An alternative foundation for the planning and evaluation of linkage analysis. II. Implications for multiple test adjustments

The 'multiple testing problem' currently bedevils the field of genetic epidemiology. Briefly stated, this problem arises with the performance of more than one statistical test and results in an increased probability of committing at least one Type I error. The accepted/conventional way of dealing with this problem is based on the classical Neyman-Pearson statistical paradigm and involves adjusting one's error probabilities. This adjustment is, however, problematic because in the process of doing that, one is also adjusting one's measure of evidence. Investigators have actually become wary of looking at their data, for fear of having to adjust the strength of the evidence they observed at a given locus on the genome every time they conduct an additional test. In a companion paper in this issue (Strug & Hodge I), we presented an alternative statistical paradigm, the 'evidential paradigm', to be used when planning and evaluating linkage studies. The evidential paradigm uses the lod score as the measure of evidence (as opposed to a p value), and provides new, alternatively defined error probabilities (alternative to Type I and Type II error rates). We showed how this paradigm separates or decouples the two concepts of error probabilities and strength of the evidence. In the current paper we apply the evidential paradigm to the multiple testing problem - specifically, multiple testing in the context of linkage analysis. We advocate using the lod score as the sole measure of the strength of evidence; we then derive the corresponding probabilities of being misled by the data under different multiple testing scenarios. We distinguish two situations: performing multiple tests of a single hypothesis, vs. performing a single test of multiple hypotheses. For the first situation the probability of being misled remains small regardless of the number of times one tests the single hypothesis, as we show. For the second situation, we provide a rigorous argument outlining how replication samples themselves (analyzed in conjunction with the original sample) constitute appropriate adjustments for conducting multiple hypothesis tests on a data set.     

An age-dependent stochastic model of population growth

A stochastic model of population growth is treated using the Bellman-Harris theory of agedependent stochastic branching processes. The probability distribution for the population size at any time and the expectation are obtained when it is assumed that there is probability (1−σ), 0≤σ<1, of the organism dividing into two at the end of its lifetime, and probability σ that division will not take place.     

A family of glutamatergic,excitatory channel types at the crayfish neuromuscular junction

Summary Outside-out patches from membrane of muscles of crayfish (Austropotamobius torrentium) were excised, and L-glutamate (glu) was applied to these patches in pulses of different duration, performing a concentration step within about 0.2 ms. While a uniform population of cationic channels is seen in equilibrium applications of glu, four kinetically different channel types were revealed by the pulse applications of glu. All these channel types had the same single channel conductance and durations of elementary short single channel openings and closings, and they thus form a family of channels. Type I, incompletely desensitizing channels reacted to a pulse of 10 mM glu with a peak open probability of 0.7 within 0.3 ms. Thereafter open probability decayed with a time constant of desensitization of about 5 ms, reaching a plateau of about 1/20 peak probability which was maintained as long as 10 mM glu were present. The peak probabilities of channel opening were proportional to approximately power 2.5 of the glu concentration, for low concentrations. Type II, completely desensitizing channels also were activated very rapidly by glu pulses, but their time constant of desensitization was 1–2 ms, and no channel openings were observed after more than 10 ms presence of a high glu concentration. The peak probabilities of channel opening rose with about the 5th power of glu concentration (for low concentrations). Type III, non-desensitizing channels, were observed relatively rarely. They were activated much more slowly and reached much lower probabilities of opening than type I and II channels. They did not show appreciable desensitization. Type IV, short-opening channels, develop sometimes from type I channels while recording, and may revert to the type I. Type IV channels show an additional open time component of 0.08 ms average duration, and a relatively long additional closed time of on average 1.3 ms. In addition to channel measurements, distributions of amplitudes and time courses of macroscopic quantal currents were determined. It is discussed in which way the different channel types may contribute to the quantal currents.     

Setting an optimal α that minimizes errors in null hypothesis significance tests

Null hypothesis significance testing has been under attack in recent years, partly owing to the arbitrary nature of setting α (the decision-making threshold and probability of Type I error) at a constant value, usually 0.05. If the goal of null hypothesis testing is to present conclusions in which we have the highest possible confidence, then the only logical decision-making threshold is the value that minimizes the probability (or occasionally, cost) of making errors. Setting α to minimize the combination of Type I and Type II error at a critical effect size can easily be accomplished for traditional statistical tests by calculating the α associated with the minimum average of α and β at the critical effect size. This technique also has the flexibility to incorporate prior probabilities of null and alternate hypotheses and/or relative costs of Type I and Type II errors, if known. Using an optimal α results in stronger scientific inferences because it estimates and minimizes both Type I errors and relevant Type II errors for a test. It also results in greater transparency concerning assumptions about relevant effect size(s) and the relative costs of Type I and II errors. By contrast, the use of α = 0.05 results in arbitrary decisions about what effect sizes will likely be considered significant, if real, and results in arbitrary amounts of Type II error for meaningful potential effect sizes. We cannot identify a rationale for continuing to arbitrarily use α = 0.05 for null hypothesis significance tests in any field, when it is possible to determine an optimal α.     

Optimal lineage principle for age-structured populations

We present a formulation of branching and aging processes that allows age distributions along lineages to be studied within populations, and provides a new interpretation of classical results in the theory of aging. We establish a variational principle for the stable age distribution along lineages. Using this optimal lineage principle, we show that the response of a population's growth rate to age-specific changes in mortality and fecundity--a key quantity that was first calculated by Hamilton--is given directly by the age distribution along lineages. We apply our method also to the Bellman-Harris process, in which both mother and progeny are rejuvenated at each reproduction event, and show that this process can be mapped to the classic aging process such that age statistics in the population and along lineages are identical. Our approach provides both a theoretical framework for understanding the statistics of aging in a population, and a new method of analytical calculations for populations with age structure. We discuss generalizations for populations with multiple phenotypes, and more complex aging processes. We also provide a first experimental test of our theory applied to bacterial populations growing in a microfluidics device.     

Probability distribution of molecular evolutionary trees: A new method of phylogenetic inference

A new method is presented for inferring evolutionary trees using nucleotide sequence data. The birth-death process is used as a model of speciation and extinction to specify the prior distribution of phylogenies and branching times. Nucleotide substitution is modeled by a continuous-time Markov process. Parameters of the branching model and the substitution model are estimated by maximum likelihood. The posterior probabilities of different phylogenies are calculated and the phylogeny with the highest posterior probability is chosen as the best estimate of the evolutionary relationship among species. We refer to this as the maximum posterior probability (MAP) tree. The posterior probability provides a natural measure of the reliability of the estimated phylogeny. Two example data sets are analyzed to infer the phylogenetic relationship of human, chimpanzee, gorilla, and orangutan. The best trees estimated by the new method are the same as those from the maximum likelihood analysis of separate topologies, but the posterior probabilities are quite different from the bootstrap proportions. The results of the method are found to be insensitive to changes in the rate parameter of the branching process. Correspondence to: Z. Yang     

Production of a unique antibody specific for membrane ruffles and its use to characterize the behavior of two distinct types of ruffles

I have produced a new monoclonal antibody, YF-169, against membrane ruffle specific 55-kD protein. YF-169 stained membrane ruffles of chick embryo fibroblasts so definitely that it enabled clear and reliable analyses of membrane ruffles. Fibroblasts organized two distinct types of membrane ruffles. One type of the ruffles were transiently formed in serum-starved cells (Type I) when stimulated by serum or platelet- derived growth factor. After spontaneous degradation of Type I ruffles, the other type of ruffles containing many microspikes were gradually organized at leading edges (Type II). The formation of Type I ruffles was not affected by either nocodazole, a microtubule-disrupting drug, or taxol, a microtubule-stabilizing reagent. However, Type II ruffles were entirely destroyed not only by nocodazole but also by taxol, suggesting that regulated organization of microtubule network is important to maintain Type II ruffles. H8, a protein kinase inhibitor prevented the spontaneous degradation of Type I ruffles and also reduced the destructive effect of nocodazole on Type II ruffles without affecting microtubule-disrupting activity. Protein kinases may be involved in the degradation processes of both types of ruffles. W7, a calmodulin antagonist, strongly inhibited Type I ruffle formation and completely destroyed Type II ruffles. W7 was also found to induce a remarkable change of 55-kD protein localization. After degradation of Type II ruffles, most of 55-kD protein was incorporated into newly formed unusual thick fibers. These results suggest that regulated organization of microtubule network is not necessary to form Type I ruffles but is important to maintain Type II ruffles, while calmodulin function is essential for both types of membrane ruffles.     

An alternative foundation for the planning and evaluation of linkage analysis. I. Decoupling "error probabilities" from "measures of evidence"

The lod score, which is based on the likelihood ratio (LR), is central to linkage analysis. Users interpret lods by translating them into standard statistical concepts such as p values, alpha levels and power. An alternative statistical paradigm, the Evidential Framework, in contrast, works directly with the LR. A key feature of this paradigm is that it decouples error probabilities from measures of evidence. We describe the philosophy behind and the operating characteristics of this paradigm--based on new, alternatively-defined error probabilities. We then apply this approach to linkage studies of a genetic trait for: I. fully informative gametes, II. double backcross sibling pairs, and III. nuclear families. We consider complete and incomplete penetrance for the disease model, as well as using an incorrect penetrance. We calculate the error probabilities (exactly for situations I and II, via simulation for III), over a range of recombination fractions, sample sizes, and linkage criteria. We show how to choose linkage criteria and plan linkage studies, such that the probabilities of being misled by the data (i.e. concluding either that there is strong evidence favouring linkage when there is no linkage, or that there is strong evidence against linkage when there is linkage) are low, and the probability of observing strong evidence in favour of the truth is high. We lay the groundwork for applying this paradigm in genetic studies and for understanding its implications for multiple tests.     

Insulin-like growth factor (IGF)/somatomedin receptor subtypes: structure, function, and relationships to insulin receptors and IGF carrier proteins

The insulin-like growth factors IGF-I and IGF-II are mitogenic polypeptides with a high degree of chemical homology. Two distinct subtypes of receptors for the IGFs have been identified on the basis of structure and binding specificity. Type I IGF receptors bind IGF-I with equal or greater affinity than IGF-II, and also bind insulin with a low but definite affinity. They are structurally homologous to insulin receptors, containing disulfide-linked a-subunits that bind the peptides and beta-subunits that have intrinsic tyrosine-specific kinase activity. Type II IGF receptors typically bind IGF-II with greater affinity than IGF-I, and do not interact with insulin. They consist of a single polypeptide and lack tyrosine kinase activity. Because of the extensive cross-reactivity of IGF-I and IGF-II with both type I and type II receptors, we believe that potentially either receptor may mediate the biological responses of either peptide. Type I IGF receptors have been shown to mediate the mitogenic effects of the IGFs in some cell types. Whether type II IGF receptors mediate the same or different functions remains to be elucidated.     

Direct studies of dikaryotization in Schizophyllum commune

Compatible matings of Schizophyllum commune were performed on glucose-peptone-yeast extract medium appended with gelatin (18%) and studied by phase contrast microscopy during nuclear migration. Three categories of nuclear migration were observed. Type I involved a pulsatile jerking of the entire cytoplasmic contents of the hypha, changed direction periodically, and, during periods of cytoplasmic tranquility, the nucleus continued to migrate. Type II A migration of nuclei occurred in the absence of visible cytoplasmic flow. Both Type I and Type II A nuclear movements exceeded the hyphal growth rate by 10--20-fold. Type II B nuclear migration also occurred in the absence of visible cytoplasmic flow and the velocity was within the range of the hyphal growth rate. No specific organelles that were detected either directed or facilitated Type II A or Type II B nuclear movements. The nucleolus could either lead or trail relative to the direction of nuclear movement. Nuclear migration can be attributed to both cytoplasmic flow and self motility, depending upon the particular regions of the migration hypha in which it occurs.     

Dose-finding based on efficacy-toxicity trade-offs

We present an adaptive Bayesian method for dose-finding in phase I/II clinical trials based on trade-offs between the probabilities of treatment efficacy and toxicity. The method accommodates either trinary or bivariate binary outcomes, as well as efficacy probabilities that possibly are nonmonotone in dose. Doses are selected for successive patient cohorts based on a set of efficacy-toxicity trade-off contours that partition the two-dimensional outcome probability domain. Priors are established by solving for hyperparameters that optimize the fit of the model to elicited mean outcome probabilities. For trinary outcomes, the new algorithm is compared to the method of Thall and Russell (1998, Biometrics 54, 251-264) by application to a trial of rapid treatment for ischemic stroke. The bivariate binary outcome case is illustrated by a trial of graft-versus-host disease treatment in allogeneic bone marrow transplantation. Computer simulations show that, under a wide rage of dose-outcome scenarios, the new method has high probabilities of making correct decisions and treats most patients at doses with desirable efficacy-toxicity trade-offs.     

The probability of treatment induced drug resistance

We propose a discrete time branching process to model the appearance of drug resistance under treatment. Under our assumptions at every discrete time a pathogen may die with probability 1−p or divide in two with probability p. Each newborn pathogen is drug resistant with probability μ. We start with N drug sensitive pathogens and with no drug resistant pathogens. We declare the treatment successful if all pathogens are eradicated before drug resistance appears. The model predicts that success is possible only if p<1/2. Even in this case the probability of success decreases exponentially with the parameter m=μN. In particular, even with a very potent drug (i.e. p very small) drug resistance is likely if m is large.     

Comparison of Coding Capabilities of Type I and Type II Neurons

We consider the dependence of information transfer by neurons on the Type I vs. Type II classification of their dynamics. Our computational study is based on Type I and II implementations of the Morris-Lecar model. It mainly concerns neurons, such as those in the auditory or electrosensory system, which encode band-limited amplitude modulations of a periodic carrier signal, and which fire at random cycles yet preferred phases of this carrier. We first show that the Morris-Lecar model with additive broadband noise ("synaptic noise") can exhibit such firing patterns with either Type I or II dynamics, with or without amplitude modulations of the carrier. We then compare the encoding of band-limited random amplitude modulations for both dynamical types. The comparison relies on a parameter calibration that closely matches firing rates for both models across a range of parameters. In the absence of synaptic noise, Type I performs slightly better than Type II, and its performance is optimal for perithreshold signals. However, Type II performs well over a slightly larger range of inputs, and this range lies mostly in the subthreshold region. Further, Type II performs marginally better than Type I when synaptic noise, which yields more realistic baseline firing patterns, is present in both models. These results are discussed in terms of the tuning and phase locking properties of the models with deterministic and stochastic inputs.     

Conversion of specific to nonspecific cytotoxic T lymphocytes

The type of cytotoxic T lymphocyte (CTL) generated during a mixed leukocyte culture has been shown to depend on the purity of interleukin 2 (IL 2) used to stimulate growth. Antigen-specific CTL requiring both antigen and IL 2 to proliferate or express cytotoxicity (designated Type I in this work) are generated and maintained with highly purified IL 2. In the presence of IL 2 alone, they persist in a quiescent, noncytotoxic state, and on its removal they rapidly die. A second type of CTL (Type II), of nonspecific cytotoxicity, and dependent only on IL 2 for growth, is generated by exposure to an impure lymphokine preparation containing IL 2. Type I cells are T lymphocytes which are nongranular and nonadherent, whereas Type II cells are larger, adhere to plastic, and contain many granules. Cloned Type I cells are converted to Type II under three conditions: by low levels of IL 2 in the presence of a crude lymphokine preparation; by high levels of IL 2 in the presence of antigen; or by high levels of IL 2 in the presence of the phorbol diester PMA. Conversion results from an effect of the growth conditions on individual cells, and not from selection of a minor population.     

Stem Cell-Like Gene Expression in Ovarian Cancer Predicts Type II Subtype and Prognosis

Although ovarian cancer is often initially chemotherapy-sensitive, the vast majority of tumors eventually relapse and patients die of increasingly aggressive disease. Cancer stem cells are believed to have properties that allow them to survive therapy and may drive recurrent tumor growth. Cancer stem cells or cancer-initiating cells are a rare cell population and difficult to isolate experimentally. Genes that are expressed by stem cells may characterize a subset of less differentiated tumors and aid in prognostic classification of ovarian cancer. The purpose of this study was the genomic identification and characterization of a subtype of ovarian cancer that has stem cell-like gene expression. Using human and mouse gene signatures of embryonic, adult, or cancer stem cells, we performed an unsupervised bipartition class discovery on expression profiles from 145 serous ovarian tumors to identify a stem-like and more differentiated subgroup. Subtypes were reproducible and were further characterized in four independent, heterogeneous ovarian cancer datasets. We identified a stem-like subtype characterized by a 51-gene signature, which is significantly enriched in tumors with properties of Type II ovarian cancer; high grade, serous tumors, and poor survival. Conversely, the differentiated tumors share properties with Type I, including lower grade and mixed histological subtypes. The stem cell-like signature was prognostic within high-stage serous ovarian cancer, classifying a small subset of high-stage tumors with better prognosis, in the differentiated subtype. In multivariate models that adjusted for common clinical factors (including grade, stage, age), the subtype classification was still a significant predictor of relapse. The prognostic stem-like gene signature yields new insights into prognostic differences in ovarian cancer, provides a genomic context for defining Type I/II subtypes, and potential gene targets which following further validation may be valuable in the clinical management or treatment of ovarian cancer.     

A Note on Testing Hypotheses about Trimmed Means

A well known result is that skewness can cause problems when testing hypotheses about measures of location, particulary when a one-sided test is of interest. Wilcox (1994) reports both theoretical and simulation results showing that when testing hypotheses about trimmed means, control over Type I error probabilities can be substantially better than methods for means. However, at least in some situations, control over the probability of a Type I error might still be judged to be inadequate. One way of adressing this concern is to combine trimmed means with the bootsrap method advocated by Westfall and Yuong (1993). This note reports simulation results indicating that there are situations where substantial improvements over Type I error probabilities are indeed obtained.     

HGF-Induced Tubulogenesis and Branching of Epithelial Cells Is Modulated by Extracellular Matrix and TGF-β

Beginning with the observation that hepatocyte growth factor (HGF) induces the formation of branching tubular structures in Madin-Darby canine kidney (MDCK) cells cultured in Type I collagen gels but not in basement membrane Matrigel, we examined the individual components within this complex basement membrane extract to determine the effect of these proteins on the morphogenetic changes mediated by HGF. After extraction of several growth factors from Matrigel, HGF was still unable to induce process formation, an early event in tubulogenesis, indicating that one or more of the remaining extracellular matrix (ECM) proteins or growth factors were exerting the inhibitory effect. By individually adding back these components to MDCK cells grown in Type I collagen gels in the presence of HGF, we were able to establish that: (1) certain ECM proteins, such as laminin, entactin, and fibronectln, actually facilitated the formation of branching tubular structures and increased their complexity; (2) other ECM proteins, such as Type IV collagen, heparan sulfate proteoglycan, and vitronectin, caused marked inhibition of HGF-induced morphogenesis; and (3) not only did transforming growth factor-β (TGF-β) inhibit the formation of tubular structures, but those which did form exhibited little branching, thereby suggesting that TGF-β modulates tubulogenesis as well as branching. These results suggest that a tubulogenic morphogen such as HGF and a tubulogenesis-inhibitory morphogen such as TGF-β can, in the context of the dynamic matrix known to exist during epithelial tissue development, modulate the degree of tubule (or ductal) formation, the length of these tubules, and the extent of their arborization. The relevance of these findings to tubulogenesis and branching during kidney development is discussed.     

Critical Evaluation of Branch Polarity and Apical Dominance as Dictators of Colony Astogeny in a Branching Coral

The high morphological resemblance between branching corals and trees, can lead to comparative studies on pattern formation traits, best exemplified in plants and in some cnidarians. Here, 81 branches of similar size of the hermatypic coral Stylophora pistillata were lopped of three different genets, their skeletons marked with alizarin red-S, and divided haphazardly into three morphometric treatment groups: (I) upright position; (II) horizontal position, intact tip; and (III) horizontal position, cut tip. After 1 y of in-situ growth, the 45 surviving ramets were brought to the laboratory, their tissues removed and their architectures analyzed by 22 morphological parameters (MPs). We found that within 1 y, isolated branches developed into small coral colonies by growing new branches from all branch termini, in all directions. No architectural dissimilarity was assigned among the three studied genets of treatment I colonies. However, a major architectural disparity between treatment I colonies and colonies of treatments II and III was documented as the development of mirror structures from both sides of treatments II and III settings as compared to tip-borne architectures in treatment I colonies. We did not observe apical dominance since fragments grew equally from all branch sides without documented dominant polarity along branch axis. In treatment II colonies, no MP for new branches originating either from tips or from branch bases differed significantly. In treatment III colonies, growth from the cut tip areas was significantly lower compared to the base, again, suggesting lack of apical dominance in this species. Changes in branch polarity revealed genet associated plasticity, which in one of the studied genets, led to enhanced growth. Different genets exhibited canalization flexibility of growth patterns towards either lateral growth, or branch axis extension (skeletal weight and not porosity was measured). This study revealed that colony astogeny in S. pistillata is a regulated process expressed through programmed events and not directly related to simple energy trade-off principles or to environmental conditions, and that branch polarity and apical dominance do not dictate colony astogeny. Therefore, plasticity and astogenic disparities encompass a diversity of genetic (fixed and flexible) induced responses.