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.     

GENETIC AND SOCIAL INHERITANCE OF BODY AND EGG SIZE IN THE BARNACLE GOOSE (BRANTA LEUCOPSIS)

We present heritability estimates for final size of body traits and egg size as well as phenotypic and genetic correlations between body and egg traits in a recently established population of the barnacle goose (Branta leucopsis) in the Baltic area. Body traits as well as egg size were heritable and, hence, could respond evolutionarily to phenotypic selection. Genetic correlations between body size traits were significantly positive and of similar magnitude or higher than the corresponding phenotypic correlations. Heritability estimates for tarsus length obtained from full-sib analyses were higher than those obtained from midoffspring-midparent regressions, and this indicates common environment effects on siblings. Heritabilities for tarsus length obtained from midoffspring-mother regressions were significantly higher than estimates from midoffspring-father regressions. The results suggest that this discrepancy is not caused by maternal effects through egg size, nor by extra-pair fertilizations, but by a socially inherited foraging site fidelity in females.     

Birth Weight and Its Relationship to Size Attained and Relative Fat Distribution at 7 to 12 Years of Age

The relationship between birth weight and relative subcutaneous fat distribution at school age was considered in 131 boys and 106 girls 7 to 12 years of age. Relative fat distribution at school age was estimated with the ratio of the subscapular to triceps skinfolds (S/T) for the total sample, and with the ratio of the sum of two trunk (subscapular, midaxillary) to the sum of two extremity (triceps, medial calf) skinfolds (T/E) for subsamples of 102 boys and 63 girls. There were no sex differences in the S/T ratio (mm/mm), boys 0.62 ± 0.15, girls 0.63 ± 0.18; T/E ratio (mm/mm), boys 0.58 ± 0.13, girls 0.59 ± 0.16; and BMI (kg/m²), boys 17.1 ± 2.4, girls 16.9 ± 2.2. Second order partial correlations, controlling for age and the BMI or age and sum of skinfolds, between birth weight and the skinfold ratios are, respectively, ?0.22 and ?0.20 (p<0.01) for S/T and ?0.29 and ?032 (p<0.01) for T/E in girls, and ?0.18 and ?0.17 (p<0.05) for S/T and ?0.06 and ?0.6 for T/E in boys. Though low, the correlations suggest that as birth weight decreases proportionally more subcutaneous fat is accumulated on the trunk than on the extremities, more so in females than in males. Results of stepwise multiple regression analyses indicate that birth weight accounts for from 2% to 8% of the variance in relative subcutaneous fat distribution at school age.     

Differences in Body Image and Depression Among Obese Women With and Without Binge Eating Disorder

Obese individuals with binge eating disorder (BED) differ from obese non-binge eating (NBE) individuals in a number of clinically relevant ways. This study examined attitudinal responses to various measures of body image in women seeking obesity treatment, by comparing NBE participants (n=80) to those with BED (n=48). It was hypothesized that women with BED would demonstrate greater attitudinal disturbance of body image compared to NBE individuals. It was further hypothesized that significant differences between groups would remain after statistically controlling for degree of depression. Consistent with the primary hypothesis, BED participants reported significantly increased attitudinal disturbance in body dissatisfaction and size perception compared to NBE participants. Although shared variance was observed between measures of depression and body image on some items, several aspects of increased body image disturbance remained after statistically controlling for depression. Treatment implications and recommendations for future research are discussed.     

Geographical and latitudinal variation in growth patterns and adult body size of Swedish moose (Alces alces)

We examined the geographical pattern in growth and adult body size among 14 populations of Swedish moose (Alces alces) using data from 4,294 moose (1.5 years old) killed during the hunting season in 1989–1992. In both sexes, adult body mass was significantly positively correlated with latitude. Moose in northern populations had a 15–20% larger adult body mass than moose in the south. Juvenile body mass was correlated with neither latitude nor adult body mass. Thus, variation in time (years) and rate of body growth after the juvenile stage were responsible for most of the variation in adult body mass among populations. Moose in northern populations grew for approximately 2 more years of life than southern moose. In contrast to adult body mass, skeletal size (measured as jawbone length) was not correlated with latitude, suggesting that variation in adult body mass was primarily due to differences in fat reserves. Discrimination between population characteristics, such as moose density, climate, and the amount of browse available to moose, showed climatic harshness to be the most important variable explaining geographical variation in body mass among populations. The results support the notion that in mammals body size increases with latitude in accordance with Bergmann's rule. We conclude that (1) variation in patterns of growth after the juvenile stage is the main cause of the latitudinal trend in adult body size in moose, and (2) climatic conditions are a more important factor than population density and availability of food in explaining geographical variation in growth patterns and adult body mass between populations of Swedish moose.     

Condition factor and hepatosomatic index as estimates of energy status in male three-spined stickleback

Seasonal variation in direct and indirect measures of energy status was examined using estimates of glycogen, lipid and protein levels in a single cohort of male three-spined sticklebacks from an annual population collected each month over one complete year. Condition factor, somatic condition factor and hepatosomatic index (HSI) were calculated as indirect indices of energy status and the accuracy of these indirect measures as predictors of energy status was investigated. Results indicate that both condition factors were significant predictors of energy reserves (lipid, protein, glycogen and total energy), but that the proportion of variance accounted for was small. Both condition factors perform better as predictors of energy content per unit body weight. The HSI was a significant, but a weak predictor of total glycogen levels over the whole year. On a seasonal basis the relationship between HSI and energy reserves was highly variable. These indices are therefore poor predictors of energy reserves in male three-spined sticklebacks.     

Body water content over a range of ambient salinities in the sheepshead minnow

Body water content was determined on groups of Cyprinodon variegatus after sequential acclimation to ambient salinities in the range from fresh water to 100%. A multiple linear regression model applied to the data included body mass ( M ) of individuals and acclimation salinity ( S ) as independent variables, and body water content ( W ) as the dependent variable. The model that described the relationship was W (g) = 0·059 + 0·723 M (g)–0001 S (%). Converting values of body water content to percent of wet body mass produced a range of values from 74·5% in fresh water to 72·0% at 100%, only a 2·5% difference in body water content over this wide range of ambient salinities.     

Conformation of P22 tailspike folding and aggregation intermediates probed by monoclonal antibodies.

The partitioning of partially folded polypeptide chains between correctly folded native states and off-pathway inclusion bodies is a critical reaction in biotechnology. Multimeric partially folded intermediates, representing early stages of the aggregation pathway for the P22 tailspike protein, have been trapped in the cold and isolated by nondenaturing polyacrylamide gel electrophoresis (PAGE) (speed MA, Wang DIC, King J. 1995. Protein Sci 4:900-908). Monoclonal antibodies against tailspike chains discriminate between folding intermediates and native states (Friguet B, Djavadi-Ohaniance L, King J, Goldberg ME. 1994. J Biol Chem 269:15945-15949). Here we describe a nondenaturing Western blot procedure to probe the conformation of productive folding intermediates and off-pathway aggregation intermediates. The aggregation intermediates displayed epitopes in common with productive folding intermediates but were not recognized by antibodies against native epitopes. The nonnative epitope on the folding and aggregation intermediates was located on the partially folded N-terminus, indicating that the N-terminus remained accessible and nonnative in the aggregated state. Antibodies against native epitopes blocked folding, but the monoclonal directed against the N-terminal epitope did not, indicating that the conformation of the N-terminus is not a key determinant of the productive folding and chain association pathway.