Box-Jenkins modelling in medical research
Abstract
Notifications of diseases, entries in a hospital, injuries due to accidents, etc., are frequently collected in fixed equally spaced intervals. Such observations are likely to be dependent. In environmental medicine, where series such as daily concentrations of pollutants are collected and analysed, it is evident that dependence of consecutive measurements may be important. A high concentration of a pollutant today has a certain 'inertia', i.e. a tendency to be high tomorrow as well. Dependence of consecutive obser vations may be equally important when data such as blood glucose are recorded within a single patient. ARIMA models (autoregressive integrated moving average models, Box-Jenkins models), which allow the stochastic dependence of consecutive data to be modelled, have become well established in such fields as economics. This article reviews basic concepts of Box-Jenkins modelling. The methods are illustrated by applications. In particular, the following topics are presented: the ARIMA model, transfer function models (assessment of relations between time series) and intervention analysis (assessment of changes of time series).
Get full access to this article
View all access and purchase options for this article.
References
Box Gep, Jenkins GM Time series analysis: forecasting and control, revised edition. San Francisco: Holden Day, 1976 .
Jenkins GM Practical experiences with modelling and forecasting time series St Helier: Gwilym Jenkins & Partners (Overseas) Ltd., 1979.
Harvey AC Time series models. Oxford: P Allan, 1981.
Hipel KW, McLeod AI, Lennox WC Advances in Box-Jenkins modelling, 1. Model construction Water Resources Research 1977; 13: 567-75.
McLeod AI, Hipel KW, Lennox WC Advances in Box-Jenkins modelling, 2. Applications. Water Resources Research 1977; 13: 577-86.
Box Gep, Tiao GC Intervention analysis with applications to economic and environmental problems Journal of the American Statistical Association 1975; 70: 70-79.
Tiao GC, Box Gep, Hamming WJ Analysis of Los Angeles photochemical smog data: a statistical overview . Journal of the Air Pollution Control Association 1975; 25: 260-68.
Tiao GC, Box Gep, Hamming WJ A statistical analysis of the Los Angeles ambient carbon monoxide data 1955-1972 Journal of the Air Pollution Control Association 1975; 25: 1129-36.
Hipel KW, Lennox WC, Unny TE, McLeod AI Intervention analysis in water resources Water Resources Research 1975; 11 : 855-61.
Cleveland WS The inverse autocorrelations of a time series and their applications Technometrics 1972; 14: 277-98.
Chatfield C. Inverse autocorrelations. Journal of the Royal Statistical Society, Series A 1979 ; 142: 363-77.
Helfenstein U., Ackermann-Liebrich U., Braun-Fahrländer Ch, Wanner HU Air pollution and diseases of the respiratory tracts in pre-school children: a transfer function model. Journal of Environmental Monitoring and Assessment 1991; 17 : 147-56.
Ljung GM, Box Gep. On a measure of lack of fit in time series models Biometrika 1978; 65: 297-303.
Bartlett MS Some aspects of the time-correlation problem in regard to tests of significance Journal of the Royal Statistical Society 1935; 98: 536-43.
Box Gep, Newbold P. Some comments on a paper of Cohen, Gomme and Kendall Journal of the Royal Statistical Society, Series A 1979 ; 134: 229-40.
Haugh LD Checking the independence of two covariance-stationary time series: a univariate residual cross-correlation approach. Journal of the American Statistical Association 1976; 71: 378-85.
Haugh LD, Box Gep. Identification of dynamic regression (distributed lag) models connecting two time series Journal of the American Statistical Association 1977; 72: 121-30.
Anon. Europe's river Rhine has suffered one of the worst chemical spills ever Environmental Science and Technology 1987; 21: 5.
Anon. A fishy smell in Basle. Lancet 1987; i: 95.
Capel PD, Giger W., Wanner O. Accidental input of pesticides into the Rhine river Environmental Science and Technology 1988; 22: 992-97.
Helfenstein U., Ackermann-Liebrich U., Braun-Fahrländer Ch, Wanner HU The environmental accident of 'Schweizerhalle' and respiratory diseases: a time series analysis Statistics in Medicine 1991; 10: 1481-92.
Ackermann-Liebrich U., Braun Ch, Rapp RC Epidemiologic analysis of an environmental disaster: the Schweizerhalle experience. Environmental Research 1992; 58 : 1-14.
Crabtree BF, Ray SC, Schmidt PM, O'Connor PJ, Schmidt DD The individual over time: time series applications in health care research Journal of Clinical Epidemiology 1990; 43: 241-60.
Helfenstein U. When did a reduced speed limit show an effect? Exploratory identification of an intervention time. Accident Analysis and Prevention 1990; 22: 79-87.
Katzoff M. The application of time series forecasting methods to an estimation problem using provisional mortality statistics Statistics in Medicine 1989; 8 : 353-62.
Schnell D., Zaidi A., Reynolds G. A time series analysis of gonorrhea surveillance data. Statistics in Medicine 1989; 8: 343-52.
Zaidi A., Schnell D., Reynolds G. Time series analysis of syphilis surveillance data Statistics in Medicine 1989; 8 : 353-62.
Watier L., Richardson S., Hubert B. A time series construction of an alert threshold with application to S. bovismorbificans in France Statistics in Medicine 1991; 10: 1493-509.
Box Gep, Tiao GC Comparison of forecast and actuality Applied Statistics 1976; 25: 195-200.
Bhattacharyya MN, Layton AP Effectiveness of seat belt legislation on the Queensland Road Toll. An Australian case study in intervention analysis . Journal of the American Statistical Association 1979; 74: 596-603.
Gruchow HW, Rimm AA, Hoffmann G. Alcohol consumption and ischemic heart disease mortality: are time series correlations meaningful? American Journal of Epidemiology 1983; 118: 641-50.
Chatfield C. The analysis of time series: an introduction, fourth edition. London: Chapman and Hall, 1989 .
Helfenstein U. Detecting hidden relations between time series of mortality rates Methods of Information in Medicine 1990; 29: 57-60.
Abraham B., Ledolter J. Statistical methods for forecasting New York: John Wiley, 1983.
Haines LM, Munoz WP, Van Gelderen CJ ARIMA modelling of birth data. Journal of Applied Statistics 1989; 16 : 55-67.
Bowie C., Prothero D. Finding causes of seasonal diseases using time series analysis International Journal of Epidemiology 1981 ; 10: 87-92.
Murphy Mfg, Campbell MJ Sudden infant death syndrome and environmental temperature: an analysis using vital statistics. Journal of Epidemiology and Community Health 1987; 41: 63-71.
Derriennic F., Richardson S., Mollié A., Lellouch J. Short-term effects of sulphur dioxide pollution on mortality in two French cities International Journal of Epidemiology 1989; 18: 186-97.
Helfenstein U. Box-Jenkins modelling of some viral infectious diseases Statistics in Medicine 1986 ; 5: 37-47.
Choi K., Thacker SB An evaluation of influenza mortality surveillance, 1962-1979. I. Time series forecasts of expected pneumonia and influenza deaths American Journal of Epidemiology 1981; 13: 215-26.
Lassare S., Tan SH Evaluation of safety measures on the frequency and gravity of traffic accidents in France by means of intervention analysis. In: Anderson OD ed. Time series analysis, theory and practice 1. Amsterdam: North-Holland Publishing Company, 1982: 297-306.
Martinez-Schnell B., Zaidi A. Time series analysis of injuries . Statistics in Medicine 1989; 8: 1497-508.
Sali GJ Evaluation of Boise selective traffic enforcement project Transportation Research Report 1983; 910: 68-74.
Amick DR, Marshall PB Evaluation of the Bonneville County, Idaho, DUI accident prevention program . Transportation Research Report 1983 ; 910: 81-93.
Harvey AC, Durbin J. The effects of seat belt legislation on British road casualities: a case study in structural time series modelling (with Discussion) Journal of the Royal Statistical Society, series A 1986; 149: 187-227.
Tsouros AD, Young RJ Applications of time series analysis: A case study on the impact of computer tomography Statistics in Medicine 1986; 5: 593-606.
Cite article
Cite article
Cite article
OR
Download to reference manager
If you have citation software installed, you can download article citation data to the citation manager of your choice
Information, rights and permissions
Information
Published In
Article first published: March 1996
Issue published: March 1996
PubMed: 8743076
Authors
Metrics and citations
Metrics
Journals metrics
This article was published in Statistical Methods in Medical Research.
VIEW ALL JOURNAL METRICSArticle usage*
Total views and downloads: 206
*Article usage tracking started in December 2016
Articles citing this one
Receive email alerts when this article is cited
Web of Science: 0
Crossref: 114
- Geo-epidemiology of malaria incidence in the Vhembe District to guide ...
- Does the 80 km/h speed limit save lives in France?
- A newly combination model based on data denoising strategy and advance...
- Japanese encephalitis transmission trends in Gansu, China: A time seri...
- Impact of the COVID-19 pandemic on prescription refills for immune-med...
- Incidence of pulmonary tuberculosis under the regular COVID-19 epidemi...
- Time series forecasting for tuberculosis incidence employing neural ne...
- Trends in Systemic Antifungal Use in Australia, 2005–2016: a Time-Seri...
- Antimicrobial use and antimicrobial resistance in Enterobacterales and...
- Impact of the COVID-19 pandemic on cardiovascular heart disease medica...
- Investigating seasonal patterns in enteric infections: a systematic re...
- Time series analysis of hemorrhagic fever with renal syndrome in mainl...
- Prospective correlational time-series analysis of the influence of wea...
- Trends in Postpartum Opioid Prescribing: A Time Series Analysis
- Rising co-payments and continuity of healthcare for Dutch patients wit...
- ICU Patients’ Antibiotic Exposure and Triazole-Resistance in Invasive ...
- Impact of antibiotic prescription on the resistance of Klebsiella pneu...
- Contemporary Treatment Patterns for Non-muscle-invasive Bladder Cancer...
- Forecasting Migration Intention Using Multivariate Time Series
- Do extreme summers increase blood vitamin D (25-hydroxyvitamin D) leve...
- Modeling and analysis of a time series of equine infectious anemia cas...
- COVID-19 Cases in Iraq; Forecasting Incidents Using Box - Jenkins ARIM...
- Trends, seasonality and the association between outpatient antibiotic ...
- Early Prediction of Vital Signs Using Generative Boosting via LSTM Net...
- Rising co-payments coincide with unwanted effects on continuity of hea...
- Management Strategies and Patient Selection After a Hospital Funding R...
- The impact of randomized trial results on abdominal aortic aneurysm re...
- A novel hybrid model on the prediction of time series and its applicat...
- Temporal Changes in Characteristics, Treatment and Outcomes of Heart F...
- The Association Between Internet Searches and Moisturizer Prescription...
- Statistical methods applied in pharmacotherapy
- Global trends in the awareness of sepsis: insights from search engine ...
- Temporal association between antibiotic use and resistance in Klebsiel...
- Prevalence of Elective and Ruptured Abdominal Aortic Aneurysm Repairs ...
- Shorter waiting time, better emergency healthcare: Forecasting Stockho...
- A Data Assimilation-Based Approach for Estimating Land Surface Variabl...
- Combined influence of multiple climatic factors on the incidence of ba...
- Construction and evaluation of two computational models for predicting...
- Cancer mortality in former East and West Germany: a story of unificati...
- Practice patterns in the care of acute Achilles tendon ruptures
- Decrease in mortality rate and hospital admissions for acute myocardia...
- Impact of Clinical Trial Results on the Temporal Trends of Carotid End...
- The accuracy and timeliness of neuraminidase inhibitor dispensing data...
- Snapshot of the prescribing practice for the clopidogrel and esomepraz...
- The Terror Attacks of 9/11 and Suicides in Germany
- Use of Internet Search Queries to Enhance Surveillance of Foodborne Il...
- Understanding weekly cycles in suicide: an analysis of Austrian and Sw...
- Unintentional Discontinuation of Chronic Medications for Seniors in Nu...
- Influence of antimicrobial consumption on gram-negative bacteria in in...
- Predicting CCHF incidence and its related factors using time-series an...
- Can Didactic Continuing Education Improve Clinical Decision Making and...
- The Guyana Diabetes and Foot Care Project: Improved Diabetic Foot Eval...
- Frequency and tendency of malaria in Colombia, 1990 to 2011: a descrip...
- Forecasting ESKAPE infections through a time-varying auto-adaptive alg...
- Intervention Analysis in Time Series
- The Effect of an Organizational Network for Patient Safety on Safety E...
- Towards tailored physical activity health intervention: Predicting dro...
- Mortality on match days of the German national soccer team: a time ser...
- Forecasting Tuberculosis Incidence in Iran Using Box-Jenkins Models
- Impact of the JUPITER Trial on Statin Pres...
- Outpatient Antibiotic Use in France between 2000 and 2010: after the N...
- Climate Variability, Weather and Enteric Disease Incidence in New Zeal...
- Did Media Attention of the 2009 A(H1N1) Influenza Epidemic Increase Ou...
- Patented Drug Extension Strategies on Healthcare Spending: A Cost-Eval...
- Effect of 9/11 on suicide: appropriateness of a time series model
- Antibiotic Consumption and Healthcare-Associated Infections Caused by ...
- Seasonality of Acute Otitis Media and the Role of Respiratory Viral Ac...
- Safety and cost savings of reducing adult dengue hospitalization in a ...
- An evaluation of the impact of antibiotic stewardship on reducing the ...
- Seasonality and Temporal Correlation between Community Antibiotic Use ...
- Death has a preference for birthdays—an analysis of death time series
- Clinical Evidence, Practice Guidelines, and β-Blocker Utilization Befo...
- The impact of antibiotic use on the incidence and resistance pattern o...
- Time-series analysis of the relationship of antimicrobial use and hand...
- Surveillance of Dengue Fever Virus: A Review of Epidemiological Models...
- Seasonal Variations in Clostridium difficile Infections Are Associated...
- Outpatient physician billing data for age and setting specific syndrom...
- Modelling the impact of antibiotic use on antibiotic-resistant Escheri...
- Multihospital Outbreak of Clostridium difficile ...
- Conventional and advanced time series estimation: application to the A...
- Real-time retrieval of Leaf Area Index from MODIS time series data
- The Need for Validation of Statistical Methods for Estimating Respirat...
- Analysis of an outbreak of Clostridium difficile infection controlled ...
- Temporal effects of antibiotic use and Clostridium difficile infection...
- Quasiexperimental Study of the Effects of Antibiotic Use, Gastric Acid...
- Activity and impact on antibiotic use and costs of a dedicated infecti...
- The relationship of short-term air pollution and weather to ED visits ...
- Understanding Detection Performance in Public Health Surveillance: Mod...
- Effects of meteorological factors on the onset of subarachnoid hemorrh...
- Modelling the impact of antibiotic use and infection control practices...
- Temporal effects of antibiotic use and hand rub consumption on the inc...
- Time series analysis of ultraviolet B radiation and type 1 diabetes in...
- Reduction in the suicide rate during Advent—a time series analysis
- Statistical Analysis and Application of Quasi Experiments to Antimicro...
- Weather Variability and the Incidence of Cryptosporidiosis: Comparison...
- The Effect of Antidepressant Warnings on Prescribing Trends in Ontario...
- Using Interrupted Time Series Analysis To Assess Associations of Fluor...
- Comparação do registro da produção ambulatorial em oncologia no Sistem...
- Impact of the Pravastatin or Atorvastatin Evaluation and Infection The...
- Evolution of fluoroquinolone resistance among Escherichia coli urinary...
- Transfer Function Models
- Intervention Analysis in Time Series
- ARMA and ARIMA Models
- Applications of Time-series Analysis to Antibiotic Resistance and Cons...
- Rates of Hyperkalemia after Publication of the Randomized Aldactone Ev...
- Antimicrobial Drug Use and Methicillin-resistant Staphyl...
- El Niño Southern Oscillation and the transmission of hepatitis A virus...
- Climate variability and Ross River virus transmission in Townsville Re...
- Evaluating Disease Management Program Effectiveness: An Introduction t...
- MODELING PULSE DISTURBANCE IMPACT ON COD POPULATION DYNAMICS: THE 1988...
- Stimulating Adverse Drug Reaction Reporting
- Óbitos por desnutrição em idosos, São Paulo e Rio de Janeiro: análise ...
- Making sense of antimicrobial use and resistance surveillance data: ap...
- Modelling and forecasting antimicrobial resistance and its dynamic rel...
Figures and tables
Figures & Media
Tables
View Options
Get access
Access options
If you have access to journal content via a personal subscription, university, library, employer or society, select from the options below:
loading institutional access options
Alternatively, view purchase options below:
Purchase 24 hour online access to view and download content.
Access journal content via a DeepDyve subscription or find out more about this option.
