Modeling and Analysis of Longitudinal Data

Presenter: Daniel John Tolhurst

Session Synopsis:

Pseudo-replication in Canola Chemistry Trials

The Australian National Variety Trials (NVT) system evaluates current and potential crop varieties in order to provide information for growers. NVT covers a range of crops and for most it involves a series of standard replicated variety trials. Testing for canola differs because the varieties are classified according to their tolerance to several widely used herbicides (chemistries). The current design protocol for canola trials allocates these chemistry treatments to field blocks (ChemBlocks) in a one-to-one fashion. Randomisation is then restricted so varieties in the same ChemBlock are tolerant to the applied spray. However, as the number of chemistries and ChemBlocks are equal, every class in chemistry is also a class in ChemBlock, and both are strictly aliased. This is referred to as pseudo-replication of the treatments and has important implications on the statistical analysis that must be addressed at the single-site level. The canola trial at 2013 Diggora will be presented as a motivating example. This environment comprises 96 varieties with specific tolerance to four chemistries and three with dual tolerance. Adjacent ChemBlocks are separated by six buffer rows that minimise spray drift and the trial has 27 filler plots; both of which contain material not relevant to NVT. The treatment structure is a combination of Chemistry and Variety (for single tolerant varieties) and Chemistry crossed with Variety (for dual tolerant varieties). Clearly formulation of the linear mixed model (LMM) is non-trivial and must accommodate the non-orthogonality of the design and respect the aliasing of treatments. This is achieved via Design Tableau, which is a simple but general approach to LMM specification of comparative experiments. Design Tableau also ensures the modelling of buffer and filler plots respect the integrity of the contiguous spatial array while fitting a single residual and genetic variance that is commensurate with the plot and treatment structures. The Design Tableau formulated here is then easily extended to the multi-environment trial (MET) analysis and a sensible model for the variety by environment interaction (VEI) in NVT canola. Finally, new experimental designs are presented that eliminate any aliasing with minimal increases in field size and spray effort. Unfortunately, however, these are yet to be adopted in NVT canola so growers are limited to comparing varieties with the same tolerance only.

Presenter: Luzia Aparecida Trinca

Session Synopsis:

Methods for constructing multi-stratum experiments

Multi-stratum experiments are frequently performed in many areas as, for example, laboratory biology, agriculture and engineering. Data analysis from such experiments are performed by fitting appropriated mixed models. In multi-stratum experiments the relationship among the units within each strata can be of nesting, crossing, or both. Often experimental cost does not allow the use of orthogonal layouts and it is important to have general methods to construct efficent designs for the practical problems. The stratum-by-stratum approach is quite flexible and can be used to design multi-stratum experiments in general. Any design criteria including compound criteria can be used to construct the designs. For several types of relationships among the units we stablish the steps to be followed in order to obtain the whole design. We use examples from biotechnological area to illustrate the methods.

Presenter: Clayton Forknall

Session Synopsis:

Modelling grain yield against disease progression across leaf layers and time using a one stage random coefficients regression approach.

Limiting the impact of foliar diseases is a challenge faced by the Australian grains industry. Foliar diseases infect the leaf tissue of plants, adversely affecting the function of photosynthesis, grain fill and ultimately grain yield. Disease infection typically initiates on the lower leaf layers early in the growing season and progresses towards the topmost leaf layers over time. Modelling the complicated dynamics of disease progression in field crops requires the assessment of the proportion of leaf area diseased (LAD) on successive leaf layers at multiple times throughout the season. Previously, the Area Under the Disease Progress Curve (AUDPC) has been used to provide a simple measure of LAD and disease duration on a given leaf layer, where the AUDPC is formed by applying the trapezoid rule to LAD assessments over time. Using a two stage approach, the AUDPC, often averaged over leaf layers, is correlated to yield at either a treatment or experimental unit level to derive relationships describing yield losses to foliar disease. A limitation of the AUDPC is that it weights the LAD measured on each leaf layer, at each time of assessment equally; there is no allowance for the differential contribution of different leaf layers to grain fill across the growing season. A fully efficient one stage approach to model the response variable of yield against disease progression across leaf layers and time is proposed. Using a linear mixed model framework, the LAD measurements on each leaf layer at each time of assessment are included as random covariates in the analysis of grain yield. The flexibility of the linear mixed model is explored to capture the structure implicit between the covariates across time and leaf layers. This modelling approach provides reliable estimates of the impact of disease on yield. Additionally, it models disease development over time and how this loss of leaf area across different leaf layers impacts upon yield.

Presenter: Izabela Oliveira

Session Synopsis:

Censored Regression Models For Complex Longitudinal Data On Animal Welfare

Air quality in horse stables is an important factor in maintaining animal health. Ammonia gas produced in the process of excrement/bedding mixture is one of the most noxious gases present in stable air. At high concentrations it can damage the respiratory tract of animals and health of handlers. An experiment was carried out in Lavras, Brazil, to evaluate the efficacy of a commercial biological product in reducing NH3 particles in horse stalls. Ten animals were randomly assigned to stalls having the same conditions (except for the treatment application) and concentration of ammonia was measured over a 23 days period. Daily measurements were taken at four different times (8am, 11am, 2pm and 5pm). The response of interest is NH3, in ppm, assessed by a device fixed to the stalls and limited to reporting measures between 0 and 99, that is, data are censored due to the measuring instrument. Ammonia gas was detected from the 3rd day; from the 5th day concentrations above the maximum acceptable for human and animal health (25 ppm) were observed; and the 99s frequency increased over the period. This work presents several modeling strategies for these complex longitudinal data using the GAMLSS R package. In addition to the classical approach (Tobit model), asymmetric distributions (censored gamma) and smoothers were considered. We conclude that concentration of ammonia was significantly affected by period and treatment use. Acknowledgments: The authors thank Global Saúde Brasil, DEG/UFLA and NEQUI-UFLA (www.nequi.com.br) for support during the research.

Presenter: Girma Taye Aweke

Session Synopsis:

Modeling effect of climate variability on malaria in Ethiopia

Temperature in Ethiopia has increased at about 0.2°C per decade. This coupled with global evidences on relationship between weather and disease outcome suggest that climate variability facilitates and exacerbates transmission of several infectious diseases. Despite wide recognition of impact of climate variability on health, there is scanty information on climate variability and its implication on specific disease outcome in Ethiopia. Statistical methods for studying relationship of climate variability and disease outcome has not been widely considered in Ethiopia. This study models climate variability and its impact on burden of malaria. Twenty one year weather data from National Metrology Agency of Ethiopia and 11 years Malaria prevalence data, from Federal Ministry of Health (FMoH) was used in the analysis. Box plot, time series plot, time series based models (ARIMA with different parameters and smoothing methods) and poison regression were employed to identify pattern of climate variability over a period of 21 years; determine vulnerability of disease to climate change and forecast future burden of the disease The result shows that average maximum and minimum temperatures and total annual rainfall are characterized by high inter-annual variability for all regions during the last 21 years. Minimum temperature was associated with high malaria prevalence in Tigray (p=0.01), Gambella (p=0.01), Dire Dawa (p=0.025) and Afar regions (p=0.03). Conversely maximum temperature was associated with high malaria prevalence in SNNP (p=0.05), Oromia (p=0.01), Benishangul-Gumuz (p=0.01), Amhara (p=0.01), and Afar regions (p=0.01). Malaria prevalence, projected until 2020, showed increasing trend over years for all regions indicating that climate change exacerbate malaria cases if no intervention is in place. Effect of climate variability is felt on malaria cases through changing magnitude and seasonality of rainfall and temperature. Forecasts of standardized malaria cases showed wide confidence interval and increasing trend in the coming five years for all regions and require intervention in the years to come Poison regression is useful to study relationship between weather and disease prevalence, while selection of appropriate time series model is important to forecast future disease burden. In view of this, it is recommended to choose appropriate model parameters to obtain accurate disease burden forecasts.