1. 


2. 
 Andersson, Eva M., 1968
(författare)

Effect of dependency in systems for multivariate surveillance.
 2007

Rapport (övrigt vetenskapligt)abstract
 In many situations we need a system for detecting changes early. Examples are early detection of disease outbreaks, of patients at risk and of financial instability. In influenza outbreaks, for example, we want to detect an increase in the number of cases. Important indicators might be the number of cases of influenzalike illness and pharmacy sales (e.g. aspirin). By continually monitoring these indicators, we can early detect a change in the process of interest. The methodology of statistical surveillance is used. Often, the conclusions about the process(es) of interest is improved if the surveillance is based on several indicators. Here three systems for multivariate surveillance are compared. One system, called LRpar, is based on parallel likelihood ratio methods, since the likelihood ratio has been shown to have several optimality properties. In LRpar, the marginal density of each indicator is monitored and an alarm is called as soon as one of the likelihood ratios exceeds its alarm limit. The LRpar is compared to an optimal alarm system, called LRjoint, which is derived from the full likelihood ratio for the joint density. The performances of LRpar and LRjoint are compared to a system where the Hotellings T2 is monitored. The evaluation is made using the delay of a motivated alarm, as a function of the times of the changes. The effect of dependency is investigated: both dependency between the monitored processes and correlation between the time points when the changes occur. When the first change occurs immediately, the three methods work rather similarly, for independent processes and zero correlation between the change times. But when all processes change later, the T2 has much longer delay than LRjoint and LRpar. This holds both when the processes are independent and when they have a positive covariance. When we assume a positive correlation between the change times, the LRjoint yields a shorter delay than LRpar when the changes actually do occur simultaneously, whereas the opposite is true when the changes do actually occur at different time point.


3. 
 Andersson, Eva M., 1968, et al.
(författare)

Exploratory analysis of Swedish influenza data
 2006

Rapport (övrigt vetenskapligt)abstract
 Information about the stochastic properties of Swedish influenza data can be used for many purposes. In this report we describe and discuss statistical models that can be used in the construction of automated detection systems. Statistical models for influenza data, which are suggested in the literature, are reviewed and the possibility to use them for analyses of Swedish data is discussed. To describe how the influenza incidence changes from one week to another exponential functions are found to work better than earlier suggested models. Data are available for several periods and the parameters are estimated for each. The parameters are found to vary considerably. The conclusion is that nonparametric methods will be more robust to the variation between periods and should therefore be used in a detection system. However the spectrum of parametric models is useful to consider in the evaluations of the detection systems. Data on influenzalike illness (ILI) and data on laboratory diagnoses (LD) were available for several periods of influenza. The possibility of using different leading indicators is discussed. Special interest is given to whether ILI can be used as a leading indicator for LD. The conclusion is that the complicated relation between these variables (in the present form) hampers this. Automated detection systems could be developed for several purposes; the most obvious one is outbreak detection, but in search of new infectious diseases it could also be of interest to have a system for detecting decline in the “ordinary” influenza. For outbreak detection we focus on ILI data since the first indications of an outbreak can be expected to be in the ILI data. Very sparse data are available for nonepidemic periods in the present data sets. The lack of good baseline data is a serious problem for the detection of a change from a baseline. A detection system which relies on an estimate of the baseline level is very vulnerable to errors in the estimate. Instead, we suggest that the fact that there is a rise in level at the start of an epidemic is utilized. Thus, a detection system which utilizes the monotonicity property at a rise in level rather than an estimate of the nonepidemic level is suggested. It is concluded that the Gaussian distribution is not useful for ILI data at the outbreak phase but that the Poisson distributions can be used as a first approximation. For detection of the decline of the influenza we focus on LD data. We conclude that a Gaussian distribution can be used near the peak. It is suggested that the monotonicity properties of a peak is utilized. Some suggestions of how to predict the time and height of the peak of the influenza incidence are given.


4. 
 Andersson, Eva M., 1968
(författare)

Hotelling´s T2 Method in Multivariate Online Surveillance. On the Delay of an Alarm
 2008

Rapport (övrigt vetenskapligt)abstract
 A system for detecting changes in an ongoing process is needed in many situations. Online monitoring (surveillance) is used in early detection of disease outbreaks, of patients at risk and of financial instability. By continually monitoring one or several indicators, we can, early, detect a change in the processes of interest. There are several suggested methods for multivariate surveillance, one of which is the Hotelling’s T2. Since one aim in surveillance is quick detection of a change, it is important to use evaluation measures that reflect the timeliness of an alarm. One suggested measure is the expected delay of an alarm, in relation to the time of change () in the process. Here we investigate a delay measure for the bivariate situation. Generally, the measure depends on both change times (i.e. 1 and 2). We show that, for a bivariate situation using the T2 method, the delay only depends on 1 and 2 through the distance 12.


5. 


6. 
 Andersson, Eva M., 1968, et al.
(författare)

Modeling influenza incidence for the purpose of online monitoring
 2007

Rapport (övrigt vetenskapligt)abstract
 We describe and discuss statistical models of Swedish influenza data, with special focus on aspects which are important in online monitoring. Earlier suggested statistical models are reviewed and the possibility of using them to describe the variation in influenzalike illness (ILI) and laboratory diagnoses (LDI) is discussed. Exponential functions were found to work better than earlier suggested models for describing the influenza incidence. However, the parameters of the estimated functions varied considerably between years. For monitoring purposes we need models which focus on stable indicators of the change at the outbreak and at the peak. For outbreak detection we focus on ILI data. Instead of a parametric estimate of the baseline (which could be very uncertain,), we suggest a model utilizing the monotonicity property of a rise in the incidence. For ILI data at the outbreak, Poisson distributions can be used as a first approximation. To confirm that the peak has occurred and the decline has started, we focus on LDI data. A Gaussian distribution is a reasonable approximation near the peak. In view of the variability of the shape of the peak, we suggest that a detection system use the monotonicity properties of a peak.


7. 


8. 
 Andersson, Eva M., 1968, et al.
(författare)

Predictions by early indicators of the time and height of yearly influenza outbreaks in Sweden
 2007

Rapport (övrigt vetenskapligt)abstract
 Aims: Methods for prediction of the peak of the influenza from early observations are suggested. These predictions can be used for planning purposes. Methods: In this study, new robust methods are described and applied on weekly Swedish data on influenzalike illness (ILI) and weekly laboratory diagnoses of influenza (LDI). Both simple and advanced rules for how to predict the time and height of the peak of LDI are suggested. The predictions are made using covariates calculated from data in early LDI reports. The simple rules are based on the observed LDI values while the advanced ones are based on smoothing by unimodal regression. The suggested predictors were evaluated by crossvalidation and by application to the observed seasons. Results: The relation between ILI and LDI was investigated and it was found that the ILI variable is not a good proxy for the LDI variable. The advanced prediction rule regarding the time of the peak of LDI had a median error of 0.9 weeks, and the advanced prediction rule for the height of the peak had a median deviation of 28%. Conclusions: The statistical methods for predictions have practical usefulness.


9. 
 Andersson, Eva M., 1968, et al.
(författare)

Statistiska varningssystem för hälsorisker
 2008

Rapport (övrigt vetenskapligt)abstract
 Varningssystem behövs t.ex. vid intensivövervakning, smittskydd, miljörisker och kvalitetskontroll av vården. Statistiska varningssystem signalerar när det skett en väsentlig ändring och man vet vilka egenskaper systemet har. För varningssystem är det viktigt att larmet kommer snabbt efter förändringen utan att det blir många falsklarm. I ett varningssystem kan inte hypotesprövning på vanligt sätt användas. Det behövs istället speciell metodik. Enbart subjektiv övervakning av data medför stor bedömarvariation varför en kombination med ett statistiskt system kan vara av värde. Metodiken exemplifieras för influensaövervakning.


10. 

