܘܗܝ (2003، ܦܐܬܐ 596) ܟܟܬܒܝ ܐܗܐ ܗܕܟܐ: ܟܡܐ ܙܒܢܐ ܟܫܩܠܐ ܕܫܚܠܦ ܐܝܟܢܝܘܬܐ (status) ܕܬܪܝܢ ܛܝ̈ܡܐ – "ܡܝܬܐ، ܚܠܡܐ، ܓܘܪܐ ܝܢ ܡܨܠܚܐ" – ܘܐܢ ܐܗܐ ܦܪܝܫܐ ܝܠܗ ܒܝܢܝ ܓܘ̈ܕܐ.

ܬܠܬܐ ܐܘܪ̈ܚܬܐ ܕܡܬܦܠܚ̈ܢ ܣܓܝ (Jesussek & Volk-Jesussek, 2025, p. 401) ܐܢܝ ܝܢܐ ܬܠܬܐ ܡܢܘ̈ܬܐ ܕܡܦܩܢܐ (output): ܣܪܛܐ ܟܦܝܦܐ ܕ-Kaplan-Meier – ܩܐ ܬܚܘܝܬܐ؛ ܒܘܚܪܢܐ ܕ-log-rank – ܩܐ ܦܘܚܡܐ ܕܓܘ̈ܕܐ؛ ܪܝܓܪܫܢ ܕ-Cox – ܩܐ ܒܘܚܪܢܐ ܕܟܡܐ ܡܫܬܚܠܦ̈ܢܐ (variables) ܐܟܚܕܐ، ܐܦ ܡܬܡܫܚ̈ܢܐ. ܩܐ ܥܠܬܐ (factor) ܚܕܐ ܥܡ ܬܪܝܢ ܕܪ̈ܓܐ ܣܦܩ log-rank؛ ܐܡܢ ܕܒܥܝܚ ܕܡܘܣܦܚ ܐܦ ܥܘܡܪܐ، ܡܬܠܐ – Cox (ܬܡܢ، ܦܐܬܐ 425).

ܦܣܝܩܘܬܐ: ܩܐ ܡܘܕܝ ܠܐ ܪܝܓܪܫܢ ܦܫܝܛܐ

ܟܠ ܒܘܨܝܐ ܟܫܠܡ ܚܕ ܙܒܢܐ، ܘܓܘ ܚܪܬܗ ܐܝܬ ܡܫܬܘܬܦ̈ܢܐ (participants) ܕܓܕܫܐ ܗܠ ܗܫܐ ܠܐ ܗܘܐ ܝܠܗ ܓܘܝܗܘܢ؛ ܐܚܪ̈ܢܐ ܫܒܩܠܗܘܢ ܓܘ ܦܠܓܐ، ܫܚܠܦܠܗܘܢ ܒܝܬܐ ܝܢ ܠܐ ܐܬܝܠܗܘܢ ܒܬܪ ܗܕܐ (Jesussek & Volk-Jesussek, 2025, pp. 400-401; Kleinbaum & Klein, 2012, pp. 6-7). ܓܘܝܗܘܢ ܝܕܝܥܐ ܝܠܗ ܒܣ ܕܙܒܢܐ ܐܪܝܟ ܝܬܝܪ ܝܠܗ ܡܢ ܙܒܢܐ ܕܢܛܪܬܐ (follow-up) – ܐܗܐ ܝܠܗ̇ ܦܣܝܩܘܬܐ ܡܢ ܝܡܝܢܐ (right censoring)، ܘܐܝܗ̇ ܝܠܗ̇ ܕܡܬܚܙܝܐ ܣܓܝ ܝܬܝܪ (Cohen et al., 2003, p. 597; Kleinbaum & Klein, 2012, p. 7). ܐܝܬ ܐܦ ܦܣܝܩܘܬܐ ܡܢ ܣܡܠܐ (ܓܕܫܐ ܗܘܐ ܝܠܗ ܩܕܡ ܕܢܛܪܬܐ ܫܪܐ) ܘܦܣܝܩܘܬܐ ܓܘ ܡܨܥܬܐ (ܝܕܝܥܐ ܝܠܗ ܒܣ ܕܗܘܐ ܝܠܗ ܒܝܢܝ ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ؛ Kleinbaum & Klein, 2012، ܦܐܬܐ 8) – ܦܐܬܐ ܟܥܒܕܐ ܒܣ ܥܡ ܦܣܝܩܘܬܐ ܡܢ ܝܡܝܢܐ. ܫܩܠܬܐ ܕܦܣܝ̈ܩܐ، ܝܢ ܡܥܠܬܐ ܕܙܒܢܐ ܕܢܛܪܬܐ ܕܝܠܗܘܢ ܐܝܟ ܕܐܝܬܘܗܝ ܙܒܢܐ ܕܓܕܫܐ، ܟܡܨܠܐ ܦܐܪܐ: ܓܘ ܡܬܠܐ ܕ-Cohen ܘܚܒܪ̈ܘܗܝ ܡܨܥܝܬܐ (mean) ܕܐܢܝ ܕܡܛܝܠܗܘܢ ܠܓܕܫܐ ܗܘܐ ܝܠܗ̇ 3.88 ܚܕܝܘ̈ܬܐ ܕܙܒܢܐ، ܩܘܒܠ 5.16 ܐܢ ܒܘܨܝܐ ܗܘܐ ܡܬܡܫܚܐ ܗܠ ܕܟܠܗܘܢ ܡܛܝܠܗܘܢ – ܫܘܥܪܐ ܒܨܝܪܐ ܕ-25% (ܦܐ̈ܬܐ 596-597). ܐܘܪ̈ܚܬܐ ܕܩܘܝܡܐ ܒܚܝ̈ܐ ܟܡܦܠܚ̈ܢ ܒܝܕܥܬܐ ܕܦܣܝ̈ܩܐ ܐܝܟ ܕܐܝܬܝܗ̇: ܗܠ ܙܒܢܐ ܕܦܣܝܩܘܬܐ ܐܢܝ ܡܬܡܢܝ̈ܢܐ ܝܢܐ ܓܘ ܐܢܝ ܕܐܝܬܠܗܘܢ ܒܣܘܟܢܐ (at risk)، ܘܒܬܪܗ ܟܦܠܛܝ.

ܫܪܛܐ: ܦܣܝܩܘܬܐ ܠܐ ܐܣܝܪܬܐ ܝܠܗ̇ ܥܡ ܣܟܘܝܐ ܕܓܕܫܐ. Kleinbaum ܘ-Klein (Kleinbaum & Klein, 2012, pp. 37-43) ܟܦܪܫܝ ܒܝܢܝ ܦܣܝܩܘܬܐ "ܠܐ ܬܠܝܬܐ" (ܓܕܫܢܝܬܐ ܓܘ ܟܠ ܓܘܕܐ ܡܢܬܢܝܐ)، "ܓܕܫܢܝܬܐ" ܘ"ܠܐ ܡܘܕܥܢܝܬܐ" – ܡܠ̈ܐ ܕ"ܣܓܝ ܙܒ̈ܢܐ ܟܡܬܚܠܛ̈ܢ" ܐܝܟ ܕܐܝܬܝܗܝ ܫܡ̈ܗܐ ܚܕ ܥܢܝܢܐ – ܘ-Kaplan-Meier، log-rank ܘ-Cox ܟܣܡܟܝ ܥܠ ܩܕܡܝܬܐ. ܓܘ ܥܒܕܐ: ܡܦܠܛܐ ܕܡܫܬܘܬܦ̈ܢܐ (participants) ܡܢ ܢܛܪܬܐ ܩܐ ܕܐܝܟܢܝܘܬܐ ܕܝܠܗܘܢ ܒܝܫܐ ܗܘܝܠܗ̇ ܟܡܨܠܐ ܫܘ̈ܥܪܐ (Harrell, 2015, p. 402).

ܓܘ ܦܐܝܠ: ܥܡܘܕܐ ܕܙܒܢܐ (ܡܢ ܢܘܩܙܐ ܕܫܘܪܝܐ ܕܟܠ ܡܫܬܘܬܦܢܐ ܗܠ ܓܕܫܐ ܝܢ ܗܠ ܦܣܝܩܘܬܐ) ܘܥܡܘܕܐ ܕܐܝܟܢܝܘܬܐ (status) – 1 ܩܐ ܓܕܫܐ، 0 ܩܐ ܦܣܝܩܘܬܐ. ܩܐ ܟܠ ܡܫܬܘܬܦܢܐ ܣܕܪܐ ܚܕ. ܕܠܐ ܥܡܘܕܐ ܕܐܝܟܢܝܘܬܐ، ܟܠ ܡܫܬܘܬܦ̈ܢܐ ܟܡܬܚܫܒܝ ܐܝܟ ܐܢܝ ܕܚܙܝܠܗܘܢ ܓܕܫܐ (Jesussek & Volk-Jesussek, 2025, p. 410) – ܓܘ ܦܐܬܐ: "ܕܠܐ ܡܫܬܚܠܦܢܐ ܕܐܝܟܢܝܘܬܐ". ܗܕܟܐ ܟܡܬܩܒܠ ܐܦ ܡܬܠܐ ܩܕܡܝܐ ܓܘ ܟܬܒܐ، ܕܠܐ ܦܣܝܩܘܬܐ: 0.9 ܒܬܪ 3 ܫܢ̈ܐ، 0.7 ܒܬܪ 4، 0.6 ܒܬܪ 6 (ܬܡܢ، ܦܐ̈ܬܐ 405-406).

ܣܪܛܐ ܟܦܝܦܐ ܕ-Kaplan-Meier

ܣܪܛܐ ܟܦܝܦܐ ܟܡܚܘܐ ܓܘ ܟܠ ܙܒܢܐ ܡܣܬܒܪܢܘܬܐ (probability) ܕܓܕܫܐ ܗܠ ܗܫܐ ܠܐ ܗܘܐ ܝܠܗ – "ܡܢܬܐ ܕܩܘܝܡܐ" (survival rate؛ Jesussek & Volk-Jesussek, 2025, pp. 402-403). ܚܘܫܒܢܐ: ܓܘ ܟܠ ܙܒܢܐ ܕܓܘܗ ܗܘܐ ܝܠܗ ܓܕܫܐ، ܟܦܠܓܚ ܐܢܝ ܕܩܝܡܠܗܘܢ ܡܢܗ ܥܠ ܐܢܝ ܕܗܘܘ ܒܣܘܟܢܐ ܩܕܡܗ ܒܚܕ ܓܢܒܐ، (n − d)/n، ܘܟܡܣܓܝܚ ܒܡܐ ܕܗܘܐ ܗܠ ܗܝܟ – ܡܥܠܝܬܐ ܕ"product-limit" (Kleinbaum & Klein, 2012, pp. 63-67; Jesussek & Volk-Jesussek, 2025, pp. 407-408). ܦܣܝܩܐ ܠܐ ܟܡܚܬܬ ܣܪܛܐ ܟܦܝܦܐ، ܐܠܐ ܟܦܠܛ ܡܢ ܓܘܕܐ ܕܣܘܟܢܐ ܕܙܒ̈ܢܐ ܕܒܬܪܗ. ܗܕܟܐ ܣܪܛܐ ܟܦܝܦܐ ܟܢܚܬ ܒܕܪ̈ܓܐ ܒܣ ܓܘ ܙܒ̈ܢܐ ܕܓܕܫܐ، ܘ"ܡܨܠܝܢܘܬܐ (slope) ܩܫܝܬܐ ܝܬܝܪ ܟܡܚܘܝܐ ܪܗܛܐ ܪܡܐ ܝܬܝܪ ܕܓܕܫ̈ܐ" (Jesussek & Volk-Jesussek, 2025, p. 404).

ܛܝܡܐ ܡܨܥܝܐ (median) – ܙܒܢܐ ܕܓܘܗ ܣܪܛܐ ܟܦܝܦܐ ܟܢܚܬ ܠ-50% – ܐܝܗܘ ܝܠܗ ܡܢܝܢܐ ܡܩܒܠܐ ܩܐ ܟܢܘܫܝܐ؛ ܡܨܥܝܬܐ (mean) ܡܨܠܝܬܐ ܝܠܗ̇ ܐܡܢ ܕܐܝܬ ܦܣܝܩܘܬܐ. ܐܢ ܝܬܝܪ ܡܢ ܦܠܓܐ ܕܓܘܕܐ ܠܐ ܚܙܝܠܗܘܢ ܓܕܫܐ ܗܠ ܐܚܪܝܬ ܕܢܛܪܬܐ، ܛܝܡܐ ܡܨܥܝܐ "ܠܐ ܡܛܝܐ ܝܠܗ" – ܘܐܗܐ ܡܫܟܚܢܘܬܐ ܝܠܗ̇ ܒܓܢܒܗ̇. ܦܐܬܐ ܟܚܫܒܐ ܛܝܡܐ ܡܨܥܝܐ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܐܝܟ survfit ܓܘ R، ܘܐܦ ܡܨܥܝܬܐ ܟܪܝܬܐ (restricted mean؛ ܫܛܝܚܘܬܐ ܬܚܘܬ ܣܪܛܐ ܟܦܝܦܐ ܗܠ ܙܒܢܐ ܐܚܪܝܐ) – ܐܝܟ Mean ܕ-SPSS. ܡܣܬܒܪܢܘܬܐ ܕܩܘܝܡܐ ܗܠ ܙܒܢܐ ܡܚܬܡܐ ("70% ܡܢ ܡܠܝ̈ܬܐ ܕܫܢ̈ܐ ܟܩܝܡ̈ܢ ܝܬܝܪ ܡܢ ܚܡܫ ܫܢ̈ܐ"؛ Jesussek & Volk-Jesussek, 2025، ܦܐܬܐ 403) – ܓܘ ܬܘܩ̈ܢܐ "ܡܣܬܒܪܢܘܬܐ ܕܩܘܝܡܐ ܗܠ ܙܒܢܐ".

ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܩܐ ܣܪܛܐ ܟܦܝܦܐ – "ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ". ܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܕ-Greenwood ܝܠܗ̇ ܓܘ ܟܠ ܐܘܪ̈ܚܬܐ؛ ܦܘܪܫܢܐ ܝܠܗ ܓܘ ܣܒܠܬܐ ܕܓܘܗ̇ ܟܒܢܝܚ ܬܚܘܡܐ. ܓܘ ܬܚܘܡܐ "ܦܫܝܛܐ" (plain)، S ± 1.96·SE، ܕ-Kleinbaum ܘ-Klein ܟܡܠܦܝ (Kleinbaum & Klein, 2012, pp. 78-79)، ܬܚܘ̈ܡܐ ܡܨܝ ܕܦܠܛܝ ܠܒܪ ܡܢ 0 ܘ-1، ܘܐܗܐ ܝܠܗ̇ "ܒܨܝܪܘܬܐ ܓܠܝܬܐ" ܕܥܠܗ̇ ܟܠ ܒܘܨ̈ܝܐ ܫܠܝܡܝ ܝܢܐ (Therneau & Grambsch, 2000, p. 16)؛ ܐܢܝ ܟܡܩܪܒܝ ܣܒܠܬܐ ܕܠܘܓ ܝܢ ܠܘܓܝܬ (ܦܐܬܐ 17)، ܘ-Harrell (2015، ܦܐ̈ܬܐ 412-413) – ܣܒܠܬܐ ܕܠܘܓ ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ (default). ܐܗܐ ܝܠܗ ܐܦ ܓܘܒܝܐ ܡܩܕܡܐ ܕ-R ܘܕܦܐܬܐ؛ log-log (ܕܒܗ ܟܡܦܠܚܝ SAS ܘ-Stata) ܘܠܘܓܝܬ – ܓܘ ܬܘܩ̈ܢܐ. ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕܛܝܡܐ ܡܨܥܝܐ ܡܦܩܐ ܝܠܗ ܡܢ ܣܪ̈ܛܐ ܟܦܝ̈ܦܐ ܕܬܚܘ̈ܡܐ، ܐܝܟ ܓܘ R؛ Kleinbaum ܘ-Klein (Kleinbaum & Klein, 2012, p. 80) ܟܡܚܘܝ ܐܘܪܚܐ ܕ-Brookmeyer-Crowley، ܕܒܗ̇ ܟܡܦܠܚ SAS – ܘܡܛܠ ܗܕܐ ܬܚܘ̈ܡܐ ܡܨܝ ܕܗܘܝ ܦܪ̈ܝܫܐ ܩܠܝܠ ܒܝܢܝ ܦܪܘܓܪ̈ܡܐ.

ܦܘܚܡܐ ܕܓܘ̈ܕܐ: log-rank

ܒܘܚܪܢܐ ܕ-log-rank ܟܒܚܪ ܐܢ ܠܬܪܬܝܢ ܓܘ̈ܕܐ ܝܢ ܝܬܝܪ ܐܝܬ ܗܘ ܣܪܛܐ ܟܦܝܦܐ ܕܩܘܝܡܐ: ܗܘܦܘܬܣܝܣ ܕܣܦܝܩܘܬܐ (null hypothesis) – "ܠܬܪܬܝܢ ܓܘ̈ܕܐ ܐܝܬ ܣܪ̈ܛܐ ܟܦܝ̈ܦܐ ܕܦܘܠܓܐ ܚܕ ܓܢܣܐ" (Jesussek & Volk-Jesussek, 2025, p. 414). ܓܘ ܟܠ ܙܒܢܐ ܕܓܕܫܐ ܟܦܚܡ ܡܢܝܢܐ ܕܓܕܫ̈ܐ ܓܘ ܟܠ ܓܘܕܐ (O) ܥܡ ܡܢܝܢܐ ܡܣܟܝܐ ܐܢ ܣܘܟܢܐ ܫܘܝܐ ܝܠܗ – ܠܦܘܬ ܡܢܬܐ ܕܓܘܕܐ ܓܘ ܐܢܝ ܕܐܝܬܠܗܘܢ ܒܣܘܟܢܐ (E) – ܘܟܟܢܫ ܦܘܪ̈ܫܢܐ ܥܠ ܟܠ ܙܒ̈ܢܐ؛ ܣܛܐܛܝܣܛܝܩ ܦܠܝܓ ܝܠܗ χ² ܥܡ ܡܢܝܢܐ ܕܓܘ̈ܕܐ ܒܨܝܪ 1 ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (Kleinbaum & Klein, 2012, pp. 68-72; Jesussek & Volk-Jesussek, 2025, pp. 415-419). ܙܒ̈ܢܐ ܕܓܘܝܗܘܢ ܒܣ ܡܫܬܘܬܦ̈ܢܐ ܦܣܝ̈ܩܐ ܗܘܘ ܠܐ ܟܥܐܠܝ ܓܘ ܚܘܫܒܢܐ (Jesussek & Volk-Jesussek, 2025, p. 416). ܩܘܪܒܐ ܕܡܬܚܙܐ ܣܓܝ Σ(O − E)²/E ܙܥܘܪܐ ܝܠܗ ܩܠܝܠ ܡܢ ܣܛܐܛܝܣܛܝܩ ܚܬܝܬܐ (Kleinbaum & Klein, 2012, p. 71) – ܦܐܬܐ ܟܚܫܒܐ ܚܬܝܬܐ. log-rank ܝܠܗ ܚܬܝܬܐܝܬ ܒܘܚܪܢܐ ܕ-Score ܕܪܝܓܪܫܢ ܕ-Cox ܥܡ ܓܘܕܐ ܐܝܟ ܡܫܬܚܠܦܢܐ ܝܚܝܕܝܐ، ܘܡܛܠ ܗܕܐ ܟܡܣܡ ܡܐ ܕ-Cox ܟܡܣܡ – ܣܘܟ̈ܢܐ ܦܘܚܡܝ̈ܐ (proportional hazards؛ Harrell, 2015, pp. 486-487; Therneau & Grambsch, 2000, p. 54).

SPSS ܟܡܩܪܒ ܬܪܝܢ ܒܘܚܪ̈ܢܐ ܐܚܪ̈ܢܐ ܡܢ ܗܝ̇ ܫܪܒܬܐ، ܘܦܐܬܐ ܟܚܫܒܐ ܬܠܬܝܗܘܢ. ܟܠܗܘܢ "log-rank ܡܬܩܠܐ" ܝܢܐ: Breslow – ܕܓܘ ܦܪܘܓܪ̈ܡܐ ܐܚܪ̈ܢܐ ܟܡܬܩܪܐ Wilcoxon – ܟܝܗܒ ܡܬܩܠܐ ܠܟܠ ܙܒܢܐ ܠܦܘܬ ܡܢܝܢܐ ܕܡܫܬܘܬܦ̈ܢܐ ܒܣܘܟܢܐ، ܘܡܛܠ ܗܕܐ "ܟܣܐܡ ܝܬܝܪ ܚܝܠܐ ܥܠ ܝܕܥܬܐ ܓܘ ܫܘܪܝܐ ܕܣܪܛܐ ܟܦܝܦܐ"؛ Tarone-Ware – ܠܦܘܬ ܫܪܫܐ ܕܡܢܝܢܐ، ܐܦ ܐܝܗܘ ܟܓܒܐ ܫܘܪܝܐ، ܐܠܐ ܒܨܝܪ (Kleinbaum & Klein, 2012, p. 74). log-rank ܟܝܗܒ ܠܟܠ ܙܒ̈ܢܐ ܡܬܩܠܐ ܫܘܝܐ، ܘܐܝܗܘ ܝܠܗ ܚܝܠܢܐ ܝܬܝܪ ܐܡܢ ܕܣܘܟ̈ܢܐ ܦܘܚܡܝ̈ܐ ܝܢܐ. ܒܘܚܪܢܐ ܟܓܒܝܚ ܡܢ ܩܕܡ، ܠܦܘܬ ܐܘܪܚܐ ܕܦܘܪܫܢܐ ܡܣܟܝܐ ܝܠܗ – ܠܐ "ܨܝܕܐ" ܕܛܝܡܐ ܕ-p ܕܒܥܝܚ (ܬܡܢ، ܦܐܬܐ 76). ܥܡ ܬܠܬܐ ܓܘ̈ܕܐ ܝܢ ܝܬܝܪ ܦܐܬܐ ܟܡܘܣܦܐ ܦܘܚܡ̈ܐ ܙܘܓܢ̈ܝܐ (pairwise comparisons)، ܥܡ ܬܘܪܨܐ ܦܐܝܐ – ܒܬܪ ܒܘܚܪܢܐ ܟܠܢܝܐ ܪܫܝܡܐ (Harrell, 2015, p. 32).

ܪܝܓܪܫܢ ܕ-Cox

ܪܝܓܪܫܢ ܕ-Cox ܟܒܚܪ ܡܥܒܕܢܘܬܐ ܕܟܡܐ ܡܫܬܚܠܦ̈ܢܐ (variables) ܐܟܚܕܐ – ܡܬܡܫܚ̈ܢܐ، ܕܬܪܝܢ ܛܝ̈ܡܐ ܝܢ ܕܓܢ̈ܣܐ – ܥܠ ܙܒܢܐ ܗܠ ܓܕܫܐ (Jesussek & Volk-Jesussek, 2025, p. 423). ܠܐ ܟܡܢܒܐ ܠܙܒܢܐ ܒܓܢܒܗ ܐܠܐ ܣܘܟܢܐ (hazard): ܪܗܛܐ ܕܒܗ ܓܕܫܐ ܟܗܘܐ ܓܘ ܪܦܦܐ ܡܚܬܡܐ ܩܐ ܐܢܐ ܕܗܠ ܗܫܐ ܠܐ ܚܙܝܠܗ ܠܗ – "ܪܗܛܐ ܕܠܐ ܡܨܠܚܢܘܬܐ ܬܠܝܐ"، ܘܠܐ ܡܣܬܒܪܢܘܬܐ (Kleinbaum & Klein, 2012, pp. 11-12). ܡܘܕܝܠ (model) ܟܡܣܡ ܕܠܘܓ ܕܣܘܟܢܐ ܚܘܠܛܐ ܣܪܛܢܝܐ (linear) ܝܠܗ ܕܡܫܬܚܠܦ̈ܢܐ، ܕ"ܟܡܙܝܥ" ܣܘܟܢܐ ܫܬܐܣܝܐ ܡܫܘܬܦܐ ܕܐܣܟܝܡܐ ܕܝܠܗ ܠܐ ܡܬܚܡܐ ܝܠܗ – ܘܡܛܠ ܗܕܐ ܐܝܗܘ ܝܠܗ "ܦܠܓܐ-ܦܪܡܝܛܪܝܐ" (semi-parametric)، ܘܦܘܚܡܐ ܕܣܘܟܢܐ (hazard ratio) ܚܫܝܒܐ ܝܠܗ ܕܠܐ ܫܘܥܪܐ ܕܣܘܟܢܐ ܫܬܐܣܝܐ (Kleinbaum & Klein, 2012, pp. 109-111). ܐܗܐ ܝܠܗ ܐܘܪܚܐ ܕ-Cox (1972, as cited in Cohen et al., 2003, p. 598)، ܕܡܬܚܙܝܐ ܣܓܝ ܝܬܝܪ؛ ܟܣܡܟܐ ܒܣ ܥܠ ܛܟܣܐ ܕܙܒ̈ܢܐ ܕܓܕܫܐ (Harrell, 2015, p. 475; Kleinbaum & Klein, 2012, p. 130).

ܡܦܩܢܐ (output): ܩܐ ܟܠ ܡܫܬܚܠܦܢܐ B ܘ-HR = exp(B) – ܦܘܚܡܐ ܕܣܘܟܢܐ (hazard ratio). HR = 1.34 ܩܐ ܐܦܠܝܩܝܫܢ ܩܘܒܠ ܡܥܕܪܢܘܬܐ ܕܓܘܕܐ ܟܐܡܪ ܕܓܘ ܟܠ ܪܦܦܐ، ܪܗܛܐ ܕܒܗ ܡܫܬܘܬܦ̈ܢܐ ܕܐܦܠܝܩܝܫܢ ܟܕܥܪܝ ܠܫܬܝܐ ܕܬܬܘܢ ܪܡܐ ܝܠܗ ܒ-34%؛ HR = 0.73 – ܢܚܝܬܐ ܒ-27%. ܓܘ ܡܫܬܚܠܦܢܐ ܡܬܡܫܚܢܐ – ܩܐ ܟܠ ܚܕܝܘܬܐ؛ ܛܒܐ ܝܬܝܪ ܝܠܗ ܬܘܢܝܐ ܩܐ ܫܘܢܝܐ ܕܐܝܬܠܗ ܣܘܟܠܐ (ܥܣܪܐ ܫܢ̈ܐ ܕܥܘܡܪܐ، ܡܬܠܐ؛ Harrell, 2015، ܦܐ̈ܬܐ 429، 509-510). "ܛܝ̈ܡܐ ܕܐܝܬܠܗܘܢ ܐܪܙܐ ܝܬܝܪ" ܓܘ ܠܘܚܐ ܐܢܝ ܝܢܐ ܡܢܝܢܐ ܡܫܘܬܦܐ (coefficient) ܘܛܝܡܐ ܕ-p ܕܝܠܗ (Jesussek & Volk-Jesussek, 2025, p. 428). ܡܫܬܚܠܦܢܐ ܕܓܢ̈ܣܐ (categorical) ܟܥܐܠ ܒܪܡܙܢܘܬܐ ܕܡ̈ܠܐ ܕܘ̈ܡܝܐ (dummy coding) – ܟܠ ܓܢܣܐ ܩܘܒܠ ܩܕܡܝܐ – ܥܡ ܒܘܚܪܢܐ ܕ-Wald ܩܐ ܟܠ ܓܢ̈ܣܐ ܐܟܚܕܐ (Harrell, 2015, p. 481). ܘܦܘܚܡܐ ܕܣܘܟܢܐ ܩܝܡܐ ܠܐ ܝܠܗ ܦܐܝܕܐ ܫܪܝܪܐ ܩܝܡܐ: ܗܘ HR ܟܐܡܪ ܦܘܪܫܢܐ ܙܥܘܪܐ ܐܡܢ ܕܣܘܟܢܐ ܫܬܐܣܝܐ ܢܚܝܬܐ ܝܠܗ ܘܪܒܐ ܐܡܢ ܕܪܡܐ ܝܠܗ (ܬܡܢ، ܦܐ̈ܬܐ 430-431).

ܒܘܚܪ̈ܢܐ ܕܡܘܕܝܠ. ܦܘܚܡܐ ܕܡܬܚܙܝܢܘܬܐ (likelihood ratio, LR)، Score ܘ-Wald ܟܒܚܪܝ ܐܢ ܟܠ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܨܦܪܐ ܝܢܐ؛ LR "ܒܪܘܫܡܐ ܟܡܬܚܫܒ ܫܪܝܪܐ ܝܬܝܪ، ܘ-Wald – ܒܨܝܪ ܫܪܝܪܐ" (Therneau & Grambsch, 2000, p. 53)، ܘ"ܐܡܢ ܕܐܝܬ ܦܘܠܓ ܪܥܝܢܐ – ܦܠܘܚܘܢ ܒ-LR" (Kleinbaum & Klein, 2012, p. 104). ܐܡܢ ܕܡܢܝܢܐ ܡܫܘܬܦܐ ܟܐܙܠ ܠܠܐ ܬܚܘܡܐ (ܓܘܕܐ ܕܠܐ ܓܕܫ̈ܐ)، Wald ܟܢܦܠ ܘܬܪܝܢ ܐܚܪ̈ܢܐ ܠܐ (Therneau & Grambsch, 2000, pp. 58-61). ܡܚܘܝܢܐ ܕܦܐܝܘܬܐ C ܕ-Harrell – ܡܢܬܐ ܕܙܘܓ̈ܐ ܕܡܘܕܝܠ ܟܡܛܟܣ ܬܪܝܨܐܝܬ (Harrell, 2015, p. 505) – ܚܫܝܒܐ ܝܠܗ ܥܠ ܗܢܝ ܝܗܝ̈ܒܬܐ، ܘܡܛܠ ܗܕܐ ܡܣܒܪܢܐ ܝܬܝܪ ܝܠܗ (ܬܡܢ، ܦܐ̈ܬܐ 506-509).

ܛܝ̈ܡܐ ܫܘ̈ܝܐ. ܐܡܢ ܕܟܡܐ ܡܫܬܘܬܦ̈ܢܐ ܚܙܝܠܗܘܢ ܓܕܫܐ ܒܚܕ ܙܒܢܐ (ܐܡܢ ܕܙܒܢܐ ܡܫܘܚܐ ܝܠܗ ܒܫܒܘ̈ܥܐ ܝܢ ܒܝܪ̈ܚܐ ܐܗܐ ܣܓܝ ܟܗܘܐ)، ܓܪܓ ܕܦܣܩܚ ܐܝܟܢܐ ܕܦܠܓܚ ܒܝܢܬܘܗܝ ܓܘܕܐ ܕܣܘܟܢܐ. Breslow ܝܠܗ "ܗܠ ܗܫܐ ܓܘܒܝܐ ܡܩܕܡܐ ܓܘ ܩܪܝܒ ܟܠ ܦܪܘܓܪ̈ܡܐ"، ܘܦܘܫܪܐ ܕܝܠܗ "ܒܨܝܪ ܚܬܝܬܐ ܝܠܗ" – ܟܡܩܪܒ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܠܨܦܪܐ؛ Efron "ܚܬܝܬܐ ܝܠܗ ܒܡܫܘܚܬܐ" ܘܥܓܠܐ ܐܝܟ ܗܘ (Therneau & Grambsch, 2000, pp. 48-53)، "ܚܬܝܬܐ ܝܬܝܪ ܒܣܓܝ" (Harrell, 2015, p. 477) – ܐܦܢ ܓܘ ܡܬܠܐ ܕ-Harrell ܕܘܟ Breslow ܗܘܐ ܩܪܝܒܐ ܝܬܝܪ ܠܚܘܫܒܢܐ ܚܬܝܬܐ (ܦܐܬܐ 479). R ܟܡܦܠܚ ܒ-Efron، ܘ-SPSS، SAS ܘ-Stata ܒ-Breslow (Kleinbaum & Klein, 2012, p. 635). ܦܐܬܐ ܟܝܗܒܐ ܬܪܘܝܗܘܢ، ܕܡܨܝܚ ܕܦܚܡܚ ܥܡ ܟܠ ܚܕ ܡܢ ܦܪܘܓܪ̈ܡܐ.

ܟܡܐ ܓܕܫ̈ܐ ܓܪܓ. ܓܘ ܦܘܫܩܐ ܕܩܘܝܡܐ ܒܚܝ̈ܐ (survival analysis) "ܪܒܘܬܐ ܡܥܒܕܢܝܬܐ ܕܕܘܡܝܐ" ܝܠܗ̇ ܡܢܝܢܐ ܕܓܕܫ̈ܐ، ܠܐ ܡܢܝܢܐ ܕܡܫܬܘܬܦ̈ܢܐ (Harrell, 2015, p. 73). Harrell (ܦܐ̈ܬܐ 72-73) ܟܡܩܪܒ ܠܐ ܝܬܝܪ ܡܢ ܡܢܝܢܐ ܡܫܘܬܦܐ ܚܕ ܩܐ ܟܠ 10-20 ܓܕܫ̈ܐ – ܒܡܨܥܝܬܐ 15 – ܘܟܡܢܐ ܟܠ ܡܢܝܢܐ ܡܫܘܬܦܐ، ܥܡ ܟܠ ܡܫܬܚܠܦܢܐ ܕܘܡܝܐ (dummy)؛ ܦܐܬܐ ܟܙܗܪܐ ܬܚܘܬ 10.

ܫܪܛܐ ܕܣܘܟ̈ܢܐ ܦܘܚܡܝ̈ܐ

"ܫܪܛܐ ܪܫܝܐ ܕܪܝܓܪܫܢ ܕ-Cox": ܦܘܚܡܐ ܕܣܘܟܢܐ (hazard ratio) ܒܝܢܝ ܬܪܬܝܢ ܓܘ̈ܕܐ ܩܝܡܐ ܝܠܗ ܒܐܘܪܟܐ ܕܙܒܢܐ (Jesussek & Volk-Jesussek, 2025, p. 428) – ܐܢ ܐܦܠܝܩܝܫܢ ܟܡܪܡܐ ܣܘܟܢܐ ܒ-34%، ܐܗܐ ܫܪܝܪܐ ܝܠܗ ܓܘ ܫܒܘܥܐ ܩܕܡܝܐ ܘܓܘ ܫܒܘܥܐ ܕܐܪܒܥܝܢ. ܐܦ log-rank ܟܡܣܡ ܐܗܐ (ܬܡܢ، ܦܐܬܐ 415). "ܐܢ ܣܘܟ̈ܢܐ ܟܦܣܩܝ ܚܕ̈ܕܐ، ܫܪܛܐ ܠܐ ܡܨܐ ܕܩܐܡ" – ܐܠܐ ܡܨܐ ܕܗܘܐ ܡܬܒܪܐ ܐܦ ܕܠܐ ܕܦܣܩܝ (Kleinbaum & Klein, 2012, pp. 126, 165). ܘܒܗܦܟܐ: ܐܡܢ ܕܠܝܬ ܡܥܒܕܢܘܬܐ ܟܠܗ̇، ܣܪ̈ܛܐ ܟܦܝ̈ܦܐ "ܟܡܬܥܦܝ" ܚܕ ܥܠ ܚܕ، ܘܗܝܟ "ܫܪܛܐ ܠܐ ܝܠܗ ܥܣܩܘܬܐ" (Harrell, 2015, p. 434).

ܦܐܬܐ ܟܒܚܪܐ ܫܪܛܐ ܩܐ ܟܠ ܡܫܬܚܠܦܢܐ ܘܩܐ ܡܘܕܝܠ ܟܠܗ، ܐܝܟ cox.zph ܓܘ R – ܒܘܚܪܢܐ ܕ-score ܩܐ ܡܘܣܦܐ ܕ-g(t)·x ܠܡܘܕܝܠ: ܐܢ ܡܥܒܕܢܘܬܐ ܕܡܫܬܚܠܦܢܐ ܟܫܚܠܦ̇ ܥܡ ܙܒܢܐ. ܩܪܝܒ ܟܠ ܒܘܚܪ̈ܢܐ ܕܦܘܚܡܝܘܬܐ ܒܘܚܪܢܐ ܗܕܟܐ ܝܢܐ، ܘܦܪ̈ܝܫܐ ܝܢܐ ܒܣ ܒܓܘܒܝܐ ܕ-g(t) (Therneau & Grambsch, 2000, p. 132). ܓܘܒܝܐ ܡܩܕܡܐ (default) – 1 − S(t) ܕ-Kaplan-Meier: ܩܪܝܒ ܫܘܝܐ ܝܠܗ ܠܛܟܣܐ ܕܙܒ̈ܢܐ، ܐܠܐ "ܒܨܝܪ ܪܓܝܫܐ ܠܨܘܪ̈ܬܐ ܕܦܣܝܩܘܬܐ"، ܘܟܒܕܪ ܙܒ̈ܢܐ ܫܘܝܐܝܬ ܘܟܟܠܐ ܚܙ̈ܝܬܐ ܡܪ̈ܚܩܬܐ ܕܦܩܕܝ ܦܐܪܐ (ܬܡܢ، ܦܐܬܐ 136). ܒܘܚܪܢܐ ܐܬܝܠܗ ܓܘ Harrell ܐܝܟ ܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation) ܕܫܪ̈ܟܐ (residuals) ܕ-Schoenfeld ܥܡ ܛܟܣܐ ܕܙܒܢܐ (Harrell, 2015, pp. 499, 517; Kleinbaum & Klein, 2012, pp. 181-183). ܡܢܝ̈ܢܐ ܕܓܘ ܟܬܒ̈ܐ ܥܬܝ̈ܩܐ ܡܨܝ ܕܗܘܝ ܦܪ̈ܝܫܐ ܩܠܝܠ: ܗܠ ܢܘܣܚܐ 3 ܕ-survival، cox.zph ܗܘܐ ܚܫܒܐ ܩܘܪܒܐ ܕܒܘܚܪܢܐ (Therneau & Grambsch, 2000, p. 134).

ܒܘܚܪܢܐ "ܡܨܐ ܕܛܥܐ" ܬܘܒܪ̈ܐ، ܘܓܘ ܕܘܡܝܐ (sample) ܪܒܐ ܐܦ ܬܘܒܪܐ ܙܥܘܪܐ ܛܒܐ ܪܫܝܡܐ ܝܠܗ – ܡܛܠ ܗܕܐ ܩܕܡܝܐ ܟܫܐܠܚ "ܐܢ ܐܗܐ ܟܫܚܠܦ ܡܕܡ" ܘ"ܐܢ ܐܗܐ ܫܪܝܪܐ ܝܠܗ" (Therneau & Grambsch, 2000, pp. 140-143)، ܘܡܩܪܒܐ ܝܠܗ ܕܡܦܠܚܚ "ܠܟܡܝܘܬܐ ܒܬܪܬܝܢ ܐܘܪ̈ܚܬܐ" – ܒܘܚܪܢܐ ܘܨܘܪܬܐ (Kleinbaum & Klein, 2012, p. 187). ܐܡܢ ܕܫܪܛܐ ܡܬܒܪܐ ܝܠܗ: ܦܘܠܓܐ ܠ-strata ܠܦܘܬ ܡܫܬܚܠܦܢܐ (stratification؛ ܣܘܟܢܐ ܫܬܐܣܝܐ ܦܪܝܫܐ ܩܐ ܟܠ ܓܘܕܐ، ܕܠܐ HR ܩܐ ܐܗܐ ܡܫܬܚܠܦܢܐ)، ܦܘܠܓܐ ܕܙܒܢܐ ܕܢܛܪܬܐ ܠܥܕ̈ܢܐ، ܝܢ ܡܘܣܦܐ ܕܡܫܬܚܠܦܢܐ ܕܬܠܐ ܒܙܒܢܐ (Kleinbaum & Klein, 2012, pp. 126, 204-207; Therneau & Grambsch, 2000, pp. 145-147; Harrell, 2015, pp. 501-503) – ܟܠ ܗܢܝ ܠܒܪ ܡܢ ܦܐܬܐ ܝܢܐ.

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1 – ܩܐ ܟܠ ܓܘܕܐ: ܡܢܝܢܐ ܕܡܫܬܘܬܦ̈ܢܐ، ܕܓܕܫ̈ܐ ܘܕܦܣܝ̈ܩܐ، ܛܝܡܐ ܡܨܥܝܐ (median) ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval)، ܡܨܥܝܬܐ ܟܪܝܬܐ، ܘܡܣܬܒܪܢܘܬܐ ܕܩܘܝܡܐ ܗܠ ܙܒܢܐ ܕܓܒܝܠܘܟܘܢ. ܨܘܪܬܐ 1 – ܣܪ̈ܛܐ ܟܦܝ̈ܦܐ، ܥܡ ܣܪܛܐ ܙܥܘܪܐ ܩܐ ܟܠ ܦܣܝܩܐ ܘܣܕܪܐ ܕ"ܒܣܘܟܢܐ" ܠܬܚܬ: ܐܡܢ ܕܩܠܝܠ̈ܐ ܝܢܐ ܒܣܘܟܢܐ، ܚܪܬܐ ܕܣܪܛܐ ܟܦܝܦܐ ܠܐ ܩܝܡܬܐ ܝܠܗ̇. ܠܘܚܐ 2 – ܬܠܬܐ ܒܘܚܪ̈ܢܐ ܩܐ ܦܘܚܡܐ ܕܓܘ̈ܕܐ، ܥܡ O ܘ-E ܩܐ ܟܠ ܓܘܕܐ ܓܘ ܡܥܝܪܢܘܬܐ؛ ܥܡ ܬܠܬܐ ܓܘ̈ܕܐ ܝܢ ܝܬܝܪ – ܐܦ ܦܘܚܡ̈ܐ ܙܘܓܢ̈ܝܐ. ܒܕܚܝܬܐ – ܠܘܚܐ ܓܡܝܪܐ ܕ-Kaplan-Meier ܩܐ ܟܠ ܓܘܕܐ.

ܐܡܢ ܕܓܒܝܚ ܡܫܬܚܠܦ̈ܢܐ ܡܦܫ̈ܩܢܐ – ܠܘܚܐ ܕܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܕ-Cox (B, SE, Wald, p, HR ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ)، ܒܘܚܪ̈ܢܐ ܕܡܘܕܝܠ (−2LL، ܦܘܚܡܐ ܕܡܬܚܙܝܢܘܬܐ، Score، Wald ܘܡܚܘܝܢܐ C) ܘܒܘܚܪܢܐ ܕܦܘܚܡܝܘܬܐ. ܓܘ ܚܪܬܐ – ܦܣܩܐ ܕܡܫܟܚ̈ܢܘܬܐ (results paragraph) ܒܣܘܪܝܬ ܘܒܐܢܓܠܝܙܝܐ ܘܩܘܛܝܐ ܕ"ܩܪܝܢܐ ܕܦܐܪܐ"، ܕܟܦܢܝܐ ܠܝܗܝ̈ܒܬܐ.

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܦܣܝܩܘܬܐ ܠܐ ܬܠܝܬܐ – ܚܙܝܡܘܢ ܠܥܠ (Kleinbaum & Klein, 2012, p. 43; Jesussek & Volk-Jesussek, 2025, pp. 409, 415; Cohen et al., 2003, p. 598). ܡܫܬܘܬܦܢܐ ܕܠܐ ܐܬܝܠܗ ܒܬܪ ܗܕܐ ܩܐ ܕܕܥܪܠܗ ܠܫܬܝܐ ܕܬܬܘܢ ܠܐ ܝܠܗ ܦܣܝܩܐ "ܬܡܝܡܐ". ܠܐ ܬܠܝܘܬܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ (Jesussek & Volk-Jesussek, 2025, p. 415). ܠܝܬ ܣܘܟ̈ܢܐ ܡܬܟܬܫ̈ܢܐ (competing risks): ܐܢ ܓܕܫܐ ܐܚܪܢܐ ܟܡܟܠܐ ܓܕܫܐ ܕܡܬܒܨܐ (ܡܘܬܐ، ܐܡܢ ܕܓܕܫܐ ܕܥܪܬܐ ܝܠܗ̇ ܠܦܠܚܐ)، Kaplan-Meier ܟܡܣܡ ܕܐܢܝ ܠܐ ܬܠܝ̈ܐ ܝܢܐ – ܫܪܛܐ ܕܠܐ ܡܨܝܚ ܕܒܚܪܚ – ܘܟܡܪܒܐ ܣܘܟܢܐ؛ ܣܪܛܐ ܟܦܝܦܐ ܕܣܓܝܐܘܬܐ ܟܢܝܫܬܐ (CIC) ܠܐ ܣܢܩܐ ܝܠܗ ܠܐܗܐ ܫܪܛܐ (Kleinbaum & Klein, 2012, p. 447; Jesussek & Volk-Jesussek, 2025, p. 409). ܐܝܗ̇ ܠܝܬ ܓܘ ܦܐܬܐ.

ܓܘ Cox (Jesussek & Volk-Jesussek, 2025, pp. 428-429): ܣܘܟ̈ܢܐ ܦܘܚܡܝ̈ܐ (proportional hazards)؛ ܣܪܛܢܝܘܬܐ (linearity) ܕܡܫܬܚܠܦܢܐ ܡܬܡܫܚܢܐ ܓܘ ܠܘܓ ܕܣܘܟܢܐ – ܘܐܗܐ ܠܐ ܟܫܪܚ ܒܦܘܠܓܐ ܕܡܫܬܚܠܦܢܐ ܠܓܘ̈ܕܐ، ܐܠܐ ܒܦܘܢܩܣܝ̈ܘܢܐ ܪ̈ܟܝܟܐ (Harrell, 2015, pp. 19-21, 489-494)؛ ܕܠܐ multicollinearity؛ ܕܠܐ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ (outliers) ܡܪ̈ܚܩܐ؛ ܘܕܠܐ ܥܒ̈ܕܐ ܕܚܕ̈ܕܐ (interactions) ܕܠܐ ܥܠܝ̈ܠܐ ܝܢܐ. ܘܓܕܫ̈ܐ ܣܦܝ̈ܩܐ – ܚܙܝܡܘܢ ܠܥܠ.

ܡܘܕܝ ܠܐ ܟܥܒܕܐ ܐܗܐ ܦܐܬܐ. ܡܫܬܚܠܦ̈ܢܐ ܕܟܫܚܠܦܝ ܥܡ ܙܒܢܐ، ܓܕܫ̈ܐ ܕܟܗܘܝ ܡܢ ܪܝܫ، ܣܘܟ̈ܢܐ ܡܬܟܬܫ̈ܢܐ، ܦܘܠܓܐ ܠ-strata، ܡܘܕܝ̈ܠܐ ܦܪܡܝܛܪ̈ܝܐ (Weibull، exponential – Nag, 2022، ܦܐ̈ܬܐ 24، 33) ܘܡܘܕܝܠ ܓܘ ܙܒܢܐ ܦܪܝܫܐ (discrete time). Cohen ܘܚܒܪ̈ܘܗܝ (2003، ܦܐ̈ܬܐ 599-600) ܟܡܚܘܝ ܐܘܪܚܐ ܦܫܝܛܐ ܩܐ ܡܢܬܐ ܡܢܝܗܝ: ܦܐܝܠ ܕܓܘܗ ܩܐ ܟܠ ܡܫܬܘܬܦܢܐ ܐܝܬ ܣܕܪܐ ܩܐ ܟܠ ܥܕܢܐ، ܘܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܥܡ ܙܒܢܐ ܐܝܟ ܡܢܒܝܢܐ (predictor) – ܗܕܟܐ ܡܨܝܚ ܐܦ ܕܫܚܠܦܚ ܛܝ̈ܡܐ ܕܡܫܬܚܠܦ̈ܢܐ ܡܢ ܥܕܢܐ ܠܥܕܢܐ.

ܘܕܟܝ ܟܥܒܕܚ ܐܗܐ ܒ-SPSS؟ (And how do you do it in SPSS?)

Analyze › Survival › Kaplan-Meier: ܙܒܢܐ ܓܘ Time، ܐܝܟܢܝܘܬܐ ܓܘ Status (ܥܡ Define Event)، ܓܘܕܐ ܓܘ Factor؛ ܓܘ Compare Factor – Log rank، Breslow، Tarone-Ware (Kleinbaum & Klein, 2012, pp. 610-611)، ܘ-Pairwise over strata ܩܐ ܦܘܚܡ̈ܐ ܙܘܓܢ̈ܝܐ. Analyze › Survival › Cox Regression: ܡܫܬܚܠܦ̈ܢܐ ܓܘ Covariates، ܘܓܘ Categorical – ܐܢܝ ܕܓܢ̈ܣܐ، ܥܡ Reference Category: First ܐܝܟ ܓܘ ܦܐܬܐ. SPSS ܟܚܫܒ Cox ܥܡ Breslow ܩܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ (Kleinbaum & Klein, 2012, p. 635) – ܓܒܘܘܢ Breslow ܓܘ ܦܐܬܐ ܕܫܩܠܝܬܘܢ ܗܢܝ ܡܢܝ̈ܢܐ. ܒܘܚܪܢܐ ܕܦܘܚܡܝܘܬܐ ܠܝܬ ܓܘ ܪܫܝܡܬܐ: "SPSS ܠܐ ܟܝܗܒ ܒܦܫܝܩܘܬܐ" ܠܒܘܚܪܢܐ، ܘܟܥܒܕܚ ܠܗ ܒܟܡܐ ܕܪ̈ܓܐ – ܟܢܛܪܚ ܫܪ̈ܟܐ ܕ-Schoenfeld، ܟܡܛܟܣܚ ܙܒܢܐ ܘܟܚܫܒܚ ܐܣܘܪܐ ܕܚܕ̈ܕܐ (ܬܡܢ، ܦܐ̈ܬܐ 615-617)؛ ܦܐܪܐ ܩܪܝܒܐ ܝܠܗ ܠcox.zph ܐܠܐ ܠܐ ܫܘܝܐ ܝܠܗ. ܣܝܢܬܐܟܣ ܕܦܐܬܐ ܟܡܚܬܬܐ ܟܒܢܐ KM ܘ-COXREG؛ ܠܐ ܪܗܝܛܐ ܝܠܗ ܓܘ SPSS – ܓܘ PSPP، ܚܠܦܐ ܕܡܓܢ، ܗܢܝ ܦܘܩ̈ܕܢܐ ܗܠ ܗܫܐ ܠܐ ܥܒܝ̈ܕܐ ܝܢܐ.

ܘܕܟܝ ܟܥܒܕܚ ܐܗܐ ܒ-R؟ (And how do you do it in R?)

ܚܒܝܫܘܬܐ survival، ܕ-Therneau ܟܬܒܠܗ̇ (Therneau & Grambsch, 2000, p. 1): survfit ܩܐ Kaplan-Meier، survdiff ܩܐ log-rank، coxph ܩܐ Cox ܘ-cox.zph ܩܐ ܒܘܚܪܢܐ ܕܦܘܚܡܝܘܬܐ. ܦܐܬܐ ܫܪܝܪܬܐ ܝܠܗ̇ ܩܘܒܠ ܚܒܝܫܘܬܐ، ܘܣܩܪܝܦܬ (script) ܕܠܬܚܬ ܪܗܝܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ (ܛܝ̈ܡܐ ܓܘ ܡܥܝܪ̈ܢܘܬܐ). ܦܐܬܐ ܟܡܚܬܬܐ ܐܦ ܣܩܪܝܦܬ R ܥܡ ܝܗܝ̈ܒܬܐ ܕܝܘܟܘܢ ܕܥܝܠ̈ܬܐ ܓܘܗ.

# ܦܘܫܩܐ ܕܩܘܝܡܐ ܒܚܝ̈ܐ – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ
library(readxl)     # ܩܪܝܢܐ ܕܐܩܣܠ
library(survival)   # ܚܒܝܫܘܬܐ: Kaplan-Meier، log-rank، Cox

# ܛܥܢܐ: ܣܕܪܐ = ܡܫܬܘܬܦܢܐ؛ ܓܠܝܘܢܐ "Data"
d <- read_excel("C:/Rdata/DATA_survival_example_eng.xlsx", sheet = "Data")
d <- d[complete.cases(d[, c("weeks", "relapse", "program", "sex", "age", "prior_attempts")]), ]   # 237 ܡܢ 240

# ܣܪܛܐ ܟܦܝܦܐ ܕ-Kaplan-Meier ܠܦܘܬ ܦܪܘܓܪܡܐ: ܛܝܡܐ ܡܨܥܝܐ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (ܠܘܚܐ 1)
fit <- survfit(Surv(weeks, relapse) ~ program, data = d)
print(fit, rmean = "individual")   # ܛܝܡܐ ܡܨܥܝܐ: ܕܓܘܕܐ 31 [22, –]، ܐܦܠܝܩܝܫܢ 20 [15, 31]، ܝܚܝܕܝܐ ܠܐ ܡܛܝܐ [31, –]
summary(fit, times = 26)           # S(26): .545 [.444, .669], .421 [.324, .547], .645 [.547, .760]
plot(fit, col = 1:3, mark.time = TRUE, xlab = "weeks", ylab = "S(t)")

# ܒܘܚܪܢܐ ܕ-log-rank (ܠܘܚܐ 2)
survdiff(Surv(weeks, relapse) ~ program, data = d)   # χ²(2) = 9.23, p = .010

# ܪܝܓܪܫܢ ܕ-Cox – Efron (ܓܘܒܝܐ ܡܩܕܡܐ)؛ ties = "breslow" ܟܝܗܒ ܡܢܝ̈ܢܐ ܕ-SPSS
m <- coxph(Surv(weeks, relapse) ~ factor(program) + factor(sex) + age + prior_attempts, data = d)
summary(m)   # LR χ²(5) = 12.93, p = .024؛ ܐܦܠܝܩܝܫܢ ܩܘܒܠ ܕܓܘܕܐ HR = 1.34 [0.91, 1.99]

# ܫܪܛܐ ܕܣܘܟ̈ܢܐ ܦܘܚܡܝ̈ܐ
cox.zph(m, transform = "km")   # ܟܠܢܝܐ: χ²(5) = 1.72, p = .886

ܘܕܟܝ ܟܥܒܕܚ ܐܗܐ ܒ-Python؟

ܓܘ ܚܒܝܫܘܬܐ lifelines، ܕܥܠܗ̇ ܒܢܝܐ ܝܠܗ Nag (2022, p. vii): KaplanMeierFitter ܩܐ Kaplan-Meier (ܦܐܬܐ 43)، logrank_test ܩܐ log-rank (ܦܐ̈ܬܐ 52-53) ܘ-CoxPHFitter ܩܐ Cox (ܦܐܬܐ 72)؛ fit ܟܩܒܠ ܥܡܘܕܐ ܕܙܒܢܐ ܘܥܡܘܕܐ ܕܐܝܟܢܝܘܬܐ (ܦܐܬܐ 16). ܒܚܘܪܘܢ ܓܘ ܬܚܘܝܬܐ ܕܚܒܝܫܘܬܐ ܓܘܒܝ̈ܐ ܡܩܕܡ̈ܐ – ܙܢܐ ܕܬܚܘܡܐ ܕܬܘܟܠܢܐ ܩܐ ܣܪܛܐ ܟܦܝܦܐ ܘܥܒܕܐ ܥܡ ܛܝ̈ܡܐ ܫܘ̈ܝܐ – ܩܕܡ ܕܦܚܡܝܬܘܢ ܥܡ ܦܐܬܐ.

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܟܡܘܕܥܚ: ܡܘܢܐ ܝܠܗ ܓܕܫܐ ܘܡܘܢܐ ܝܠܗ ܢܘܩܙܐ ܕܫܘܪܝܐ؛ ܐܘܪܟܐ ܕܢܛܪܬܐ (follow-up) ܘܡܢܝܢܐ ܕܦܣܝ̈ܩܐ؛ ܛܝܡܐ ܡܨܥܝܐ (median؛ ܝܢ "ܠܐ ܡܛܝܐ ܝܠܗ") ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܩܐ ܟܠ ܓܘܕܐ، ܝܢ ܡܣܬܒܪܢܘܬܐ ܕܩܘܝܡܐ ܗܠ ܙܒܢܐ ܡܚܬܡܐ؛ ܒܘܚܪܢܐ ܕ-log-rank ܥܡ χ²، ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ ܘ-p؛ ܘܓܘ Cox – HR ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܩܐ ܟܠ ܡܫܬܚܠܦܢܐ، ܩܐ ܫܘܢܝܐ ܕܐܝܬܠܗ ܣܘܟܠܐ (Harrell, 2015, pp. 509-510)، ܒܘܚܪܢܐ ܕܡܘܕܝܠ، ܐܘܪܚܐ ܕܛܝ̈ܡܐ ܫܘ̈ܝܐ، ܘܒܘܚܪܢܐ ܕܫܪܛܐ ܕܦܘܚܡܝܘܬܐ. ܨܘܪܬܐ ܕ-Kaplan-Meier ܡܢܬܐ ܝܠܗ̇ ܡܢ ܬܘܢܝܐ – "ܒܪܘܫܡܐ" ܟܡܚܘܚ ܦܘܢܩܣܝ̈ܘܢܐ ܕܩܘܝܡܐ ܒܨܘܪܬܐ، ܘܨܘܪܬܐ "ܡܨܝܐ ܕܗܘܝܐ ܡܘܕܥܢܝܬܐ" ܐܝܟ ܦܘܫܩܐ ܒܓܢܒܗ (Cohen et al., 2003, p. 599). ܦܣܩܐ ܕܦܐܬܐ ܟܒܢܝܐ ܢܘܩܙܐ ܕܫܘܪܝܐ ܝܠܗ̇.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܫܩܠܬܐ ܕܦܣܝ̈ܩܐ، ܝܢ ܦܘܫܩܐ ܕܙܒܢܐ ܕܢܛܪܬܐ ܕܝܠܗܘܢ ܐܝܟ ܙܒܢܐ ܕܓܕܫܐ – ܬܪܬܝܢ ܐܘܪ̈ܚܬܐ ܟܡܩܨܪ̈ܢ ܙܒ̈ܢܐ (Cohen et al., 2003, pp. 596-597).

ܬܘܢܝܐ ܕܡܨܥܝܬܐ ܒܕܘܟܬܐ ܕܛܝܡܐ ܡܨܥܝܐ ܐܡܢ ܕܐܝܬ ܦܣܝܩܘܬܐ، ܝܢ ܬܘܢܝܐ ܕܚܪܬܐ ܕܢܛܪܬܐ ܐܝܟ "ܛܝܡܐ ܡܨܥܝܐ" ܐܡܢ ܕܛܝܡܐ ܡܨܥܝܐ ܠܐ ܡܛܝܐ ܝܠܗ.

ܩܪܝܢܐ ܕܚܪܬܐ ܕܣܪܛܐ ܟܦܝܦܐ ܐܡܢ ܕܦܝܫܝܠܗܘܢ ܓܘܗ̇ ܩܠܝܠ ܡܫܬܘܬܦ̈ܢܐ ܒܣܘܟܢܐ – ܢܚܬܬܐ ܕܕܪܓܐ ܓܡܝܪܐ ܡܨܝܐ ܕܗܘܝܐ ܓܕܫܐ ܚܕ.

ܦܘܫܩܐ ܕ-HR ܐܝܟ ܦܘܚܡܐ ܕܡܣܬܒܪ̈ܢܘܬܐ ܝܢ ܐܝܟ ܦܘܚܡܐ ܕܙܒ̈ܢܐ: HR = 2 ܠܐ ܝܠܗ "ܬܪܝܢ ܚܕ̈ܐ ܣܟܘܝܐ" ܘܠܐ "ܦܠܓܐ ܕܙܒܢܐ"؛ ܣܘܟܢܐ ܪܗܛܐ ܝܠܗ ܘܠܐ ܡܣܬܒܪܢܘܬܐ (Kleinbaum & Klein, 2012, p. 12).

ܓܘܒܝܐ ܕܒܘܚܪܢܐ ܠܦܘܬ ܦܐܪܐ – ܡܪܗܛܐ ܕ-log-rank، Breslow ܘ-Tarone-Ware ܘܬܘܢܝܐ ܕܗܘ ܕܪܫܝܡܐ ܝܠܗ (Kleinbaum & Klein, 2012, p. 76).

ܦܘܠܓܐ ܕܡܫܬܚܠܦܢܐ ܡܬܡܫܚܢܐ ܠܓܘ̈ܕܐ ܩܐ ܦܘܚܡܐ ܕܣܪ̈ܛܐ ܟܦܝ̈ܦܐ ܘܬܘܢܝܐ ܕܐܗܐ ܐܝܟ ܡܫܟܚܢܘܬܐ – "ܠܝܬ ܡܕܡ ܡܚܪܒܢܐ ܝܬܝܪ" (Harrell, 2015, p. 19)؛ ܐܝܟ ܬܚܘܝܬܐ – ܛܒܐ ܝܠܗ، ܐܠܐ ܐܣܘܪܐ ܟܒܚܪܚ ܠܗ ܓܘ Cox ܥܡ ܡܫܬܚܠܦܢܐ ܡܬܡܫܚܢܐ.

ܛܥܝܐ ܡܢ ܣܪ̈ܛܐ ܟܦܝ̈ܦܐ ܕܟܦܣܩܝ ܚܕ̈ܕܐ – log-rank ܟܡܘܒܕ ܚܝܠܐ، ܘ-HR ܕ-Cox ܡܨܥܝܬܐ ܝܠܗ̇ ܕܠܡܐ ܠܐ ܟܡܚܘܝܐ ܚܕ ܥܕܢܐ ܡܢܝܗܝ.

ܪܡܙܢܘܬܐ ܕܐܝܟܢܝܘܬܐ ܒܗܦܟܐ – 1 ܩܐ ܦܣܝܩܐ ܘ-0 ܩܐ ܓܕܫܐ. ܦܐܬܐ ܟܫܐܠܐ ܐܝܢܐ ܛܝܡܐ ܟܡܚܘܐ ܓܕܫܐ؛ ܒܚܘܪܘܢ ܕܡܢܝܢܐ ܕܓܕܫ̈ܐ ܓܘ ܠܘܚܐ 1 ܡܬܩܒܠܐ ܝܠܗ ܒܗܘܢܐ.

ܡܒܘ̈ܥܐ

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Lawrence Erlbaum Associates.

Harrell, F. E., Jr. (2015). Regression modeling strategies: With applications to linear models, logistic and ordinal regression, and survival analysis (2nd ed.). Springer. https://doi.org/10.1007/978-3-319-19425-7

Jesussek, M., & Volk-Jesussek, H. (2025). Statistics made easy: A clear and simple introduction (7th ed.). numiqo e.U.

Kleinbaum, D. G., & Klein, M. (2012). Survival analysis: A self-learning text (3rd ed.). Springer. https://doi.org/10.1007/978-1-4419-6646-9

Nag, A. (2022). Survival analysis with Python. CRC Press. https://doi.org/10.1201/9781003255499

Therneau, T. M., & Grambsch, P. M. (2000). Modeling survival data: Extending the Cox model. Springer. https://doi.org/10.1007/978-1-4757-3294-8

Cox (1972) – ܐܝܟ ܕܡܬܝܐ ܝܠܗ ܓܘ Cohen ܘܚܒܪ̈ܘܗܝ (2003). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܓܘ ܫܪܫܐ ܕܝܗܝ؛ ܡܬ̈ܝܬܐ ܠܦܘܬ ܦܐܬܐ ܛܒܝܥܬܐ. ܢܘܣܚܐ 1 ܒܢܝܐ ܝܠܗ ܡܢ ܨܚ̈ܚܐ 24-25 ܓܘ ܟܬܒܐ ܕ-numiqo (ܓܘ folder: Jesussek & Volk-Jesussek, 2024, DATAtab) ܘܡܢ ܦܣܩܐ 15.7 ܓܘ Cohen ܘܚܒܪ̈ܘܗܝ؛ ܢܘܣܚܐ 2 – ܡܢ ܐܪܒܥܐ ܟܬܒ̈ܐ ܕܓܘ folder "ܦܘܫܩܐ ܕܩܘܝܡܐ ܒܚܝ̈ܐ" (ܓܘ ܟܬܒܐ ܕ-Nag ܫܡܐ ܕܦܐܝܠ 2021، ܘܓܘ ܦܐܬܐ ܕܙܕܩ̈ܐ – 2022). ܚܘܫܒܢܐ ܓܘ ܦܐܬܐ ܫܪܝܪܐ ܝܠܗ ܩܘܒܠ R 4.3.3 ܘܚܒܝܫܘܬܐ survival 3.5-8 (survfit ܒܐܪܒܥܐ ܙܢ̈ܐ ܕܬܚܘܡܐ ܕܬܘܟܠܢܐ، survdiff، coxph، concordance، cox.zph)، ܘܩܘܒܠ ܡܢܝ̈ܢܐ ܛܒܝ̈ܥܐ ܓܘ ܟܬܒ̈ܐ: ܝܗܝ̈ܒܬܐ ܕܢܝܚܬܐ ܕܡܪܥܐ (remission) ܘܝܗܝ̈ܒܬܐ ܕ-Evans County ܓܘ Kleinbaum ܘ-Klein (2012، ܦܐ̈ܬܐ 62-80، 95، 156 – Kaplan-Meier، Greenwood، log-rank، Wilcoxon، Tarone-Ware ܘ-Cox)، ܝܗܝ̈ܒܬܐ ܕܥܘܩܒ̈ܪܐ ܕ-Pike ܓܘ Harrell (2015, p. 480 – Efron & Breslow)، ܘܝܗܝ̈ܒܬܐ ܕܒܘܚܪܢܐ ܕ-Therneau ܘ-Grambsch (2000، ܦܐ̈ܬܐ 323-327).