Predicting meningococcal disease outbreaks in structured populations.

Rational decision making on whether some form of intervention would be necessary to control the spread of a meningococcal epidemic is based on predictions concerning its potential natural progression. Unfortunately, reliable predictions are difficult to make during the early stages of an outbreak. A stochastic discrete time epidemic model was applied to adaptively predict the development of outbreaks of meningococcal disease in 'closed' populations such as military garrisons or boarding schools, which are further divided into subgroups called 'units'. The performance of the adaptive method was assessed by using 3 simulated epidemics representing substantially different realizations in a 'garrison' of 20 units, with 68 men in each. Predictions of the weekly number of disease cases, of the number of carriers, and of the number of new infections were computed. Simulations suggest that predictions based only on the observed numbers of disease cases are generally inaccurate. These predictions can be improved if temporal observations on asymptomatic carriers in different units are utilized together with observed time series of the disease. A sample of 15 per cent from all units can be sufficient for a major improvement if the alternative is to obtain a full sample of only some units. Exploiting fully such information requires computer intensive Markov chain Monte Carlo methods.

Applying modern survival analysis methods to longitudinal dental caries studies.

Before the 1960s, tooth-specific caries risk was reported to be highest at 2 to 4 years after eruption. We studied the tooth-specific caries risk in three contemporary age cohorts in Finland. All together, 4072 boys and girls were followed annually from age 6 to age 18+ years in three age cohorts born in the 1960s, 1970s, and 1980s. We used a survival model and Bayesian inferential methods in the statistical analyses to establish the secular changes during this period. The analysis was based on the caries risk in individual teeth as a function of tooth age instead of summary measures, such as DMFS values. Our first finding was a marked overall decrease of caries. Moreover, analyses of the 1960 and 1970 cohorts revealed that the risk in molar teeth was highest immediately after eruption; in the youngest cohort, however, the risks of individual teeth were so low that no such dependencies on tooth age could be established.

Poliovirus surveillance by examining sewage water specimens: studies on detection probability using simulation models.

Efficiency of environmental surveillance of poliovirus circulation was studied using simulation models. First, three transmission models were defined for describing different scenarios of poliovirus infections in a large unstructured population. Second, environmental factors, such as the total volume of the sewage network and losses of viruses, were modeled for computing the virus output at the sewage sampling site. Third, the effect of sampling and laboratory procedures was accounted for in the probability of detection, given the amount of polioviruses in a specimen. The simulation model can be used for theoretical assessments of the likely efficiency of environmental surveillance, compared with acute flaccid paralysis (AFP) surveillance. Under reasonable assumptions in a vaccinated population, the AFP surveillance can be outperformed if the poliovirus outbreak is not large. However, this depends on the assumed case-to-infection ratio and on the sampling frequency of the sewage water specimens. Increasing the latter will lead to a higher detection probability, which will further enhance the method based on environmental surveillance.

Genetic basis of climatic adaptation in scots pine by bayesian quantitative trait locus analysis.

We examined the genetic basis of large adaptive differences in timing of bud set and frost hardiness between natural populations of Scots pine. As a mapping population, we considered an "open-pollinated backcross" progeny by collecting seeds of a single F(1) tree (cross between trees from southern and northern Finland) growing in southern Finland. Due to the special features of the design (no marker information available on grandparents or the father), we applied a Bayesian quantitative trait locus (QTL) mapping method developed previously for outcrossed offspring. We found four potential QTL for timing of bud set and seven for frost hardiness. Bayesian analyses detected more QTL than ANOVA for frost hardiness, but the opposite was true for bud set. These QTL included alleles with rather large effects, and additionally smaller QTL were supported. The largest QTL for bud set date accounted for about a fourth of the mean difference between populations. Thus, natural selection during adaptation has resulted in selection of at least some alleles of rather large effect.

Predictive inference, causal reasoning, and model assessment in nonparametric Bayesian analysis: a case study.

This paper continues our earlier analysis of a data set on acute ear infections in small children, presented in Andreev and Arjas (1998). The main goal here is to provide a method, based on the use of predictive distributions, for assessing the possible causal influence which the type of day care will have on the incidence of ear infections. A closely related technique is used for the assessment of the nonparametric Bayesian intensity model applied in the paper. Two graphical methods, supported by formal tests, are suggested for this purpose.

Estimation of transmission probabilities in families ascertained through a proband with variable age-at-onset disease: application to the HLA A, B and DR loci in Finnish families with type 1 diabetes. The DiMe Study Group.

An open problem of some interest in the study of HLA has been the possible existence of transmission distortion in the human HLA complex. In this paper, transmission probabilities are estimated and tested using data on HLA A, B and DR loci genotypes of parents and offspring ascertained from the entire population of Finland (Childhood Diabetes in Finland Study) through one or more offspring diagnosed with insulin-dependent diabetes mellitus (IDDM) during the recruitment period from September 1986 to July 1989. First, we show how to get unbiased estimates of transmission probabilities from the family data collected in the disease registry of incident cases. This is accomplished by assuming that transmission of HLA genes to children in the general population is conditionally independent given the parents' genotypes, and the birth dates of all offspring. Based on the sampling (ascertainment) process in the study on Childhood Diabetes in Finland, younger siblings of the index child (the oldest proband) are independent of the ascertainment and therefore give rise to unbiased inference regarding allele transmission. The hypothesis of Mendelian transmission of alleles at each locus was tested using the standard chi(2) test. Goodness-of-fit of the Mendelian inheritance model to the individual locus data is calculated by maximizing the likelihood function over allele transmission intensities at each locus. The existence of a strong transmission distortion is not supported by this study at the loci considered.

Bayesian mapping of multiple quantitative trait loci from incomplete outbred offspring data.

A general fine-scale Bayesian quantitative trait locus (QTL) mapping method for outcrossing species is presented. It is suitable for an analysis of complete and incomplete data from experimental designs of F2 families or backcrosses. The amount of genotyping of parents and grandparents is optional, as well as the assumption that the QTL alleles in the crossed lines are fixed. Grandparental origin indicators are used, but without forgetting the original genotype or allelic origin information. The method treats the number of QTL in the analyzed chromosome as a random variable and allows some QTL effects from other chromosomes to be taken into account in a composite interval mapping manner. A block-update of ordered genotypes (haplotypes) of the whole family is sampled once in each marker locus during every round of the Markov Chain Monte Carlo algorithm used in the numerical estimation. As a byproduct, the method gives the posterior distributions for linkage phases in the family and therefore it can also be used as a haplotyping algorithm. The Bayesian method is tested and compared with two frequentist methods using simulated data sets, considering two different parental crosses and three different levels of available parental information. The method is implemented as a software package and is freely available under the name Multimapper/outbred at URL http://www.rni.helsinki.fi/mjs/.

Modeling a Poisson forest in variable elevations: a nonparametric Bayesian approach.

A nonparametric Bayesian formulation is given to the problem of modeling nonhomogeneous spatial point patterns influenced by concomitant variables. Only incomplete information on the concomitant variables is assumed, consisting of a relatively small number of point measurements. Residual variation, caused by other unmeasured influential factors, is modeled in terms of a spatially varying baseline intensity function. A Markov chain Monte Carlo scheme is proposed for the simultaneous nonparametric estimation of each unknown function in the model. The suggested method is illustrated by reanalysing a data set in Rathbun (1996, Biometrics 52, 226-242), and the estimated models are compared with those obtained by Rathbun.

A hierarchical Bayesian model to predict the duration of immunity to Haemophilus influenzae type b.

A hierarchical Bayesian regression model is fitted to longitudinal data on Haemophilus influenzae type b (Hib) serum antibodies. To estimate the decline rate of the antibody concentration, the model accommodates the possibility of unobserved subclinical infections with Hib bacteria that cause increasing concentrations during the study period. The computations rely on Markov chain Monte Carlo simulation of the joint posterior distribution of the model parameters. The model is used to predict the duration of immunity to subclinical Hib infection and to a serious invasive Hib disease.

Predicting the course of meningococcal disease outbreaks in closed subpopulations.

A stochastic epidemic model was applied to meningococcal disease outbreaks in defined small populations such as military garrisons and schools. Meningococci are spread primarily by asymptomatic carriers and only a small proportion of those infected develop invasive disease. Bayesian predictions of numbers of invasive cases were developed, based on observed data using a stochastic epidemic model. We used additional data sets to model both disease probability and duration of carriage. Markov chain Monte Carlo sampling techniques were used to compute the full posterior distribution which summarized all information drawn together from multiple sources.

Acute middle ear infection in small children: a Bayesian analysis using multiple time scales.

The study is based on a sample of 965 children living in Oulu region (Finland), who were monitored for acute middle ear infections from birth to the age of two years. We introduce a nonparametrically defined intensity model for ear infections, which involves both fixed and time dependent covariates, such as calendar time, current age, length of breast-feeding time until present, or current type of day care. Unmeasured heterogeneity, which manifests itself in frequent infections in some children and rare in others and which cannot be explained in terms of the known covariates, is modelled by using individual frailty parameters. A Bayesian approach is proposed to solve the inferential problem. The numerical work is carried out by Monte Carlo integration (Metropolis-Hastings algorithm).

Bayesian mapping of multiple quantitative trait loci from incomplete inbred line cross data.

A novel fine structure mapping method for quantitative traits is presented. It is based on Bayesian modeling and inference, treating the number of quantitative trait loci (QTLs) as an unobserved random variable and using ideas similar to composite interval mapping to account for the effects of QTLs in other chromosomes. The method is introduced for inbred lines and it can be applied also in situations involving frequent missing genotypes. We propose that two new probabilistic measures be used to summarize the results from the statistical analysis: (1) the (posterior) QTL intensity, for estimating the number of QTLs in a chromosome and for localizing them into some particular chromosomal regions, and (2) the locationwise (posterior) distributions of the phenotypic effects of the QTLs. Both these measures will be viewed as functions of the putative QTL locus, over the marker range in the linkage group. The method is tested and compared with standard interval and composite interval mapping techniques by using simulated backcross progeny data. It is implemented as a software package. Its initial version is freely available for research purposes under the name Multimapper at URL http://www.rni.helsinki.fi/mjs.

Analysis of contraceptive failure data in intrauterine device studies. Modern competing risks approach.

The life table method used heretofore in case of intrauterine device (IUD) failure data requires grouping of data into intervals. If the termination times are recorded exactly along with the reason of termination, grouping of data results in some loss of information. Modern competing risks techniques are suggested here for the exact IUD failure data. The uses of cumulative incidence functions, which are essentially the quantity given by Potter's net rate, and cause-specific hazard rates are stressed. Also, this paper focuses on the flaws of life table estimates of net and gross rates, which have been widely used during the past three decades in the analysis of contraceptive failures. The methods suggested in this paper can be used in any other situation where the failure times and reasons of failure are recorded.

A statistical model of transmission of Hib bacteria in a family.

The simultaneous estimation of family and community transmission rates as well as cure rates from panel data in a recurrent Hib (Haemophilus influenzae type b bacteria) infection is considered. An individual-based stationary Markov process model with constant hazards in two age groups is applied to describe recurrent asymptomatic Hib infection in a family with small children. The problem of estimation is solved in terms of the Bayesian posterior of the model parameters. The model is used to predict prevalence and incidence of Hib carriage in families as a function of the family size and age structure.

Non-parametric Bayesian approach to hazard regression: a case study with a large number of missing covariate values.

A 'packaged' non-parametric multiplicative hazard regression model is proposed, and applied to a study of the effects of some genetic and viral factors in the development of spontaneous leukaemia in mice. Hierarchical modelling and data augmentation are used to deal with the large number of missing covariate values. A Bayesian procedure is adopted, and the Metropolis-Hastings algorithm is used in the numerical computation of the posterior distribution.