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Capturing Heterogeneous Time-Variation in Covariate Effects in Non-Proportional Hazard Regression Models.

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  1. [1] § Brain Tumor Case Study ↔ CaseStudy.R, lines 41 to 119 · score 0.58 · admission, day, died, fraction, age, genome · Report a mismatch

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The authors' code

R · 174 lines · 6.8 KB · no license · 1 match

  1. # ==============================================================================
  2. # Capturing heterogeneous time-variation in covariate effects in non-proportional hazard regression models
  3. # Niklas Hagemann, Thomas Kneib and Kathrin Moellenhoff
  4. #
  5. # Code for the case study
  6. # ==============================================================================
  8. # Packages =====================================================================
  10. library(dplyr) # package for data manipulation
  11. library(pammtools) # package for PEM data transformation
  12. library(mgcv) # package for fitting GAMs
  13. library(survival) # package for handling survival datasets
  14. library(pec) # package for IBS
  16. # Dataset 1 ====================================================================
  18. data1 <- read.delim("difg_tcga_gdc_clinical_data.tsv", stringsAsFactors = TRUE)
  20. data1 <- data1 %>% dplyr::filter(! is.na(Overall.Survival..Months.), ! is.na(Overall.Survival.Status))
  21. data1$event <- as.numeric(data1$Overall.Survival.Status =="1:DECEASED")
  22. data1$time <- data1$Overall.Survival..Months.
  23. names(data1)[c(4)] <- c("Age")
  24. data1 <- data1 %>% filter(Sample.Type == "Primary solid Tumor")
  25. data1 <- data1 %>% select(Patient.ID, Age, Fraction.Genome.Altered, Primary.Diagnosis, Sex, event, time)
  27. # Dataset 2 ====================================================================
  29. data2 <- read.delim("gbm_tcga_gdc_clinical_data.tsv", stringsAsFactors = TRUE)
  31. data2 <- data2 %>% dplyr::filter(! is.na(Overall.Survival..Months.), ! is.na(Overall.Survival.Status))
  32. data2$event <- as.numeric(data2$Overall.Survival.Status =="1:DECEASED")
  33. data2$time <- data2$Overall.Survival..Months.
  34. names(data2)[c(4)] <- c("Age")
  35. data2 <- data2 %>% filter(Sample.Type == "Primary solid Tumor")
  36. data2 <- data2 %>% select(Patient.ID, Age, Fraction.Genome.Altered, Primary.Diagnosis, Sex, event, time)
  39. data <- bind_rows(data1, data2)
  41. # Remove patients with missing values and survival times <0 ====================
  42. data <- data %>% filter(time >= 0)
  43. data <- data %>% na.omit()
  45. # Set survival time to half a day for patients who died on their admission date
  46. data$time[data$time == 0] <- 1/60
  48. # Add end of study after 8 years ===============================================
  50. data$event[data$time >96] <- 0
  51. data$time[data$time >96] <- 96
  53. # Transform data for PAMM ======================================================
  55. data_ped <- data %>% as_ped(Surv(time = time, event = event)~., cut = unique(data$time), id = "id")
  57. # Fit models ===================================================================
  59. set.seed(123456)
  60. model_fs <- pamm(formula = ped_status ~
  61. s(tend,bs = "ps", k = 12, m = c(3, 1)) +
  62. s(tend, Primary.Diagnosis, bs = "fs", xt = list(bs = "ps"), k = 12, m = c(3, 1), by = Fraction.Genome.Altered) +
  63. Age +
  64. Primary.Diagnosis +
  65. Sex,
  66. data = data_ped,
  67. family = poisson(),
  68. offset = offset,
  69. method = "REML")
  71. set.seed(123456)
  72. model_add <- pamm(formula = ped_status ~
  73. s(tend, bs = "ps", k = 12, m = c(3, 1)) +
  74. s(tend, bs = "ps", k = 12, m = c(3, 1), by = Fraction.Genome.Altered) +
  75. s(Fraction.Genome.Altered, Primary.Diagnosis, bs = "re") +
  76. Age +
  77. Primary.Diagnosis +
  78. Sex,
  79. data = data_ped,
  80. family = poisson(),
  81. offset = offset,
  82. method = "REML")
  85. set.seed(123456)
  86. model_re <- pamm(formula = ped_status ~
  87. s(tend,bs = "ps", k = 12, m = c(3, 1)) +
  88. s(Fraction.Genome.Altered, Primary.Diagnosis, bs = "re") +
  89. Age +
  90. Primary.Diagnosis +
  91. Sex,
  92. data = data_ped,
  93. family = poisson(),
  94. offset = offset,
  95. method = "REML")
  97. set.seed(123456)
  98. model_ps <- pamm(formula = ped_status ~
  99. s(tend, bs = "ps", k = 12, m = c(3, 1)) +
  100. s(tend, bs = "ps", k = 12, m = c(3, 1), by = Fraction.Genome.Altered) +
  101. Age +
  102. Primary.Diagnosis +
  103. Sex,
  104. data = data_ped,
  105. family = poisson(),
  106. offset = offset,
  107. method = "REML")
  109. set.seed(123456)
  110. model_linear <- pamm(formula = ped_status ~
  111. s(tend, bs = "ps", k = 12, m = c(3, 1)) +
  112. Fraction.Genome.Altered +
  113. Age +
  114. Primary.Diagnosis +
  115. Sex,
  116. data = data_ped,
  117. family = poisson(),
  118. offset = offset,
  119. method = "REML")
  121. # Calculate fit measures =======================================================
  123. pec_fs = pec(model_fs,
  124. Surv(time, event) ~ 1,
  125. data = data,
  126. times = sort(unique(data$time)),
  127. start = min(unique(data$time)),
  128. exact = FALSE,
  129. verbose = FALSE)
  131. pec_add = pec(model_add,
  132. Surv(time, event) ~ 1,
  133. data = data,
  134. times = sort(unique(data$time)),
  135. start = min(unique(data$time)),
  136. exact = FALSE,
  137. verbose = FALSE)
  139. pec_ps = pec(model_ps,
  140. Surv(time, event) ~ 1,
  141. data = data,
  142. times = sort(unique(data$time)),
  143. start = min(unique(data$time)),
  144. exact = FALSE,
  145. verbose = FALSE)
  147. pec_re = pec(model_re,
  148. Surv(time, event) ~ 1,
  149. data = data,
  150. times = sort(unique(data$time)),
  151. start = min(unique(data$time)),
  152. exact = FALSE,
  153. verbose = FALSE)
  155. pec_lin = pec(model_linear,
  156. Surv(time, event) ~ 1,
  157. data = data,
  158. times = sort(unique(data$time)),
  159. start = min(unique(data$time)),
  160. exact = FALSE,
  161. verbose = FALSE)
  163. fit_measures <- cbind(c("FS", "ADD", "RE", "PS", "LIN"),
  164. round(c(logLik(model_fs), logLik(model_add), logLik(model_re), logLik(model_ps), logLik(model_linear)), 2),
  165. round(c(
  166. pec::crps(pec_fs)[2,1],
  167. pec::crps(pec_add)[2,1],
  168. pec::crps(pec_re)[2,1],
  169. pec::crps(pec_ps)[2,1],
  170. pec::crps(pec_lin)[2,1]), 4),
  171. round(c(AIC(model_fs), AIC(model_add), AIC(model_re), AIC(model_ps), AIC(model_linear)), 2)
  172. )
  174. print(fit_measures)

CaseStudy.R at commit cf61eac, no license · at the source

Overview

Authors: Niklas Hagemann1,2, Thomas Kneib3, Kathrin Möllenhoff2
ORCID iDs: Niklas Hagemann, Thomas Kneib, Kathrin Möllenhoff
  1. Department of Biostatistics, Harvard T.H. Chan School of Public Health, Harvard University, Boston, USA
  2. Institute of Medical Statistics and Computational Biology, Faculty of Medicine, University of Cologne, Göttingen, Germany
  3. Chair of Statistics and Campus Institute Data Science, Georg August University Göttingen, Cologne, Germany
Institutions: Harvard University (United States); University of Cologne (Germany); Campus-Institut Data Science (CIDAS) (Germany); University of Göttingen (Germany)
Journal: Biometrical journal. Biometrische Zeitschrift, volume 68, issue 5, article e70179
Dates: received 10 December 2025; accepted 30 July 2026; published online 20 September 2026; in print October 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1002/bimj.70179 · PMID 42764422 · PMCID PMC13590908 · OpenAlex W4406786254
Open access: hybrid, a free copy (OpenAlex)
Preprint: arxiv:2501.13525
Status: code verified (how the code is found and verified)
Categories: human (organism), clinical / translational (subfield)
Methods: Statistics
Keywords: effect heterogeneity, factor smooth interactions, functional random coefficients, functional random effects, hazard regression, non‐proportional hazards, piecewise exponential model, penalized splines, random wiggly curves, time‐varying effects
MeSH: Biometry*, Models, Statistical*, Humans, Proportional Hazards Models, Regression Analysis, Survival Analysis, Time Factors (* major topic)
Topic: Risk and Safety Analysis (Statistics, Probability and Uncertainty, Decision Sciences), according to OpenAlex
Funding: Deutsche Forschungsgemeinschaft (RTG 2624, 427806116)
Citations: not cited yet (Europe PMC); 45 references in the paper

Abstract

A central focus in survival analysis is examining how covariates affect survival time. These covariate effects are often found to be either time‐varying, heterogeneous—such as being specific to patients, treatments, or subgroups—or exhibit both characteristics simultaneously. While the standard model, the Cox proportional hazards model, allows neither time‐varying nor heterogeneous effects, several extensions to the Cox model as well as alternative modeling frameworks have been introduced. However, no unified framework for incorporating heterogeneously time‐varying effects of covariates has been proposed. Such effects occur when a covariate affects survival not only in a heterogeneous and time‐varying manner, but when the time‐variation is also heterogeneous. We propose to model such effects by introducing heterogeneously time‐varying coefficients to piecewise exponential additive mixed models. We deploy functional random effects, also known as factor smooths, to model such coefficients as the interaction effect of heterogeneity and time‐variation. Our approach allows for non‐linear time‐effects due to being based on penalized splines and uses an efficient random effects basis to model the heterogeneity. Using a penalized basis prevents overfitting in case of absence of such effects. In addition, the penalization mostly solves the problem of choosing the number of intervals which is usually present in unregularized piecewise exponential approaches. We demonstrate the superiority of our approach in comparison to competitors by means of a simulation study. Finally, the practical application and relevance are outlined by presenting a brain tumor case study.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above, with 1 match between paragraphs and lines of code.

Niklas191/heterogeneous_time-variation

License: none: the authors keep all their rights
State: the link answers, verified on 31 October 2026
Evidence: files inventoried
Commit: cf61eaccce784f10ef8502b20efcf295cf8cdb61, 28 July 2025
Languages: R (3)
Size: 5 files, 3 scripts
Software Heritage: not archived
Found in: “Data Availability Statement”
Holds: README
Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: mgcv (2 files), survival (2 files), tidyverse (2 files)
Availability: 2 checks, the latest on 31 October 2026: the link answers
  • 31 October 2026: the link answers
  • 1 October 2026: the link answers
4 files
At the source: github.com/Niklas191/heterogeneous_time-variation

The paper's code and data availability statement is in the Data section.

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Data

No dataset and no data link were found in the paper.

Data Availability Statement

The R code and data necessary to reproduce the reported results, figures, and tables are available in the Supporting Information. All R functions are also available at https://github.com/Niklas191/heterogeneous_time‐variation (https://github.com/Niklas191/heterogeneous_time-variation). The current version of the case study data set is publicly available at the cBioPortal database with IDs gbm_tcga_gdc (https://www.cbioportal.org/study/clinicalData?id=gbm_tcga_gdc) and difg_tcga_gdc (https://www.cbioportal.org/study/clinicalData?id=difg_tcga_gdc).

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Version 1, 1 October 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 10 keywords, 7 MeSH terms, 1 funder, 17 references.

Cite

This paper

Hagemann, N., Kneib, T., & Möllenhoff, K. (2026). Capturing Heterogeneous Time-Variation in Covariate Effects in Non-Proportional Hazard Regression Models. Biometrical journal. Biometrische Zeitschrift, 68(5), e70179. https://doi.org/10.1002/bimj.70179

BibTeX

@article{hagemann2026capturing,
author = {Hagemann, Niklas and Kneib, Thomas and Möllenhoff, Kathrin},
title = {{Capturing Heterogeneous Time-Variation in Covariate Effects in Non-Proportional Hazard Regression Models}},
journal = {Biometrical journal. Biometrische Zeitschrift},
year = {2026},
month = oct,
volume = {68},
number = {5},
pages = {e70179},
publisher = {Wiley},
issn = {0323-3847},
doi = {10.1002/bimj.70179},
url = {https://doi.org/10.1002/bimj.70179},
pmid = {42764422},
pmcid = {PMC13590908}
}

RIS

TY - JOUR
AU - Hagemann, Niklas
AU - Kneib, Thomas
AU - Möllenhoff, Kathrin
TI - Capturing Heterogeneous Time-Variation in Covariate Effects in Non-Proportional Hazard Regression Models
T2 - Biometrical journal. Biometrische Zeitschrift
J2 - Biom J
PY - 2026
DA - 2026/10/01
VL - 68
IS - 5
SP - e70179
SN - 0323-3847
PB - Wiley
DO - 10.1002/bimj.70179
UR - https://doi.org/10.1002/bimj.70179
LA - en
ER -

CSL-JSON

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