Continuous data covariates

As we shall see later the data type to a large extent determines the class of statistical tests that we undertake. Commonly for continuous data we use the t-tests and their extensions analysis of variance and analysis of covariance. For binary, categorical and ordinal data we use the class of chi-square tests (Pearson chi-square for categorical data and the Mantel-Haenszel chi-square for ordinal data) and their extension, logistic regression. 

LCA and CCK, on the other hand, appear to be strikingly dissimilar. All CCK procedures require at least one quasi-continuous indicator, and if there are none, the investigator has to create such an indicator (e.g., SSMAXCOV procedure). In contrast, LCA does not require continuous indicators and only deals with categorical data. In the case of categorical data, the patterns of interest are usually apparent, so there is no need to summarize the data with correlations. Therefore, LCA evaluates cross-tabulations and compares the number of cases across cells. This shift in representation of the data necessitates other basic changes. For example, LCA operates with proportions instead of covariances and yields tables rather than plots. These differences aside, the two approaches share a lot in common. LCA, like CCK, starts with a set of correlated indicators. It also makes the assumption of zero nuisance covariance-—in the LCA literature this is called the assumption of local independence, and it means that the indicators are presumed to be independent (i.e., uncorrelated) within latent classes. Moreover, LCA and CCK (MAXCOV in particular) use similar procedures for group assignment and both of them involve Bayes s theorem. 

In Chapter 6 we covered methods for adjusted analyses and analysis of covariance in relation to continuous (ANOVA and ANCOVA) and binary and ordinal data (CMH tests and logistic regression). Similar methods exist for survival data. As with these earlier methods, particularly in relation to binary and ordinal data, there are numerous advantages in accounting for such factors in the analysis. If the randomisation has been stratified, then such factors should be incorporated into the analysis in order to preserve the properties of the resultant p-values. 

Generalized additive modeling (GAM) was applied to each of the output data sets. A selection criteria of a = 0.05 and a frequency cutoff of 0.50 was applied for continued investigation of a covariate that is, GAM had to select a covariate for inclusion in 50% or more of the models from the 100 bootstrap fits for the covariate to be considered for further investigation. 

This chapter endeavors to show that a population PK/PD approach to the analysis of count data can be a valuable addition to the pharmacometrician s toolkit. Nonlinear mixed effects modeling does not need to be relegated to the analysis of continuously valued variables only. The opportunity to integrate disease progression, subject level covariates, and exposure-response models in the analysis of count data provides an important foundation for understanding and quantifying drug effect. Such parametric models are invaluable as input into clinical trial and development path simulation projects. 

Percentile division is a systematic approach to finding a specific value of a covariate that can split data into subgroups to maximize the probability structure in revealing explanatory variables that can be used as predictors of the response variable in a data set. The response variable could be binary, categorical, or continuous. In a data set with a binary outcome variable, for instance, the procedure would be as follows ... 

Two variants of a technique which relies on input-output models developed from operation data are presented the first uses PLS and the second CVSS models. PLS regression based on the zero lag covariance of the process measurements was introduced in Section 4.3. A Multipass PLS algorith-m is developed for detecting simultaneous multiple sensor abnormalities. This algorithm is only suitable for process measurements where the successive measurements are not correlated. The negligible autocorrelation assumption is justified for a continuous process operating at steady-state and having only random noise on measurements. 

Table 6.8 Summary of linear mixed effect model analysis to tumor growth data using a repeated measures analysis of covariance treating time as a continuous variable.

Figure 9.11 Scatter plots and box and whisker plots for continuous and categorical covariates against the EBE for baseline systemic clearance under the base model. Solid lines in the scatter plots are the LOESS smooth the data using a 0.3 sampling proportion.

Here, we briefly describe MFDA. Considering the usual situations where the trajectory is sampled with discrete time steps, we focus on discrete time and continuous frequency spaces. For simplicity, we set the sampling time interval of the trajectory data. At, to unity. We define the spectral density matrix S(f) as the inverse Fourier transform of a lagged variance-covariance matrix C(r) = (v(f)v (f+x)). 

The analysis involved deconvolution by iterative reconvolution, background subtraction, and optional correction for shift of the instrument response function. Statistical tests included chi-square, the Durbin-Watson test, the covariance matrix, a runs test, and the autocorrelation function [6]. An alternative form of data analysis involves distributions of lifetimes rather than a series of exponentials. Differentiation of systems obeying a decay law made up of three discrete components from systems where there exists a continuous distribution of lifetimes, or a distribution plus one or more discrete components, is a nontrivial analytical problem. Methods involving the minimization of the chi-square parameter are commonly used, but recently the maximum entropy method (MEM) has gained popularity [7]. Inherent in the MEM method is the theoretical lack of bias and the potential for recovering the coefficients of an exponential series with fixed lifetimes which are free of correlation effects and artificial oscillations. Recent work has compared the MEM with a new version of the exponential series method (ESM) which allows use of the same size probe function as the MEM and found that the two methods gave comparable results [8]. 

Statistical analyses were chosen systematically and multiple regression procedures were used throughout after preliminary univariate analyses. Decisions about the statistical procedures and analytical strategies were decided before the data collection was complete rather than being derived by an ad hoc process afterwards. Throughout the analyses, blood lead was treated as a continuously distributed variable and children were not grouped on the basis of their blood lead concentrations. Covariates were selected on... 

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