Biopsychosocial determinants of pregnancy length and fetal growth

PDFlib PLOP: PDF Linearization, Optimization, Protection Page inserted by evaluation version www.pdflib.com – sales@pdflib.com 240 doi: 10.1111/j.1365-3016.2008.00926.x Biopsychosocial determinants of pregnancy length and fetal growth Jennifer St-Laurenta, Philippe De Walsb, Jean-Marie Moutquinc, Theophile Niyonsengaf, Manon Noiseuxd and Loretta Czernise a Clinical Research Centre, Sherbrooke University Hospital Centre, Sherbrooke, bDepartment of Social and Preventive Medicine, Laval University, Quebec City, cDepartment of Obstetrics and Gynecology, University of Sherbrooke, Sherbrooke, dMontérégie Health and Social Services Agency, Longueuil, eDepartment of Sociology, Bishop’s University, Lennoxville, Quebec, Canada, and fRobert Stempel School of Public Health, Florida International University, Miami, FL, USA Summary Correspondence: Philippe De Wals, MD, PhD, Department of Social and Preventive Medicine, Laval University, Pavillon de l’Est, Local 1110, Quebec, G1K 7P4, Canada. E-mail: philippe.dewals@msp.ulaval.ca St-Laurent J, De Wals P, Moutquin J-M, Niyonsenga T, Noiseux M, Czernis L. Biopsychosocial determinants of pregnancy length and fetal growth. Paediatric and Perinatal Epidemiology 2008; 22: 240–248. The causes and mechanisms related to preterm delivery and intrauterine growth restriction are poorly understood. Our objective was to assess the direct and indirect effects of psychosocial and biomedical factors on the duration of pregnancy and fetal growth. A self-administered questionnaire was distributed to pregnant women attending prenatal ultrasound clinics in nine hospitals in the Montérégie region in the province of Quebec, Canada, from November 1997 to May 1998. Prenatal questionnaires were linked with birth certificates. Theoretical models explaining pregnancy length and fetal growth were developed and tested, using path analysis. In order to reduce the number of variables from the questionnaire, a principal component analysis was performed, and the three most important new dimensions were retained as explanatory variables in the final models. Data were available for 1602 singleton pregnancies. The biophysical score, covering both maternal age and the pre-pregnancy body mass index, was the only variable statistically associated with pregnancy length. Smoking, obstetric history, maternal health and biophysical indices were direct predictors of fetal growth. Perceived stress, social support and self-esteem were not directly related to pregnancy outcomes, but were determinants of smoking and the above-mentioned biomedical variables. More studies are needed to identify the mechanisms by which adverse psychosocial factors are translated into adverse biological effects. Keywords: fetal growth, pregnancy length, stress, path analysis. Introduction Preterm delivery and intrauterine growth restriction constitute important public health problems worldwide; their causes and causal pathways are still poorly understood.1,2 In developed countries, iatrogenic delivery is responsible for almost half of the births between gestational ages of 28 and 35 weeks, and other recognised risk factors for preterm birth include multiple pregnancies, hypertension and pre-eclampsia, maternal stress, smoking, genital tract infection, incompetent cervix, heavy physical work and inadequate prenatal care. For intrauterine growth restriction, risk factors include maternal smoking, short maternal stature, low pre-pregnancy body mass index (BMI), low gestational weight gain, pregnancy-induced hypertension and specific fetal anomalies. Stress can be defined as a pathological process resulting from the reaction of the body to external forces and abnormal conditions that tend to disturb the organism’s homeostasis; the term refers to the emotional, psychological and physical effects as well as the sources of disturbance.3 An association between stress and adverse pregnancy outcome has been reported in a large number of studies, and different pathogenic Paediatric and Perinatal Epidemiology, 22, 240–248. ©2008 The Authors, Journal Compilation ©2008 Blackwell Publishing Ltd. Biopsychosocial determinants of pregnancy length and fetal growth mechanisms have been hypothesised including hormonal, vascular, toxic and nutritional mediators, as well as immune and infectious processes.4,5 Social support is a multi-faceted concept that may be described and measured in many different ways.6 In the context of pregnancy, social support has a positive effect on psychological well-being and may limit the magnitude of negative stress reactions.7 Although many observational studies have suggested that social support has a mediating influence on the relationship between life stress, regardless of the causes of stress, and the development of pregnancy complications, interventions offering additional social support for at-risk pregnant women were not associated with improvements in perinatal outcomes.8 Self-esteem is also a complex concept that may be both an explanation and a consequence of psychological disorders and has been shown to be a predictor of various kinds of deviant and risky behaviour.9 The association between measures of self-esteem and adverse pregnancy outcomes is not well known, but a hypothesis is that high self-esteem may limit depression in the face of stress by enhancing a positive sense of self throughout life circumstances and alleviating the negative perception of stressors.7 An important issue in research on the causes of adverse pregnancy outcomes is to identify the complex pathways relating distant socio-economic and psychological factors with more proximate biological variables. Analytical methods usually rely on multivariable regression models, in which all the independent variables are treated on equal terms.10 Path analysis is a subset of structural equation modelling, which allows the examination of direct and indirect relationships among measured variables.11 This technique may be useful to better understand the complex interrelations and interactions between psychological, social and biological factors and the pathways leading to preterm delivery and/or intrauterine growth restriction. In 1997, the Regional Public Health Board of Montérégie (one of the 18 regions in the province of Quebec, Canada) undertook a survey to estimate the prevalence of risk factors for adverse pregnancy outcomes.12 Women attending prenatal ultrasound clinics were invited to complete a questionnaire, which was then linked with birth certificates. Applying a path analysis technique, the data set was used to construct and test theoretical models explaining the variability of pregnancy length and fetal growth, focusing on 241 the effects of perceived stress, social support and self-esteem. Methods Study population The population in the Montérégie region is approximately 1.3 million, with about 13 000 births per year. Seventy-five per cent of births take place in the nine public hospitals located in the region, and most of the remaining births take place in hospitals located in the nearby Montreal region. Pregnant women referred to the prenatal ultrasound clinics in the nine hospitals in the Montérégie region were invited to complete a selfadministered questionnaire in French while waiting for an examination. A total of 2685 questionnaires were distributed, in proportion to the annual number of examinations in each of the participating hospitals. Women residing outside the study region or with insufficient knowledge of French were not invited. Data collection extended from November 1997 to May 1998. The study protocol was approved by the Research and Ethics Committee of the Regional Public Health Board of Montérégie and by the medical directors of participating hospitals. Questionnaire and explanatory variables The questionnaire (available on request from the authors) included information on age and stage of pregnancy. Responders were asked to provide the highest level of education achieved. This ordinal scale was arbitrarily transformed into a numerical scale using the following values: 6 years for elementary education completed, 12 years for secondary education, 13 years for advanced secondary training, 14 years for community college and 16 years representing completion of a university degree. The question pertaining to annual family income was designed with eight categories, the lowest being <$10 000 and the highest being ⱖ$70 000. Regarding tobacco consumption, responses were recorded in one of two possible categories: current smokers and those who smoked during pregnancy, and never smoking women and those who stopped smoking completely before pregnancy. Five Likert-scale questions were used to assess social support. The first two questions were derived from a provincial survey on the health of the population and identified the presence or absence of a partner.13 The Paediatric and Perinatal Epidemiology, 22, 240–248. ©2008 The Authors, Journal Compilation ©2008 Blackwell Publishing Ltd. 242 J. St-Laurent et al. quality of the relationship was also evaluated. The remaining three questions were derived from an index elaborated for the Quebec Health Survey 1992–93. These questions identified the presence or absence of friends or family members in whom the responders said that they could confide, and to whom they would turn to for help and affection.14 Self-esteem was evaluated using six items from the Rosenberg scale.15 Eleven questions from the ‘Prenatal Psychosocial Profile’ were used to measure stress,16 including financial situation, family life, unstable living conditions, the loss of a loved one, tolerance for the current pregnancy, psychological and physical abuse, drug or alcohol use, work, friends and daily life hassles. For social support, selfesteem and perceived stress, global scores were created by adding the scores of all of the variables pertaining to each of these three dimensions. Obstetric history was also obtained, as well as information on health problems before and during pregnancy. Weight and height before pregnancy was used for calculation of the BMI. In order to reduce the number of biomedical variables, a principal component analysis was performed using spss-catpca software.17 This technique aims to identify newly constructed continuous dimensions which are highly correlated with the initial variables and having a distribution of scores that explains the largest portion of the variance of observations in the sample. The three most important factors emerging from the analysis were retained as explanatory variables in the model. Birth certificates and outcome variables Self-administered questionnaires were linked to singleton livebirth certificates of women residing in the Montérégie region. The length of pregnancy was measured as the number of completed weeks recorded on the birth certificate. The fetal growth index was calculated as the observed birthweight minus the expected gestational age-specific and sex-specific birthweight, divided by the expected gestational age- and sexspecific birthweight.18 Model development and testing The development of a theoretical explanatory model was initiated after the study questionnaire was designed and implemented. The first step was to perform an extensive review of published studies and reviews on the determinants of preterm delivery and intrauterine growth restriction (the list is available on request to the authors). A single initial theoretical model was developed (Model I) specifying the causal relationships between the explanatory variables and Figure 1. Theoretical model constructed from the literature review (Model I). Paediatric and Perinatal Epidemiology, 22, 240–248. ©2008 The Authors, Journal Compilation ©2008 Blackwell Publishing Ltd. Biopsychosocial determinants of pregnancy length and fetal growth the two outcomes (Fig. 1). A constraint was to use the variables included in the questionnaire. The path diagram was then converted into a set of structural equations, using Amos 4.0 software.19 Model I was tested, using a two-thirds random sample of the observations. Standardised regression weights and their significance levels were calculated for duration of pregnancy and for fetal growth. Goodness of fit was evaluated using three different indices. CMIN/DF is the minimum value of discrepancy divided by its degrees of freedom, and values lower than 3 are indicative of an acceptable fit between the hypothetical model and the sample data.20 The comparative fit index (CFI) measures the degree to which the specified model is better than no model at all, and values close to 1 indicate a very good fit.21 Finally, the root mean square error of approximation (RMSEA) measures the residual variance per degree of freedom, and values of 0.05 or less indicate a close fit.22 In a second step, results from Model I were scrutinised, leading to the elimination of relationships that were poorly predictive or not statistically significant (P value > 0.05). New pathways were tried until more predictive and significant ones emerged that improved the fit. A new theoretical model (Model II) was identified and tested using the initial two-thirds sample and then, the remaining one-third of the observations in order to check its superiority over Model 1. Finally, Model II was applied to the whole data set in order to derive the most precise coefficients possible. Results Characteristics of participants A total of 1860 questionnaires were completed and of these, 1602 were from singleton pregnancies and successfully linked with a birth certificate. In the final study sample, the mean pregnancy length was 39.1 weeks (s.d. = 1.7 weeks), and 6.6% of women gave birth prematurely <37 weeks). The mean birthweight was 3383 g (s.d. = 533 g), and 5.2% of all newborns weighed <2500 g. Skewness was -1.8 and kurtosis was 6.8 for the gestational age distribution, while skewness was -0.5 and kurtosis was 1.2 for birthweight. The socio-economic and demographic characteristics of participants are shown in Table 1. Forty-four per cent of participants did not complete a college or university degree, and the mean duration of schooling 243 Table 1. Socio-economic and demographic characteristics of participants (n = 1602) Characteristics Highest degree completed Elementary Secondary Advanced secondary Community college University Family income <$10 000 $10 000–$19 999 $20 000–$29 999 $30 000–$39 999 $40 000–$49 999 $50 000–$59 999 $60 000–$69 999 ⱖ$70 000 Unknown Age (years) ⱕ18 19–34 ⱖ35 Body mass index <20 20–25 >25 n (%) 23 457 227 430 465 (1.4) (28.5) (14.2) (26.8) (29.0) 89 127 171 206 222 185 172 267 100 (5.6) (7.9) (10.7) (12.9) (13.9) (11.5) (10.7) (16.7) (6.2) 24 (1.5) 1458 (91.0) 120 (7.5) 366 (22.8) 765 (47.8) 410 (25.6) was 14.1 years (s.d. = 2.2 years). Fourteen per cent of women reported a family income of <$20 000, an indication of poverty. The mean age of participants was 27.9 years (s.d. = 4.6 years). The mean BMI before pregnancy was 23.4 (s.d. = 4.9). As seen in Table 2, a large majority of participants were living with a partner (94.9%) and less than 10% were not satisfied with the quality of their relationship. The level of social support was generally high in the study sample. The global score, expressed as the percentage of maximal support, was 90.7 (s.d. = 18.1). Answers pertaining to self-esteem are shown in Table 3. Overall, women had a high level of self-esteem and 5% or less indicated a negative self-perception. The global score was 15.1 (s.d. = 2.7). The majority of participants reported not being highly or moderately stressed (Table 4). The most frequent sources of stress were financial problems (7.3%) and the impression of being continuously overwhelmed (5.9%). The global score for stress was 38.1 (s.d. = 4.9), for a maximum value of 44 meaning no stress at all. The proportion of participants who reported a chronic medical condition before pregnancy was Paediatric and Perinatal Epidemiology, 22, 240–248. ©2008 The Authors, Journal Compilation ©2008 Blackwell Publishing Ltd. 244 J. St-Laurent et al. Table 2. Social support of participants n (%) Social support Living with a partner Your partner doesn’t understand you Your partner doesn’t give you enough affection Your partner is not involved enough in your relationship Is there one person in your family or friends to whom you can confide or speak freely about your problems? Is there someone in your family or friends who will help you when you are in trouble? Is there someone in your family or friends to whom you feel close and who will be affectionate with you? 18.9%, while 16.5% reported a chronic condition during pregnancy. The most frequent condition reported was asthma or another chronic respiratory problem (18.9% before pregnancy and 16.4% during pregnancy). Hypertension during pregnancy was reported by 3.1% of participants. Thirty-six per cent of women reported at least one infection during early pregnancy, the most common infection being a cold. A history of spontaneous abortion was reported by 30.0% of women and induced abortion by 14.5%. The proportion of women who had at least one previous birth was 53.6%. A previous preterm birth was reported by 4.9% 1602 1369 1365 1367 1585 1586 1582 (94.9) (8.9) (9.1) (6.1) (92.8) (97.2) (95.4) of participants and a low-birthweight infant by 3.2%. Finally, smoking during pregnancy was reported by 24.8% of women. Principal component analysis Three main dimensions were identified in the principal component analysis, which explained, respectively, 58.6%, 22.5% and 18.9% of the variance of 10 biomedical variables from the questionnaire (based on Eigenvalues). The correlation between the original risk factors and the three new dimensions is indicated in Table 3. Self-esteem of participants Statements I feel that I have a number of good qualities I feel that I’m a person of worth, at least on an equal plane with others I am able to do things as well as most other people I have a positive attitude toward myself On the whole, I am satisfied with myself I am inclined to feel that I am a failure n Strongly agree (%) Agree (%) Disagree (%) Strongly disagree (%) 1575 1574 0.4 0.4 0.4 0.9 42.8 35.0 54.7 62.0 1569 1565 1567 1568 0.3 0.5 0.4 79.9 1.2 4.6 3.4 14.0 38.8 51.7 53.4 2.3 57.6 40.9 40.6 1.6 Table 4. Maternal participants’ perceived stress level Item Financial concerns (groceries, rent, transport) Other financial preoccupations (debts, bankruptcy) Family-related problems (partner, children, parents) Recent or future relocation Recent loss of a loved one Current pregnancy Sexual, psychological or physical abuse Alcohol- or drug-related problems. Work-related problems Problems with friends Feeling of being continually overwhelmed n No stress (%) Low stress (%) Moderate stress (%) High stress (%) 1566 1562 1556 1551 1553 1547 1552 1555 1550 1555 1552 28.9 49.6 56.1 70.8 88.1 38.0 93.4 94.6 57.7 86.6 44.2 34.7 28.0 25.6 13.2 4.9 38.8 2.3 1.8 19.5 8.8 28.0 26.8 16.3 11.7 9.6 2.4 17.5 0.9 0.2 14.8 1.5 18.8 7.3 4.7 3.7 3.2 1.6 2.3 0.3 0.4 4.7 0.2 5.9 Paediatric and Perinatal Epidemiology, 22, 240–248. ©2008 The Authors, Journal Compilation ©2008 Blackwell Publishing Ltd. Biopsychosocial determinants of pregnancy length and fetal growth 245 Table 5. Results from the principal component analysis indicating the correlation (component loading coefficient) between the original risk factors and three new dimensions Dimensions Risk factors Obstetric history Maternal health Biophysical index 0.936 0.895 1.144 0.882 −0.907 0.098 −0.015 0.111 −0.498 −0.009 0.049 0.056 −0.024 0.038 −0.024 0.676 0.747 0.683 0.339 −0.505 0.135 0.176 0.087 0.092 0.223 0.240 −0.076 0 . 21 9 0.610 0.983 Previous miscarriage and/or ectopic pregnancy Previous termination Previous low-birthweight infant Previous preterm birth Parity Disease before pregnancy Infection during pregnancy Other disease during pregnancy Maternal age Body mass index Table 5 (based on component loading coefficients). The pattern of correlations leads to a meaningful labelling of the three dimensions being, respectively, ‘obstetric history’, ‘maternal health’ and ‘biophysical index’. Explanatory models The final explanatory model (Model II) for length of pregnancy is presented in Fig. 2. Values of the CMIN/DF (3.284), CFI (0.999) and RMSEA (0.038) indices indicated a satisfactory level of fit of the model. No direct relationship existed between self-esteem and social support on the one hand, and length of pregnancy on the other hand. The effect of perceived stress was not significant. The same holds true for tobacco usage. The only variable predicting pregnancy length was the biophysical index, constructed from maternal age and BMI. The final explanatory model (Model II) for fetal growth is shown in Fig. 3. Values of the CMIN/DF Figure 2. Final model for pregnancy length (Model II). *P < 0.05, **P < 0.001. Paediatric and Perinatal Epidemiology, 22, 240–248. ©2008 The Authors, Journal Compilation ©2008 Blackwell Publishing Ltd. 246 J. St-Laurent et al. Figure 3. Final model for fetal growth (Model II). *P < 0.05, **P < 0.001. (3.022), CFI (0.998) and RMSEA (0.036) indices indicated a satisfactory level of fit of the model. The fetal growth index was directly predicted by four factors being, in order of importance, smoking, biophysical index, obstetric history and maternal health. In the two models, social support was influenced by income, while perceived stress and self-esteem were influenced by education. Social support directly influenced perceived stress and also indirectly through self-esteem. Unexpectedly, the relationship between perceived stress and smoking was not statistically significant. Discussion In this study, based on a relatively large sample, the risk factors for adverse pregnancy outcomes were measured during pregnancy, thus preventing memory bias. Well-tested questions were used to measure perceived stress during pregnancy, social support and self-esteem. An index of fetal growth, statistically independent of the length of gestation, was applied, and both outcomes were treated as continuous variables in order to enhance the power of analysis. A theoretical model of causality was developed and tested within the framework of path analysis. The results showed that the level of perceived stress was influenced both by social support and by self-esteem, while these sociopsychological variables did not directly affect the length of gestation or fetal growth but instead were acted upon by intermediary behavioural and biomedical factors. This finding is consistent with the results of a study among 5295 inner-city women in Connecticut using a very similar methodology: birthweight was directly influenced by medical risk factors and addictive behaviours, while family stress and social support were direct determinants of addictive behaviours but were not independent predictors of birthweight.23 In another study among 247 women in California, prenatal social support was directly related to fetal growth, independent of obstetric risk factors.24 In the latter study, however, nutritional and biometric variables were not measured, and only 5% of participants reported smoking during pregnancy. Much more is known about the determinants of fetal growth than those of preterm birth.1,2 In our final model, fetal growth was strongly related to smoking, maternal age and BMI, diseases before and during pregnancy, and obstetric history. Perceived stress influenced maternal health and, thus, indirectly fetal growth. The physiological response to stress can affect maternal health in increasing the prevalence of hypertension and/or the incidence of infectious diseases.4,5 Paediatric and Perinatal Epidemiology, 22, 240–248. ©2008 The Authors, Journal Compilation ©2008 Blackwell Publishing Ltd. Biopsychosocial determinants of pregnancy length and fetal growth Many of these factors can be modified through appropriate intervention, smoking cessation or prevention in the first place. Pregnancy length was positively influenced by maternal age and BMI. No other factor was statistically associated with this outcome, meaning that prevention is still elusive. There are several limitations in our study. The survey was conducted in a region with favourable socioeconomic conditions, and participants were of a higher level of education than the population of pregnant women in the region.12 In the questionnaire, some answers may be perceived as undesirable and a systematic bias towards acceptable statements cannot be excluded. A low prevalence of adverse psychosocial factors in the data set certainly limits the power of analyses. Perceived stress, social support and selfesteem are complex concepts that are imperfectly measured through a questionnaire administered only once during pregnancy.25 Repeated measurements could improve both the validity and reliability of estimates. In addition, we did not define for every risk factor a critical exposure period in terms of when the variable may act such as before or during pregnancy, and this could dilute any true effect. In a study in California, the patterns of exposure variability across pregnancy were examined, and inter-trimester concordance was shown to be high for smoking and factors related to residence, to be moderately high for many occupational exposures, and to be low for illnesses and environmental exposures of short duration.26 In our study, perceived stress was measured in the first part of gestation and it is known that as pregnancy advances, women become less responsive to stressors. During the second trimester of pregnancy, the cardiovascular response to demanding tasks is reduced, relative to pre-pregnancy levels.27 The affective response to an earthquake was shown to be lower in early than in late pregnancy.28 These observations are concordant with the hypothesis that the hypothalamic-pituitary-adrenal response to stressors may be diminished or masked when levels of placental corticotrophin-releasing factor increased during pregnancy.29 The original survey was designed for descriptive epidemiology and not for analytical research. Medical risk factors were measured from a self-administered questionnaire and medical charts were not reviewed, which could generate imprecision. No biological measurement could be made in order to obtain unbiased information on potentially important predictors of adverse pregnancy outcomes such as hormonal and 247 immunological status. Birth certificates in Quebec do not contain information on induction of labour and on the cause of caesarean section, and it was thus impossible to perform a separate analysis for spontaneous preterm delivery. Finally, the model assumes linear relationships between variables19 and this may not always be the case. The effect of smoking on gestation length, for instance, could be masked if a threshold is present.1 Some other risk factors were not included in the model such as the use of illicit drugs, physical activity, dietary habits or gestational weight gain, and this is a limitation. In order to reduce the number of dependent variables in the model, a principal component analysis was performed. In this approach, no a priori assumption has to be made for grouping. As the three main dimensions generated by the principal component analysis were highly correlated with three different sets of clinically meaningful variables, this approach was retained in the path analysis. Using latent variables based on the information provided by the principal component analysis in full structural equation models would have generated new dimensions best representing the initial variables, and would have reduced measurement errors. However, the magnitude of the gain in terms of power would have been minimal as indicated by the values of the component loading coefficients presented in Table 5. The most important assumption in path analysis is a normal distribution of the endogenous (dependent) variable.19 For exogenous (independent) variables, departure from normality has much less consequence. In this study, the gestational age and birthweight distributions were close to normality, as indicated by the values of their skewness and kurtosis indices. This was not the case for the measure of social support, selfesteem and perceived stress. As a consequence, path regression coefficients leading to these variables may be biased and their statistical significance overestimated. Conclusions Structural equation modelling and path analysis constitute an interesting avenue for the analysis of the complex interactions between psychological, social and biological factors leading to preterm delivery and intrauterine growth restriction. Results showed that the level of perceived stress was influenced both by social support and self-esteem, while these psychosocial variables did not directly affect the length of ges- Paediatric and Perinatal Epidemiology, 22, 240–248. ©2008 The Authors, Journal Compilation ©2008 Blackwell Publishing Ltd. 248 J. St-Laurent et al. tation or fetal growth but instead were acted upon by intermediary behavioural and biomedical factors. However, there are many limitations in our analysis and more studies are needed to identify the mechanisms by which adverse psychosocial factors are translated into biological effects resulting in adverse pregnancy outcomes. Acknowledgements The study was supported by research grants from the ‘Direction de la santé publique de la Montérégie’ and from the ‘Fondation pour la recherche sur les maladies infantiles’. It was the subject matter of a Master degree in Clinical Sciences at the University of Sherbrooke. References 1 Kramer MS. Determinants of low birth weight: methodological assessment and meta-analysis. Bulletin of the World Health Organization 1987; 65:663–737. 2 Steer P. The epidemiology of preterm labour. BJOG 2005; 112(Suppl. 1):1–3. 3 U.S. National Library of Medicine. Unified Medical Language System. Stress Definition(s). http://ghr.nlm.nih.gov/ghr/ glossary/stress [last accessed 21 March 2008]. 4 Kramer MS, Goulet L, Lydon J, Seguin L, McNamara H, Dassa C, et al. 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