Ian B. MacNeill

Seasonality in six enterically transmitted diseases and ambient temperature

We propose an analytical and conceptual framework for a systematic and comprehensive assessment of disease seasonality to detect changes and to quantify and compare temporal patterns. To demonstrate the proposed technique, we examined seasonal patterns of six enterically transmitted reportable diseases (EDs) in Massachusetts collected over a 10-year period (1992-2001). We quantified the timing and intensity of seasonal peaks of ED incidence and examined the synchronization in timing of these peaks with respect to ambient temperature. All EDs, except hepatitis A, exhibited well-defined seasonal patterns which clustered into two groups. The peak in daily incidence of Campylobacter and Salmonella closely followed the peak in ambient temperature with the lag of 2-14 days. Cryptosporidium, Shigella, and Giardia exhibited significant delays relative to the peak in temperature (approximately 40 days, P<0.02). The proposed approach provides a detailed quantification of seasonality that enabled us to detect significant differences in the seasonal peaks of enteric infections which would have been lost in an analysis using monthly or weekly cumulative information. This highly relevant to disease surveillance approach can be used to generate and test hypotheses related to disease seasonality and potential routes of transmission with respect to environmental factors.

Seasonality Assessment for Biosurveillance Systems

Biosurveillance systems for infectious diseases typically deal with nonlinear time series. This nonlinearity is due to the non-Gaussian and nonstationary nature of an outcome process. Infectious diseases (ID), waterborne and foodborne enteric infections in particular, are typically characterized by a sequence of sudden outbreaks, which are often followed by long low endemic levels. Multiple outbreaks occurring within a relatively short time interval form a seasonal pattern typical for a specific pathogen in a given population. Seasonal variability in the probability of exposure combined with a partial immunity to a pathogen adds to the complexity of seasonal patterns. Although seasonal variation is a well-known phenomenon in the epidemiology of enteric infections, simple analytical tools for examination, evaluation, and comparison of seasonal patterns are limited. This obstacle also limits analysis of factors associated with seasonal variations. The objectives of this paper are to outline the notion of seasonality, to define characteristics of seasonality, and to demonstrate tools for assessing seasonal patterns and the effects of environmental factors on such patterns. To demonstrate these techniques, we conducted a comparative study of seasonality in Salmonella cases as reported by the state surveillance system in relation to seasonality in ambient temperature, and found that the incidence in Salmonella infection peaked two weeks after a peak in temperature. The results suggest that ambient temperature can be a potential predictor of Salmonella infections at a seasonal scale.

Time series analysis of human foetal breathing activity at 30–39 weeks gestation

Thirty-one healthy human fetuses were each observed with a real-time scanner continuously for 24 h. The percentage of time spent breathing was computed for each 5 min observation period during the 24 h which produced a time series of 288 observations for each fetus. Box-Jenkins modelling techniques and analysis of frequency spectrum distribution were used to quantify mathematically the human fetal breathing data. The data was described mathematically by a first-order auto-regression z(t)=0.7 z(t-1) + epsilon(t) which confirmed and quantified the episodic nature of foetal breathing activity. Evaluation of the spectral distribution of the fetal breathing movements identified a significant band of pseudo-periodic components with repeat periods ranging from 100 to 500 min (P less than 0.001). Results of this study indicated that the occurrence of fetal breathing movements were non-random and that Box-Jenkins modelling results and spectral power distribution may be useful in identification and description of any fetal breathing patterns which differ from normal patterns.

Lagged regression residuals and serial-correlation tests

A new family of statistics is proposed to test for the presence of serial correlation in linear regression models. The tests are based on partial sums of lagged cross-products of regression residuals that define a class of interesting Gaussian processes. These processes are characterized in terms of regressor functions, the serial-correlation structure, the distribution of the noise process, and the order of the lag of the cross-products of residuals. It is shown that these four factors affect the lagged residual processes independently. Large-sample distributional results are presented for test statistics under the null hypothesis of no serial correlation or for alternatives from a range of interesting hypotheses. Some indication of the circumstances to which the asymptotic results apply in finite-sample situations and of those to which they should be applied with some caution are obtained through a simulation study. Tables of selected quantiles of the proposed tests are also given. The tests are illustr...

Modeling heteroscedastic age-period-cohort cancer data

The extent to which cancer will be a burden on the Canadian health-care system will be determined by future cancer rates and future population levels in the high-risk age groups. Parametric models of incidence and mortality rates for various cancers may be used to obtain medium-term forecasts of rates, which then can be used in conjunction with population projections to obtain forecasts of total incidence and mortality. Age-period-cohort cancer data often exhibit marked heteroscedasticity, which complicates the modeling of the data. Methods to allow for the effects of this heteroscedasticity on residual processes are developed and discussed in the context of modeling Canadian female breast-cancer incidence data.

Effects of screening errors and differential mortality on the estimation of the incidence of dementia in the Canadian Study of Health and Aging.

The Canadian Study of Health and Aging produced an estimate of the incidence of dementia among elderly Canadians by following up, after 5 years, the undemented found in an initial prevalence survey. Initial and follow-up estimates could be biased by false-negative error in the screening tool used for subjects living in the community, and by erroneous classification of subjects who died in the interim. Here, we use a deterministic model to quantify those possible biases. We conclude that, using the estimates of the errors from control samples, the incidence among community subjects would be overestimated by 15%, and the incidence among the institutional subjects would be underestimated by 37%. The overall incidence would be underestimated by 14%. Most of the bias can be attributed to inaccuracies in the classification of deaths.

Monitoring Statistics Which Have Increased Power over a Reduced Time Range.

The problem of monitoring trends for changes at unknown times is considered. Statistics which permit one to focus high power on a segment of the monitored period are studied. Numerical procedures are developed to compute the null distribution of these statistics.

The effect of autocorrelated errors on change-detection statistics.

In this paper, regression models with error terms generated by lower order ARMA schemes are analyzed. Methods are discussed for estimating the parameters of the regression coefficients and the ARMA processes. The problem of detecting changes in the regression parameters is considered. A change-detection statistic proposed by MacNeill (1978) for regression problems is modified for application to ARMA processes. The effect of autocorrelated errors on this statistic is briefly discussed.

Detection of Interventions at Unknown Times

Publisher Summary While the detection of changes in parameters when the time of change is a relatively standard statistical problem; the detection of changes when the time of change is unknown is a non-standard problem that is currently receiving considerable attention. A method of detecting change of regression parameters at unknown times has been presented in this chapter. A derivation of a likelihood ratio type statistic for detecting changes in regression parameters at unknown times is presented and distributional properties of the statistic are discussed in the chapter. The statistic is then applied to several periodic series. Models are then considered for improving the short and intermediate-term forecasting capacity of periodic models, yet, preserving both long-term predictive capacity and the clear meaning of the model parameters. The models are constructed so as to have certain properties of the autoregressive schemes, but to retain the basic properties of periodicity. The effect of present observations on the amplitude disappears in the long term; hence, the basic cycle defines the long-term prediction. An adaptive harmonic regression model of a doubly stochastic nature fitted to data indicates that such models are capable of improving both fits to the data and forecasts of future observations.

Likelihood and clinical trials

The history of the application of statistical theory to the analysis of clinical trials is reviewed. The current orthodoxy is a somewhat illogical hybrid of the original theory of significance tests of Edgeworth, Karl Pearson, and Fisher, and the subsequent decision theory approach of Neyman, Egon Pearson, and Wald. This hegemony is under threat from Bayesian statisticians. A third approach is that of likelihood, stemming from the work of Fisher and Barnard. This approach is illustrated using hypothetical data from the Lancet articles by Bradford Hill, which introduced clinicians to statistical theory.