Methods for clustered encouragement design studies with noncompliance and missing data

Encouragement design studies are particularly useful for estimating the effect of an intervention that cannot itself be randomly administered to some and not to others. They require a randomly selected group receive extra encouragement to undertake the treatment of interest, where the encouragement typically takes the form of additional information or incentives. We consider a "clustered encouragement design" (CED), where the randomization is at the level of the clusters (e.g. physicians), but the compliance with assignment is at the level of the units (e.g. patients) within clusters. Noncompliance and missing data are particular problems in encouragement design studies, where encouragement to take the treatment, rather than the treatment itself, is randomized. The motivating study looks at whether computer-based care suggestions can improve patient outcomes in veterans with chronic heart failure. Since physician adherence has been inadequate, the original study focused on methods to improve physician adherence, although an equally important question is whether physician adherence improves patient outcomes. Here, we reanalyze the data to determine the effect of physician adherence on patient outcomes. We propose causal inference methodology for the effect of a treatment versus a control in a randomized CED study with all-or-none compliance at the unit level. These methods extend the current approaches to account for nonignorable missing data and use an alternative approach to inference using multiple imputation methods, which have been successfully applied to a wide variety of missing data problems and have recently been applied to the potential outcomes framework of causal inference (Taylor and Zhou, 2009b).     

Epigenetic Variations in Plant Hybrids and Their Potential Roles in Heterosis

Heterosis,one of the most important biological phenomena,refers to the phenotypic superiority of a hybrid over its genetically diverse parents with respect to many traits such as biomass,growth rate and yield.Despite its successful application in breeding and agronomic production of many crop and animal varieties,the molecular basis of heterosis remains elusive.The classic genetic explanations for heterosis centered on three hypotheses:dominance (Davenport,1908;Bruce,1910;Keeble and Pellew,1910;Jones,1917),overdominance (East,1908;Shull,1908) and epistasis (Powers,1944;Yu et al.,1997).However,these hypotheses are largely conceptual and not connected to molecular principles,and are therefore insufficient to explain the molecular basis of heterosis (Birchler et al.,2003).Recently,many studies have explored the molecular mechanism of heterosis in plants at a genome-wide level.These studies suggest that global differential gene expression between hybrids and parental lines potentially contributes to heterosis in plants (e.g.,Swanson-Wagner et al.,2006;Zhang et al.,2008;Wei et al.,2009;Song et al.,2010).Research suggests that genetic components,including cis-acting elements and trans-acting factors,are critical regulators of differential gene expression in hybrids (Hochholdinger and Hoecker,2007;Springer and Stupar,2007;Zhang et al.,2008).However,other research indicates that epigenetic components,the regulators of chromatin states and genome activity,also have the potential to impact heterosis (e.g.,Ha et al.,2009;He et al.,2010;Groszmann et al.,2011;Barber et al.,2012;Chodavarapu et al.,2012;Greaves et al.,2012a;Shen et al.,2012).     

Protein fold recognition using sequence-derived predictions.

In protein fold recognition, one assigns a probe amino acid sequence of unknown structure to one of a library of target 3D structures. Correct assignment depends on effective scoring of the probe sequence for its compatibility with each of the target structures. Here we show that, in addition to the amino acid sequence of the probe, sequence-derived properties of the probe sequence (such as the predicted secondary structure) are useful in fold assignment. The additional measure of compatibility between probe and target is the level of agreement between the predicted secondary structure of the probe and the known secondary structure of the target fold. That is, we recommend a sequence-structure compatibility function that combines previously developed compatibility functions (such as the 3D-1D scores of Bowie et al. [1991] or sequence-sequence replacement tables) with the predicted secondary structure of the probe sequence. The effect on fold assignment of adding predicted secondary structure is evaluated here by using a benchmark set of proteins (Fischer et al., 1996a). The 3D structures of the probe sequences of the benchmark are actually known, but are ignored by our method. The results show that the inclusion of the predicted secondary structure improves fold assignment by about 25%. The results also show that, if the true secondary structure of the probe were known, correct fold assignment would increase by an additional 8-32%. We conclude that incorporating sequence-derived predictions significantly improves assignment of sequences to known 3D folds. Finally, we apply the new method to assign folds to sequences in the SWISSPROT database; six fold assignments are given that are not detectable by standard sequence-sequence comparison methods; for two of these, the fold is known from X-ray crystallography and the fold assignment is correct.     

The Wilcoxon signed rank test for paired comparisons of clustered data

The Wilcoxon signed rank test is a frequently used nonparametric test for paired data (e.g., consisting of pre- and posttreatment measurements) based on independent units of analysis. This test cannot be used for paired comparisons arising from clustered data (e.g., if paired comparisons are available for each of two eyes of an individual). To incorporate clustering, a generalization of the randomization test formulation for the signed rank test is proposed, where the unit of randomization is at the cluster level (e.g., person), while the individual paired units of analysis are at the subunit within cluster level (e.g., eye within person). An adjusted variance estimate of the signed rank test statistic is then derived, which can be used for either balanced (same number of subunits per cluster) or unbalanced (different number of subunits per cluster) data, with an exchangeable correlation structure, with or without tied values. The resulting test statistic is shown to be asymptotically normal as the number of clusters becomes large, if the cluster size is bounded. Simulation studies are performed based on simulating correlated ranked data from a signed log-normal distribution. These studies indicate appropriate type I error for data sets with > or =20 clusters and a superior power profile compared with either the ordinary signed rank test based on the average cluster difference score or the multivariate signed rank test of Puri and Sen. Finally, the methods are illustrated with two data sets, (i) an ophthalmologic data set involving a comparison of electroretinogram (ERG) data in retinitis pigmentosa (RP) patients before and after undergoing an experimental surgical procedure, and (ii) a nutritional data set based on a randomized prospective study of nutritional supplements in RP patients where vitamin E intake outside of study capsules is compared before and after randomization to monitor compliance with nutritional protocols.     

Sensitivity analyses comparing time-to-event outcomes only existing in a subset selected postrandomization and relaxing monotonicity

In randomized studies researchers may be interested in the effect of treatment assignment on a time-to-event outcome that only exists in a subset selected after randomization. For example, in preventative HIV vaccine trials, it is of interest to determine whether randomization to vaccine affects the time from infection diagnosis until initiation of antiretroviral therapy. Earlier work assessed the effect of treatment on outcome among the principal stratum of individuals who would have been selected regardless of treatment assignment. These studies assumed monotonicity, that one of the principal strata was empty (e.g., every person infected in the vaccine arm would have been infected if randomized to placebo). Here, we present a sensitivity analysis approach for relaxing monotonicity with a time-to-event outcome. We also consider scenarios where selection is unknown for some subjects because of noninformative censoring (e.g., infection status k years after randomization is unknown for some because of staggered study entry). We illustrate our method using data from an HIV vaccine trial.     

Frailty modeling for spatially correlated survival data,with application to infant mortality in Minnesota

The use of survival models involving a random effect or 'frailty' term is becoming more common. Usually the random effects are assumed to represent different clusters, and clusters are assumed to be independent. In this paper, we consider random effects corresponding to clusters that are spatially arranged, such as clinical sites or geographical regions. That is, we might suspect that random effects corresponding to strata in closer proximity to each other might also be similar in magnitude. Such spatial arrangement of the strata can be modeled in several ways, but we group these ways into two general settings: geostatistical approaches, where we use the exact geographic locations (e.g. latitude and longitude) of the strata, and lattice approaches, where we use only the positions of the strata relative to each other (e.g. which counties neighbor which others). We compare our approaches in the context of a dataset on infant mortality in Minnesota counties between 1992 and 1996. Our main substantive goal here is to explain the pattern of infant mortality using important covariates (sex, race, birth weight, age of mother, etc.) while accounting for possible (spatially correlated) differences in hazard among the counties. We use the GIS ArcView to map resulting fitted hazard rates, to help search for possible lingering spatial correlation. The DIC criterion (Spiegelhalter et al., Journal of the Royal Statistical Society, Series B 2002, to appear) is used to choose among various competing models. We investigate the quality of fit of our chosen model, and compare its results when used to investigate neonatal versus post-neonatal mortality. We also compare use of our time-to-event outcome survival model with the simpler dichotomous outcome logistic model. Finally, we summarize our findings and suggest directions for future research.     

Parameter estimation in longitudinal studies with outcome-dependent follow-up

In many observational studies, individuals are measured repeatedly over time, although not necessarily at a set of prespecified occasions. Instead, individuals may be measured at irregular intervals, with those having a history of poorer health outcomes being measured with somewhat greater frequency and regularity; i.e., those individuals with poorer health outcomes may have more frequent follow-up measurements and the intervals between their repeated measurements may be shorter. In this article, we consider estimation of regression parameters in models for longitudinal data where the follow-up times are not fixed by design but can depend on previous outcomes. In particular, we focus on general linear models for longitudinal data where the repeated measures are assumed to have a multivariate Gaussian distribution. We consider assumptions regarding the follow-up time process that result in the likelihood function separating into two components: one for the follow-up time process, the other for the outcome process. The practical implication of this separation is that the former process can be ignored when making likelihood-based inferences about the latter; i.e., maximum likelihood (ML) estimation of the regression parameters relating the mean of the longitudinal outcomes to covariates does not require that a model for the distribution of follow-up times be specified. As a result, standard statistical software, e.g., SAS PROC MIXED (Littell et al., 1996, SAS System for Mixed Models), can be used to analyze the data. However, we also demonstrate that misspecification of the model for the covariance among the repeated measures will, in general, result in regression parameter estimates that are biased. Furthermore, results of a simulation study indicate that the potential bias due to misspecification of the covariance can be quite considerable in this setting. Finally, we illustrate these results using data from a longitudinal observational study (Lipshultz et al., 1995, New England Journal of Medicine 332, 1738-1743) that explored the cardiotoxic effects of doxorubicin chemotherapy for the treatment of acute lymphoblastic leukemia in children.     

The ups and downs of signalling between root and shoot

It is becoming increasingly apparent that the long-distance signalling associated with many developmental processes is complex and that novel hormone-like signals may play substantial roles. The past decades have seen several substances (e.g. brassinosteroids, systemin and other polypeptides, mevalonic and jasmonic acids, polyamines, oligosaccharides, flavonoids, and quinones) vie for a place among the classical plant hormones (e.g. Spaink, 1996). Recent microinjection and grafting studies have also shown that RNA may act as a long-distance signal (Jorgensen et al ., 1998; Xoconostle-Cázares et al ., 1999). In this issue, Hannah et al . describe long-distance signalling and the regulation of root–shoot partitioning in dwarf lethal or dosage-dependent lethal ( DL ) mutants of common bean (Shii et al ., 1980, 1981), and present evidence indicating that substances in addition to classical plant hormones (e.g. cytokinins) may be involved.
As in the report by Hannah et al ., much of the evidence for roles of unidentified long-distance signals in the control of plant development is indirect. The possibility that a small number of long-distance signals might control a multitude of developmental processes arises through the potential for differences in tissue sensitivity, fluctuations in hormone levels and differences in the nature of responses of different tissues to the same hormone. Consequently, particular hormones may influence numerous processes seemingly simultaneously, yet independently. Even so, long-distance signalling is involved in processes as diverse as root–shoot balance, senescence, branching, flowering, nodulation, stress responses and nutrient uptake. Through comparison of even a few different developmental processes, progress can be made to reveal the true complexity of plant development. Using this approach it is also clear that many unknown signals may be involved.     

The sustainable neighborhoods for happiness (SNfH) decision tool: Assessing neighborhood level sustainability and happiness

The relationship between sustainability and happiness is an intriguing and growing research area (Cloutier et al., 2013; Montgomery, 2013; Florida et al., 2013; Leyden et al., 2011). However, a review of primary literature and research indicates a missing gap in neighborhood level assessments of sustainability and happiness. The Sustainable Neighborhoods for Happiness Index (SNHI) was developed using city level data and studies (Cloutier et al., 2014), but was created with the intent of serving as a neighborhood measure. Within this paper, we detail the development of the Sustainable Neighborhoods for Happiness (SNfH) Decision Tool – a neighborhood level assessment tool, derived from the SNHI, to assist in decisions around future strategies for sustainable community development. While several sustainability decision tools exist, there is a need for those that are easily understood and accessible to neighborhood stakeholders (e.g., residents, community leaders, city employees). The SNfH Decision Tool was created with a user-friendly graphical front-end and embedded back-end calculations to inform users. The goal is to help neighborhood stakeholders identify the needs of their community to swiftly take action to alleviate issues and promote a sustainable and happy future.     

Validation of surrogate markers in multiple randomized clinical trials with repeated measurements: canonical correlation approach

Part of the recent literature on the evaluation of biomarkers as surrogate endpoints starts from a multitrial context, which leads to a definition of validity in terms of the quality of both trial-level and individual-level association between the surrogate and true endpoints (Buyse et al., 2000, Biostatistics1, 49-67). These authors concentrated on cross-sectional continuous responses. However, in many randomized clinical studies, repeated measurements are encountered on either or both endpoints. A challenge in this setting is the formulation of a simple and meaningful concept of "surrogacy."Alonso et al. (2003, Biometrical Journal45, 931-945) proposed the variance reduction factor (VRF) to evaluate surrogacy at the individual level. They also showed how and when this concept should be extended to study surrogacy at the trial level. Here, we approach the problem from the natural canonical correlation perspective. We define a class of canonical correlation functions that can be used to study surrogacy at the trial and individual level. We show that the VRF and the R2 measure defined by Buyse et al. (2000) follow as special cases. Simulations are conducted to evaluate the performance of different members of this family. The methodology is illustrated on data from a meta-analysis of five clinical trials comparing antipsychotic agents for the treatment of chronic schizophrenia.     

Evolution of metal hyperaccumulation and phytoremediation hype

Cadmium accumulation and tolerance are discussed in a New Phytologist article by Krämer (2000), which comments on a paper by Lombi et al . (2000). In this context, a number of additional points should be made, putting the role of humans in the evolution of metal resistance into context and emphasizing what is the 'hype' of phytoremediation.
It is important that sites created by humans should not be overemphasized in considering the evolution of metal resistance. Plants resistant to heavy metals have their primary sites not on these, but on soils where ores are outcropping, the so-called metalliferous or orogenic soils (Ernst, 1974). Over thousands of years, natural exposure to a surplus of various metals, depending on the mineralization process, has driven the evolution of metal resistance in many plant species under the local environmental conditions. Many publications have shown that Thlaspi caerulescens can hyperaccumulate Zn (e.g. Vázquez et al ., 1992), and accumulate other heavy metals such as Cu and Pb depending on soil chemistry (e.g. Baker et al ., 1994). It has been known for more than 30 years that T. caerulescens gives a good response to experimentally supplied high Zn levels (Ernst, 1968). One of the ecological effects of hyperaccumulation of heavy metals is a defence against herbivorous insects (Boyd & Martens, 1994). This effect is enhanced by a preferential accumulation of heavy metals in the epidermal leaf layer (Heath et al ., 1997).     

Assessing model accuracy using the homology modeling automatically software

Homology modeling is a powerful technique that greatly increases the value of experimental structure determination by using the structural information of one protein to predict the structures of homologous proteins. We have previously described a method of homology modeling by satisfaction of spatial restraints (Li et al., Protein Sci 1997;6:956-970). The Homology Modeling Automatically (HOMA) web site, , is a new tool, using this method to predict 3D structure of a target protein based on the sequence alignment of the target protein to a template protein and the structure coordinates of the template. The user is presented with the resulting models, together with an extensive structure validation report providing critical assessments of the quality of the resulting homology models. The homology modeling method employed by HOMA was assessed and validated using twenty-four groups of homologous proteins. Using HOMA, homology models were generated for 510 proteins, including 264 proteins modeled with correct folds and 246 modeled with incorrect folds. Accuracies of these models were assessed by superimposition on the corresponding experimentally determined structures. A subset of these results was compared with parallel studies of modeling accuracy using several other automated homology modeling approaches. Overall, HOMA provides prediction accuracies similar to other state-of-the-art homology modeling methods. We also provide an evaluation of several structure quality validation tools in assessing the accuracy of homology models generated with HOMA. This study demonstrates that Verify3D (Luthy et al., Nature 1992;356:83-85) and ProsaII (Sippl, Proteins 1993;17:355-362) are most sensitive in distinguishing between homology models with correct or incorrect folds. For homology models that have the correct fold, the steric conformational energy (including primarily the Van der Waals energy), MolProbity clashscore (Word et al., Protein Sci 2000;9:2251-2259), and the PROCHECK G-factors (Laskowski et al., J Biomol NMR 1996;8:477-486) provide sensitive and consistent methods for assessing accuracy and can distinguish between homology models of higher and lower accuracy. As demonstrated in the accompanying paper (Bhattacharya et al., accompanying paper), combinations of these scores for models generated with HOMA provide a basis for distinguishing low from high accuracy models.     

Plant diversity and ecology on the Qinghai–Tibet Plateau

The Qinghai–Tibet Plateau (QTP) comprises a platform (sometimes called the Qinghai–Tibet Plateau sensu stricto), the Himalayas, and Hengduan Mountains (Liang et al.,2018; Mao et al.,2021). The latter two parts and adjacent highlands are also called the Pan-Himalaya. Numerous plants are distributed there with many endemic species, probably because of the high diverse landscapes created by continuous geological and climatic activities (Favre et al.,2015; Mao et al.,2021). As the well known biodiversity hotspot of the alpine plants in the world (Sun et al.,2017), many studies have been conducted on evolutionary origin and ecological adaptation of those species occurring in the QTP (e.g., Wen et al.,2014, 2019; Zhang et al.,2019). In the present special issue, we collected 15 related papers on this topic. Among them, two are invited reviews. Mao et al. (2021) provide a comprehensive review of evolutionary origin of species diversity on the QTP. Especially, they outlined major disputes and likely causes in this research topic, including circumscribing and naming the QTP, the QTP uplifts, dating of molecular phylogenetic trees, non-causal correlations between QTP uplifts and species diversification and the unified ice sheet. The authors also summarized genomic advancements related to high-altitude adaptation of both plants and animals. Tong et al. (2021) reviewed the reproductive strategies of animal-pollinated alpine plants on the QTP, involving pollination system, pollen limitation, self-pollination, and sexual system. In this region, 95.4% of animal-pollinated plants are pollinated by insects (i.e., bees, moths, butterflies, and flies) with only 4% by vertebrates (i.e., bats and birds). Self-pollination through self-compatibility shift from outcrossing has become an effective reproductive strategy to overcome pollen limitation in alpine plants. The other 13 research papers aimed to address origin and adaptation of alpine flora involving three major lines of evidence: genomics, ecology, and paleobotany. We hope that the collection of these papers will increase our understanding of the origin, speciation, and adaptation of alpine species on the QTP.     

Metal hyperaccumulation: a model system for coevolutionary studies

Recent years have seen a flurry of research activity concerning the hyperaccumulation of heavy metals by plants. Much of the interest in hyperaccumulation has been fueled by the commercial potential of phytoremediation, the use of plants to clean up contaminated soils (Baker et al ., 1994; Salt et al ., 1995; Chaney et al ., 1997, 2000). These applications have in turn spurred many studies of the genetics and physiology of metal uptake (e.g. Krämer et al ., 1996; Lasat et al ., 1996; Salt & Krämer, 1999; Baker et al ., 2000; see also Krämer, 2000; Lombi et al ., 2000). Although phytoremediation provides an intriguing and potentially profitable backdrop, the ecology and evolution of hyperaccumulation in natural populations are interesting subjects in their own right. Two papers in this issue (Ghaderian et al ., pp. 219–224; Davis & Boyd, pp. 211–217) are exciting contributions to the growing consensus that hyperaccumulation may act as a defense against herbivores and pathogens, and suggest that hyperaccumulation may become a model system for research in this area.     

Structural mechanisms of constitutive activation in the C5a receptors with mutations in the extracellular loops: molecular modeling study

Previously we demonstrated by random saturation mutagenesis a set of mutations in the extracellular (EC) loops that constitutively activate the C5a receptor (C5aR) (Klco et al., Nat Struct Mol Biol 2005;12:320-326; Klco et al., J Biol Chem 2006;281:12010-12019). In this study, molecular modeling revealed possible conformations for the extracellular loops of the C5a receptors with mutations in the EC2 loop or in the EC3 loop. Comparison of low-energy conformations of the EC loops defined two distinct clusters of conformations typical either for strongly constitutively active mutants of C5aR (the CAM cluster) or for nonconstitutively active mutants (the non-CAM cluster). In the CAM cluster, the EC3 loop was turned towards the transmembrane (TM) helical bundle and more closely interacted with EC2 than in the non-CAM cluster. This suggested a structural mechanism of constitutive activity where EC3 contacts EC2 leading to EC2 interactions with helix TM3, thus triggering movement of TM7 towards TM2 and TM3. The movement initiates rearrangement of the system of hydrogen bonds between TM2, TM3 and TM7 including formation of the hydrogen bond between the side chains of D82(2.50) in TM2 and N296(7.49) in TM7, which is crucial for formation of the activated states of the C5a receptors (Nikiforovich et al., Proteins: Struct Funct Gene 2011;79:787-802). Since the relative large length of EC3 in C5aR (13 residues) is comparable with those in many other members of rhodopsin family of GPCRs (13-19 residues), our findings might reflect general mechanisms of receptor constitutive activation. The very recent X-ray structure of the agonist-induced constitutively active mutant of rhodopsin (Standfuss et al., Nature 2011;471:656-660) is discussed in view of our modeling results.     

Non-stationary aging dynamics in ant societies

In recent experiments by Richardson et al. (2010) [Richardson, T.O., Robinson, E.J.H., Christensen, K., Jensen, H.J., Franks, N.R., Sendova-Franks, A.B., 2010. PLoS ONE 5, e9621.] ant motion out of the nest is shown to be a non-stationary process intriguingly similar to the dynamics encountered in physical aging of glassy systems. Specifically, exit events can be described as a Poisson process in logarithmic time, or, for short, a log-Poisson process. Nouvellet et al. (2010) [Nouvellet, P., Bacon, J.P.,Waxman, D., 2010. J. Theor. Biol. 266, 573.] criticized these conclusions and performed new experiments where the exit process could more simply be described by standard Poisson statistics. In their reply Richardson et al. (2011b) [Richardson, T.O., Robinson, E.J.H., Christensen, K., Jensen, J.H., Christensen, K., Jensen, H.J., Franks, N.R., Sendova-Franks, A.B., 2011b. J. Theor. Biol. 269, 356-358.] stressed that the two sets of experiments were performed under very different conditions and claimed that this was the likely source of the discrepancy. Ignoring any technical issues which are part of the above discussion, the focal point of this work is to ascertain whether or not both log-Poisson and Poisson statistics are possible in an ant society under different external conditions. To this end, a model is introduced where interacting ants move in a stochastic fashion from one site to a neighboring site on a finite 2D lattice. The probability of each move is determined by the ensuing changes of a utility function which is a sum of pairwise interactions between ants, weighted by distance. Depending on how the interactions are defined and on a control parameter dubbed ‘degree of stochasticity’ (DS), the dynamics either quickly converges to a stationary state, where movements are a standard Poisson process, or may enter a non-stationary regime, where exits can be described as suggested by Richardson et al. Other aspects of the model behavior are also discussed, i.e. the time dependence of the average value of the utility function, and the statistics of spatial re-arrangements happening anywhere in the system. Finally, we discuss the role of record events and their statistics in the context of ant societies and suggest the possibility that a transition from non-stationary to stationary dynamics can be triggered experimentally.     

Nested Markov compliance class model in the presence of time-varying noncompliance

Summary .  We consider a Markov structure for partially unobserved time-varying compliance classes in the Imbens–Rubin (1997, The Annals of Statistics 25, 305–327) compliance model framework. The context is a longitudinal randomized intervention study where subjects are randomized once at baseline, outcomes and patient adherence are measured at multiple follow-ups, and patient adherence to their randomized treatment could vary over time. We propose a nested latent compliance class model where we use time-invariant subject-specific compliance principal strata to summarize longitudinal trends of subject-specific time-varying compliance patterns. The principal strata are formed using Markov models that relate current compliance behavior to compliance history. Treatment effects are estimated as intent-to-treat effects within the compliance principal strata.     

Compliance Mixture Modelling with a Zero‐Effect Complier Class and Missing Data

Summary Randomized experiments are the gold standard for evaluating proposed treatments. The intent to treat estimand measures the effect of treatment assignment, but not the effect of treatment if subjects take treatments to which they are not assigned. The desire to estimate the efficacy of the treatment in this case has been the impetus for a substantial literature on compliance over the last 15 years. In papers dealing with this issue, it is typically assumed there are different types of subjects, for example, those who will follow treatment assignment (compliers), and those who will always take a particular treatment irrespective of treatment assignment. The estimands of primary interest are the complier proportion and the complier average treatment effect (CACE). To estimate CACE, researchers have used various methods, for example, instrumental variables and parametric mixture models, treating compliers as a single class. However, it is often unreasonable to believe all compliers will be affected. This article therefore treats compliers as a mixture of two types, those belonging to a zero‐effect class, others to an effect class. Second, in most experiments, some subjects drop out or simply do not report the value of the outcome variable, and the failure to take into account missing data can lead to biased estimates of treatment effects. Recent work on compliance in randomized experiments has addressed this issue by assuming missing data are missing at random or latently ignorable. We extend this work to the case where compliers are a mixture of types and also examine alternative types of nonignorable missing data assumptions.     

Role of afferent input in muscle atrophy.

It is well known that soleus muscle of rat atrophies following spaceflight or hindlimb suspension (Ohira et al., 1992). It is, further, reported that the electromyogram (EMG) of soleus muscle disappears immediately in response to unloading by exposure to actual micro-g environment (Kawano et al., 2002; Leterme and Falempin, 1998) and by hindlimb suspension of rats (Alford et al., 1987; Ohira et al., 2000). However, the EMG level is increased gradually to the control level following 7-10 days of continuous hindlimb suspension (Alford et al., 1987; Ohira, 2000), while muscle atrophy is progressing (Winiarski et al., 1987). We previously reported that reduction of the EMG level of rat soleus in response to actual micro-g environment, created by a parabolic flight of a jet airplane, was closely associated with a decrease of the afferent input recorded at the L5 segmental level of spinal cord (Kawano et al., 2002). However, it is still unclear how the EMG level of soleus muscle adapts to unloading condition. The current study was performed to investigate the responses of soleus EMG and both afferent and efferent neurogram at the L5 segmental level of spinal cord to acute (20 seconds) and chronic (14 days) unloading.