Biopharmaceutical statistics in a pharmaceutical regulated environment: past, present, and future.

The practice of statistics in the pharmaceutical industry has changed markedly over the last 25 years. This paper examines the evolution of clinical trial statistics in relationship to advances in statistical methodology and computational power as well as the changing regulatory environment. The current role of the biopharmaceutical statistician is assessed along with the drivers for future change.

Statistical methods for a three-period crossover design in which high dose cannot be used first.

Design and analysis methods for the three-period crossover trial defined by the sequences: (D0, D1, D2), (D1, D0, D2), and (D1, D2, D0), where D0 is a placebo, and D1 and D2 are a low dose and a high dose of a drug, respectively, are developed. This design may be used when investigators are unwilling to administer a higher dose of a new drug to a patient before administering a lower dose. In using this design, patients should be randomized to sequences in blocks that are integer multiples of 3. Both parametric and non-parametric analysis methods are based on contrasts that capture intrapatient variability only and provide unbiased estimates and hypothesis tests of pairwise differences between carryover, direct dose, and period effects. The design and methods are illustrated with data reflecting the cognitive component of the Alzheimer's disease assessment scale collected in a large clinical trial of Tacrine at doses of 0, 40, and 80 mg/day.

Exposure analysis of dichotomous response measures in long-term studies.

Differential exposure to study medications in long-term studies of some cardiovascular compounds complicates analyses, particularly the usual intention-to-treat analyses and inferences therefrom of the data collected. Analysis methods that incorporate exposure are developed, presented, and illustrated by applying them to primary response data from a long-term, placebo-controlled, ancillary trial of gemfibrozil. The analysis methods address the extent to which end-points are correlated with the actual use of the compound rather than the extent to which end-points are correlated with the random assignment to double-blind study medications.

Methodologic aspects of a population pharmacodynamic model for cognitive effects in Alzheimer patients treated with tacrine.

Tacrine is a cholinesterase inhibitor with activity in the central nervous system originally marketed for the reversal of competitive neuromuscular blockade. Because a marked reduction in cholinergic neurons is a hallmark of brain changes in Alzheimer disease, tacrine has been studied in two placebo-controlled clinical trials of patients with probable Alzheimer disease. Standard analysis of variance (ANOVA) and analysis of covariance (ANCOVA) have shown a difference between the tacrine group and the placebo group in terms of the cognitive component of the Alzheimer disease assessment scale at the end of the placebo-controlled phase. Due to limitations of ANOVA and ANCOVA, only a selected group of patients could be analyzed by those methods. A population pharmacodynamic model has been developed that allows the use of all observations from one or more trials to be combined. It can incorporate any sequence of active or placebo treatments and account for carryover effects of both placebo and active drug. The time courses of active or placebo treatment response and the development of tolerance to active drug or placebo can be defined. The model describes disease progression without treatment, the placebo effect, and the effect of tacrine as a function of daily dose. Placebo effect and active drug effects are modeled by effect site concentration components.

Results and validation of a population pharmacodynamic model for cognitive effects in Alzheimer patients treated with tacrine.

Tacrine has been studied in two clinical trials of identical design in patients with probable Alzheimer disease. One trial enrolled patients in the United States, while the other enrolled patients in France. A population pharmacodynamic model has been used to describe the cognitive component of the Alzheimer disease assessment scale (ADASC) using mixed effects nonlinear regression. The model parameters and their population variability and covariance were estimated by using NONMEM. During an observation period of up to 5 months, the rate of disease progression was 6.17 ADASC units/year. The effect of tacrine was described best by a shift in the disease progress curve (-2.99 ADASC units or 177.6 days at a dose of 80 mg/day). The placebo effects associated with tacrine and placebo treatment were similar in magnitude and time course. There was no evidence of tolerance to tacrine but tolerance to the placebo treatment developed during the study. The size of the placebo effect in the French population was 76% larger than in the United States population, and the response to placebo diminished more slowly in the French population.

One-sided or two-sided p values: which most appropriately address the question of drug efficacy?

Whether a one-sided or a two-sided p value should be used for reporting the results of an analysis should be determined by the a priori question the investigation seeks to answer. It is concluded that one-sided p values are appropriate in clinical trials whose objective is to provide definitive, confirmatory evidence of efficacy of pharmaceutical compounds.

Assessment of bioequivalence using a multiplicative model.

In many bioavailability/bioequivalence studies, the distributions of responses such as AUC and Cmax are often positively skewed and exhibit a lack of homogeneity of variances. In this situation, a logarithmic transformation is usually considered for reduction of skewness and achievement of an additive model with relatively homogeneous variance. In this paper, consideration is given to a multiplicative model based on empirical evidence. A method is proposed using individual subject ratios for assessing the bioequivalence of two different formulations. This method is then subsequently extended to several commonly used crossover experiments.

The alternative hypothesis: one-sided or two-sided?

The appropriateness of a one-sided alternative hypothesis rather than the more conservative, boiler-plate, two-sided hypothesis is discussed and examples provided. It is concluded that confirmatory efficacy clinical trials of pharmaceutical compounds should always be viewed within the one-sided alternative hypothesis testing framework.

The treatment of gastric ulcer with antisecretory drugs. Relationship of pharmacological effect to healing rates.

Published clinical trials (N = 56) of antisecretory drugs in the treatment of benign gastric ulcer were reviewed. Composite healing rates for various drug regimens were calculated using a method previously described for duodenal ulcer. Healing rates were compared with data on suppression of intragastric acidity to see if any relationship was evident. No significant correlations between the two existed, unless placebo data were included in the analysis. Correlations were stronger with suppression of total 24-hr rather than nocturnal acidity. Using Williams' method for assessing trends, it was found that an increase in antisecretory effect is not associated with a concomitant increase in healing rates. Duration of medical treatment is the single most important factor in healing of benign gastric ulcer; healing rates for all drug regimens and placebo show a consistent increase with prolongation of treatment.

Comparison of equal-weight oral dosages of verapamil hydrochloride and diltiazem hydrochloride in patients with mild to moderate hypertension.

The clinical efficacy, safety, and tolerability of oral verapamil and diltiazem, at total daily dosages of equal weight, were evaluated in a placebo-controlled, double-blind crossover study. Thirty-six ambulatory patients with chronic, stable, mild to moderate hypertension (supine diastolic blood pressure of 94-116 mm Hg) received a dosage of either verapamil or diltiazem 80 mg t.i.d. as the hydrochloride salt for one week after an antihypertensive-drug washout period. Each then received 120 mg of the same drug t.i.d. for one week. After another two-week washout period, the patients were crossed over to the other drug. Each patient had a 12-lead electrocardiogram and measurement of supine and standing blood pressure weekly. In the 32 patients completing the study, low-dose verapamil reduced supine diastolic blood pressure (DBP) from a mean of 101.5 +/- 5.2 to 95.3 +/- 9.5 mm Hg; high dose verapamil reduced DBP to 90.9 +/- 7.4 mm Hg. Standing DBP was reduced to a similar degree. Diltiazem showed an almost identical effect: Supine DBP was reduced from a mean of 101.7 +/- 5.3 to 94.0 +/- 10.1 mm Hg with the low dose and to 91.0 +/- 8.6 mm Hg with the high dose, with similar effects on standing DBP. The high dose of both drugs significantly increased the QTc interval, and both doses of diltiazem significantly increased the PR interval compared with baseline. Both drugs exhibited consistent efficacy with minimal adverse effects. The electrophysiologic safety profile of verapamil was superior to that of diltiazem.

p-value and power computations in multiple look trials.

This paper presents at an instructive level detailed design, decision and computational aspects of p-values and power for clinical trials in which interim looks at accumulating data are planned. Background theory and an application are presented. In addition, a definition of the term p-value, appropriate for a trial in which interim looks are planned is proposed. The definition is intuitively consistent with that for a fixed sample size trial. That is, the p-value reflects the strength of the data against the null hypothesis. For trials incorporating group sequential methods, the p-value at a particular look reflects the conditional nature of the data collected through that look on the data collected through earlier looks.

Design, monitoring, and analysis issues relative to adverse events.

In the clinical development of new drugs for market approval, it is frequently impossible to design trials to provide definitive information about safety--particularly about adverse events. It is possible, however, to design most trials to provide definitive information about efficacy. Efficacy trials with new drugs should therefore be monitored for safety, and the safety profile described within and across trials. Confidence intervals are recommended as the appropriate statistical methodology for doing this. Such intervals provide an interval estimate on the unknown incidences of adverse experiences among patients who could be treated with each regimen, as well as permit a conclusion that two regimens are different.

The effect of single intravenous doses of cimetidine or ranitidine on gastric secretion.

Intravenous cimetidine, 300 mg or 400 mg, or ranitidine, 50 mg, was administered as a single dose to 36 volunteers in a randomized, crossover fashion. Aspirates of gastric juice were obtained after dosing, and the pH, titratable acidity, gastric fluid volume, and gastric acid output were determined from baseline through 71/2 hours for each subject. Each intervention significantly increased pH and suppressed hydrogen ion concentration, gastric fluid volume, and gastric acid output. Both the magnitudes of the changes when compared with baseline and the time of the mean maximum effects were similar in all three drug regimens. The effect of all three interventions on gastric fluid volume and gastric acid output diminished sharply after 6 hours. The data indicate that the gastric secretory response to all three interventions did not differ substantially.

The effect of age on theophylline clearance in normal subjects.

Dose-interval AUC and clearance of theophylline at steady-state were determined in healthy male subjects in each of three age groups (18-35, 36-54 and 55-70 years old). Mean AUC in the oldest group was significantly higher than in the youngest and clearance in both the middle and oldest groups was significantly lower than in the youngest. Though clearance was significantly correlated with age, age alone accounted for only 31% of the variability in clearance.