Recommendations for the primary analysis of continuous endpoints in longitudinal clinical trials
Craig Mallinckrodt & Peter Lane
Abstract: This position paper summarizes relevant theory and current practice regarding the analysis of longitudinal clinical trials intended to support regulatory approval of medicinal products, and it reviews published research regarding methods for handling missing data. It is one strand of the PhRMA initiative to improve efficiency of late-stage clinical research and gives recommendations from a cross-industry team. We concentrate specifically on continuous response measures analyzed using a linear model, when the goal is to estimate and test treatment differences at a given time point. Traditionally, the primary analysis of such trials handled missing data by simple imputation using the last, or baseline, observation carried forward method (LOCF, BOCF) followed by analysis of (co)variance at the chosen time point. However, the general statistical and scientific community has moved away from these simple methods in favor of joint analysis of data from all time points based on a multivariate model (eg, of a mixed-effects type). One such newer method, a likelihood-based mixed-effects model repeated measures (MMRM) approach, has received considerable attention in the clinical trials literature. We discuss specific concerns raised by regulatory agencies with regard to MMRM and review published evidence comparing LOCF and MMRM in terms of validity, bias, power, and type I error. Our main conclusion is that the mixed model approach is more efficient and reliable as a method of primary analysis, and should be preferred to the inherently biased and statistically invalid simple imputation approaches. We also summarize other methods of handling missing data that are useful as sensitivity analyses for assessing the potential effect of data missing not at random.
Recommendations for the primary analysis of continuous endpoints in longitudinal clinical trials
Craig Mallinckrodt & Peter Lane
Joint with Craig Mallinckrodt (Lilly)
Abstract: This position paper summarizes relevant theory and current practice regarding the analysis of longitudinal clinical trials intended to support regulatory approval of medicinal products, and it reviews published research regarding methods for handling missing data. It is one strand of the PhRMA initiative to improve efficiency of late-stage clinical research and gives recommendations from a cross-industry team. We concentrate specifically on continuous response measures analyzed using a linear model, when the goal is to estimate and test treatment differences at a given time point. Traditionally, the primary analysis of such trials handled missing data by simple imputation using the last, or baseline, observation carried forward method (LOCF, BOCF) followed by analysis of (co)variance at the chosen time point. However, the general statistical and scientific community has moved away from these simple methods in favor of joint analysis of data from all time points based on a multivariate model (eg, of a mixed-effects type). One such newer method, a likelihood-based mixed-effects model repeated measures (MMRM) approach, has received considerable attention in the clinical trials literature. We discuss specific concerns raised by regulatory agencies with regard to MMRM and review published evidence comparing LOCF and MMRM in terms of validity, bias, power, and type I error. Our main conclusion is that the mixed model approach is more efficient and reliable as a method of primary analysis, and should be preferred to the inherently biased and statistically invalid simple imputation approaches. We also summarize other methods of handling missing data that are useful as sensitivity analyses for assessing the potential effect of data missing not at random.
Kenward MG, Roger JH (2009). An improved approximation to the precision of fixed effects from restricted maximum likelihood. Computational Statistics and Data Analysis53:2583–2595.
Abstract: An approximate small sample variance estimator for fixed effects from the multivariate normal linear model, together with appropriate inference tools based on a scaled F pivot, is now well established in practice and there is a growing literature on its properties in a variety of settings. Although effective under linear covariance structures, there are examples of nonlinear structures for which it does not perform as well. The cause of this problem is shown to be a missing term in the underlying Taylor series expansion which accommodates the bias in the estimators of the parameters of the covariance structure. The form of this missing term is derived, and then used to adjust the small sample variance estimator. The behaviour of the resulting estimator is explored in terms of invariance under transformation of the covariance parameters and also using a simulation study. It is seen to perform successfully in the way predicted from its derivation.
A Review of Synergy Concepts of Nonlinear Blending and Dose-Reduction Profiles
John J. Peterson
Abstract: This article presents two dose-response surface analyses of combinations of trimetrexate (TMQ) and a compound known as AG2034 in the presence of low and high levels of folic acid, respectively. The data come from an experiment published by Faessel et al. (1). The dose-response surface models employed are obtained using a hierarchical logistic model approach. Using these dose-response models, an investigation of possible drug synergy is performed using a methodology based upon mixture-amount-experiments. The first analysis uses the nonlinear blending approach. The nonlinear blending analysis shows that there is little or nothing to be gained by blending AG2034 with TMQ. In most cases, replacing TMQ molecules with AG2034 molecules simply dilutes the combination drug effect in the sense that there is insufficient Loewe synergy to overcome the loss of efficacy obtained by adding the less potent AG2034.
As a secondary analysis, a series of “dose reduction profile” plots are created. These plots are created to show how much each drug can be reduced in amount and yet achieve the same efficacy as larger amounts of each drug used individually. While this is not a true synergy analysis, such an analysis may nonetheless have utility in situations where smaller amounts of two drugs used together produce less frequent or less serious adverse reactions than larger amounts of either drug used one alone.
For both the low and high folic acid experiments a mixture-amount-experiment analysis shows that for virtually all of the total doses studied there is no reason to blend AG2034 and TMQ for enhanced efficacy or potency. However, for the high folic acid experiment, the blending of these two compounds appears to produce some dose combinations on an isobole contour that have concentrations of AG2034 and TMQ that are 10% (or less) of their respective concentrations needed to produce the same mean response alone. This holds for isoboles that produce inhibition levels of 90% to 20% of the control mean level. This means that AG2034 and TMQ appear to have very good dose reduction potential when used in certain combinations. In particular, in the presence of a high level of folic acid, only a small amount of TMQ is needed to make a large reduction in the amount of AG2034 required to maintain the same mean response.
