On time series analysis of public health and biomedical data

Conventional and advanced time series estimation: application to the Australian and New Zealand Intensive Care Society (ANZICS) adult patient database, 1993-2006

RATIONALE

Time series analysis has seen limited application in the biomedical Literature. The utility of conventional and advanced time series estimators was explored for intensive care unit (ICU) outcome series.

METHODS

Monthly mean time series, 1993-2006, for hospital mortality, severity-of-illness score (APACHE III), ventilation fraction and patient type (medical and surgical), were generated from the Australia and New Zealand Intensive Care Society adult patient database. Analyses encompassed geographical seasonal mortality patterns, series structural time changes, mortality series volatility using autoregressive moving average and Generalized Autoregressive Conditional Heteroscedasticity models in which predicted variances are updated adaptively, and bivariate and multivariate (vector error correction models) cointegrating relationships between series.

RESULTS

The mortality series exhibited marked seasonality, declining mortality trend and substantial autocorrelation beyond 24 lags. Mortality increased in winter months (July-August); the medical series featured annual cycling, whereas the surgical demonstrated long and short (3-4 months) cycling. Series structural breaks were apparent in January 1995 and December 2002. The covariance stationary first-differenced mortality series was consistent with a seasonal autoregressive moving average process; the observed conditional-variance volatility (1993-1995) and residual Autoregressive Conditional Heteroscedasticity effects entailed a Generalized Autoregressive Conditional Heteroscedasticity model, preferred by information criterion and mean model forecast performance. Bivariate cointegration, indicating long-term equilibrium relationships, was established between mortality and severity-of-illness scores at the database level and for categories of ICUs. Multivariate cointegration was demonstrated for {log APACHE III score, log ICU length of stay, ICU mortality and ventilation fraction}.

CONCLUSIONS

A system approach to understanding series time-dependence may be established using conventional and advanced econometric time series estimators.

Stock volatility as a risk factor for coronary heart disease death

AIMS

The volatility of financial markets may cause substantial emotional and physical stress among investors. We hypothesize that this may have adverse effects on cardiovascular health. The Chinese stock markets were extremely volatile between 2006 and 2008. We, therefore, examined the relationship between daily change of the Shanghai Stock Exchange (SSE) Composite Index (referred as the Index) and coronary heart disease (CHD) deaths from 1 January 2006 to 31 December 2008 in Shanghai, the financial capital of China.

METHODS AND RESULTS

Daily death and stock performance data were collected from the Shanghai Center for Disease Control and Prevention and SSE, respectively. Data were analysed with over-dispersed generalized linear Poisson models, controlling for long-term and seasonal trends of CHD mortality, day of the week, Index closing value, weather conditions, and air pollution levels. We observed a U-shaped relationship between the Index change and CHD deaths: both rising and falling of the Index were associated with more deaths and the fewest deaths coincided with little or no change of the index. We also examined the absolute daily change of the Index in relation to CHD deaths: in a 1-day lag model, each 100-point change of the Index corresponded to 5.17% (95% confidence interval: 1.71, 8.63%) increase in CHD deaths. Further analysis showed that the association was stronger for out-of-hospital CHD death than for in-hospital death.

CONCLUSION

We found that CHD deaths fluctuated with daily stock changes in Shanghai, suggesting that stock volatility may adversely affect cardiovascular health.

An Assessment of Mixed-Modeling Approaches for Characterizing Profiles of Time-Varying Response and Predictor Variables

A general statistical modeling approach was tested for characterizing the relationship between pathogen inoculum density (or other biological response variables) and environmental variables when the data are collected as temporal profiles of observations within multiple locations or years. The approach, based on the use of linear mixed models, simultaneously accounts for serial correlations of the observations within each time profile, the random effects of location–year (or other grouping factors), and the cross-correlation of the environmental variables, and is appropriate when the environmental effects on the response variable or its transformation (Y) are distributed over several times (e.g., days). Stability and precision of parameter estimates for environmental effects over multiple time lags were achieved through the use of polynomial constraints within a likelihood-based full mixed-model fit; from the parameter estimates, marginal effects of environmental variables and weights for individual time lags were determined. The mixed model was directly expanded, through the incorporation of smoothing functions, to potentially account for possible longer-term trends in the temporal profiles unrelated to the environmental variables being considered. The new approach described here (with or without a smoothing function) generalizes a previously used—and computationally less demanding—two-stage (composite) approach. In the previous approach, constrained parameter estimates and associated weights were first determined without consideration of serial correlation, cross-correlation of environmental variables, and the random effects of location–year; then, a mixed-model fit was accomplished using the fixed time-lag weights derived in the first step. Using data for inoculum density of Gibberella zeae on wheat spikes from 27 location–years, similar results were achieved with the full mixed model and the two-stage approaches, in terms of both the calculated parameters and predictions of Y. With the use of smoothing functions, the precision of the predictions was improved but the general conclusions regarding environmental effects on Y were not affected. Thus, in the particular example data set, previously derived conclusions regarding environmental effects on inoculum density were robust in terms of the statistical methodology used in analysis; most researchers will find the two-stage approach much easier to implement for the analysis of multiple profiles of time-varying observations.

Time series analysis on the health effects of temperature: advancements and limitations

The association between extreme temperatures and health outcomes has been frequently investigated during the last few years. This assessment is usually based on a time series design, a framework which has gained a substantial development in the last two decades. In this contribution we offer an overview of the recent methodological advancements which provide new statistical tools to examine the health effects of temperature in a time series setting, highlighting at the same time the main limitations that still affect this research area.

Computerized general practice based networks yield comparable performance with sentinel data in monitoring epidemiological time-course of influenza-like illness and acute respiratory illness

Background

Computerized morbidity registration networks might serve as early warning systems in a time where natural epidemics such as the H₁N₁ flu can easily spread from one region to another.

Methods

In this contribution we examine whether general practice based broad-spectrum computerized morbidity registration networks have the potential to act as a valid surveillance instrument of frequently occurring diseases. We compare general practice based computerized data assessing the frequency of influenza-like illness (ILI) and acute respiratory infections (ARI) with data from a well established case-specific sentinel network, the European Influenza Surveillance Scheme (EISS). The overall frequency and trends of weekly ILI and ARI data are compared using both networks.

Results

Detection of influenza-like illness and acute respiratory illness occurs equally fast in EISS and the computerized network. The overall frequency data for ARI are the same for both networks, the overall trends are similar, but the increases and decreases in frequency do not occur in exactly the same weeks. For ILI, the overall rate was slightly higher for the computerized network population, especially before the increase of ILI, the overall trend was almost identical and the increases and decreases occur in the same weeks for both networks.

Conclusions

Computerized morbidity registration networks are a valid tool for monitoring frequent occurring respiratory diseases and the detection of sudden outbreaks.

Stability of symptoms across major depressive episodes in bipolar disorder

OBJECTIVE

Some studies suggest that depressive subtypes, defined by groups of symptoms, have predictive or diagnostic utility. These studies make the implicit assumption of stability of symptoms across episodes in mood disorders, which has rarely been investigated.

METHODS

We examined prospective data from a cohort of 3,750 individuals with bipolar I or II disorder participating in the Systematic Treatment Enhancement Program for Bipolar Disorder study, selecting a subset of individuals who experienced two depressive episodes during up to two years of follow-up. Across-episode association of individual depressive or hypomanic/mixed symptoms was examined using the weighted kappa measure of agreement as well as logistic regression.

RESULTS

A total of 583 subjects experienced two prospectively observed depressive episodes, with 149 of those subjects experiencing a third. Greatest evidence of stability was observed for neurovegetative features, suicidality, and guilt/rumination. Loss of interest and fatigue were not consistent across episodes. Structural equation modeling suggested that the dimensional structure of symptoms was not invariant across episodes.

CONCLUSION

While the overall dimensional structure of depressive symptoms lacks temporal stability, individual symptoms including suicidality, mood, psychomotor, and neurovegetative symptoms are stable across major depressive episodes in bipolar disorder and should be considered in future investigations of course and pathophysiology in bipolar disorder.

Association of ambient air pollution with hospital outpatient and emergency room visits in Shanghai, China

Few studies exist in China examining the association of ambient air pollution with morbidity outcomes. We conducted a time-series analysis to examine the association of outdoor air pollutants (PM(10), SO(2), and NO(2)) with hospital outpatient and emergency room visits in Shanghai, China, using 3 years of daily data (2005-2007). Hospital and air pollution data were collected from the Shanghai Health Insurance Bureau and Shanghai Environmental Monitoring Center. Using a natural spline model, we examined effect of air pollutants with different lag structures including both single-day lag and multi-day lag. We examined effects of air pollution for the warm season (from April to September) and cool season (from October to March) separately. We found outdoor air pollution (SO(2) and NO(2)) was associated with increased risk of hospital outpatient and emergency room visits in Shanghai. The effect estimates varied for different lag structures of pollutants' concentrations. For lag 3, a 10 microg/m(3) increase in concentration of PM(10), SO(2) and NO(2) corresponded to 0.11% (95%CI: -0.03%, 0.26%), 0.34% (95%CI: 0.06%, 0.61%) and 0.55% (95%CI: 0.14%, 0.97%) increase of outpatient visit; and 0.01% (95%CI: -0.09%, 0.10%), 0.17% (95%CI: 0.00%, 0.35%) and 0.08% (95%CI: -0.18%, 0.33%) increase of emergency room visit. The associations appeared to be more evident in the cool season than in the warm season. In conclusion, short-term exposure to outdoor air pollution was associated with increased risk of hospital outpatient and emergency room visits in Shanghai. Our analyses provide evidence that the current air pollution level has an adverse health effect and strengthen the rationale for further limiting air pollution levels in the city.

What is population health intervention research?

Population-level health interventions are policies or programs that shift the distribution of health risk by addressing the underlying social, economic and environmental conditions. These interventions might be programs or policies designed and developed in the health sector, but they are more likely to be in sectors elsewhere, such as education, housing or employment. Population health intervention research attempts to capture the value and differential effect of these interventions, the processes by which they bring about change and the contexts within which they work best. In health research, unhelpful distinctions maintained in the past between research and evaluation have retarded the development of knowledge and led to patchy evidence about policies and programs. Myths about what can and cannot be achieved within community-level intervention research have similarly held the field back. The pathway forward integrates systematic inquiry approaches from a variety of disciplines.

[Profile of paediatric admissions and emergencies during an epidemic period of rotavirus in Valladolid [Spain]. Utility of a predictive model]

INTRODUCTION

The aim of this study was to determine the weeks of high rotavirus circulation in Valladolid (Spain) and to compare the characteristics of hospitalizations and emergencies in epidemic and nonepidemic periods.

METHODS

The information sources consisted of the weekly notifications to the Microbiological Information System, the Minimum Data Set, and the Emergency Registry. Expected cases for 2006 were calculated using a previously developed model. Weeks with observed cases over the upper limit of the 95% confidence interval for expected cases were considered epidemic periods. Hospitalization and emergencies in epidemic and nonepidemic periods were compared.

RESULTS

The number of cases in 2006 was 42% less than the expected number. The mean number of daily admissions was higher in epidemic periods (d=1.49; p=0.01) and the length of admissions was longer.

CONCLUSION

The activity of the paediatric service increased during the epidemic period. Consequently, implementation of surveillance activities and prevention and control programs for rotavirus in hospitals would seem advisable.

Support vector machine versus logistic regression modeling for prediction of hospital mortality in critically ill patients with haematological malignancies

Background

Several models for mortality prediction have been constructed for critically ill patients with haematological malignancies in recent years. These models have proven to be equally or more accurate in predicting hospital mortality in patients with haematological malignancies than ICU severity of illness scores such as the APACHE II or SAPS II [1]. The objective of this study is to compare the accuracy of predicting hospital mortality in patients with haematological malignancies admitted to the ICU between models based on multiple logistic regression (MLR) and support vector machine (SVM) based models.

Methods

352 patients with haematological malignancies admitted to the ICU between 1997 and 2006 for a life-threatening complication were included. 252 patient records were used for training of the models and 100 were used for validation. In a first model 12 input variables were included for comparison between MLR and SVM. In a second more complex model 17 input variables were used. MLR and SVM analysis were performed independently from each other. Discrimination was evaluated using the area under the receiver operating characteristic (ROC) curves (± SE).

Results

The area under ROC curve for the MLR and SVM in the validation data set were 0.768 (± 0.04) vs. 0.802 (± 0.04) in the first model (p = 0.19) and 0.781 (± 0.05) vs. 0.808 (± 0.04) in the second more complex model (p = 0.44). SVM needed only 4 variables to make its prediction in both models, whereas MLR needed 7 and 8 variables in the first and second model respectively.

Conclusion

The discriminative power of both the MLR and SVM models was good. No statistically significant differences were found in discriminative power between MLR and SVM for prediction of hospital mortality in critically ill patients with haematological malignancies.

Methods for estimating confidence intervals in interrupted time series analyses of health interventions

OBJECTIVE

Interrupted time series (ITS) is a strong quasi-experimental research design, which is increasingly applied to estimate the effects of health services and policy interventions. We describe and illustrate two methods for estimating confidence intervals (CIs) around absolute and relative changes in outcomes calculated from segmented regression parameter estimates.

STUDY DESIGN AND SETTING

We used multivariate delta and bootstrapping methods (BMs) to construct CIs around relative changes in level and trend, and around absolute changes in outcome based on segmented linear regression analyses of time series data corrected for autocorrelated errors.

RESULTS

Using previously published time series data, we estimated CIs around the effect of prescription alerts for interacting medications with warfarin on the rate of prescriptions per 10,000 warfarin users per month. Both the multivariate delta method (MDM) and the BM produced similar results.

CONCLUSION

BM is preferred for calculating CIs of relative changes in outcomes of time series studies, because it does not require large sample sizes when parameter estimates are obtained correctly from the model. Caution is needed when sample size is small.

Trends in pediatric and adult bicycling deaths before and after passage of a bicycle helmet law

OBJECTIVES

The goals were to examine bicycle-related mortality rates in Ontario, Canada, from 1991 to 2002 among bicyclists 1 to 15 years of age and 16 years of age through adulthood and to determine the effect of legislation (introduced in October 1995 for bicyclists <18 years of age) on mortality rates.

METHODS

The average numbers of deaths per year and mortality rates per 100000 person-years for the prelegislation and postlegislation periods, and the percentage changes, were calculated for each of the 2 age groups (1-15 years and >/=16 years). Differences before and after legislation in the 2 age groups were modeled in a time series analysis.

RESULTS

There were 362 bicycle-related deaths in the 12-year period (1-15 years: 107 deaths; >/=16 years: 255 deaths). For bicyclists 1 to 15 years of age, the average number of deaths per year decreased 52%, the mortality rate per 100000 person-years decreased 55%, and the time series analysis demonstrated a significant reduction in deaths after legislation. The estimated change in the number of deaths per month was -0.59 deaths per month. For bicyclists >/=16 years of age, there were only slight changes in the average number of deaths per year and the mortality rate per 100000 person-years, and the time series analysis demonstrated no significant change in deaths after legislation.

CONCLUSIONS

The bicycle-related mortality rate in children 1 to 15 years of age has decreased significantly, which may be attributable in part to helmet legislation. A similar reduction for bicyclists 16 years of age through adulthood was not identified. These findings support promotion of helmet use, enforcement of the existing law, and extension of the law to adult bicyclists.

Bayesian semiparametric regression for longitudinal binary processes with missing data

Longitudinal studies with binary repeated measures are widespread in biomedical research. Marginal regression approaches for balanced binary data are well developed, whereas for binary process data, where measurement times are irregular and may differ by individuals, likelihood-based methods for marginal regression analysis are less well developed. In this article, we develop a Bayesian regression model for analyzing longitudinal binary process data, with emphasis on dealing with missingness. We focus on the settings where data are missing at random (MAR), which require a correctly specified joint distribution for the repeated measures in order to draw valid likelihood-based inference about the marginal mean. To provide maximum flexibility, the proposed model specifies both the marginal mean and serial dependence structures using nonparametric smooth functions. Serial dependence is allowed to depend on the time lag between adjacent outcomes as well as other relevant covariates. Inference is fully Bayesian. Using simulations, we show that adequate modeling of the serial dependence structure is necessary for valid inference of the marginal mean when the binary process data are MAR. Longitudinal viral load data from the HIV Epidemiology Research Study are analyzed for illustration.

Evidence-based macro practice: addressing the challenges and opportunities

Steps involved in the process of evidence-based practice are reviewed in terms of their applicability to macro-level social work. These steps include (1) posing answerable questions; (2) locating credible research studies, (3) critically evaluating this research and its applicability to a practice situation; 4. selecting an intervention(s) by integrating research evidence with professional expertise, ethical standards, and the situation's unique circumstance; and (5) evaluating outcomes. This process has clear and compelling applications to macro-practice. A substantial body of research applicable to macro-level social work currently exists. Widespread adoption of EBP has great potential to improve social work programs and policies.

Seasonality of infectious diseases

Seasonality, a periodic surge in disease incidence corresponding to seasons or other calendar periods, characterizes many infectious diseases of public health importance. The recognition of seasonal patterns in infectious disease occurrence dates back at least as far as the Hippocratic era, but mechanisms underlying seasonality of person-to-person transmitted diseases are not well understood. Improved understanding will enhance understanding of host-pathogen interactions and will improve the accuracy of public health surveillance and forecasting systems. Insight into seasonal disease patterns may be gained through the use of autocorrelation methods or construction of periodograms, while seasonal oscillation of infectious diseases can be easily simulated using simple transmission models. Models demonstrate that small seasonal changes in host or pathogen factors may be sufficient to create large seasonal surges in disease incidence, which may be important particularly in the context of global climate change. Seasonality represents a rich area for future research.

Statistical Analysis and Application of Quasi Experiments to Antimicrobial Resistance Intervention Studies

Quasi-experimental study designs are frequently used to assess interventions that aim to limit the emergence of antimicrobial-resistant pathogens. However, previous studies using these designs have often used suboptimal statistical methods, which may result in researchers making spurious conclusions. Methods used to analyze quasi-experimental data include 2-group tests, regression analysis, and time-series analysis, and they all have specific assumptions, data requirements, strengths, and limitations. An example of a hospital-based intervention to reduce methicillin-resistant Staphylococcus aureus infection rates and reduce overall length of stay is used to explore these methods.

Procedures for numerical analysis of circadian rhythms

This article reviews various procedures used in the analysis of circadian rhythms at the populational, organismal, cellular and molecular levels. The procedures range from visual inspection of time plots and actograms to several mathematical methods of time series analysis. Computational steps are described in some detail, and additional bibliographic resources and computer programs are listed.

Diurnal temperature range and daily mortality in Shanghai, China

Although the relationship between temperature level and mortality outcomes has been well established, it is still unknown whether within-day variation in temperature, e.g. diurnal temperature range (DTR), is a risk factor for death independent of the corresponding temperature. Moreover, DTR is a meteorological indicator associated with global climate change which may be related to a variety of health outcomes. We hypothesized that large diurnal temperature change might be a source of additional environmental stress and therefore a risk factor for death. We used daily weather and mortality data from Shanghai, China to test this hypothesis. We conducted a time-series study to examine the association between DTR and mortality outcomes from 2001 to 2004. A semi-parametric generalized additive model (GAM) was used to assess the acute effect of DTR on mortality after controlling for covariates including time trend, day of the week (DOW), temperature, humidity, and outdoor air pollution. We found a strong association between DTR and daily mortality after adjustment for those potential confounders. A 1 degrees C increment of the 3-day moving average of DTR corresponded to a 1.37% (95% CI 1.08-1.65%) increase in total non-accidental mortality, a 1.86% (95% CI 1.40-2.32%) increase in cardiovascular mortality, and a 1.29% (95% CI 0.49-2.09%) increase in respiratory mortality. The effects of DTR on total non-accidental and cardiovascular mortality were significant on both "cold" (below 23 degrees C) and "warm" (at least 23 degrees C) days, although respiratory mortality was only significantly associated with DTR on "cold" days. This study suggests within-day variation in temperature may be a novel risk factor for death.

Finding leading indicators for disease outbreaks: filtering, cross-correlation, and caveats

Bioterrorism and emerging infectious diseases such as influenza have spurred research into rapid outbreak detection. One primary thrust of this research has been to identify data sources that provide early indication of a disease outbreak by being leading indicators relative to other established data sources. Researchers tend to rely on the sample cross-correlation function (CCF) to quantify the association between two data sources. There has been, however, little consideration by medical informatics researchers of the influence of methodological choices on the ability of the CCF to identify a lead-lag relationship between time series. We draw on experience from the econometric and environmental health communities, and we use simulation to demonstrate that the sample CCF is highly prone to bias. Specifically, long-scale phenomena tend to overwhelm the CCF, obscuring phenomena at shorter wave lengths. Researchers seeking lead-lag relationships in surveillance data must therefore stipulate the scale length of the features of interest (e.g., short-scale spikes versus long-scale seasonal fluctuations) and then filter the data appropriately--to diminish the influence of other features, which may mask the features of interest. Otherwise, conclusions drawn from the sample CCF of bi-variate time-series data will inevitably be ambiguous and often altogether misleading.

On the equivalence of case-crossover and time series methods in environmental epidemiology

The case-crossover design was introduced in epidemiology 15 years ago as a method for studying the effects of a risk factor on a health event using only cases. The idea is to compare a case's exposure immediately prior to or during the case-defining event with that same person's exposure at otherwise similar "reference" times. An alternative approach to the analysis of daily exposure and case-only data is time series analysis. Here, log-linear regression models express the expected total number of events on each day as a function of the exposure level and potential confounding variables. In time series analyses of air pollution, smooth functions of time and weather are the main confounders. Time series and case-crossover methods are often viewed as competing methods. In this paper, we show that case-crossover using conditional logistic regression is a special case of time series analysis when there is a common exposure such as in air pollution studies. This equivalence provides computational convenience for case-crossover analyses and a better understanding of time series models. Time series log-linear regression accounts for overdispersion of the Poisson variance, while case-crossover analyses typically do not. This equivalence also permits model checking for case-crossover data using standard log-linear model diagnostics.