In praise of Prais-Winsten: An evaluation of methods used to account for autocorrelation in interrupted time series.

Interrupted time series are increasingly being used to assess the population impact of public health interventions. These data are usually correlated over time (auto correlated) and this must be accounted for in the analysis. Typically, this is done using either the Prais-Winsten method, the Newey-West method, or autoregressive-moving-average (ARMA) modeling. In this paper, we illustrate these methods via a study of pneumococcal vaccine introduction and explore their performance under 20 simulated autocorrelation scenarios with sample sizes ranging between 20 and 300. We show that in terms of mean square error, the Prais-Winsten and ARMA methods perform best, while in terms of coverage the Prais-Winsten method generally performs better than other methods. All three methods are unbiased. As well as having good statistical properties, the Prais-Winsten method is attractive because it is decision-free and produces a single measure of autocorrelation that can be compared between studies and used to guide sample size calculations. We would therefore encourage analysts to consider using this simple method to analyze interrupted time series.

Seasonality of suicide: a multi-country multi-community observational study.

AIMS: We aimed to investigate the heterogeneity of seasonal suicide patterns among multiple geographically, demographically and socioeconomically diverse populations. METHODS: Weekly time-series data of suicide counts for 354 communities in 12 countries during 1986-2016 were analysed. Two-stage analysis was performed. In the first stage, a generalised linear model, including cyclic splines, was used to estimate seasonal patterns of suicide for each community. In the second stage, the community-specific seasonal patterns were combined for each country using meta-regression. In addition, the community-specific seasonal patterns were regressed onto community-level socioeconomic, demographic and environmental indicators using meta-regression. RESULTS: We observed seasonal patterns in suicide, with the counts peaking in spring and declining to a trough in winter in most of the countries. However, the shape of seasonal patterns varied among countries from bimodal to unimodal seasonality. The amplitude of seasonal patterns (i.e. the peak/trough relative risk) also varied from 1.47 (95% confidence interval [CI]: 1.33-1.62) to 1.05 (95% CI: 1.01-1.1) among 12 countries. The subgroup difference in the seasonal pattern also varied over countries. In some countries, larger amplitude was shown for females and for the elderly population (≥65 years of age) than for males and for younger people, respectively. The subperiod difference also varied; some countries showed increasing seasonality while others showed a decrease or little change. Finally, the amplitude was larger for communities with colder climates, higher proportions of elderly people and lower unemployment rates (p-values < 0.05). CONCLUSIONS: Despite the common features of a spring peak and a winter trough, seasonal suicide patterns were largely heterogeneous in shape, amplitude, subgroup differences and temporal changes among different populations, as influenced by climate, demographic and socioeconomic conditions. Our findings may help elucidate the underlying mechanisms of seasonal suicide patterns and aid in improving the design of population-specific suicide prevention programmes based on these patterns.

A methodological framework for model selection in interrupted time series studies.

Interrupted time series (ITS) is a powerful and increasingly popular design for evaluating public health and health service interventions. The design involves analyzing trends in the outcome of interest and estimating the change in trend following an intervention relative to the counterfactual (the expected ongoing trend if the intervention had not occurred). There are two key components to modeling this effect: first, defining the counterfactual; second, defining the type of effect that the intervention is expected to have on the outcome, known as the impact model. The counterfactual is defined by extrapolating the underlying trends observed before the intervention to the postintervention period. In doing this, authors must consider the preintervention period that will be included, any time-varying confounders, whether trends may vary within different subgroups of the population and whether trends are linear or nonlinear. Defining the impact model involves specifying the parameters that model the intervention, including for instance whether to allow for an abrupt level change or a gradual slope change, whether to allow for a lag before any effect on the outcome, whether to allow a transition period during which the intervention is being implemented, and whether a ceiling or floor effect might be expected. Inappropriate model specification can bias the results of an ITS analysis and using a model that is not closely tailored to the intervention or testing multiple models increases the risk of false positives being detected. It is important that authors use substantive knowledge to customize their ITS model a priori to the intervention and outcome under study. Where there is uncertainty in model specification, authors should consider using separate data sources to define the intervention, running limited sensitivity analyses or undertaking initial exploratory studies.

Multivariate meta-analysis for non-linear and other multi-parameter associations.

In this paper, we formalize the application of multivariate meta-analysis and meta-regression to synthesize estimates of multi-parameter associations obtained from different studies. This modelling approach extends the standard two-stage analysis used to combine results across different sub-groups or populations. The most straightforward application is for the meta-analysis of non-linear relationships, described for example by regression coefficients of splines or other functions, but the methodology easily generalizes to any setting where complex associations are described by multiple correlated parameters. The modelling framework of multivariate meta-analysis is implemented in the package mvmeta within the statistical environment R. As an illustrative example, we propose a two-stage analysis for investigating the non-linear exposure-response relationship between temperature and non-accidental mortality using time-series data from multiple cities. Multivariate meta-analysis represents a useful analytical tool for studying complex associations through a two-stage procedure.

Cold and heat waves in the United States.

Extreme cold and heat waves, characterized by a number of cold or hot days in succession, place a strain on people's cardiovascular and respiratory systems. The increase in deaths due to these waves may be greater than that predicted by extreme temperatures alone. We examined cold and heat waves in 99 US cities for 14 years (1987-2000) and investigated how the risk of death depended on the temperature threshold used to define a wave, and a wave's timing, duration and intensity. We defined cold and heat waves using temperatures above and below cold and heat thresholds for two or more days. We tried five cold thresholds using the first to fifth percentiles of temperature, and five heat thresholds using the 95-99 percentiles. The extra wave effects were estimated using a two-stage model to ensure that their effects were estimated after removing the general effects of temperature. The increases in deaths associated with cold waves were generally small and not statistically significant, and there was even evidence of a decreased risk during the coldest waves. Heat waves generally increased the risk of death, particularly for the hottest heat threshold. Cold waves of a colder intensity or longer duration were not more dangerous. Cold waves earlier in the cool season were more dangerous, as were heat waves earlier in the warm season. In general there was no increased risk of death during cold waves above the known increased risk associated with cold temperatures. Cold or heat waves earlier in the cool or warm season may be more dangerous because of a build up in the susceptible pool or a lack of preparedness for extreme temperatures.

Multivariate meta-analysis: a method to summarize non-linear associations.

Multivariate meta-analysis represents a promising statistical tool in several research areas. Here, we provide a brief overview of the application of this methodology to combining complex multi-parameterized relationships, such as non-linear or delayed associations, in multi-site studies. The discussion focuses on the advantages over simpler univariate methods, estimation and computational issues and directions for further research.

Distributed lag non-linear models.

Environmental stressors often show effects that are delayed in time, requiring the use of statistical models that are flexible enough to describe the additional time dimension of the exposure-response relationship. Here we develop the family of distributed lag non-linear models (DLNM), a modelling framework that can simultaneously represent non-linear exposure-response dependencies and delayed effects. This methodology is based on the definition of a 'cross-basis', a bi-dimensional space of functions that describes simultaneously the shape of the relationship along both the space of the predictor and the lag dimension of its occurrence. In this way the approach provides a unified framework for a range of models that have previously been used in this setting, and new more flexible variants. This family of models is implemented in the package dlnm within the statistical environment R. To illustrate the methodology we use examples of DLNMs to represent the relationship between temperature and mortality, using data from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) for New York during the period 1987-2000.

Italy and Austria before and after study: second-hand smoke exposure in hospitality premises before and after 2 years from the introduction of the Italian smoking ban.

UNLABELLED: The aim of this paper was to compare nicotine concentration in 28 hospitality premises (HPs) in Florence and Belluno, Italy, where a smoking ban was introduced in 2005, and in 19 HPs in Vienna, Austria, where no anti-smoking law entered into force up to now. Airborne nicotine concentrations were measured in the same HPs in winter 2002 or 2004 (pre-ban measurements) and winter 2007 (post-ban measurements). In Florence and Belluno, medians decreased significantly (P < 0.001) from 8.86 [interquartile range (IQR): 2.41-45.07)] before the ban to 0.01 microg/m3 (IQR: 0.01-0.41) afterwards. In Austria (no smoking ban) the medians collected in winters 2004 and 2007 were, respectively, 11.00 (IQR: 2.53-30.38) and 15.76 microg/m3 (IQR: 2.22-31.93), with no significant differences. Measurements collected in winter 2007 in 28 HPs located in Naples, Turin, Milan (0.01 microg/m3; IQR: 0.01-0.16) confirmed post-ban results in Florence and Belluno. The medians of nicotine concentrations in Italy and Austria before the Italian ban translates, using the risk model of Repace and Lowery, into a lifetime excess lung cancer mortality risk for hospitality workers of 11.81 and 14.67 per 10,000, respectively. Lifetime excess lung cancer mortality risks for bar and disco-pub workers were 10-20 times higher than that calculated for restaurant workers, both in Italy and Austria. In winter 2007, it dropped to 0.01 per 10,000 in Italy, whereas in Austria it remained at the same levels. The drop of second-hand smoke exposure indicates a substantial improvement in air quality in Italian HPs even after 2 years from the ban. PRACTICAL IMPLICATIONS: The nation-wide smoking ban introduced in Italy on January 10, 2005, resulted in a drop in second-hand smoke exposure in hospitality premises, whereas in Austria, where there is no similar nation-wide smoking ban, the exposure to second-hand smoke in hospitality premises remains high. Given that second-hand smoke is considered a group 1 carcinogen according to the International Agency for Research on Cancer classification, the World Health Organization Framework Convention on Tobacco Control strongly recommends the implementation of nation-wide smoke-free policies in order to improve the indoor air quality of hospitality premises and workplaces. Results from our study strongly supports this recommendation.

[Occupational exposure to nickel in Tuscany: analysis of a biological monitoring register for the period 1991-1998]. / Esposizione occupazionale a Nichel in Toscana: analisi di un registro di monitoraggio biologico per il periodo 1991-1998.

OBJECTIVE: The study assesses the time trend in exposure to nickel among factory workers in Florence, via data on biological monitoring. A data-base of nickel in urinary samples (Ni-U mg/l) was created for the period 1991 to 1998. METHODS: The data-base contained 2.138 samples, measured by atomic absorption (GF-AAS),from 893 workers. Subjects came from 157 factories in various manufacturing sectors, especially electroplating, mechanical workshops, jewellery. RESULTS: Ni-U levels were correlated with manufacturing sector. The highest levels were found among workers from electroplating industries, where exposure was mainly due to water-soluble nickel compounds. The eight-year time trend showed a statistically significant decrease in Ni-U values, with a sharper drop during the last two-year period. Age, sex and number of samples per subject were not statistically related to this trend. CONCLUSION: The observed Ni-U decrease could be related to the efficacy of new legislation introduced in Italy during the study period (Law 626/94 and subsequent laws), but also to the intense labour inspection activities that officials of National Health Service performed, which were rightly focused on nickel exposure in different manufacturing sectors. This study confirms the usefulness for occupational risk evaluation of a biological monitoring data-base of routinely collected data.