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A quick count seeks to estimate the voting trends of an election and communicate them to the population on the evening of the same day of the election. In quick counts, the sampling is based on a stratified design of polling stations. Voting information is gathered gradually, often with no guarantee of obtaining the complete sample or even information in all the strata. However, accurate interval estimates with partial information must be obtained. Furthermore, this becomes more challenging if the strata are additionally study domains. To produce partial estimates, two strategies are proposed: (1) a Bayesian model using a dynamic post-stratification strategy and a single imputation process defined after a thorough analysis of historic voting information; additionally, a credibility level correction is included to solve the underestimation of the variance and (2) a frequentist alternative that combines standard multiple imputation ideas with classic sampling techniques to obtain estimates under a missing information framework. Both solutions are illustrated and compared using information from the 2021 quick count. The aim was to estimate the composition of the Chamber of Deputies in Mexico.
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BACKGROUND: The main objective of this study was to describe the relationship between working conditions, sleep and psycho-affective variables and medical errors. METHODS: This was an observational, analytical and cross-sectional study in which 661 medical residents answered questionnaires about working conditions, sleep and psycho-affective variables. Actigraphic sleep parameters and peripheral temperature circadian rhythm were measured in a subgroup of 38 subjects. Bivariate and multivariate predictors of medical errors were assessed. RESULTS: Medical residents reported working 66.2 ± 21.9 weekly hours. The longest continuous shift was of 28.4 ± 10.9 h. They reported sleeping 6.1 ± 1.6 h per day, with a sleep debt of 94 ± 129 min in workdays. A high percentage of them reported symptoms related to psycho-affective disorders. The longest continuous shift duration (OR = 1.03 [95% CI, 1.00-1.05], p = 0.01), working more than six monthly on-call shifts (OR = 1.87 [95% CI, 1.16-3.02], p = 0.01) and sleeping less than six hours per working day (OR = 1.66 [95% CI, 1.10-2.51], p = 0.02) were independently associated with self-reported medical errors. The report of medical errors was associated with an increase in the percentage of diurnal sleep (2.2% [95% CI, 0.1-4.3] vs 14.5% [95% CI, 5.9-23.0]; p = 0.01) in the actigraphic recording. CONCLUSIONS: Medical residents have a high working hour load that affect their sleep opportunities, circadian rhythms and psycho-affective health, which are also related to the report of medical errors. These results highlight the importance of implementing multidimensional strategies to improve medical trainees' sleep and wellbeing, increasing in turn their own and patients' safety.
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Sono , Tolerância ao Trabalho Programado , Humanos , Tolerância ao Trabalho Programado/psicologia , Estudos Transversais , Análise Multivariada , Erros MédicosRESUMO
Resumo: Introdução: Não se sabe se a ausência de estudantes de Medicina ao Teste de Progresso (TP) se dá de forma aleatória ou por alguma característica sistemática deles, o que poderia influenciar a representatividade dos resultados obtidos pelos participantes. Objetivo: Este estudo teve como objetivos comparar os índices de desempenho acadêmico, no curso de Medicina da UFSC, dos alunos presentes e ausentes ao TP em 2019; propor uma maneira de estimar, a partir desses índices, quais seriam as notas dos faltantes se tivessem participado do TP; e identificar fatores associados à ausência ao TP. Método: Foram comparadas as médias dos índices de desempenho acadêmico, globais e nas diferentes fases (semestres) dos grupos de alunos presentes e ausentes ao TP, utilizando teste t de Student para amostras independentes. Por meio de uma técnica de regressão linear, foram imputadas as prováveis notas no TP ao grupo de alunos ausentes. Resultado: As médias globais dos três indicadores acadêmicos foram significativamente menores nos alunos ausentes ao TP (p variando de < 0,03 a < 0,0001); em dez das 11 fases (semestres) analisadas do curso, os indicadores acadêmicos dos faltosos foram piores do que dos presentes. A imputação de notas no TP aos ausentes permitiu verificar que existe correlação (R = 0,62) entre a porcentagem destes e a diferença de notas entre os grupos que realizaram e os que faltaram ao TP. Entre os alunos do gênero masculino, 25,8% não fizeram o TP, enquanto no gênero feminino foram 16,6% (diferença com p < 0,01). Conclusão: A ausência de alunos ao TP não se dá de forma aleatória. Entre os faltosos, há uma tendência sistemática de existirem alunos com piores índices de desempenho acadêmico. O uso de imputação múltipla de dados evidencia uma correlação entre a porcentagem de faltosos e a diferença na média da nota no TP, desse grupo, comparada à média da nota dos participantes. A proporção de homens que faltaram ao TP foi significativamente maior do que a de mulheres.
Abstract: Introduction: It is not known whether the absence of medical students at the Progress Test (PT) is random event or if it due to some systematic characteristic of the students, which could influence the representativeness of the results obtained by the participants. Objectives: 1) to compare the academic performance indexes, in UFSC Medical School, of students who were present and absent from the PT in 2019; 2) to propose a way to estimate, based on these indexes, what the absentee's grades would be if they had participated in the PT; 3) to identify factors associated with absence from the PT. Method: The averages of academic performance indexes, overall and in the different phases (semesters) in the groups of students who were present and absent from the PT, were compared using Student's t test for independent samples. Using a linear regression technique, the probable PT scores were assigned to the group of absent students. Results: The global averages of the three academic indicators were significantly lower in students absent from the PT (p ranging from < 0.03 to < 0.0001); in 10 of the 11 analyzed course phases (semesters), the academic indicators of absentees were worse than those present at the test. The attribution of PT grades to the absentees allowed us to verify that there is a correlation (R=0.62) between the percentage of these students and the difference in grades between the groups that took and those that did not take the PT. Among male students, 25.8% did not attend the PT, while among female students the number of absentees was 16.6% (difference with p <0.01). Conclusions: The absence of students at the PT does not occur randomly. Among the absentees, there is a systematic tendency to have students with worse academic performance. The use of multiple imputation of data demonstrate a correlation between the percentage of absentees and the difference in the average of grades in the PT of this group, compared to the average of the participants' grades. The proportion of male students who missed the PT was significantly higher than that of female students.
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OBJECTIVE: We study how life course objective socioeconomic position (SEP) predicts subjective social status (SSS) and the extent to which SSS mediates the association of objective SEP with nutritional status and mental health outcomes. METHODS: We use data from participants of the INCAP Longitudinal Study 1969-2018 (n = 1258) from Guatemala. We use the MacArthur ladder for two measures of SSS - perceived community respect and perceived economic status. We estimate the association of SSS with health outcomes after adjusting for early life characteristics and life course objective SEP (wealth, schooling, employment) using linear regression. We use path analysis to study the extent of mediation by SSS on the health outcomes of body mass index (BMI; kg/m2), psychological distress (using the WHO Self-Reported Questionnaire; SRQ-20) and happiness, using the Subjective Happiness Scale (SHS). RESULTS: Median participant rating was 5 [IQR: 3-8] for the perceived community respect and 3 [IQR: 1-5] for the perceived economic status, with no differences by sex. Objective SEP in early life and adulthood were predictive of both measures of SSS in middle adulthood as well as health outcomes (BMI, SRQ-20 and SHS). Perceived community respect (z-scores; 1 z = 3.1 units) was positively associated with happiness (0.13, 95 % CI: 0.07, 0.19). Perceived economic status (z-scores; 1 z = 2.3 units) was inversely associated with psychological distress (-0.28, 95 % CI: -0.47, -0.09). Neither measure of SSS was associated with BMI. Neither perceived community respect nor perceived economic status attenuated associations of objective SEP with health outcomes on inclusion as a mediator. CONCLUSIONS: Subjective social status was independently associated with happiness and psychological distress in middle adulthood after adjusting for objective SEP. Moreover, association of objective SEP with health was not mediated by SSS, suggesting potentially independent pathways.
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BACKGROUND AND AIMS: Syringe-sharing among people who inject drugs, which can occur during incarceration and post-release, has been linked with increased risk of blood-borne infections. We aimed to investigate the cumulative effect of repeated incarceration and the post-release period on receptive syringe-sharing. DESIGN: Ongoing community-based cohort, recruited through targeted sampling between 2011 and 2012 with 6-month follow-ups. SETTING: Tijuana, Mexico. PARTICIPANTS: Sample of 185 participants (median age 35 years; 67% female) with no history of incarceration at study entry, followed to 2017. MEASUREMENTS: Cumulative incarceration and post-release period were constructed from incarceration events reported in the past 6 months for each study visit. Receptive syringe-sharing in the past 6 months was assessed as a binary variable. We used logistic regression with generalized estimating equations to examine the association between cumulative incarceration events and the post-release period with receptive syringe-sharing over time. Missing data were handled through multiple imputation. FINDINGS: At baseline, 65% of participants engaged in receptive syringe-sharing in the prior 6 months. At follow-up, 150 (81%) participants experienced a total of 358 incarceration events [median = 2, interquartile range (IQR) = 1-3]. The risk of receptive syringe-sharing increased with the number of repeated incarcerations. Compared with never incarcerated, those with one incarceration had 1.28 [95% confidence interval (CI) = 0.97-1.68] higher adjusted odds of syringe-sharing; two to three incarcerations, 1.42 (95% CI = 1.02-1.99) and more than three incarcerations, 2.10 (95% CI = 1.15-3.85). Participants released within the past 6 months had 1.53 (95% CI = 1.14-2.05) higher odds of sharing syringes compared with those never incarcerated. This post-release risk continued up to 1.5 years post-incarceration (adjusted odds ratio = 1.41, 95% CI = 1.04-1.91), but then waned. CONCLUSIONS: A longitudinal community cohort study among people who inject drugs suggested that the effects of incarceration on increased injecting risk, measured through syringe-sharing, are cumulative and persist during the post-release period.
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Infecções por HIV , Preparações Farmacêuticas , Abuso de Substâncias por Via Intravenosa , Estudos de Coortes , Feminino , Humanos , Recém-Nascido , Masculino , México/epidemiologia , Uso Comum de Agulhas e Seringas , Abuso de Substâncias por Via Intravenosa/epidemiologia , SeringasRESUMO
During analysis of scientific research data, it is customary to encounter anomalous values or missing data. Anomalous values can be the result of errors of recording, typing, measurement by instruments, or may be true outliers. This review discusses concepts, examples and methods for identifying and dealing with such contingencies. In the case of missing data, techniques for imputation of the values are discussed in, order to avoid exclusion of the research subject, if it is not possible to retrieve information from registration forms or to re-address the participant.
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Durante a análise dos dados de uma pesquisa científica, é habitual deparar-se com valores anômalos ou dados faltantes. Valores anômalos podem ser resultado de erros de registro, de digitação, de aferição instrumental, ou configurarem verdadeiros outliers. Nesta revisão, são discutidos conceitos, exemplos e formas de identificar e de lidar com tais contingências. No caso de dados faltantes, discutem-se técnicas de imputação dos valores para evitar a exclusão do sujeito da pesquisa, caso não seja possível recuperar a informação das fichas de registro ou reabordar o participante
During analysis of scientific research data, it is customary to encounter anomalous values or missing data. Anomalous values can be the result of errors of recording, typing, measurement by instruments, or may be true outliers. This review discusses concepts, examples and methods for identifying and dealing with such contingencies. In the case of missing data, techniques for imputation of the values are discussed in, order to avoid exclusion of the research subject, if it is not possible to retrieve information from registration forms or to re-address the participant
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Humanos , Masculino , Feminino , Estudos Clínicos como Assunto , Análise de Dados , Análise de Variância , Base de DadosRESUMO
BACKGROUND: HIV programs are often assessed by the proportion of patients who are alive and retained in care; however some patients are categorized as lost to follow-up (LTF) and have unknown vital status. LTF is not an outcome but a mixed category of patients who have undocumented death, transfer and disengagement from care. Estimating vital status (dead versus alive) among this category is critical for survival analyses and program evaluation. METHODS: We used three methods to estimate survival in the cohort and to ascertain factors associated with death among the first cohort of HIV positive patients to receive antiretroviral therapy in Haiti: complete case (CC) (drops missing), Inverse Probability Weights (IPW) (uses tracking data) and Multiple Imputation with Chained Equations (MICE) (imputes missing data). Logistic regression was used to calculate odds ratios and 95% confidence intervals for adjusted models for death at 10 years. The logistic regression models controlled for sex, age, severe poverty (living on <$1 USD per day), Port-au-Prince residence and baseline clinical characteristics of weight, CD4, WHO stage and tuberculosis diagnosis. RESULTS: Age, severe poverty, baseline weight and WHO stage were statistically significant predictors of AIDS related mortality across all models. Gender was only statistically significant in the MICE model but had at least a 10% difference in odds ratios across all models. CONCLUSION: Each of these methods had different assumptions and differed in the number of observations included due to how missing values were addressed. We found MICE to be most robust in predicting survival status as it allowed us to impute missing data so that we had the maximum number of observations to perform regression analyses. MICE also provides a complementary alternative for estimating survival among patients with unassigned vital status. Additionally, the results were easier to interpret, less likely to be biased and provided an alternative to a problem that is often commented upon in the extant literature.
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Interpretação Estatística de Dados , Conjuntos de Dados como Assunto , Infecções por HIV/tratamento farmacológico , Perda de Seguimento , Adulto , Antirretrovirais/uso terapêutico , Feminino , Haiti , Humanos , Modelos Logísticos , Estudos Longitudinais , Masculino , Pessoa de Meia-Idade , Análise de Regressão , Análise de SobrevidaRESUMO
A number of studies have evidenced the effect of modifiable lifestyle factors such as diet, breastfeeding and nutritional status on breast cancer risk. However, none have addressed the missing data problem in nutritional epidemiologic research in South America. Missing data is a frequent problem in breast cancer studies and epidemiological settings in general. Estimates of effect obtained from these studies may be biased, if no appropriate method for handling missing data is applied. We performed Multiple Imputation for missing values on covariates in a breast cancer case-control study of Córdoba (Argentina) to optimize risk estimates. Data was obtained from a breast cancer case control study from 2008 to 2015 (318 cases, 526 controls). Complete case analysis and multiple imputation using chained equations were the methods applied to estimate the effects of a Traditional dietary pattern and other recognized factors associated with breast cancer. Physical activity and socioeconomic status were imputed. Logistic regression models were performed. When complete case analysis was performed only 31% of women were considered. Although a positive association of Traditional dietary pattern and breast cancer was observed from both approaches (complete case analysis OR=1.3, 95%CI=1.0-1.7; multiple imputation OR=1.4, 95%CI=1.2-1.7), effects of other covariates, like BMI and breastfeeding, were only identified when multiple imputation was considered. A Traditional dietary pattern, BMI and breastfeeding are associated with the occurrence of breast cancer in this Argentinean population when multiple imputation is appropriately performed. Multiple Imputation is suggested in Latin America's epidemiologic studies to optimize effect estimates in the future.
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External validation of food recall over 24 h in schoolchildren is often restricted to eating events in schools and is based on direct observation as the reference method. The aim of this study was to estimate the dietary intake out of school, and consequently the bias in such research design based on only part-time validated food recall, using multiple imputation (MI) conditioned on the information on child age, sex, BMI, family income, parental education and the school attended. The previous-day, web-based questionnaire WebCAAFE, structured as six meals/snacks and thirty-two foods/beverage, was answered by a sample of 7-11-year-old Brazilian schoolchildren (n 602) from five public schools. Food/beverage intake recalled by children was compared with the records provided by trained observers during school meals. Sensitivity analysis was performed with artificial data emulating those recalled by children on WebCAAFE in order to evaluate the impact of both differential and non-differential bias. Estimated bias was within ±30 % interval for 84·4 % of the thirty-two foods/beverages evaluated in WebCAAFE, and half of the latter reached statistical significance (P<0·05). Rarely (<3 %) consumed dietary items were often under-reported (fish/seafood, vegetable soup, cheese bread, French fries), whereas some of those most frequently reported (meat, bread/biscuits, fruits) showed large overestimation. Compared with the analysis restricted to fully validated data, MI reduced differential bias in sensitivity analysis but the bias still remained large in most cases. MI provided a suitable statistical framework for part-time validation design of dietary intake over six daily eating events.
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Registros de Dieta , Ingestão de Alimentos , Rememoração Mental , Instituições Acadêmicas , Índice de Massa Corporal , Brasil , Criança , Feminino , Humanos , MasculinoRESUMO
La mayoría de los datos en ciencias sociales y educación presentan valores perdidos debido al abandono del estudio o la ausencia de respuesta. Los métodos para el manejo de datos perdidos han mejorado dramáticamente en los últimos años, y los programas computacionales ofrecen en la actualidad una variedad de opciones sofisticadas. A pesar de la amplia disponibilidad de métodos considerablemente justificados, muchos investigadores e investigadoras siguen confiando en técnicas viejas de imputación que pueden crear análisis sesgados. Este artículo presenta una introducción conceptual a los patrones de datos perdidos. Seguidamente, se introduce el manejo de datos perdidos y el análisis de los mismos con base en los mecanismos modernos del método de máxima verosimilitud con información completa (FIML, siglas en inglés) y la imputación múltiple (IM). Asimismo, se incluye una introducción a los diseños de datos perdidos así como nuevas herramientas computacionales tales como la función Quark y el paquete semTools. Se espera que este artículo incentive el uso de métodos modernos para el análisis de los datos perdidos.
Most of the social and educational data have missing observations due to either attrition or nonresponse. Missing data methodology has improved dramatically in recent years, and popular computer programs as well as software now offer a variety of sophisticated options. Despite the widespread availability of theoretically justified methods, many researchers still rely on old imputation techniques that can create biased analysis. This article provides conceptual introductions to the patterns of missing data. In line with that, this article introduces how to handle and analyze the missing information based on modern mechanisms of full-information maximum likelihood (FIML) and multiple imputation (MI). An introduction about planned missing designs is also included and new computational tools like Quark function, and semTools package are also mentioned. The authors hope that this paper encourages researchers to implement modern methods for analyzing missing data.
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OBJECTIVE: To assess the utility of imputing race/ethnicity using U.S. Census race/ethnicity, residential address, and surname information compared to standard missing data methods in a pediatric cohort. DATA SOURCES/STUDY SETTING: Electronic health record data from 30 pediatric practices with known race/ethnicity. STUDY DESIGN: In a simulation experiment, we constructed dichotomous and continuous outcomes with pre-specified associations with known race/ethnicity. Bias was introduced by nonrandomly setting race/ethnicity to missing. We compared typical methods for handling missing race/ethnicity (multiple imputation alone with clinical factors, complete case analysis, indicator variables) to multiple imputation incorporating surname and address information. PRINCIPAL FINDINGS: Imputation using U.S. Census information reduced bias for both continuous and dichotomous outcomes. CONCLUSIONS: The new method reduces bias when race/ethnicity is partially, nonrandomly missing.
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Censos , Coleta de Dados/métodos , Registros Eletrônicos de Saúde/estatística & dados numéricos , Etnicidade/estatística & dados numéricos , Grupos Raciais/estatística & dados numéricos , Adolescente , Negro ou Afro-Americano/estatística & dados numéricos , Fatores Etários , Asma/etnologia , Transtorno do Deficit de Atenção com Hiperatividade/etnologia , Viés , Criança , Pré-Escolar , Feminino , Hispânico ou Latino/estatística & dados numéricos , Humanos , Lactente , Recém-Nascido , Masculino , Nomes , Projetos de Pesquisa , Fatores Sexuais , Fatores Socioeconômicos , Estados UnidosRESUMO
INTRODUÇÃO: A perda de informações é um problema frequente em estudos realizados na área da Saúde. Na literatura essa perda é chamada de missing data ou dados faltantes. Através da imputação dos dados faltantes são criados conjuntos de dados artificialmente completos que podem ser analisados por técnicas estatísticas tradicionais. O objetivo desse artigo foi comparar, em um exemplo baseado em dados reais, a utilização de três técnicas de imputações diferentes. MÉTODO: Os dados utilizados referem-se a um estudo de desenvolvimento de modelo de risco cirúrgico, sendo que o tamanho da amostra foi de 450 pacientes. Os métodos de imputação empregados foram duas imputações únicas e uma imputação múltipla (IM), e a suposição sobre o mecanismo de não-resposta foi MAR (Missing at Random). RESULTADOS: A variável com dados faltantes foi a albumina sérica, com 27,1 por cento de perda. Os modelos obtidos pelas imputações únicas foram semelhantes entre si, mas diferentes dos obtidos com os dados imputados pela IM quanto à inclusão de variáveis nos modelos. CONCLUSÕES: Os resultados indicam que faz diferença levar em conta a relação da albumina com outras variáveis observadas, pois foram obtidos modelos diferentes nas imputações única e múltipla. A imputação única subestima a variabilidade, gerando intervalos de confiança mais estreitos. É importante se considerar o uso de métodos de imputação quando há dados faltantes, especialmente a IM que leva em conta a variabilidade entre imputações para as estimativas do modelo.
INTRODUCTION: It is common for studies in health to face problems with missing data. Through imputation, complete data sets are built artificially and can be analyzed by traditional statistical analysis. The objective of this paper is to compare three types of imputation based on real data. METHODS: The data used came from a study on the development of risk models for surgical mortality. The sample size was 450 patients. The imputation methods applied were: two single imputations and one multiple imputation and the assumption was MAR (Missing at Random). RESULTS: The variable with missing data was serum albumin with 27.1 percent of missing rate. The logistic models adjusted by simple imputation were similar, but differed from models obtained by multiple imputation in relation to the inclusion of variables. CONCLUSIONS: The results indicate that it is important to take into account the relationship of albumin to other variables observed, because different models were obtained in single and multiple imputations. Single imputation underestimates the variability generating narrower confidence intervals. It is important to consider the use of imputation methods when there is missing data, especially multiple imputation that takes into account the variability between imputations for estimates of the model.
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Humanos , Métodos Epidemiológicos , Modelos Estatísticos , Procedimentos Cirúrgicos Operatórios/mortalidade , RiscoRESUMO
The study of pest distributions in space and time in agricultural systems provides important information for the optimization of integrated pest management programs and for the planning of experiments. Two statistical problems commonly associated to the space-time modelling of data that hinder its implementation are the excess of zero counts and the presence of missing values due to the adopted sampling scheme. These problems are considered in the present article. Data of coffee berry borer infestation collected under Colombian field conditions are used to study the spatio-temporal evolution of the pest infestation. The dispersion of the pest starting from initial focuses of infestation was modelled considering linear and quadratic infestation growth trends as well as different combinations of random effects representing both spatially and not spatially structured variability. The analysis was accomplished under a hierarchical Bayesian approach. The missing values were dealt with by means of multiple imputation. Additionally, a mixture model was proposed to take into account the excess of zeroes in the beginning of the infestation. In general, quadratic models had a better fit than linear models. The use of spatially structured parameters also allowed a clearer identification of the temporal increase or decrease of infestation patterns. However, neither of the space-time models based on standard distributions was able to properly describe the excess of zero counts in the beginning of the infestation. This overdispersed pattern was correctly modelled by the mixture space-time models, which had a better performance than their counterpart without a mixture component.
O estudo da distribuição de pragas em espaço e tempo em sistemas agrícolas fornece informação importante para a otimização de programas de manejo integrado de pragas e para o planejamento de experimentos. Dois problemas estatísticos comumente associados à modelagem espaço-temporal desse tipo de dados que dificultam sua implementação são o excesso de zeros nas contagens e a presença de dados faltantes devido ao esquema de amostragem adotado. Esses problemas são considerados no presente artigo. Para estudar a evolução da infestação da broca do café a partir de focos iniciais de infestação foram usados dados de infestação da praga coletados em condições de campo na Colômbia. Foram considerados modelos com tendência de crescimento da infestação linear e quadrática, assim como diferentes combinações de efeitos aleatórios representando variabilidade espacialmente estruturada e não estruturada. As análises foram feitas sob uma abordagem Bayesiana hierárquica. O método de imputação múltipla foi usado para abordar o problema de dados faltantes. Adicionalmente, foi proposto um modelo de mistura para levar em consideração o excesso de zeros nas contagens no início da infestação. Em geral, os modelos quadráticos tiveram um melhor ajuste que os modelos lineares. O uso de parâmetros espacialmente estruturados permitiu uma identificação mais clara dos padrões temporais de acréscimo ou decréscimo na infestação. No entanto, nenhum dos modelos espaço-tempo baseados em distribuições padrões descreveu, apropriadamente, o excesso de zeros no início da infestação. Esse padrão de sobredispersão foi corretamente modelado pelos modelos de mistura espaço-tempo, os quais tiveram um melhor desempenho que seus homólogos sem mistura.
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The study of pest distributions in space and time in agricultural systems provides important information for the optimization of integrated pest management programs and for the planning of experiments. Two statistical problems commonly associated to the space-time modelling of data that hinder its implementation are the excess of zero counts and the presence of missing values due to the adopted sampling scheme. These problems are considered in the present article. Data of coffee berry borer infestation collected under Colombian field conditions are used to study the spatio-temporal evolution of the pest infestation. The dispersion of the pest starting from initial focuses of infestation was modelled considering linear and quadratic infestation growth trends as well as different combinations of random effects representing both spatially and not spatially structured variability. The analysis was accomplished under a hierarchical Bayesian approach. The missing values were dealt with by means of multiple imputation. Additionally, a mixture model was proposed to take into account the excess of zeroes in the beginning of the infestation. In general, quadratic models had a better fit than linear models. The use of spatially structured parameters also allowed a clearer identification of the temporal increase or decrease of infestation patterns. However, neither of the space-time models based on standard distributions was able to properly describe the excess of zero counts in the beginning of the infestation. This overdispersed pattern was correctly modelled by the mixture space-time models, which had a better performance than their counterpart without a mixture component.
O estudo da distribuição de pragas em espaço e tempo em sistemas agrícolas fornece informação importante para a otimização de programas de manejo integrado de pragas e para o planejamento de experimentos. Dois problemas estatísticos comumente associados à modelagem espaço-temporal desse tipo de dados que dificultam sua implementação são o excesso de zeros nas contagens e a presença de dados faltantes devido ao esquema de amostragem adotado. Esses problemas são considerados no presente artigo. Para estudar a evolução da infestação da broca do café a partir de focos iniciais de infestação foram usados dados de infestação da praga coletados em condições de campo na Colômbia. Foram considerados modelos com tendência de crescimento da infestação linear e quadrática, assim como diferentes combinações de efeitos aleatórios representando variabilidade espacialmente estruturada e não estruturada. As análises foram feitas sob uma abordagem Bayesiana hierárquica. O método de imputação múltipla foi usado para abordar o problema de dados faltantes. Adicionalmente, foi proposto um modelo de mistura para levar em consideração o excesso de zeros nas contagens no início da infestação. Em geral, os modelos quadráticos tiveram um melhor ajuste que os modelos lineares. O uso de parâmetros espacialmente estruturados permitiu uma identificação mais clara dos padrões temporais de acréscimo ou decréscimo na infestação. No entanto, nenhum dos modelos espaço-tempo baseados em distribuições padrões descreveu, apropriadamente, o excesso de zeros no início da infestação. Esse padrão de sobredispersão foi corretamente modelado pelos modelos de mistura espaço-tempo, os quais tiveram um melhor desempenho que seus homólogos sem mistura.