Using hidden Markov models with raw,triaxial wrist accelerometry data to determine sleep stages

Accelerometry is a low‐cost and noninvasive method that has been used to discriminate sleep from wake, however, its utility to detect sleep stages is unclear. We detail the development and comparison of methods which utilise raw, triaxial accelerometry data to classify varying stages of sleep, ranging from sleep/wake detection to discriminating rapid eye movement sleep, stage one sleep, stage two sleep, deep sleep and wake. First‐ and second‐order hidden Markov models (HMMs) with time‐homogeneous and time‐varying transition probability matrices, along with continuous acceleration observations in the form of a Gaussian‐observation HMM and K‐means classified acceleration in a discrete‐observation HMM were explored. In addition, generalised linear mixed models (GLMMs) with binary and multinomial responses and logit link functions were considered as was whether incorporating adjoining acceleration information into the models improved prediction. Model predictions were compared to the reference‐standard in sleep detection (polysomnography) and outcome accuracies were calculated. Consistently, HMMs yielded greater sleep stage detection than GLMMs but there was little difference between first‐ and second‐order HMMs. Varying degrees of difference were observed when comparing Gaussian‐observation HMMs to discrete‐observation HMMs, and time‐varying HMMs yielded greater discrimination than time‐homogeneous HMMs, as did models which considered adjoining acceleration information. These results suggest that wrist‐worn accelerometry data may be able to detect sleep stages but that further investigation is required to optimise classification accuracy.     

Some Notes on Refereeing

Analysis of longitudinal data using a general linear mixed model requires the specification of a form for the covariance matrix of within-subject observations. Graphical diagnostics, such as the scatterplot matrix, can be of substantial help in making this specification. I introduce another graphical diagnostic, the Partial-Regression-on-Intervenors Scatterplot Matrix (PRISM), which complements the ordinary scatterplot matrix and which is more useful for identifying certain kinds of correlation structures. PRISMs corresponding to several commonly used correlation structures are displayed. The PRISM's usefulness in model specification is illustrated with an example of longitudinal data from a 100-kilometer road race.     

Modified kolmogorov-smirnov tests of goodness of fit

The Kolmogorov-Smirnov (K–S) one-sided and two-sided tests of goodness of fit based on the test statistics D⁺ _n D^? _n and D_n are equivalent to tests based on taking the cumulative probability of the i–th order statistic of a sample of size n to be (i–.5)/n. Modified test statistics C⁺ _n, C^? _n and C_n are obtained by taking the cumulative probability to be i/(n+l). More generally, the cumula-tive probability may be taken to be (i?δ)/(n+l?2δ), as suggested by Blom (1958), where 0 less than or equal δ less than or equal .5. Critical values of the test statis-tics can be found by interpolating inversely in tables of the proba-bility integrals obtained by setting a=l/(n+l?2δ) in an expression given by Pyke (1959). Critical values for the D's (corresponding to δ=.5) have been tabulated to 5DP by Miller (1956) for n=1(1)100. The authors have made analogous tabulations for the C's (corresponding to δ=0) [previously tabulated by Durbin (1969) for n=1(1)60(2)100] and for the test statistics E⁺ _n, E^? _n and E_n corresponding to δ f.3. They have also made a Monte Carlo comparison of the power of the modified tests with that of the K–S test for several hypothetical distributions. In a number of cases, the power of the modified tests is greater than that of the K–S test, especially when the standard deviation is greater under the alternative than under the null hypo-thesis.     

One-Sample Likelihood Ratio Tests for Mixed Data

In this paper we present a procedure for finding the optimal order of a response polynomial. the procedure is based on the prediction distribution of future observations. The maximal length of the structural β - expectation tolerance region for each polynomial is calculated. The minimun of these maximal determines the optimal order of the response polynomial     

History and role of order statistics

This paper starts with an itroduction which gives definitions of order statistics,makes a clear distinction between order statistics and rank statistics, and gives an overview of the problems in which methods based on order statstics are useful.The following sections deal with the history and role of order sta¬tistics in selected areas: central tendency, dispersion, and regression; treatment of outliers and robust estimation; maximum likelihood estimators; best linear unbiased estimators; extreme-values; multiple comparisons and studentized range. The last two sections discuss a basic coverage property and some of its conse¬quences and describe the author's chronological annotated bibliography of order statistics. Finally, there is a list of references.     

Modified Asymptotic Formulas for Critical Values of the Kolmogorov Test Statistic

A brief discussion is given of the Kolmogorov test of goodness of fit. Modified asymptotic formulas for critical values of the test statistic, much more accurate for small-to-moderate sample sizes than the usual asymptotic formulas, are given.     

Health-related determinants of perceived quality of life: a comparison between first-year university students and their working peers

This study compares aspects of the health-related behaviors and working life of first-year university students with those of their working counterparts and assesses the roles of these aspects as predictors of each groups' perceived quality of life (QoL). Subjects were taken from two cross-sectional data sets (a student survey and a population survey) from the Swedish central-western region of Osterg?tland. Male and female respondents aged 20-35 years were extracted and comparison were made considering in turn socio-demographic characteristics, health-related behaviors, exposure to abusive events at work and perceived QoL. University students smoked and used oral snuff in smaller proportions, they were not as frequent drinkers as their working counterparts, but they tended to drink more when they did drink. Threats and violence were less prevalent among students, but sexual harassment, were almost as common. The strongest predictors of perceived QoL for both groups are expected and former perceived QoL, followed by current self-rated health.     

The Spacing of Births Among French-Canadian Families: An Historical Approach*

Utilisant la généalogie d'une seule famille-souche canadienne-française de 1650 à 1950, l'auteur compare l'intervalle entre les naissances dans la branehe canadienne et dans la branche américaine de cette famille. Indépendamment de la taille des families, l'intervalle s'accroit au cours des ans du côté américain. Une croissance de l'espacement ne se produit pas, par ailleurs, du côté canadien. II appert done que l'espacement progressif des naissances ne se produit que parmi les couples américains et que le comportement de ceux-ci diffère de celui des couples canadiens. La présente recherche a pour but secondaire de mettre en lumière l'utilité des généalogies en démographie, particulièrement dans l'étude de la fécondité. La comparaison des résultats obtenus ici avec ceux qui proviennent d'autres études de l'espacement des naissances illustre l'usage que Ton peut f aire de telles données historiques: on a utilisé en l'occurrence les régistres ayant trait à une seule famille pendant trois siècles. Cette famille n'est pas nécessaire-ment représentative de la famille canadienne-francaise. II s'agit plutôt de l'étude démographique d'un cas familial dans le temps et dans l'espace.     

Cultural safety and the duty of care

Rural youth, especially those of indigenous and immigrant cultures caught up in rural-urban migration, are vulnerable when the duty of care mandate transfers from families to state child welfare agents. The notion of cultural safety is examined in relation to the duty of care mandate assigned to child welfare workers when the state intervenes in family life.