Heterogeneous treatment effect estimation for observational data using model-based forests.

The estimation of heterogeneous treatment effects has attracted considerable interest in many disciplines, most prominently in medicine and economics. Contemporary research has so far primarily focused on continuous and binary responses where heterogeneous treatment effects are traditionally estimated by a linear model, which allows the estimation of constant or heterogeneous effects even under certain model misspecifications. More complex models for survival, count, or ordinal outcomes require stricter assumptions to reliably estimate the treatment effect. Most importantly, the noncollapsibility issue necessitates the joint estimation of treatment and prognostic effects. Model-based forests allow simultaneous estimation of covariate-dependent treatment and prognostic effects, but only for randomized trials. In this paper, we propose modifications to model-based forests to address the confounding issue in observational data. In particular, we evaluate an orthogonalization strategy originally proposed by Robinson (1988, Econometrica) in the context of model-based forests targeting heterogeneous treatment effect estimation in generalized linear models and transformation models. We found that this strategy reduces confounding effects in a simulated study with various outcome distributions. We demonstrate the practical aspects of heterogeneous treatment effect estimation for survival and ordinal outcomes by an assessment of the potentially heterogeneous effect of Riluzole on the progress of Amyotrophic Lateral Sclerosis.

Hill-Chao numbers allow decomposing gamma multifunctionality into alpha and beta components.

Biodiversity-ecosystem functioning (BEF) research has provided strong evidence and mechanistic underpinnings to support positive effects of biodiversity on ecosystem functioning, from single to multiple functions. This research has provided knowledge gained mainly at the local alpha scale (i.e. within ecosystems), but the increasing homogenization of landscapes in the Anthropocene has raised the potential that declining biodiversity at the beta (across ecosystems) and gamma scales is likely to also impact ecosystem functioning. Drawing on biodiversity theory, we propose a new statistical framework based on Hill-Chao numbers. The framework allows decomposition of multifunctionality at gamma scales into alpha and beta components, a critical but hitherto missing tool in BEF research; it also allows weighting of individual ecosystem functions. Through the proposed decomposition, new BEF results for beta and gamma scales are discovered. Our novel approach is applicable across ecosystems and connects local- and landscape-scale BEF assessments from experiments to natural settings.

Weather explains the decline and rise of insect biomass over 34 years.

Insects have a pivotal role in ecosystem function, thus the decline of more than 75% in insect biomass in protected areas over recent decades in Central Europe1 and elsewhere2,3 has alarmed the public, pushed decision-makers4 and stimulated research on insect population trends. However, the drivers of this decline are still not well understood. Here, we reanalysed 27 years of insect biomass data from Hallmann et al.1, using sample-specific information on weather conditions during sampling and weather anomalies during the insect life cycle. This model explained variation in temporal decline in insect biomass, including an observed increase in biomass in recent years, solely on the basis of these weather variables. Our finding that terrestrial insect biomass is largely driven by complex weather conditions challenges previous assumptions that climate change is more critical in the tropics5,6 or that negative consequences in the temperate zone might only occur in the future7. Despite the recent observed increase in biomass, new combinations of unfavourable multi-annual weather conditions might be expected to further threaten insect populations under continuing climate change. Our findings also highlight the need for more climate change research on physiological mechanisms affected by annual weather conditions and anomalies.

Treatment effect of remdesivir on the mortality of hospitalised COVID-19 patients in Switzerland across different patient groups: a tree-based model analysis.

AIMS OF THE STUDY: Remdesivir has shown benefits against COVID-19. However, it remains unclear whether, to what extent, and among whom remdesivir can reduce COVID-19-related mortality. We explored whether the treatment response to remdesivir differed by patient characteristics. METHODS: We analysed data collected from a hospital surveillance study conducted in 21 referral hospitals in Switzerland between 2020 and 2022. We applied model-based recursive partitioning to group patients by the association between treatment levels and mortality. We included either treatment (levels: none, remdesivir within 7 days of symptom onset, remdesivir after 7 days, or another treatment), age and sex, or treatment only as regression variables. Candidate partitioning variables included a range of risk factors and comorbidities (and age and sex unless included in regression). We repeated the analyses using local centring to correct the results for the propensity to receive treatment. RESULTS: Overall (n = 21,790 patients), remdesivir within 7 days was associated with increased mortality (adjusted hazard ratios 1.28-1.54 versus no treatment). The CURB-65 score caused the most instability in the regression parameters of the model. When adjusted for age and sex, patients receiving remdesivir within 7 days of onset had higher mortality than those not treated in all identified eight patient groups. When age and sex were included as partitioning variables instead, the number of groups increased to 19-20; in five to six of those branches, mortality was lower among patients who received early remdesivir. Factors determining the groups where remdesivir was potentially beneficial included the presence of oncological comorbidities, male sex, and high age. CONCLUSIONS: Some subgroups of patients, such as individuals with oncological comorbidities or elderly males, may benefit from remdesivir.

Estimating transformations for evaluating diagnostic tests with covariate adjustment.

Receiver operating characteristic analysis is one of the most popular approaches for evaluating and comparing the accuracy of medical diagnostic tests. Although various methodologies have been developed for estimating receiver operating characteristic curves and their associated summary indices, there is no consensus on a single framework that can provide consistent statistical inference while handling the complexities associated with medical data. Such complexities might include non-normal data, covariates that influence the diagnostic potential of a test, ordinal biomarkers or censored data due to instrument detection limits. We propose a regression model for the transformed test results which exploits the invariance of receiver operating characteristic curves to monotonic transformations and accommodates these features. Simulation studies show that the estimates based on transformation models are unbiased and yield coverage at nominal levels. The methodology is applied to a cross-sectional study of metabolic syndrome where we investigate the covariate-specific performance of weight-to-height ratio as a non-invasive diagnostic test. Software implementations for all the methods described in the article are provided in the tram add-on package to the R system for statistical computing and graphics.

The Impact of Prepartum Platelet Count on Postpartum Blood Loss and Its Association with Coagulation Factor XIII Activity.

Background: Postpartum hemorrhage is a leading cause of maternal morbidity and mortality worldwide. Contradictory information exists regarding the relevance of prepartum platelet count on postpartum hemorrhage. We have shown prepartum coagulation factor XIII to be associated with postpartum blood loss; however, little is known about the association of platelet count with factor XIII activity. Our objectives were, first, to evaluate the impact of prepartum platelet count on measured postpartum blood loss in the context of prepartum measurements of coagulation factors I, II, and XIII and, second, to evaluate the association of platelet count with coagulation factor XIII, both pre- and postpartum. Material and Methods: This is a secondary analysis of a prospective cohort study (PPH 1,300 study) which analyzed the impact of prepartum blood coagulation factors on postpartum blood loss in 1,300 women. Blood loss was quantified using a validated technique. The impact of prepartum platelet count on measured blood loss was assessed by continuous outcome logistic regression; the association of platelet count with factor XIII activity by Spearman rank correlation. Results: Prepartum platelet count was significantly associated with measured postpartum blood loss: every one unit (G/L) increase in prepartum thrombocytes was associated with an odds ratio of 1.002 (95% confidence interval, 1.001-1.004, p = 0.005) to keep blood loss below any given cut-off level. This means that the probability of postpartum hemorrhage decreases with increasing prepartum platelet levels. Moreover, a significant association of platelet count with factor XIII activity was shown (Spearman rank correlation coefficient for prepartum values 0.228, p < 0.001, and for postpartum values 0.293, p < 0.001). Discussion/Conclusion: The significant association of prepartum platelet count and postpartum blood loss as well as the association of platelet count with blood coagulation factor XIII activity support the likely role of platelets in preventing postpartum hemorrhage and support the new guidelines for the treatment of postpartum hemorrhage in Germany, Austria, and Switzerland, which calls for optimizing platelet counts peripartally in case of postpartum hemorrhage. A possible effect of platelets on the level of circulating factor XIII cannot be ruled out and should prompt further investigation.

Enhancing the structural diversity between forest patches-A concept and real-world experiment to study biodiversity, multifunctionality and forest resilience across spatial scales.

Intensification of land use by humans has led to a homogenization of landscapes and decreasing resilience of ecosystems globally due to a loss of biodiversity, including the majority of forests. Biodiversity-ecosystem functioning (BEF) research has provided compelling evidence for a positive effect of biodiversity on ecosystem functions and services at the local (α-diversity) scale, but we largely lack empirical evidence on how the loss of between-patch ß-diversity affects biodiversity and multifunctionality at the landscape scale (γ-diversity). Here, we present a novel concept and experimental framework for elucidating BEF patterns at α-, ß-, and γ-scales in real landscapes at a forest management-relevant scale. We examine this framework using 22 temperate broadleaf production forests, dominated by Fagus sylvatica. In 11 of these forests, we manipulated the structure between forest patches by increasing variation in canopy cover and deadwood. We hypothesized that an increase in landscape heterogeneity would enhance the ß-diversity of different trophic levels, as well as the ß-functionality of various ecosystem functions. We will develop a new statistical framework for BEF studies extending across scales and incorporating biodiversity measures from taxonomic to functional to phylogenetic diversity using Hill numbers. We will further expand the Hill number concept to multifunctionality allowing the decomposition of γ-multifunctionality into α- and ß-components. Combining this analytic framework with our experimental data will allow us to test how an increase in between patch heterogeneity affects biodiversity and multifunctionality across spatial scales and trophic levels to help inform and improve forest resilience under climate change. Such an integrative concept for biodiversity and functionality, including spatial scales and multiple aspects of diversity and multifunctionality as well as physical and environmental structure in forests, will go far beyond the current widely applied approach in forestry to increase resilience of future forests through the manipulation of tree species composition.

On the relevance of prognostic information for clinical trials: A theoretical quantification.

The question of how individual patient data from cohort studies or historical clinical trials can be leveraged for designing more powerful, or smaller yet equally powerful, clinical trials becomes increasingly important in the era of digitalization. Today, the traditional statistical analyses approaches may seem questionable to practitioners in light of ubiquitous historical prognostic information. Several methodological developments aim at incorporating historical information in the design and analysis of future clinical trials, most importantly Bayesian information borrowing, propensity score methods, stratification, and covariate adjustment. Adjusting the analysis with respect to a prognostic score, which was obtained from some model applied to historical data, received renewed interest from a machine learning perspective, and we study the potential of this approach for randomized clinical trials. In an idealized situation of a normal outcome in a two-arm trial with 1:1 allocation, we derive a simple sample size reduction formula as a function of two criteria characterizing the prognostic score: (1) the coefficient of determination R2 on historical data and (2) the correlation ρ between the estimated and the true unknown prognostic scores. While maintaining the same power, the original total sample size n planned for the unadjusted analysis reduces to ( 1 - R 2 ρ 2 ) × n $(1 - R^2 \rho ^2) \times n$ in an adjusted analysis. Robustness in less ideal situations was assessed empirically. We conclude that there is potential for substantially more powerful or smaller trials, but only when prognostic scores can be accurately estimated.

A transformation perspective on marginal and conditional models.

Clustered observations are ubiquitous in controlled and observational studies and arise naturally in multicenter trials or longitudinal surveys. We present a novel model for the analysis of clustered observations where the marginal distributions are described by a linear transformation model and the correlations by a joint multivariate normal distribution. The joint model provides an analytic formula for the marginal distribution. Owing to the richness of transformation models, the techniques are applicable to any type of response variable, including bounded, skewed, binary, ordinal, or survival responses. We demonstrate how the common normal assumption for reaction times can be relaxed in the sleep deprivation benchmark data set and report marginal odds ratios for the notoriously difficult toe nail data. We furthermore discuss the analysis of two clinical trials aiming at the estimation of marginal treatment effects. In the first trial, pain was repeatedly assessed on a bounded visual analog scale and marginal proportional-odds models are presented. The second trial reported disease-free survival in rectal cancer patients, where the marginal hazard ratio from Weibull and Cox models is of special interest. An empirical evaluation compares the performance of the novel approach to general estimation equations for binary responses and to conditional mixed-effects models for continuous responses. An implementation is available in the tram add-on package to the $\texttt{R}$ system and was benchmarked against established models in the literature.

Inclusive Trial Designs in Acute Spinal Cord Injuries: Prediction-Based Stratification of Clinical Walking Outcome and Projected Enrolment Frequencies.

BACKGROUND: New therapeutic approaches in neurological disorders are progressing into clinical development. Past failures in translational research have underlined the critical importance of selecting appropriate inclusion criteria and primary outcomes. Narrow inclusion criteria provide sensitivity, but increase trial duration and cost to the point of infeasibility, while broader requirements amplify confounding, increasing the risk of trial failure. This dilemma is perhaps most pronounced in spinal cord injury (SCI), but applies to all neurological disorders with low frequency and/or heterogeneous clinical manifestations. OBJECTIVE: Stratification of homogeneous patient cohorts to enable the design of clinical trials with broad inclusion criteria. METHODS: Prospectively-gathered data from patients with acute cervical SCI were analysed using an unbiased recursive partitioning conditional inference tree (URP-CTREE) approach. Performance in the 6-minute walk test at 6 months after injury was classified based on standardized neurological assessments within the first 15 days of injury. Functional and neurological outcomes were tracked throughout rehabilitation up to 6 months after injury. RESULTS: URP-CTREE identified homogeneous outcome cohorts in a study group of 309 SCI patients. These cohorts were validated by an internal, yet independent, validation group of 172 patients. The study group cohorts identified demonstrated distinct recovery profiles throughout rehabilitation. The baseline characteristics of the analysed groups were compared to a reference group of 477 patients. CONCLUSION: URP-CTREE enables inclusive trial design by revealing the distribution of outcome cohorts, discerning distinct recovery profiles and projecting potential patient enrolment by providing estimates of the relative frequencies of cohorts to improve the design of clinical trials in SCI and beyond.

Unbiased Recursive Partitioning Enables Robust and Reliable Outcome Prediction in Acute Spinal Cord Injury.

Neurological disorders usually present very heterogeneous recovery patterns. Nonetheless, accurate prediction of future clinical end-points and robust definition of homogeneous cohorts are necessary for scientific investigation and targeted care. For this, unbiased recursive partitioning with conditional inference trees (URP-CTREE) have received increasing attention in medical research, especially, but not limited to traumatic spinal cord injuries (SCIs). URP-CTREE was introduced to SCI as a clinical guidance tool to explore and define homogeneous outcome groups by clinical means, while providing high accuracy in predicting future clinical outcomes. The validity and predictive value of URP-CTREE to provide improvements compared with other more common approaches applied by clinicians has recently come under critical scrutiny. Therefore, a comprehensive simulation study based on traumatic, cervical complete spinal cord injuries provides a framework to investigate and quantify the issues raised. First, we assessed the replicability and robustness of URP-CTREE to identify homogeneous subgroups. Second, we implemented a prediction performance comparison of URP-CTREE with traditional statistical techniques, such as linear or logistic regression, and a novel machine learning method. URP-CTREE's ability to identify homogeneous subgroups proved to be replicable and robust. In terms of prediction, URP-CTREE yielded a high prognostic performance comparable to a machine learning algorithm. The simulation study provides strong evidence for the robustness of URP-CTREE, which is achieved without compromising prediction accuracy. The slightly lower prediction performance is offset by URP-CTREE's straightforward interpretation and application in clinical settings based on simple, data-driven decision rules.

Individual participant data meta-analysis with mixed-effects transformation models.

One-stage meta-analysis of individual participant data (IPD) poses several statistical and computational challenges. For time-to-event outcomes, the approach requires the estimation of complicated nonlinear mixed-effects models that are flexible enough to realistically capture the most important characteristics of the IPD. We present a model class that incorporates general normally distributed random effects into linear transformation models. We discuss extensions to model between-study heterogeneity in baseline risks and covariate effects and also relax the assumption of proportional hazards. Within the proposed framework, data with arbitrary random censoring patterns can be handled. The accompanying $\textsf{R}$ package tramME utilizes the Laplace approximation and automatic differentiation to perform efficient maximum likelihood estimation and inference in mixed-effects transformation models. We compare several variants of our model to predict the survival of patients with chronic obstructive pulmonary disease using a large data set of prognostic studies. Finally, a simulation study is presented that verifies the correctness of the implementation and highlights its efficiency compared to an alternative approach.

Assessing relative COVID-19 mortality during the second wave: a prospective Swiss population-based study.

OBJECTIVE: During the first COVID-19 wave in Switzerland, relative mortality was at least eight times higher compared with the uninfected general population. We aimed to assess sex-specific and age-specific relative mortality associated with a SARS-CoV-2 diagnosis during the second wave. DESIGN: Prospective population-based study. SETTING: Individuals testing positive for SARS-CoV-2 after the start of the second wave on 1 October 2020 were followed up until death or administrative censoring on 31 December 2020. PARTICIPANTS: 5 179 740 inhabitants of Switzerland in fall 2018 aged 35-95 years (without COVID-19) and 257 288 persons tested positive for SARS-CoV-2 by PCR or antigen testing during the second wave. PRIMARY AND SECONDARY OUTCOME MEASURES: The planned outcome measure was time to death from any cause, measured from the date of a SARS-CoV-2 diagnosis or 1 October in the general population. Information on confirmed SARS-CoV-2 diagnoses and deaths was matched by calendar time with the all-cause mortality of the general Swiss population of 2018. Proportional hazards models were used to estimate sex-specific and age-specific mortality rates and probabilities of death within 60 days. RESULTS: The risk of death for individuals tested positive for SARS-CoV-2 in the second wave in Switzerland increased at least sixfold compared with the general population. HRs, reflecting the risk attributable to a SARS-CoV-2 infection, were higher for men (1.40, 95% CI 1.29 to 1.52) and increased for each additional year of age (1.01, 95% CI 1.01 to 1.02). COVID-19 mortality was reduced by at least 20% compared with the first wave in spring 2020. CONCLUSION: General mortality patterns, increased for men and older persons, were similar in spring and in fall. Absolute and relative COVID-19 mortality was smaller in fall. TRIAL REGISTRATION: The protocol for this study was registered on 3 December 2020 at https://osf.io/gbd6r.

Relationship of insect biomass and richness with land use along a climate gradient.

Recently reported insect declines have raised both political and social concern. Although the declines have been attributed to land use and climate change, supporting evidence suffers from low taxonomic resolution, short time series, a focus on local scales, and the collinearity of the identified drivers. In this study, we conducted a systematic assessment of insect populations in southern Germany, which showed that differences in insect biomass and richness are highly context dependent. We found the largest difference in biomass between semi-natural and urban environments (-42%), whereas differences in total richness (-29%) and the richness of threatened species (-56%) were largest from semi-natural to agricultural environments. These results point to urbanization and agriculture as major drivers of decline. We also found that richness and biomass increase monotonously with increasing temperature, independent of habitat. The contrasting patterns of insect biomass and richness question the use of these indicators as mutual surrogates. Our study provides support for the implementation of more comprehensive measures aimed at habitat restoration in order to halt insect declines.

The contribution of insects to global forest deadwood decomposition.

The amount of carbon stored in deadwood is equivalent to about 8 per cent of the global forest carbon stocks1. The decomposition of deadwood is largely governed by climate2-5 with decomposer groups-such as microorganisms and insects-contributing to variations in the decomposition rates2,6,7. At the global scale, the contribution of insects to the decomposition of deadwood and carbon release remains poorly understood7. Here we present a field experiment of wood decomposition across 55 forest sites and 6 continents. We find that the deadwood decomposition rates increase with temperature, and the strongest temperature effect is found at high precipitation levels. Precipitation affects the decomposition rates negatively at low temperatures and positively at high temperatures. As a net effect-including the direct consumption by insects and indirect effects through interactions with microorganisms-insects accelerate the decomposition in tropical forests (3.9% median mass loss per year). In temperate and boreal forests, we find weak positive and negative effects with a median mass loss of 0.9 per cent and -0.1 per cent per year, respectively. Furthermore, we apply the experimentally derived decomposition function to a global map of deadwood carbon synthesized from empirical and remote-sensing data, obtaining an estimate of 10.9 ± 3.2 petagram of carbon per year released from deadwood globally, with 93 per cent originating from tropical forests. Globally, the net effect of insects may account for 29 per cent of the carbon flux from deadwood, which suggests a functional importance of insects in the decomposition of deadwood and the carbon cycle.

Assessing relative COVID-19 mortality: a Swiss population-based study.

OBJECTIVE: Severity of the COVID-19 has been previously reported in terms of absolute mortality in SARS-CoV-2 positive cohorts. An assessment of mortality relative to mortality in the general population is presented. DESIGN: Retrospective population-based study. SETTING: Individual information on symptomatic confirmed SARS-CoV-2 patients and subsequent deaths from any cause were compared with the all-cause mortality in the Swiss population of 2018. Starting 23 February 2020, mortality in COVID-19 patients was monitored for 80 days and compared with the population mortality observed in the same time of year starting 23 February 2018. PARTICIPANTS: 5 102 300 inhabitants of Switzerland aged 35-95 without COVID-19 (general population in spring 2018) and 20 769 persons tested positively for COVID-19 during the first wave in spring 2020. MEASUREMENTS: Sex-specific and age-specific mortality rates were estimated using Cox proportional hazards models. Absolute probabilities of death were predicted and risk was assessed in terms of relative mortality by taking the ratio between the sex-specific and age-specific absolute mortality in COVID-19 patients and the corresponding mortality in the 2018 general population. RESULTS: Absolute mortalities increased with age and were higher for males compared with females, both in the general population and in positively tested persons. A confirmed SARS-CoV-2 infection substantially increased the probability of death across all patient groups at least eightfold. The highest relative mortality risks were observed among males and younger patients. Male COVID-19 patients exceeded the population hazard for males (HR 1.21, 95% CI 1.02 to 1.44). An additional year of age increased the population hazard in COVID-19 patients only marginally (HR 1.00, 95% CI 1.00 to 1.01). CONCLUSIONS: Healthcare professionals, decision-makers and societies are provided with an additional population-adjusted assessment of COVID-19 mortality risk. In combination with absolute measures of risk, the relative risks presented here help to develop a more comprehensive understanding of the actual impact of COVID-19.

Model-based random forests for ordinal regression.

We study and compare several variants of random forests tailored to prognostic models for ordinal outcomes. Models of the conditional odds function are employed to understand the various random forest flavours. Existing random forest variants for ordinal outcomes, such as Ordinal Forests and Conditional Inference Forests, are evaluated in the presence of a non-proportional odds impact of prognostic variables. We propose two novel random forest variants in the model-based transformation forest family, only one of which explicitly assumes proportional odds. These two novel transformation forests differ in the specification of the split procedures for the underlying ordinal trees. One of these split criteria is able to detect changes in non-proportional odds situations and the other one focuses on finding proportional-odds signals. We empirically evaluate the performance of the existing and proposed methods using a simulation study and illustrate the practical aspects of the procedures by a re-analysis of the respiratory sub-item in functional rating scales of patients suffering from Amyotrophic Lateral Sclerosis (ALS).

Author Correction: Heterogeneity-diversity relationships differ between and within trophic levels in temperate forests.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Heterogeneity-diversity relationships differ between and within trophic levels in temperate forests.

The habitat heterogeneity hypothesis predicts that biodiversity increases with increasing habitat heterogeneity due to greater niche dimensionality. However, recent studies have reported that richness can decrease with high heterogeneity due to stochastic extinctions, creating trade-offs between area and heterogeneity. This suggests that greater complexity in heterogeneity-diversity relationships (HDRs) may exist, with potential for group-specific responses to different facets of heterogeneity that may only be partitioned out by a simultaneous test of HDRs of several species groups and several facets of heterogeneity. Here, we systematically decompose habitat heterogeneity into six major facets on ~500 temperate forest plots across Germany and quantify biodiversity of 12 different species groups, including bats, birds, arthropods, fungi, lichens and plants, representing 2,600 species. Heterogeneity in horizontal and vertical forest structure underpinned most HDRs, followed by plant diversity, deadwood and topographic heterogeneity, but the relative importance varied even within the same trophic level. Among substantial HDRs, 53% increased monotonically, consistent with the classical habitat heterogeneity hypothesis but 21% were hump-shaped, 25% had a monotonically decreasing slope and 1% showed no clear pattern. Overall, we found no evidence of a single generalizable mechanism determining HDR patterns.

Correction to: Baseline-adjusted proportional odds models for the quantification of treatment effects in trials with ordinal sum score outcomes.

An amendment to this paper has been published and can be accessed via the original article.