Clinical trials covariance

Time-to-event analysis in clinical trials is concerned with comparing the distributions of time to some event for various treatment regimens. The two nonparametric tests used to compare distributions are the log-rank test and the Cox proportional hazards model. The Cox proportional hazards model is more useful when you need to adjust your model for covariates. 

These particular points relate to each individual trial, but equally there will be similar considerations needed at the level of the development plan. In order for the overall, ordered programme of clinical trials to be scientifically sound there needs to be a substantial amount of commonality across the trials in terms of endpoints, definitions of analysis sets, recording of covariates and so on. This will facilitate the use of integrated summaries and meta-analysis for the evaluation and presentation of the complete programme or distinct parts of that programme, and outside of that, will allow a consistency of approach to the evaluation of the different trials. 

Berger, V.W., 2005, Selection bias and covariate imbalances in randomized clinical trials, John Wiley Sons. 

Some factors or covariates may cause deviations from the population typical value generated from system models so that each individual patient may have different PK/PD/disease progression profiles. The relevant covariate effects on drug/disease model parameters are identified in the model development process. Clinical trial simulations should make use of input/output models incorporating... 

Mould, D. R. Defining covariate distribution models for clinical trial simulation. In Kimko, H. C., Duffull, S. B., eds. Simulation for designing clinical trials. A pharmacokinetic-pharmacodynamic modeling perspective. (Drugs and the pharmaceutical sciences, volume 127) Marcel Dekker, New York, 2003. 

The covariate distribution model defines the distribution and correlation of covariates in the population to be studied. The aim of a covariate distribution model is to create a virtual patient population that reflects the target population for simulations including patients covariates. This model is of great importance for the realistic simulation of clinical trials. 

The Trial Simulator (Pharsight Corp., http //www.pharsight.com) is a comprehensive and powerful tool for the simulation of clinical trials. Population PK/PD models developed with tools mentioned in Section 17.10.3 can be implemented in a Trial Simulator. In addition, treatment protocols, inclusion criteria, and observations can be specified. Also covariate distribution models, compliance models, and drop-out models can be specified. All of these models can be implemented via a graphical user interface. For the analysis of simulation results a special version of S-Plus is implemented and results can also be exported in different formats, like SAS. 

Population pharmacokinetics can be extended to pharmacodynamics and PK/PD modeling using a link model like an effect compartment (Sheiner et al. 1979). In huge clinical trials only a limited number of patients can be included in a pharmacokinetic satellite study. The model is developed in this satellite. Knowing the demographic covariates of the patients in the whole study, concentration time curves and even effect time curves can be predicted. 

When a PPK study is designed to detect a difference between two subpopulations or to determine important covariates necessary to explain variability, attention should be paid to the sample size required for such a study. Simulation plays an important role in this situation, and Kowalski and Hutmacher (33) demonstrated the importance of using clinical trial simulations to assess the power to detect subpopulation differences in apparent drug clearance CLIP) and sample size requirements for a PPK substudy (1) of a Phase 3 clinical trial. Two subpopulations were... 

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. 

Complex pharmacokinetic/pharmacodynamic (PK/PD) simulations are usually developed in a modular manner. Each component or subsystem of the overall simulation is developed one-by-one and then each component is linked to run in a continuous manner (see Figure 33.2). Simulation of clinical trials consists of a covariate model and input-output model coupled to a trial execution model (10). The covariate model defines patient-specific characteristics (e.g., age, weight, clearance, volume of distribution). The input-output model consists of all those elements that link the known inputs into the system (e.g., dose, dosing regimen, PK model, PK/PD model, covariate-PK/PD relationships, disease progression) to the outputs of the system (e.g., exposure, PD response, outcome, or survival). In a stochastic simulation, random error is introduced into the appropriate subsystems. For example, between-subject variability may be introduced among the PK parameters, like clearance. The outputs of the system are driven by the inputs... 

Data was pooled from three clinical trials (547 patients) studying the use of darbepoetin alfa in the treatment of chemotherapy-induced anemia. Serial PK and PD (Hgb concentrations) measurements were collected throughout the studies and merged into a single database along with patient-relative covariates. A population PK/PD model was developed that simultaneously modeled darbepoetin alfa... 

One of the most potent applications of pharmacometrics is the informative construction of clinical trials by using clinical trial simulation (CTS). Population PM models are of great value when used in CTS because estimates of typical parameters along with parameter variability can be incorporated. There are three basic types of models needed to execute a CTS an input-output model, a covariate model, and an execution model. These are described in detail in Chapter 34 of this book. Clinical trial simulation can improve pediatric study structure by examining the impact of many important factors such as dropouts, choosing varying endpoints, and deviations from protocol. Pediatric PM models find great utility when applied to CTS. 

It is commonly stated that the analysis of extreme values often plays a more important role than that of the average values in clinical trials because it provides more information on the extent of safety concern at the individual level (14). Extreme values can be examined by creating frequency distributions for maximum absolute values as well as maximum increases from baseline (correcting for placebo), using reference limits of 450 and 500 ms on QT or 30 and 60 ms on AAQTc. It is important to account for covariates known to affect the distribution of QT/QTc values... 

To use genotype as one of the covariates in population PK or PD analysis of clinical trial data. 

Raab GM, Day S, Sales J (2000) How to select covariates to include in the analysis of a clinical trial. Controlled Clinical Trials 21 330-342. 

Hardly a statistician of repute can be found to defend the practice common among physicians of comparing the treatment groups in a randomized clinical trial at baseline using hypothesis/significance tests on covariates. The reason for the statistician s dislike is that such a test appears to be used to say something about the adequacy of the given allocation whereas it could only be a test of the allocation procedure the randomization process itself. 

Some statisticians have maintained that it does (Chambless and Roeback, 1993), but this is wrong in the context of the randomized clinical trial (Senn, 1994a,b, 1995b). The randomized trial permits a valid analysis even where no baselines are measured. If we take the Bayesian view, however, that information carmot be ignored, then when we have measured some covariate we have obtained information we must act on. Instead of using an analysis which corresponds to a probability-weighted average over all possible distributions of the covariate, we must replace it with one which corresponds to the particular distribution observed. However, we are only required to condition on what is observed and what we have observed is the observed covariate ... 

In an influential paper in Biometrika, Rosenbaum and Rubin discussed the possibility of using what they called the propensity score for adjusting for confounders (Rosenbaum and Rubin, 1983). The idea is that a stratification be made on the probability of assignment to treatment or control as a function of covariates. In a classic randomized clinical trial, of course, the probability of assignment to either group is 1 /2 irrespective of any covariate. The philosophy of the propensity score would then be that there is but a single stratum, that with score 1/2, and so no adjustment is necessary. This is, of course, equivalent to the familiar argument that for a classic randomized trial no adjustment is necessary. 

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