Model misspecification and bias for inverse probability weighting estimators of average causal effects

Commonly used semiparametric estimators of causal effects specify parametric models for the propensity score (PS) and the conditional outcome. An example is an augmented inverse probability weighting (IPW) estimator, frequently referred to as a doubly robust estimator, because it is consistent if at least one of the two models is correctly specified. However, in many observational studies, the role of the parametric models is often not to provide a representation of the data-generating process but rather to facilitate the adjustment for confounding, making the assumption of at least one true model unlikely to hold. In this paper, we propose a crude analytical approach to study the large-sample bias of estimators when the models are assumed to be approximations of the data-generating process, namely, when all models are misspecified. We apply our approach to three prototypical estimators of the average causal effect, two IPW estimators, using a misspecified PS model, and an augmented IPW (AIPW) estimator, using misspecified models for the outcome regression (OR) and the PS. For the two IPW estimators, we show that normalization, in addition to having a smaller variance, also offers some protection against bias due to model misspecification. To analyze the question of when the use of two misspecified models is better than one we derive necessary and sufficient conditions for when the AIPW estimator has a smaller bias than a simple IPW estimator and when it has a smaller bias than an IPW estimator with normalized weights. If the misspecification of the outcome model is moderate, the comparisons of the biases of the IPW and AIPW estimators show that the AIPW estimator has a smaller bias than the IPW estimators. However, all biases include a scaling with the PS-model error and we suggest caution in modeling the PS whenever such a model is involved. For numerical and finite sample illustrations, we include three simulation studies and corresponding approximations of the large-sample biases. In a dataset from the National Health and Nutrition Examination Survey, we estimate the effect of smoking on blood lead levels.     

Reconstructing paternal genotypes to infer patterns of sperm storage and sexual selection in the hawksbill turtle

Postcopulatory sperm storage can serve a range of functions, including ensuring fertility, allowing delayed fertilization and facilitating sexual selection. Sperm storage is likely to be particularly important in wide‐ranging animals with low population densities, but its prevalence and importance in such taxa, and its role in promoting sexual selection, are poorly known. Here, we use a powerful microsatellite array and paternal genotype reconstruction to assess the prevalence of sperm storage and test sexual selection hypotheses of genetic biases to paternity in one such species, the critically endangered hawksbill turtle, Eretmochelys imbricata. In the majority of females (90.7%, N = 43), all offspring were sired by a single male. In the few cases of multiple paternity (9.3%), two males fertilized each female. Importantly, the identity and proportional fertilization success of males were consistent across all sequential nests laid by individual females over the breeding season (up to five nests over 75 days). No males were identified as having fertilized more than one female, suggesting that a large number of males are available to females. No evidence for biases to paternity based on heterozygosity or relatedness was found. These results indicate that female hawksbill turtles are predominantly monogamous within a season, store sperm for the duration of the nesting season and do not re‐mate between nests. Furthermore, females do not appear to be using sperm storage to facilitate sexual selection. Consequently, the primary value of storing sperm in marine turtles may be to uncouple mating and fertilization in time and avoid costly re‐mating.     

A blueprint for vocal learning: auditory predispositions from brains to genomes

Memorizing and producing complex strings of sound are requirements for spoken human language. We share these behaviours with likely more than 4000 species of songbirds, making birds our primary model for studying the cognitive basis of vocal learning and, more generally, an important model for how memories are encoded in the brain. In songbirds, as in humans, the sounds that a juvenile learns later in life depend on auditory memories formed early in development. Experiments on a wide variety of songbird species suggest that the formation and lability of these auditory memories, in turn, depend on auditory predispositions that stimulate learning when a juvenile hears relevant, species-typical sounds. We review evidence that variation in key features of these auditory predispositions are determined by variation in genes underlying the development of the auditory system. We argue that increased investigation of the neuronal basis of auditory predispositions expressed early in life in combination with modern comparative genomic approaches may provide insights into the evolution of vocal learning.     

Sexual selection research on spiders: progress and biases

The renaissance of interest in sexual selection during the last decades has fuelled an extraordinary increase of scientific papers on the subject in spiders. Research has focused both on the process of sexual selection itself, for example on the signals and various modalities involved, and on the patterns, that is the outcome of mate choice and competition depending on certain parameters. Sexual selection has most clearly been demonstrated in cases involving visual and acoustical signals but most spiders are myopic and mute, relying rather on vibrations, chemical and tactile stimuli. This review argues that research has been biased towards modalities that are relatively easily accessible to the human observer. Circumstantial and comparative evidence indicates that sexual selection working via substrate-borne vibrations and tactile as well as chemical stimuli may be common and widespread in spiders. Pattern-oriented research has focused on several phenomena for which spiders offer excellent model objects, like sexual size dimorphism, nuptial feeding, sexual cannibalism, and sperm competition. The accumulating evidence argues for a highly complex set of explanations for seemingly uniform patterns like size dimorphism and sexual cannibalism. Sexual selection appears involved as well as natural selection and mechanisms that are adaptive in other contexts only. Sperm competition has resulted in a plethora of morphological and behavioural adaptations, and simplistic models like those linking reproductive morphology with behaviour and sperm priority patterns in a straightforward way are being replaced by complex models involving an array of parameters. Male mating costs are increasingly being documented in spiders, and sexual selection by male mate choice is discussed as a potential result. Research on sexual selection in spiders has come a long way since Darwin, whose spider examples are reanalysed in the context of contemporary knowledge, but the same biases and methodological constraints have persisted almost unchanged through the current boom of research.     

Responses of domestic chicks (Gallus gallus domesticus) to multimodal aposematic signals

Many aposematic prey combine their visual warning signals withadditional signals. Together, these signals constitute a multimodalor multicomponent warning display. The additional signals arethought to increase the effects of the visual signals on predators.Olfactory signals are much emphasized, but later studies haveshown that also auditory signals like the buzzing of certaininsects might have multimodal effects. The wasp displays typicalvisual aposematic signals, black and yellow stripes, but doesalso emit a characteristic buzzing. We wanted to test if, andin what way, the visual and acoustic display of the wasp hasan aversive function on the predators. We therefore conducteda 12-trial discrimination-learning task on inexperienced chicksto study whether there are innate biases toward these signalsand how they affect the speed of avoidance learning. We alsoperformed three extinction-learning trials to study how memorablethe signals were to the chicks. We show that the visual signalsin the display of the wasp contribute to the protection frompredators but in different ways; the yellow color had an aversiveeffect on inexperienced predators, while the striped patternimproved the aversion learning. The sound did not enhance theinnate aversions but increased the aversion learning of stripesin green prey.     

Comparative psychology and the grand challenge of drug discovery in psychiatry and neurodegeneration

Drug discovery for brain disorders is undergoing a period of upheaval. Faced with an empty drug pipeline and numerous failures of potential new drugs in clinical trials, many large pharmaceutical companies have been shrinking or even closing down their research divisions that focus on central nervous system (CNS) disorders. In this paper, we argue that many of the difficulties facing CNS drug discovery stem from a lack of robustness in pre-clinical (i.e., non-human animal) testing. There are two main sources for this lack of robustness. First, there is the lack of replicability of many results from the pre-clinical stage, which we argue is driven by a combination of publication bias and inappropriate selection of statistical and experimental designs. Second, there is the frequent failure to translate results in non-human animals to parallel results in humans in the clinic. This limitation can only be overcome by developing new behavioral tests for non-human animals that have predictive, construct, and etiological validity. Here, we present these translational difficulties as a “grand challenge” to researchers from comparative cognition, who are well positioned to provide new methods for testing behavior and cognition in non-human animals. These new experimental protocols will need to be both statistically robust and target behavioral and cognitive processes that allow for better connection with human CNS disorders. Our hope is that this downturn in industrial research may represent an opportunity to develop new protocols that will re-kindle the search for more effective and safer drugs for CNS disorders.     

The probability of genetic parallelism and convergence in natural populations

Genomic and genetic methods allow investigation of how frequently the same genes are used by different populations during adaptive evolution, yielding insights into the predictability of evolution at the genetic level. We estimated the probability of gene reuse in parallel and convergent phenotypic evolution in nature using data from published studies. The estimates are surprisingly high, with mean probabilities of 0.32 for genetic mapping studies and 0.55 for candidate gene studies. The probability declines with increasing age of the common ancestor of compared taxa, from about 0.8 for young nodes to 0.1–0.4 for the oldest nodes in our study. Probability of gene reuse is higher when populations begin from the same ancestor (genetic parallelism) than when they begin from divergent ancestors (genetic convergence). Our estimates are broadly consistent with genomic estimates of gene reuse during repeated adaptation to similar environments, but most genomic studies lack data on phenotypic traits affected. Frequent reuse of the same genes during repeated phenotypic evolution suggests that strong biases and constraints affect adaptive evolution, resulting in changes at a relatively small subset of available genes. Declines in the probability of gene reuse with increasing age suggest that these biases diverge with time.     

Congruence between the sexes in preexisting receiver responses

Preexisting receiver biases have been shown to affect how femalesdetect and respond to new conspecific traits in a mate choicecontext. Although preexisting biases have often been discussedin the context of female mate choice, these biases need notbe sex limited. In the genus Xiphophorus, swordtail males possessa sexually selected trait, the sword. Here I consider evidencethat the state of a bias favoring sworded conspecifics maybe generally shared by the sexes in taxa in which the sword has not arisen. In three unsworded species of poeciliid fishes,both males and females prefer members of the other sex withswords. In a fourth species, males and females share the absenceof a response to a sword. This congruity between the sexessuggests that response biases may not be sex limited and thatthe sexes could historically share common mechanisms producingshared mating responses. Alternatively, selection may tendto result in parallel changes in biases in the sexes. Thiswork expands our understanding of receiver biases by usinga phylogenetic approach to examine whether biases are historicallyshared by the sexes and suggests that there can be general congruence between the sexes in such biases.