今日の論文

論文

A fourth compartment was introduced into the model to allow a link to the PD response that was not identifiable (because of inadequate duration of PK sampling and/or the drug concentration likely to be below the lower limit of quantification of the assay) from the PK alone.

    • この複雑な PK/PD モデルはデータをよく説明するのだが，いかんせん，複雑すぎる．何が問題化というと，PK の時間軸は hours であるのに対して，PD は weeks なのだ．（エンドポイントを「骨折」ではなくて，urinary excretion of the C-telopeptide of the α chain of type I collagen (uCTX) にしているから，せいぜい weeks で済んでいる）　こういう計算は本当に大変．以前，5 分と 21 日，の測定値が共存するデータを精度よく推定したくて苦労した覚えがある．

Although the complex 'physiological' PK-PD model described the data well, its major disadvantages were the long computer run-times (〜 5 days on a Pentium 800-MHz PC) and the numerical difficulties associated with solving a rather stiff problem, i.e. where rate constant values for the PK and PD time courses varied over a wide range. (...)
The features of the ibandronate PK-PD system, with the large difference in the time courrse of ibandronate PK (hours) and the PD (weeks) response, suggested that an 'abstraction' of the PK might be appropriate.

    • 工夫の甲斐あって，この 'K-PD' モデルは 2 時間くらいで収束するようになった．しかも PD の予測性に不足はない (essentially identical performance to the PK-PD model)．
    • Pharsight Trial Simulator を使って，いろいろな投与条件を検討．投与期間が長いから，シミュレーションは必須ですね．
  • Cremers, ..., and Papapoulos (2002) EJCP, "A pharmacokinetic and pharmacodynamic model for intravenous bisphosphonate (pamidronate) in osteoporosis"
    • この時点では，この程度のことまでしかできていなかった．上の，ibandronate の解析がいかにすごいか．

The study design was admittedly not ideal; only one dose was administered, PK data were in part simulated from a related compound (alendronate のこと) and PKs was studied in a patient group other than that used for PDs. (...) PK parameters were fixed to their mean population value for the PD modelling and, therefore, interindividual variability was not accounted for.

Multivariable general linear modeling tailored to accommodate data for a dependent variable with right and left censoring was performed using the LIFEREG procedure within SAS version 8.2. For the purposes of these analyses, right- and left-censored data represented MIC values above or below the upper or lower margins of the MIC range tested, respectively. For example, a MIC observation of ≦0.25 is left censored at a censoring value of 0.25.
(...)
Despite the greater sensitivity achieved when using quantitative MIC data, the censored nature of these data presents an analytical challenge. However, the use of modeling techniques tailored to accommodate censored data, as described in this report, allowed for the estimation of thel ikelihood of higher MIC values based on the presence of certain factors.

  • Tang, Song, Belin, et al. (2005) Stat Med, "A comparison of imputation methods in a longitudinal randomized clinical trial"
    • 次の四手法を比較．
      1. One approach combines hot-deck (HD) multiple imputation using a predictive mean matching method for item non-response and the approximate Bayesian bootstrap for unit non-response.
      2. A second method is based on a multivariate normal (MVN) model using PROC MI in SAS software V8.2.
      3. LOCF
      4. Available-case analysis
    • 結論は次のとおり．

A practical approach that combines the two methods, using the HD method for highly skewed variables and MVN for other variables, might be worth pursuing and awaits further investigation.

In terms of "real-time" development, the major limitation of optimal clinical trial design is gaining speedy access to relevant information within the timelines of the development program.

    • D-optimal デザインとの併用についてのコメント．

The number of simulations that need to be performed increases exponentially with the number of trial factors and levels of those factors. (...) Optimal design theory may help to reduce the simulation burden by defining sensitive regions of the design space. Pure optimal designs tend to be unrealistic, often involving replicated experiments. Consequently, a combination of optimal design theory and simulation, taking into acount questions of logistics and ethics, offers a very pragmatic approach to clinical trial design.