Markus Kalisch

Estimating high-dimensional intervention effects from observational data

We assume that we have observational data generated from an unknown underlying directed acyclic graph (DAG) model. A DAG is typically not identifiable from observational data, but it is possible to consistently estimate the equivalence class of a DAG. Moreover, for any given DAG, causal effects can be estimated using intervention calculus. In this paper, we combine these two parts. For each DAG in the estimated equivalence class, we use intervention calculus to estimate the causal effects of the covariates on the response. This yields a collection of estimated causal effects for each covariate. We show that the distinct values in this set can be consistently estimated by an algorithm that uses only local information of the graph. This local approach is computationally fast and feasible in high-dimensional problems. We propose to use summary measures of the set of possible causal effects to determine variable importance. In particular, we use the minimum absolute value of this set, since that is a lower bound on the size of the causal effect. We demonstrate the merits of our methods in a simulation study and on a data set about riboflavin production.

Predicting causal effects in large-scale systems from observational data

Supplementary Figure 1 Comparing IDA, Lasso and Elastic-net on the five DREAM4 networks of size 10 with multifactorial data. Supplementary Table 1 Comparing IDA, Lasso and Elastic-net to random guessing on the Hughes et al. data. Supplementary Table 2 Comparing IDA, Lasso and Elastic-net to random guessing on the five DREAM4 networks of size 10, using the multifactorial data as observational data. Supplementary Methods

Learning high-dimensional directed acyclic graphs with latent and selection variables

We consider the problem of learning causal information between random variables in directed acyclic graphs (DAGs) when allowing arbitrarily many latent and selection variables. The FCI (Fast Causal Inference) algorithm has been explicitly designed to infer conditional independence and causal information in such settings. However, FCI is computationally infeasible for large graphs. We therefore propose the new RFCI algorithm, which is much faster than FCI. In some situations the output of RFCI is slightly less informative, in particular with respect to conditional independence information. However, we prove that any causal information in the output of RFCI is correct in the asymptotic limit. We also define a class of graphs on which the outputs of FCI and RFCI are identical. We prove consistency of FCI and RFCI in sparse high-dimensional settings, and demonstrate in simulations that the estimation performances of the algorithms are very similar. All software is implemented in the R-package pcalg.

Selection of Carbonic Anhydrase IX Inhibitors from One Million DNA-Encoded Compounds

DNA-encoded chemical libraries, i.e., collections of compounds individually coupled to distinctive DNA fragments serving as amplifiable identification barcodes, represent a new tool for the de novo discovery of small molecule ligands to target proteins of pharmaceutical interest. Here, we describe the design and synthesis of a novel DNA-encoded chemical library containing one million small molecules. The library was synthesized by combinatorial assembly of three sets of chemical building blocks using Diels-Alder cycloadditions and by the stepwise build-up of the DNA barcodes. Model selections were performed to test library performance and to develop a statistical method for the analysis of high-throughput sequencing data. A library selection against carbonic anhydrase IX revealed a new class of submicromolar bis(sulfonamide) inhibitors. One of these inhibitors was synthesized in the absence of the DNA-tag and showed accumulation in hypoxic tumor tissue sections in vitro and tumor targeting in vivo.

Variable selection in high-dimensional linear models: partially faithful distributions and the pc-simple algorithm

We consider variable selection in high-dimensional linear models where the number of covariates greatly exceeds the sample size. We introduce the new concept of partial faithfulness and use it to infer associations between the covariates and the response. Under partial faithfulness, we develop a simplified version of the pc algorithm (Spirtes et al., 2000), which is computationally feasible even with thousands of covariates and provides consistent variable selection under conditions on the random design matrix that are of a different nature than coherence conditions for penalty-based approaches like the lasso. Simulations and application to real data show that our method is competitive compared to penalty-based approaches. We provide an efficient implementation of the algorithm in the R-package pcalg. Copyright 2010, Oxford University Press.

The Penile Perception Score: An Instrument Enabling Evaluation by Surgeons and Patient Self-Assessment After Hypospadias Repair

PURPOSE Studies of the outcome of hypospadias repair must document quality, including assessment of complications and appraisal of appearance. To our knowledge the Pediatric Penile Perception Score is the first validated instrument for the outcome assessment of hypospadias repair in prepubertal males by surgeons and patients. We validated the instrument for adult genitalia. MATERIALS AND METHODS Standardized photographic documentation was prepared for 19 men after hypospadias repair and 3 with normal genitalia after circumcision. This was sent to 21 urologists, who rated the outcome with a questionnaire comprising items on the penile meatus, glans, shaft skin and general appearance. Each item was rated with a 4-point Likert scale. The Penile Perception Score is a sum score of all items. Patients were asked to provide a self-assessment with the same instrument. RESULTS When calculated with the ICC and the rank correlation using Kendall W, concordance among urologist scores was fair and good (0.46 and 0.64, respectively, p <0.001). Instrument stability was 0.78, indicating good reproducibility. Using the Spearman rank correlation coefficient general appearance correlated well with single items, including the meatus (r = 0.93, p = 0.000), glans (r = 0.92, p = 0.000) and shaft skin (r = 0.89, p = 0.000). No significant differences were found between patient and urologist Penile Perception Scores. CONCLUSIONS The Penile Perception Score is a reliable instrument for urologist assessment and self-assessment of postpubertal genitalia after hypospadias repair. The instrument can be recommended for all age groups because it was previously validated for the pediatric population.

Understanding human functioning using graphical models

BackgroundFunctioning and disability are universal human experiences. However, our current understanding of functioning from a comprehensive perspective is limited. The development of the International Classification of Functioning, Disability and Health (ICF) on the one hand and recent developments in graphical modeling on the other hand might be combined and open the door to a more comprehensive understanding of human functioning. The objective of our paper therefore is to explore how graphical models can be used in the study of ICF data for a range of applications.MethodsWe show the applicability of graphical models on ICF data for different tasks: Visualization of the dependence structure of the data set, dimension reduction and comparison of subpopulations. Moreover, we further developed and applied recent findings in causal inference using graphical models to estimate bounds on intervention effects in an observational study with many variables and without knowing the underlying causal structure.ResultsIn each field, graphical models could be applied giving results of high face-validity. In particular, graphical models could be used for visualization of functioning in patients with spinal cord injury. The resulting graph consisted of several connected components which can be used for dimension reduction. Moreover, we found that the differences in the dependence structures between subpopulations were relevant and could be systematically analyzed using graphical models. Finally, when estimating bounds on causal effects of ICF categories on general health perceptions among patients with chronic health conditions, we found that the five ICF categories that showed the strongest effect were plausible.ConclusionsGraphical Models are a flexible tool and lend themselves for a wide range of applications. In particular, studies involving ICF data seem to be suited for analysis using graphical models.

Robustification of the PC-Algorithm for Directed Acyclic Graphs

The PC-algorithm was shown to be a powerful method for estimating the equivalence class of a potentially very high-dimensional acyclic directed graph (DAG) with the corresponding Gaussian distribution. Here we propose a computationally eficient robustification of the PC-algorithm and prove its consistency. Furthermore, we compare the robustified and standard version of the PC-algorithm on simulated data using the new corresponding R package pcalg.

Decomposition and Model Selection for Large Contingency Tables

Large contingency tables summarizing categorical variables arise in many areas. One example is in biology, where large numbers of biomarkers are cross-tabulated according to their discrete expression level. Interactions of the variables are of great interest and are generally studied with log-linear models. The structure of a log-linear model can be visually represented by a graph from which the conditional independence structure can then be easily read off. However, since the number of parameters in a saturated model grows exponentially in the number of variables, this generally comes with a heavy computational burden. Even if we restrict ourselves to models of lower-order interactions or other sparse structures, we are faced with the problem of a large number of cells which play the role of sample size. This is in sharp contrast to high-dimensional regression or classification procedures because, in addition to a high-dimensional parameter, we also have to deal with the analogue of a huge sample size. Furthermore, high-dimensional tables naturally feature a large number of sampling zeros which often leads to the nonexistence of the maximum likelihood estimate. We therefore present a decomposition approach, where we first divide the problem into several lower-dimensional problems and then combine these to form a global solution. Our methodology is computationally feasible for log-linear interaction models with many categorical variables each or some of them having many levels. We demonstrate the proposed method on simulated data and apply it to a bio-medical problem in cancer research.

Causal Structure Learning and Inference: A Selective Review

Abstract In this paper we give a review of recent causal inference methods. First, we discuss methods for causal structure learning from observational data when confounders are not present and have a close look at methods for exact identifiability. We then turn to methods which allow for a mix of observational and interventional data, where we also touch on active learning strategies. We also discuss methods which allow arbitrarily complex structures of hidden variables. Second, we present approaches for estimating the interventional distribution and causal effects given the (true or estimated) causal structure. We close with a note on available software and two examples on real data.