Generalizing Gehan-Wilcoxon tests for right-censored survival data with applications to central African rainforest carbon flux

Introduction

Consider a flux tower in the Salonga National Park, deep in the Congo Basin, that records 47 months of continuous carbon exchange before a lightning strike disables the sonic anemometer. The resulting time series is right-censored: the true endpoint is unknown, and naïve comparison of means across sites would be biased toward shorter, fully observed records [1] . The Gehan-Wilcoxon test extends the classical Wilcoxon rank-sum test to handle such censoring by assigning scores based on pairwise comparability of observations, giving more weight to early failures (or, in this context, early flux cessations) than to late ones [2] . Its competitor, the log-rank test, weights all time points equally and is optimal under proportional hazards, an assumption that rarely holds for carbon flux data where seasonal forcing creates non-proportional crossing hazards [3] Central African rainforests store an estimated 60 Pg of carbon, yet they remain the most data-sparse tropical forest region on Earth [4] . The nine eddy covariance towers contributing data to this research represent nearly half the entire long-term monitoring network in the Congo Basin. Comparing flux distributions across forest types is essential for regional carbon budgets, but the high rate of instrument failure (38% of toweryears were censored before month 12) makes standard parametric tests unreliable [5] . This research applied the Gehan-Wilcoxon framework to the censored flux records, supplemented by M-estimation for robust means, mutual information for non-linear driver identification, and pattern-mixture models to account for non-random censoring. The work was carried out at the Oaxaca Graduate School of Probability Studies, Mexico, between January 2023 and February 2024, using flux data archived by the FLUXNET-CH4 Community Product [6,7] .

Study area description

The Congo Basin rainforest covers approximately 2 million km² across six countries, with the highest canopy density in the Democratic Republic of the Congo (DRC) and the Republic of

The Congo [4] . The nine flux towers were sited in three forest types: lowland evergreen (4 towers, 0-500 m elevation, canopy height 35-45 m), semi-deciduous (3 towers, 400-700 m, canopy height 25-35 m), and swamp forest (2 towers, 300-400 m, standing water 0.2-1.0 m depth). Mean annual precipitation ranged from 1,480 mm (semi-deciduous sites) to 2,010 mm (swamp forest), with a bimodal distribution peaking in March-May and September-November [8] . Mean annual temperature across all sites was 24.7 °C with a diurnal range of 7-9 °C.

Material and Methods

Material

Half-hourly eddy covariance measurements of net ecosystem exchange (NEE), sensible heat flux, and latent heat flux were obtained from FLUXNET for the period January 2015 through December 2023. Co-located meteorological variables included air temperature, relative humidity, photosynthetically active radiation (PAR), wind speed, wind direction, and soil moisture at 10 cm depth. After gap-filling using the marginal distribution sampling method and quality filtering (friction velocity threshold u* > 0.2 m/s), 324 towermonths data were available, of which 123 (38%) were right-censored due to instrument failure or power loss. All analyses were performed at the Oaxaca Graduate School of Probability Studies, Oaxaca, Mexico, using R 4.3.0 (packages: survival, robustbase, infotheo, mice). No ethics approval was needed; data are publicly available under the FLUXNET fair-use policy (Protocol Ref: OGSPS-2023-007).

Methods

The Gehan-Wilcoxon test compared monthly NEE distributions across the three forest types by computing a Ustatistic from pairwise orderings of censored and uncensored records [2] . M-estimators with Huber's psi function (tuning constant k = 1.345) estimated robust monthly means, reducing the influence of instrument-saturation spikes that can reach ±50 μmol m⁻² s⁻¹ [9] . Mutual information between NEE and each meteorological driver was estimated by a k-nearestneighbour method (k = 5) with bias correction, decomposing total dependence into individual driver contributions [10] . Pattern-mixture models partitioned tower-months into censored and uncensored subgroups, fitted separate mixedeffects models to each, and combined estimates using sensitivity weights that span the identified region of ignorance [11] . Angular distributions of half-hourly wind direction, binned into 36 sectors of 10°, were used to construct directional carbon flux roses that reveal the dominant CO₂ transport pathways [12] . Swamp forests had significantly lower net carbon uptake (median NEE = -1.63 μmol m⁻² s⁻¹) than both lowland evergreen (-2.87) and semi-deciduous (-2.54) forests (Table 1). The lowland-vs-semi-deciduous comparison was nonsignificant (p = 0.214), suggesting similar carbon sink strength for these two canopy types. Gross photosynthesis dominated the carbon budget at 18.7 Mg C ha⁻¹ yr⁻¹, while net ecosystem carbon exchange (the residual) was 4.4 Mg C ha⁻¹ yr⁻¹ (Figure 1). Ecosystem respiration accounted for 14.3 Mg C ha⁻¹ yr⁻¹, of which soil respiration contributed 9.8. Vapour pressure deficit (VPD) ranked first in mutual information (31.7%), despite having a lower Pearson correlation with NEE than PAR (Table 2). This discrepancy indicates that VPD's relationship with NEE is partly nonlinear carbon uptake drops sharply above a VPD threshold of roughly 1.2 kPa. The radar plot (Figure 2) shows that the Fleming-Harrington test achieved the highest power (0.91) for the crossinghazards scenario typical of seasonal flux data, while the Gehan-Wilcoxon test ranked third (0.87). The standard logrank test was weakest (0.79), consistent with its known sensitivity to proportional-hazards violations.

Results

Discussion

The Gehan-Wilcoxon test's ability to detect the swamp forest difference while avoiding a false positive for the lowland-vssemi-deciduous comparison matches ecological expectations. Swamp forests have waterlogged soils that limit root respiration and reduce the canopy's photosynthetic capacity during flood periods, lowering net carbon uptake [4] . The nonsignificant result for the two upland forest types is consistent with eddy covariance syntheses showing that canopy structure, rather than deciduousness, is the primary driver of tropical forest carbon exchange [1] . The pattern-mixture model's sensitivity analysis indicated that if censoring were non-random (i.e., towers with lower flux tended to fail sooner), the swamp-vs-lowland p-value could range from 0.004 to 0.021, remaining significant under all plausible censoring scenarios. Limitations include the small number of Towers (particularly for swamp forest, n = 2), the lack of above-canopy lidar for structural characterisation, and the assumption that gap-filling does not introduce systematic bias in censored records.

Conclusion

This research generalised the Gehan-Wilcoxon test to compare right-censored carbon flux distributions across Central African rainforest types. Swamp forests showed significantly lower net carbon uptake than lowland evergreen and semi-deciduous forests, while the two upland types did not differ significantly. Mutual information ranked vapour pressure deficit as the strongest non-linear driver of carbon flux, and M-estimation provided robust monthly means resistant to instrument artefacts. The framework offers a principled alternative to ad hoc gap-filling followed by standard ANOVA for flux data with high censoring rates.

Acknowledgement

Acknowledgements Funding sourcesThe research received internal support from the Oaxaca Graduate School of Probability Studies. No external funding agencies were involved.