Step2 convergence of t2e analysis with tied events

[paulbeele2]

REGENIE --t2e Cox null-model convergence with ordinal survival months

Hi Joelle and team,

Thanks for the survival analysis (--t2e) implementation, really helpful for our analyses.

I'm running a T2E GWAS across five separate cohorts. Most run fine, but one of the cohorts has trouble converging on the Step 2 Cox null regression for the phenotype survival_months.

It has plenty of samples (2,452) and deaths as events (1,704), but I noticed that unlike three of the cohorts, the survival months were quite “ordinal”. I.e.: most 85% of the survival times were clustered at exactly 12, 24, 36, 48, etc. months, with the remaining data as a continuous variable in between.

I managed to get the model to converge by “untying” the survival months, setting everyone to 12.00001, 12.00002, 12.00003, etc. survival months.

While the outcome Manhattan and QQ plot look reasonably well-behaved, I was wondering if you have any experience with how this affects REGENIE outcomes, to what extent this violates CoxPH assumptions, and whether this is a reasonable solution.

I noticed that the fourth cohort, which did converge on “regular” survival months as input, also had somewhat of this ordinal survival-months distribution. A P–P plot of the regular and untied survival_months GWAS showed slight inflation of p-values in the untied analysis.

Feel free to ask for any code/log files, if that helps!

Thank you in advance,

Paul

---

Output

Log of output saved in file:

../cohort/REGENIE/survival/additive/survival_months/chr22/regenie_step2_chr22.log

Options in effect

--step 2 \
--bed ../cohort/duplicate_removal/cohort_no_duplicates \
--t2e \
--firth \
--approx \
--firth-se \
--test additive \
--chr 22 \
--phenoFile ../cohort/phenotypes/regenie/regenie_pheno.txt \
--eventColList survival_status \
--phenoColList survival_months \
--covarFile ../cohort/phenotypes/regenie/regenie_covars.txt \
--covarColList sex_at_birth_bin,PC1,PC2,PC3,PC4,PC5,PC6,PC7,PC8,PC9,PC10,batch \
--catCovarList sex_at_birth_bin,batch \
--threads 4 \
--maxCatLevels 35 \
--bsize 1000 \
--maxstep-null 1 \
--maxiter-null 1000000 \
--pred ../cohort/REGENIE/regenie_step1_survival_pred.list \
--out ../cohort/REGENIE/survival/additive/survival_months/chr22/regenie_step2_chr22

Input summary

Association testing mode with fast multithreading using OpenMP

* bim              : [../cohort/duplicate_removal/cohort_no_duplicates.bim]
                     n_snps = 14800172
* fam              : [../cohort/duplicate_removal/cohort_no_duplicates.fam]
                     n_samples = 2454
* bed              : [../cohort/duplicate_removal/cohort_no_duplicates.bed]

* phenotypes       : [../cohort/phenotypes/regenie/regenie_pheno.txt]
                     n_pheno = 1
  - number of phenotyped individuals = 2452

* covariates       : [../cohort/phenotypes/regenie/regenie_covars.txt]
                     n_cov = 12
  - number of individuals with covariate data = 2452

* number of individuals used in analysis = 2452

* number of observations for each trait:
  - 'survival_months': 1704 events and 748 censors

* LOCO predictions : [../cohort/REGENIE/regenie_step1_survival_pred.list]
  - file [../cohort/REGENIE/regenie_step1_survival_2.loco]
    for phenotype 'survival_months'

* # threads        :[1]
* block size       : [1000]
* # blocks         : 
* approximate memory usage : 89MB
* using minimum MAC of 5 (variants with lower MAC are ignored)

* using fast Firth correction for logistic/cox regression p-values less than 0.05
  - using back-correction to compute Firth SE

* user specified to test only on select chromosomes

Failure output

Chromosome 22 [201 blocks in total]

-reading loco predictions for the chromosome...done (4ms)

-fitting null cox regression on time-to-event phenotypes...
Convergence issue, inner loop: cannot correct step size
Convergence issue, inner loop: cannot correct step size

WARNING: step2 cox null regression did not converge for phenotype
'survival_months'.done (39ms)

-fitting null Firth cox regression on time-to-event phenotypes...
ERROR: Firth penalized cox regression failed to converge for all phenotypes.

Try decreasing the maximum step size using `--maxstep-null` (currently=0)
and increasing the maximum number of iterations using `--maxiter-null`
(currently=5000000).

[zouyuxin]

Hi Paul,

Thanks for the detailed writeup, it is an interesting edge case.

The "untying" is likely influencing your results. The issue is that with 85% of survival times clustered at exact values, there isn't much variability left for Cox regression to use when ranking who's "at risk" relative to whom. When you assign sequential decimal values (12.00001, 12.00002, etc.), you're imposing a fixed, arbitrary order on people who were actually tied — and that order isn't random, so it can systematically bias the results. That's likely why you're seeing p-value inflation in the untied analysis.

Since REGENIE only supports Breslow's method for ties (which is known to be less robust with heavy tying), this may be a fundamental limitation for this cohort's data structure, not just a convergence quirk.

It would be best to recover the actual order of these samples, for example, if survival time is available at a finer resolution (e.g., in days rather than months). This would be the better solution because it reflects the true underlying data rather than an artificial tie-breaking method.

If that's not available, I'd suggest using random jitter instead of sequential jitter to break ties, and running it with a few different random seeds (e.g., 5–10 draws) rather than just once. If the resulting p-values/effect sizes are stable across draws, that's reassuring — it suggests the signal isn't just an artifact of how ties happened to be broken. If they vary a lot, that's a sign the tie-breaking itself is driving the result, and the signal should be treated with caution.

Yuxin