Van Der Laan Research Articles

Competitive equilibria in economies with multiple indivisible and multiple divisible commodities

In this paper we consider a general equilibrium model with a finite number of divisible and a finite number of indivisible commodities. In models with indivisibilities it is typically assumed that there is only one divisible good, which serves as money. The presence of money in the model is used to transfer the value of certain amounts of indivisible goods. For such economies with only one divisible commodity Danilov et al. showed the existence of a general equilibrium if the individual demands and supplies belong to a same class of discrete convexity. For economies with multiple divisible goods and money van der Laan et al. proved existence of a general equilibrium if the divisible goods are produced out of money using a linear production technology and no other producers are present in the model. In the model to be presented in this paper we consider an economy without production and with multiple divisible and multiple indivisible commodities. Convexity is replaced by pseudoconvexity, while the indivisible parts of individual demands should belong to some class of discrete convexity. One of the divisible commodities serves as money. Money is strictly desired by all consumers and there should be enough money present in the economy. To guarantee existence of a general equilibrium individual demands should be products of divisible and indivisible parts. In case there is no money, at least one linear production technology besides possibly other producers should be present in order to produce divisible goods.

The Role of Human HtrA1 in Arthritic Disease

Human HtrA1 belongs to a widely conserved family of serine proteases involved in various aspects of protein quality control and cell fate. Although HtrA1 has been implicated in the pathology of several diseases, its precise biological functions remain to be established. Through identification of potential HtrA1 targets, studies presented herein propose that within the context of arthritis pathology HtrA1 contributes to cartilage degradation. Elevated synovial HtrA1 levels were detected in fluids obtained from rheumatoid and osteoarthritis patients, with synovial fibroblasts identified as a major source of secreted HtrA1. Mass spectrometry analysis of potential HtrA1 substrates within synovial fluids identified fibronectin as a candidate target, and treatment of fibronectin with recombinant HtrA1 led to the generation of fibronectin-degradation products that may be involved in cartilage catabolism. Consistently, treatment of synovial fibroblasts with HtrA1 or HtrA1-generated fibronectin fragments resulted in the specific induction of matrix metalloprotease 1 and matrix metalloprotease 3 expression, suggesting that HtrA1 contributes to the destruction of extracellular matrix through both direct and indirect mechanisms.

Targeted Maximum Likelihood Learning

Suppose one observes a sample of independent and identically distributed observations from a particular data generating distribution. Suppose that one is concerned with estimation of a particular pathwise differentiable Euclidean parameter. A substitution estimator evaluating the parameter of a given likelihood based density estimator is typically too biased and might not even converge at the parametric rate: that is, the density estimator was targeted to be a good estimator of the density and might therefore result in a poor estimator of a particular smooth functional of the density. In this article we propose a one step (and, by iteration, k-th step) targeted maximum likelihood density estimator which involves 1) creating a hardest parametric submodel with parameter epsilon through the given density estimator with score equal to the efficient influence curve of the pathwise differentiable parameter at the density estimator, 2) estimating epsilon with the maximum likelihood estimator, and 3) defining a new density estimator as the corresponding update of the original density estimator. We show that iteration of this algorithm results in a targeted maximum likelihood density estimator which solves the efficient influence curve estimating equation and thereby yields a locally efficient estimator of the parameter of interest, under regularity conditions. In particular, we show that, if the parameter is linear and the model is convex, then the targeted maximum likelihood estimator is often achieved in the first step, and it results in a locally efficient estimator at an arbitrary (e.g., heavily misspecified) starting density.We also show that the targeted maximum likelihood estimators are now in full agreement with the locally efficient estimating function methodology as presented in Robins and Rotnitzky (1992) and van der Laan and Robins (2003), creating, in particular, algebraic equivalence between the double robust locally efficient estimators using the targeted maximum likelihood estimators as an estimate of its nuisance parameters, and targeted maximum likelihood estimators. In addition, it is argued that the targeted MLE has various advantages relative to the current estimating function based approach. We proceed by providing data driven methodologies to select the initial density estimator for the targeted MLE, thereby providing data adaptive targeted maximum likelihood estimation methodology. We illustrate the method with various worked out examples.

Quantile-Function Based Null Distribution in Resampling Based Multiple Testing

Simultaneously testing a collection of null hypotheses about a data generating distribution based on a sample of independent and identically distributed observations is a fundamental and important statistical problem involving many applications. Methods based on marginal null distributions (i.e., marginal p-values) are attractive since the marginal p-values can be based on a user supplied choice of marginal null distributions and they are computationally trivial, but they, by necessity, are known to either be conservative or to rely on assumptions about the dependence structure between the test-statistics. Re-sampling based multiple testing (Westfall and Young, 1993) involves sampling from a joint null distribution of the test-statistics, and controlling (possibly in a, for example, step-down fashion) the user supplied type-I error rate under this joint null distribution for the test-statistics. A generally asymptotically valid null distribution avoiding the need for the subset pivotality condition for the vector of test-statistics was proposed in Pollard, van der Laan (2003) for null hypotheses about general real valued parameters. This null distribution was generalized in Dudoit, vanderLaan, Pollard (2004) to general null hypotheses and test-statistics. In ongoing recent work van der Laan, Hubbard (2005), we propose a new generally asymptotically valid null distribution for the test-statistics and a corresponding bootstrap estimate, whose marginal distributions are user supplied, and can thus be set equal to the (most powerful) marginal null distributions one would use in univariate testing to obtain a p-value. Previous proposed null distributions either relied on a restrictive subset pivotality condition (Westfall and Young) or did not guarantee this latter property (Dudoit, vanderLaan, Pollard, 2004). It is argued and illustrated that the resulting new re-sampling based multiple testing methods provide more accurate control of the wished Type-I error in finite samples and are more powerful. We establish formal results and investigate the practical performance of this methodology in a simulation and data analysis.

Application of a Variable Importance Measure Method

Van der Laan (2005) proposed a targeted method used to construct variable importance measures coupled with respective statistical inference. This technique involves determining the importance of a variable in predicting an outcome. This method can be applied as inverse probability of treatment weighted (IPTW) or double robust inverse probability of treatment weighted (DR-IPTW) estimators. The variance and respective p-value of the estimate are calculated by estimating the influence curve. This article applies the Van der Laan (2005) variable importance measures and corresponding inference to HIV-1 sequence data. In this application, the method is targeted at every codon position. In this data application, protease and reverse transcriptase codon positions on the HIV-1 strand are assessed to determine their respective variable importance, with respect to an outcome of viral replication capacity. We estimate the DR-IPTW W-adjusted variable importance measure for a specified set of potential effect modifiers W. In addition, simulations were performed on two separate datasets to examine the DR-IPTW estimator.

A Companion to the works of Friedrich Schiller

Friedrich Schiller is not merely one of Germany's foremost poets. He is also one of the major German contributors to world literature. The undying words he gave to characters such as Marquis Posa in Don Carlos and Wilhelm Tell in the eponymous drama continue to underscore the need for human freedom. Schiller cultivated hope in the actualization of moral knowledge through aesthetic education and critical reflection, leading to his ideal of a more humane humanity. At the same time, he was fully cognizant of the problems that attend various forms of idealism. Yet for Schiller, ultimately, love remains the gravitational center of the universe and of human existence, and beyond life and death joy prevails. This collection of cutting-edge essays by some of the world's leading Schiller experts constitutes a milestone in scholarship. It includes in-depth discussions of the writer's major dramatic and poetic works, his essays on aesthetics, and his activities as historian, anthropologist, and physiologist, as well as of his relation to the ancients and of Schiller reception in 20th-century Germany. Contributors: Steven D. Martinson, Walter Hinderer, David Pugh, Otto Dann, Werner von Stransky-Stranka-Greifenfels, J. M. van der Laan, Rolf-Peter Janz, Lesley Sharpe, Norbert Oellers, Dieter Borchmeyer, Karl S. Guthke, Wulf Koepke. Steven D. Martinson is Professor of German at the University of Arizona.

Decoding Serological Response to Candida Cell Wall Immunome into Novel Diagnostic, Prognostic, and Therapeutic Candidates for Systemic Candidiasis by Proteomic and Bioinformatic Analyses

In an effort to bring novel diagnostic and prognostic biomarkers or even potential targets for vaccine design for systemic candidiasis (SC) into the open, a systematic proteomic approach coupled with bioinformatic analysis was used to decode the serological response to Candida wall immunome in SC patients. Serum levels of IgG antibodies against Candida wall-associated proteins (proteins secreted from protoplasts in active wall regeneration, separated by two-dimensional gel electrophoresis, and identified by mass spectrometry) were measured in 45 SC patients, 57 non-SC patients, and 61 healthy subjects by Western blotting. Two-way hierarchical clustering and principal component analysis of their serum anti-Candida wall antibody expression patterns discriminated SC patients from controls and highlighted the heterogeneity of their expression profiles. Multivariate logistic regression models demonstrated that high levels of antibodies against glucan 1,3-beta-glucosidase (Bgl2p) and the anti-wall phosphoglycerate kinase antibody seropositivity were the only independent predictors of SC. Receiver operating characteristic curve analysis revealed no difference between their combined evaluation and measurement of anti-Bgl2p antibodies alone. In a logistic regression model adjusted for known prognostic factors for mortality, SC patients with high anti-Bgl2p antibody levels or a positive anti-wall enolase antibody status, which correlated with each other, had a reduced 2-month risk of death. After controlling for each other, only the seropositivity for anti-wall enolase antibodies was an independent predictor of a lower risk of fatality, supporting that these mediated the protective effect. No association between serum anti-cytoplasmic enolase antibody levels and outcomes was established, suggesting a specific mechanism of enolase processing during wall biogenesis. We conclude that serum anti-Bgl2p antibodies are a novel accurate diagnostic biomarker for SC and that, at high levels, they may provide protection by modulating the anti-wall enolase antibody response. Furthermore serum anti-wall enolase antibodies are a new prognostic indicator for SC and confer protection against it. Bgl2p and wall-associated enolase could be valuable candidates for future vaccine development.

Issues of Processing and Multiple Testing of SELDI-TOF MS Proteomic Data

A new data filtering method for SELDI-TOF MS proteomic spectra data is described. We examined technical repeats (2 per subject) of intensity versus m/z (mass/charge) of bone marrow cell lysate for two groups of childhood leukemia patients: acute myeloid leukemia (AML) and acute lymphoblastic leukemia (ALL). As others have noted, the type of data processing as well as experimental variability can have a disproportionate impact on the list of "interesting'' proteins (see Baggerly et al. (2004)). We propose a list of processing and multiple testing techniques to correct for 1) background drift; 2) filtering using smooth regression and cross-validated bandwidth selection; 3) peak finding; and 4) methods to correct for multiple testing (van der Laan et al. (2005)). The result is a list of proteins (indexed by m/z) where average expression is significantly different among disease (or treatment, etc.) groups. The procedures are intended to provide a sensible and statistically driven algorithm, which we argue provides a list of proteins that have a significant difference in expression. Given no sources of unmeasured bias (such as confounding of experimental conditions with disease status), proteins found to be statistically significant using this technique have a low probability of being false positives.

Covalently Dimerized SecA Is Functional in Protein Translocation

The ATPase SecA provides the driving force for the transport of secretory proteins across the cytoplasmic membrane of Escherichia coli. SecA exists as a dimer in solution, but the exact oligomeric state of SecA during membrane binding and preprotein translocation is a topic of debate. To study the requirements of oligomeric changes in SecA during protein translocation, a non-dissociable SecA dimer was formed by oxidation of the carboxyl-terminal cysteines. The cross-linked SecA dimer interacts with the SecYEG complex with a similar stoichiometry as non-cross-linked SecA. Cross-linking reversibly disrupts the SecB binding site on SecA. However, in the absence of SecB, the activity of the disulfide-bonded SecA dimer is indistinguishable from wild-type SecA. Moreover, SecYEG binding stabilizes a cold sodium dodecylsulfate-resistant dimeric state of SecA. The results demonstrate that dissociation of the SecA dimer is not an essential feature of the protein translocation reaction.

An Adjustment to Improve the Bivariate Survivor Function Repaired NPMLE

We recently proposed a representation of the bivariate survivor function as a mapping of the hazard function for truncated failure time variates. The representation led to a class of estimators that includes van der Laan's repaired nonparametric maximum likelihood estimator (NPMLE) as an important special case. We proposed a Greenwood-like variance estimator for the repaired NPMLE but found somewhat poor agreement between the empirical variance estimates and these analytic estimates for the sample sizes and bandwidths considered in our simulation study. The simulation results also confirmed those of others in showing slightly inferior performance for the repaired NPMLE compared to other competing estimators as well as a sensitivity to bandwidth choice in moderate sized samples. Despite its attractive asymptotic properties, the repaired NPMLE has drawbacks that hinder its practical application. This paper presents a modification of the repaired NPMLE that improves its performance in moderate sized samples and renders it less sensitive to the choice of bandwidth. Along with this modified estimator, more extensive simulation studies of the repaired NPMLE and Greenwood-like variance estimates are presented. The methods are then applied to a real data example.

An inverse-probability-weighted approach to estimation of the bivariate survival function under left-truncation and right-censoring

In this note, we consider estimating the bivariate survival function when both survival times are subject to random left truncation and one of the survival times is subject to random right censoring. Motivated by Satten and Datta [2001. The Kaplan–Meier estimator as an inverse-probability-of-censoring weighted average. Amer. Statist. 55, 207–210], we propose an inverse-probability-weighted (IPW) estimator. It involves simultaneous estimation of the bivariate survival function of the truncation variables and that of the censoring variable and the truncation variable of the uncensored components. We prove that (i) when there is no censoring, the IPW estimator reduces to NPMLE of van der Laan [1996a. Nonparametric estimation of the bivariate survival function with truncated data. J. Multivariate Anal. 58, 107–131] and (ii) when there is random left truncation and right censoring on only one of the components and the other component is always observed, the IPW estimator reduces to the estimator of Gijbels and Gürler [1998. Covariance function of a bivariate distribution function estimator for left truncated and right censored data. Statist. Sin. 1219–1232]. Based on Theorem 3.1 of van der Laan [1996a. Nonparametric estimation of the bivariate survival function with truncated data. J. Multivariate Anal. 58, 107–131, 1996b. Efficient estimation of the bivariate censoring model and repairing NPMLE. Ann. Statist. 24, 596–627], we prove that the IPW estimator is consistent under certain conditions. Finally, we examine the finite sample performance of the IPW estimator in some simulation studies. For the special case that censoring time is independent of truncation time, a simulation study is conducted to compare the performances of the IPW estimator against that of the estimator proposed by van der Laan [1996a. Nonparametric estimation of the bivariate survival function with truncated data. J. Multivariate Anal. 58, 107–131, 1996b. Efficient estimation of the bivariate censoring model and repairing NPMLE. Ann. Statist. 24, 596–627]. For the special case (i), a simulation study is conducted to compare the performances of the IPW estimator against that of the estimator proposed by Huang et al. (2001. Nonnparametric estimation of marginal distributions under bivariate truncation with application to testing for age-of-onset application. Statist. Sin. 11, 1047–1068).

Temperature dependence of the magnetocrystalline anisotropy energy and projected microscopic magnetic moments in epitaxialCrO2films

Soft x-ray magnetic circular dichroism spectra and in situ element specific hysteresis loops of epitaxially grown $\mathrm{Cr}{\mathrm{O}}_{2}$ thin films have been investigated in the temperature range from $25\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}330\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ for two different crystallographic projections. The quantitative temperature dependence of the microscopic magnetic moments (spin, orbital, and magnetic dipole term) and the magnetocrystalline anisotropy energy give strong evidence for the validity of the models by Bruno and by van der Laan, which describe the generation of the orbital moment and its relation to the magnetic anisotropy energy.

Empirical Bayes and Resampling Based Multiple Testing Procedure Controlling Tail Probability of the Proportion of False Positives.

Simultaneously testing a collection of null hypotheses about a data generating distribution based on a sample of independent and identically distributed observations is a fundamental and important statistical problem involving many applications. In this article we propose a new re-sampling based multiple testing procedure asymptotically controlling the probability that the proportion of false positives among the set of rejections exceeds q at level alpha, where q and alpha are user supplied numbers. The procedure involves 1) specifying a conditional distribution for a guessed set of true null hypotheses, given the data, which asymptotically is degenerate at the true set of null hypotheses, and 2) specifying a generally valid null distribution for the vector of test-statistics proposed in Pollard & van der Laan (2003), and generalized in our subsequent article Dudoit, van der Laan, & Pollard (2004), van der Laan, Dudoit, & Pollard (2004), and van der Laan, Dudoit, & Pollard (2004b). Ingredient 1) is established by fitting the empirical Bayes two component mixture model (Efron (2001b)) to the data to obtain an upper bound for marginal posterior probabilities of the null being true, given the data. We establish the finite sample rational behind our proposal, and prove that this new multiple testing procedure asymptotically controls the wished tail probability for the proportion of false positives under general data generating distributions. In addition, we provide simulation studies establishing that this method is generally more powerful in finite samples than our previously proposed augmentation multiple testing procedure (van der Laan, Dudoit, & Pollard (2004b)) and competing procedures from the literature. Finally, we illustrate our methodology with a data analysis.

High-dimensional data: p >> n in mathematical statistics and bio-medical applications

High-dimensional data: p >> n in mathematical statistics and bio-medical applications

Multiple Testing and Data Adaptive Regression: An Application to HIV-1 Sequence Data.

Analysis of viral strand sequence data and viral replication capacity could potentially lead to biological insights regarding the replication ability of HIV-1. Determining specific target codons on the viral strand will facilitate the manufacturing of target-specific antiretrovirals. Various algorithmic and analysis techniques can be applied to this application. In this paper, we apply two techniques to a data set consisting of 317 patients, each with 282 sequenced protease and reverse transcriptase codons. The first application is recently developed multiple testing procedures to find codons which have significant univariate associations with the replication capacity of the virus. A single-step multiple testing procedure (Pollard and van der Laan 2003) method was used to control the family wise error rate (FWER) at the five percent alpha level as well as the application of augmentation multiple testing procedures to control the generalized family wise error (gFWER) or the tail probability of the proportion of false positives (TPPFP). We also applied a data adaptive multiple regression algorithm to obtain a prediction of viral replication capacity based on an entire mutant/non-mutant sequence profile. This is a loss-based, cross-validated Deletion/Substitution/Addition regression algorithm (Sinisi and van der Laan 2004), which builds candidate estimators in the prediction of a univariate outcome by minimizing an empirical risk. These methods are two separate techniques with distinct goals used to analyze this structure of viral data.

Double robust estimation in longitudinal marginal structural models

In this article we consider estimation of causal parameters in a marginal structural model for the discrete intensity of the treatment specific counting process (e.g. hazard of a treatment specific survival time) based on longitudinal observational data on treatment, covariates and survival. We define three estimators: the inverse probability of treatment weighted (IPTW) estimator, the maximum likelihood estimator (MLE), and a double robust (DR) estimator. The DR estimator is obtained by following a general methodology for constructing double robust estimating functions in censored data models as described in van der Laan and Robins (Unified Methods for Censored Longitudinal Data and Causality, 2002). The double-robust estimator is consistent and asymptotically linear when either the treatment mechanism or the partial likelihood of the observed data is consistently estimated. We illustrate the superiority of the DR estimator relative to the IPTW and ML estimators in a simulation study. The proposed methodology is also applied to estimate the causal effect of exercise on physical functioning in a longitudinal study of seniors in Sonoma County.

Book Review: Unified Methods for Censored Longitudinal Data and Causality. By Mark J. van der Laan and James M. Robins

Book Review: Unified Methods for Censored Longitudinal Data and Causality. By Mark J. van der Laan and James M. Robins

Rapid Evolution of β-Glucuronidase Specificity by Saturation Mutagenesis of an Active Site Loop

Protein engineers have widely adopted directed evolution as a design algorithm, but practitioners have not come to a consensus about the best method to evolve protein molecular recognition. We previously used DNA shuffling to direct the evolution of Escherichia coli beta-glucuronidase (GUS) variants with increased beta-galactosidase activity. Epistatic (synergistic) mutations in amino acids 557, 566, and 568, which are part of an active site loop, were identified in that experiment (Matsumura, I., and Ellington, A. D. (2001) J. Mol. Biol. 305, 331-339). Here we show that site saturation mutagenesis of these residues, overexpression of the resulting library in E. coli, and high throughput screening led to the rapid evolution of clones exhibiting increased activity in reactions with p-nitrophenyl-beta-d-xylopyranoside (pNP-xyl). The xylosidase activities of the 14 fittest clones were 30-fold higher on average than that of the wild-type GUS. The 14 corresponding plasmids were pooled, amplified by long PCR, self-ligated with T4 DNA ligase, and transformed into E. coli. Thirteen clones exhibiting an average of 80-fold improvement in xylosidase activity were isolated in a second round of screening. One of the evolved proteins exhibited a approximately 200-fold improvement over the wild type in reactivity (k(cat)/K(m)) with pNP-xyl, with a 290,000-fold inversion of specificity. Sequence analysis of the 13 round 2 isolates suggested that all were products of intermolecular recombination events that occurred during whole plasmid PCR. Further rounds of evolution using DNA shuffling and staggered extension process (StEP) resulted in modest improvement. These results underscore the importance of epistatic interactions and demonstrate that they can be optimized through variations of the facile whole plasmid PCR technique.

Hazard-Based Nonparametric Survivor Function Estimation

SummaryA representation is developed that expresses the bivariate survivor function as a function of the hazard function for truncated failure time variables. This leads to a class of nonparametric survivor function estimators that avoid negative mass. The transformation from hazard function to survivor function is weakly continuous and compact differentiable, so that such properties as strong consistency, weak convergence to a Gaussian process and bootstrap applicability for a hazard function estimator are inherited by the corresponding survivor function estimator. The set of point mass assignments for a survivor function estimator is readily obtained by using a simple matrix calculation on the set of hazard rate estimators. Special cases arise from a simple empirical hazard rate estimator, and from an empirical hazard rate estimator following the redistribution of singly censored observations within strips. The latter is shown to equal van der Laan's repaired nonparametric maximum likelihood estimator, for which a Greenwood-like variance estimator is given. Simulation studies are presented to compare the moderate sample performance of various nonparametric survivor function estimators.

Deletion/Substitution/Addition Algorithm in Learning with Applications in Genomics

van der Laan and Dudoit (2003) provide a road map for estimation and performance assessment where a parameter of interest is defined as the risk minimizer for a suitable loss function and candidate estimators are generated using a loss function. After briefly reviewing this approach, this article proposes a general deletion/substitution/addition algorithm for minimizing, over subsets of variables (e.g., basis functions), the empirical risk of subset-specific estimators of the parameter of interest. This algorithm provides us with a new class of loss-based cross-validated algorithms in prediction of univariate outcomes, which can be extended to handle multivariate outcomes, conditional density and hazard estimation, and censored outcomes such as survival. In the context of regression, using polynomial basis functions, we study the properties of the deletion/substitution/addition algorithm in simulations and apply the method to detect transcription factor binding sites in yeast gene expression experiments.