Bridging the gap between different statistical approaches: An integrated framework for modelling

This paper proposes a template for modelling complex datasets that integrates traditional statistical modelling approaches with more recent advances in statistics and modelling through an exploratory framework. Our approach builds on the well-known and long standing traditional idea of 'good practice in statistics' by establishing a comprehensive framework for modelling that focuses on exploration, prediction, interpretation and reliability assessment, a relatively new idea that allows individual assessment of predictions. The integrated framework we present comprises two stages. The first involves the use of exploratory methods to help visually understand the data and identify a parsimonious set of explanatory variables. The second encompasses a two step modelling process, where the use of non-parametric methods such as decision trees and generalized additive models are promoted to identify important variables and their modelling relationship with the response before a final predictive model is considered. We focus on fitting the predictive model using parametric, non-parametric and Bayesian approaches. This paper is motivated by a medical problem where interest focuses on developing a risk stratification system for morbidity of 1,710 cardiac patients given a suite of demographic, clinical and preoperative variables. Although the methods we use are applied specifically to this case study, these methods can be applied across any field, irrespective of the type of response.

Further evidence for the agreement between patients with stroke and their proxies on the Frenchay Activities Index

Objective: To determine item, subscale and total score agreement on the Frenchay Activities Index (FAI) between stroke patients and proxies six months after discharge from rehabilitation. Design: Prospective study design. Setting/subjects: Fifty patient-proxy pairs, interviewed separately, in the patient's residence. Main outcome measures: Modified FAI using 13 items. Individual FAI items, subscales and total score agreement as measured by weighted kappa and intraclass correlation coefficients (ICC). Results: Excellent agreement was found for the total FAI (ICC 0.87, 95% confidence interval (CI) 0.78-0.93), and domestic (ICC 0.85, 95% CI 0.73-0.91) and outdoor (ICC 0.87, 95% CI 0.78-0.95) subscales, with moderate agreement found for the work/leisure subscale (ICC 0.63, 95% CI 0.34-0.78). For the individual FAI items, good, moderate, fair and poor agreement was found for five, three, four and one item, respectively. The best agreement was for objective items of preparing meals, washing-up, washing clothes, shopping and driving. The poorest agreement was for participation in hobbies, social outings and heavy housework. Scoring biases associated with patient or proxy demographic characteristics were found. Female proxies, and those who were spouses, scored patients lower on domestic activities; male patients, and those who were younger, scored themselves higher on outdoor activities and higher patient FIM scores were positively correlated with higher FAI scores. Conclusions: While total and subscale agreement on the FAI was high, individual item agreement varied. Proxy scores should be used with caution due to bias.

Effect of changing data collection parameters on statistical motor unit number estimates

The effect of number of samples and selection of data for analysis on the calculation of surface motor unit potential (SMUP) size in the statistical method of motor unit number estimates (MUNE) was determined in 10 normal subjects and 10 with amyotrophic lateral sclerosis (ALS). We recorded 500 sequential compound muscle action potentials (CMAPs) at three different stable stimulus intensities (10–50% of maximal CMAP). Estimated mean SMUP sizes were calculated using Poisson statistical assumptions from the variance of 500 sequential CMAP obtained at each stimulus intensity. The results with the 500 data points were compared with smaller subsets from the same data set. The results using a range of 50–80% of the 500 data points were compared with the full 500. The effect of restricting analysis to data between 5–20% of the CMAP and to standard deviation limits was also assessed. No differences in mean SMUP size were found with stimulus intensity or use of different ranges of data. Consistency was improved with a greater sample number. Data within 5% of CMAP size gave both increased consistency and reduced mean SMUP size in many subjects, but excluded valid responses present at that stimulus intensity. These changes were more prominent in ALS patients in whom the presence of isolated SMUP responses was a striking difference from normal subjects. Noise, spurious data, and large SMUP limited the Poisson assumptions. When these factors are considered, consistent statistical MUNE can be calculated from a continuous sequence of data points. A 2 to 2.5 SD or 10% window are reasonable methods of limiting data for analysis. Muscle Nerve 27: 320–331, 2003

Heritability of adult body height: A comparative study of twin cohorts in eight countries

A major component of variation in body height is due to genetic differences, but environmental factors have a substantial contributory effect. In this study we aimed to analyse whether the genetic architecture of body height varies between affluent western societies. We analysed twin data from eight countries comprising 30,111 complete twin pairs by using the univariate genetic model of the Mx statistical package. Body height and zygosity were self-reported in seven populations and measured directly in one population. We found that there was substantial variation in mean body height between countries; body height was least in Italy (177 cm in men and 163 cm in women) and greatest in the Netherlands (184 cm and 171 cm, respectively). In men there was no corresponding variation in heritability of body height, heritability estimates ranging from 0.87 to 0.93 in populations under an additive genes/unique environment (AE) model. Among women the heritability estimates were generally lower than among men with greater variation between countries, ranging from 0.68 to 0.84 when an additive genes/shared environment/unique environment (ACE) model was used. In four populations where an AE model fit equally well or better, heritability ranged from 0.89 to 0.93. This difference between the sexes was mainly due to the effect of the shared environmental component of variance, which appears to be more important among women than among men in our study populations. Our results indicate that, in general, there are only minor differences in the genetic architecture of height between affluent Caucasian populations, especially among men.

Using the flexibility index to compare batch and continuous activated sludge processes

This paper considers the question of which is better: the batch or the continuous activated sludge processes? It is an important question because dissension still exists in the wastewater industry as to the relative merits of each of the processes. A review of perceived differences in the processes from the point of view of two related disciplines, process engineering and biotechnology, is presented together with the results of previous comparative studies. These reviews highlight possible areas where more understanding is required. This is provided in the paper by application of the flexibility index to two case studies. The flexibility index is a useful process design tool that measures the ability of the process to cope with long term changes in operation.

Estimation of body fatness from body mass index and bioelectrical impedance: comparison of New Zealand European, Maori and Pacific Island children

Objective: To compare percentage body fat (%BF) for a given body mass index (BMI) among New Zealand European, Maori and Pacific Island children. To develop prediction equations based on bioimpedance measurements for the estimation of fat-free mass (FFM) appropriate to children in these three ethnic groups. Design: Cross-sectional study. Purposive sampling of schoolchildren aimed at recruiting three children of each sex and ethnicity for each year of age. Double cross-validation of FFM prediction equations developed by multiple regression. Setting: Local schools in Auckland. Subjects: Healthy European, Maori and Pacific Island children (n = 172, 83 M, 89 F, mean age 9.4 +/- 2.8(s. d.), range 5 - 14 y). Measurements: Height, weight, age, sex and ethnicity were recorded. FFM was derived from measurements of total body water by deuterium dilution and resistance and reactance were measured by bioimpedance analysis. Results: For fixed BMI, the Maori and Pacific Island girls averaged 3.7% lower % BF than European girls. For boys a similar relation was not found since BMI did not significantly influence % BF of European boys ( P = 0.18). Based on bioimpedance measurements a single prediction equation was developed for all children: FFM (kg) = 0.622 height (cm)(2)/ resistance +0.234 weight (kg)+1.166, R-2 = 0.96, s. e. e. = 2.44 kg. Ethnicity, age and sex were not significant predictors. Conclusions: A robust equation for estimation of FFM in New Zealand European, Maori and Pacific Island children in the 5 - 14 y age range that is more suitable than BMI for the determination of body fatness in field studies has been developed. Sponsorship: Maurice and Phyllis Paykel Trust, Auckland University of Technology Contestable Grants Fund and the Ministry of Health.

Reliability of scores between stroke patients and significant others on the Reintegration to Normal Living (RNL) Index

Purpose: This study measured reliability between stroke patients' and significant others' scores on items on the Reintegration to Normal Living (RNL) Index and whether there were any scoring biases. Method The 11-item RNL Index was administered to 57 pairs of patients and significants six months after stroke rehabilitation. The index was scored using a 10-point visual analogue scale. Patient and significant other demographic information and data on patients' clinical, functional and cognitive status were collected. Reliability was measured using the intra-class correlation coefficient (ICC) and percent agreement. Results: Overall poor reliability was found for the RNL Index total score (ICC=.36, 95% CI. 07 to .59) and the daily functioning subscale (ICC=.24, 95% CI -.003 to .46) and moderate reliability was found for the perception of self subscale (ICC=.55, 95 % CI .28 to .73). There was a moderate bias for patients to rate themselves as achieving better reintegration than was indicated by significant others, although no demographic or clinical factors were associated with this bias. Exact match agreement was best for the subjective items and worse for items reflecting mobility around the community and participation in a work activity. Conclusions: Caution is needed when interpreting patient information reported by significant others on the RNL Index. The use of a shorter scale to rate the RNL Index requires investigation.

Genotype and environment effects on dynamics of harvest index during grain filling in sorghum

An approach based on a linear rate of increase in harvest index (141) with time after anthesis has been used as a simple means-to predict grain growth and yield in many crop simulation models. When applied to diverse situations, however, this approach has been found to introduce significant error in grain yield predictions. Accordingly, this study was undertaken to examine the stability of the HI approach for yield prediction in sorghum [Sorghum bicolor (L.) Moench]. Four field experiments were conducted under nonlimiting water. and N conditions. The experiments were sown at times that ensured a broad range in temperature and radiation conditions. Treatments consisted of two population densities and three genotypes varying in maturity. Frequent sequential harvests were used to monitor crop growth, yield, and the dynamics of 111. Experiments varied greatly in yield and final HI. There was also a tendency for lower HI with later maturity. Harvest index dynamics also varied among experiments and, to a lesser extent, among treatments within experiments. The variation was associated mostly with the linear rate of increase in HI and timing of cessation of that increase. The average rate of HI increase was 0.0198 d(-1), but this was reduced considerably (0.0147) in one experiment that matured in cool conditions. The variations found in IN dynamics could be largely explained by differences in assimilation during grain filling and remobilization of preanthesis assimilate. We concluded that this level of variation in HI dynamics limited the general applicability of the HI approach in yield prediction and suggested a potential alternative for testing.