Treatment protocols of the lupus nephritis collaborative study of plasmapheresis in severe lupus nephritis. The Lupus Nephritis Collaborative Study Group.
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Clinical Protocols↗
Biomedical subjects
J M Lachin
Publications and source records attributed to J M Lachin.
Statistical properties of randomization in clinical trials.
This is the first of five articles on the properties of different randomization procedures used in clinical trials. This paper presents definitions and discussions of the statistical properties of randomization procedures as they relate to both the design of a clinical trial and the statistical analysis of trial results. The subsequent papers consider, respectively, the properties of simple (complete), permuted-block (i.e., blocked), and urn (adaptive biased-coin) randomization. The properties described herein are the probabilities of treatment imbalances and the potential effects on the power of statistical tests; the permutational basis for statistical tests; and the potential for experimental biases in the assessment of treatment effects due either to the predictability of the random allocations (selection bias) or the susceptibility of the randomization procedure to covariate imbalances (accidental bias). For most randomization procedures, the probabilities of overall treatment imbalances are readily computed, even when a stratified randomization is used. This is important because treatment imbalance may affect statistical power. It is shown, however, that treatment imbalance must be substantial before power is more than trivially affected. The differences between a population versus a permutation model as a basis for a statistical test are reviewed. It is argued that a population model can only be invoked in clinical trials as an untestable assumption, rather than being formally based on sampling at random from a population. On the other hand, a permutational analysis based on the randomization actually employed requires no assumptions regarding the origin of the samples of patients studied. The large sample permutational distribution of the family of linear rank tests is described as a basis for easily conducting a variety of permutation tests. Subgroup (stratified) analyses, analyses when some data are missing, and regression model analyses are also discussed. The Blackwell-Hodges model for selection bias in the composition of the study groups is described. The expected selection bias associated with a randomization procedure is a function of the predictability of the treatment allocations and is readily evaluated for any sequence of treatment assignments. In an unmasked study, the potential for selection bias may be substantial with highly predictable sequences. Finally, the Efron model for accidental bias in the estimate of treatment effect in a linear model is described. This is important because the potential for accidental bias is equivalent to the potential for a covariate imbalance.(ABSTRACT TRUNCATED AT 400 WORDS)
Clinical Trials as Topic↗
Properties of simple randomization in clinical trials.
This article presents the properties of complete randomization (e.g., coin toss) and of the random allocation rule (random permutation of n/2 of n elements). The latter is principally used in cases where the total sample size n is known exactly a priori. The likelihood of treatment imbalances is readily computed and is shown to be negligible for large trials (n greater than 200), regardless of whether a stratified randomization is used. It is shown that substantial treatment imbalances are extremely unlikely in large trials, and therefore there is likely to be no substantial effect on power. The large-sample permutational distribution of the family of linear rank tests is presented for complete randomization unconditionally and conditionally, and for the random allocation rule. Asymptotically the three are equivalent to the distribution of these tests under a sampling-based population model. Permutation tests are also presented for a stratified analysis within one or more subgroups of patients defined post hoc on the basis of a covariate. This provides a basis for analysis when some patients' responses are assumed to be missing-at-random. Using the Blackwell-Hodges model, it is shown that complete randomization eliminates the potential for selection bias, but that the random allocation rule yields a substantial potential for selection bias in an unmasked trial. Finally, the Efron model for accidental bias is used to assess the potential for bias in the estimate of treatment effect due to covariate imbalance. Asymptotically, this probability approaches zero for complete randomization and for the random allocation rule. However, for finite n, complete randomization minimizes the probability of accidental bias, whereas this probability is slightly higher with a random allocation rule. It is concluded that complete randomization has merit in large clinical trials.
Clinical Trials as Topic↗
Properties of permuted-block randomization in clinical trials.
This article describes some of the important statistical properties of the commonly used permuted-block design, also known simply as blocked-randomization. Under a permutation model for statistical tests, proper analyses should employ tests that incorporate the blocking used in the randomization. These include the block-stratified Mantel-Haenszel chi-square test for binary data, the blocked analysis of variance F test, and the blocked nonparametric linear rank test. It is common, however, to ignore the blocking in the analysis. For these tests, it is shown that the size of a test obtained from an analysis incorporating the blocking (say T), versus an analysis ignoring the blocking (say TI), is related to the intrablock correlation coefficient (R) as TI = T(1-R). For blocks of common length 2m, the range of R is from -1/(2m-1) to 1. Thus, if there is a positive intrablock correlation, which is more likely than not for m greater than 1, an analysis ignoring blocking will be unduly conservative. Permutation tests are also presented for the case of stratified analyses within one or more subgroups of patients defined post hoc on the basis of a covariate. This provides a basis for the analysis when responses from some patients are assumed to be missing-at-random. An alternative strategy that requires no assumptions is to perform the analysis using only the subset of complete blocks in which no observations are missing. The Blackwell-Hodges model is used to assess the potential for selection bias induced by investigator attempts to guess which treatment is more likely to be assigned to each incoming patient. In an unmasked trial, the permuted-block design provides substantial potential for selection bias in the comparison of treatments due to the predictability of the assignments that is induced by the requirement of balance within blocks. Further, this bias is not eliminated by the use of random block sizes. We also modify the Blackwell-Hodges model to allow for selection bias only when the investigator is able to discern the next assignment with certainty. This type of bias is reduced by the use of random block sizes and is eliminated only if the possible block sizes are unknown to the investigators. Finally, the Efron model for accidental bias is used to assess the potential for bias in the estimation of treatment effects due to covariate imbalances. For the permuted-block design, the variance of this bias approaches that of complete randomization as the half-block length m----infinity.(ABSTRACT TRUNCATED AT 400 WORDS)
Analysis of Variance↗
Properties of the urn randomization in clinical trials.
In this article we review the important statistical properties of the urn randomization (design) for assigning patients to treatment groups in a clinical trial. The urn design is the most widely studied member of the family of adaptive biased-coin designs. Such designs are a compromise between designs that yield perfect balance in treatment assignments and complete randomization which eliminates experimental bias. The urn design forces a small-sized trial to be balanced but approaches complete randomization as the size of the trial (n) increases. Thus, the urn design is not as vulnerable to experimental bias as are other restricted randomization procedures. In a clinical trial it may be difficult to postulate that the study subjects constitute a random sample from a well-defined homogeneous population. In this case, a randomization model provides a preferred basis for statistical inference. We describe the large-sample permutational null distributions of linear rank statistics for testing the equality of treatment groups based on the urn design. In general, these permutation tests may be different from those based on the population model, which is equivalent to assuming complete randomization. Poststratified subgroup analyses can also be performed on the basis of the urn design permutational distribution. This provides a basis for analyzing the subset of patients with observed responses when some patients' responses can be assumed to be missing-at-random. For multiple mutually exclusive strata, these tests are correlated. For this case, a combined covariate-adjusted test of treatment effect is described. Finally, we show how to generalize the urn design to a prospectively stratified trial with a fairly large number of strata.
Clinical Trials as Topic↗
Randomization in clinical trials: conclusions and recommendations.
The statistical properties of simple (complete) randomization, permuted-block (or simply blocked) randomization, and the urn adaptive biased-coin randomization are summarized. These procedures are contrasted to covariate adaptive procedures such as minimization and to response adaptive procedures such as the play-the-winner rule. General recommendations are offered regarding the use of complete, permuted-block, or urn randomization. In a large double-masked trial, any of these procedures may be acceptable. For a given trial, the relative merits of each procedure should be carefully weighed in relation to the characteristics of the trial. Important considerations are the size of the trial, overall as well as within the smallest subgroup to be employed in a subgroup-specific analysis, whether or not the trial is to be masked, and the resources needed to perform the proper randomization-based permutational analysis.
Clinical Trials as Topic↗
Estimators and tests in the analysis of multiple nonindependent 2 x 2 tables with partially missing observations.
We present methods for the analysis of a K-variate binary measure for two independent groups where some observations may be incomplete, as in the case of K repeated measures in a comparative trial. For the K 2 X 2 tables, let theta = (theta 1,..., theta K) be a vector of association parameters where theta k is a measure of association that is a continuous function of the probabilities pi ik in each group (i = 1, 2; k = 1,..., K), such as the log odds ratio or log relative risk. The asymptotic distribution of the estimates theta = (theta 1,..., theta K) is derived. Under the assumption that theta k = theta for all k, we describe the maximally efficient linear estimator theta of the common parameter theta. Tests of contrasts on the theta are presented which provide a test of homogeneity Ha: theta k = theta l for all k not equal to l. We then present maximally efficient tests of aggregate association Hb: theta = theta 0, where theta 0 is a given value. It is shown that the test of aggregate association Hb is asymptotically independent of the preliminary test of homogeneity Ha. These methods generalize the efficient estimators of Gart (1962, Biometrics 18, 601-610), and the Cochran (1954, Biometrics 10, 417-451), Mantel-Haenszel (1959, Journal of the National Cancer Institute 22, 719-748), and Radhakrishna (1965, Biometrics 21, 86-98) tests to nonindependent tables. The methods are illustrated with an analysis of repeated morphologic evaluations of liver biopsies obtained in the National Cooperative Gallstone Study.
Analysis of Variance↗
External monitoring of a data coordinating center: experience of the National Cooperative Gallstone Study.
A Biostatistical Monitoring Committee was established to review periodically the procedures and performance of the data coordinating center of the National Cooperative Gallstone Study. The functions of this committee, the types of data coordinating center activities reviewed, the manner in which monitoring of these activities was carried out, and an assessment of the value of this committee to the study are discussed in this article.
Chenodeoxycholic Acid↗
Evaluation of sample size and power for analyses of survival with allowance for nonuniform patient entry, losses to follow-up, noncompliance, and stratification.
When designing a clinical trial to test the equality of survival distributions for two treatment groups, the usual assumptions are exponential survival, uniform patient entry, full compliance, and censoring only administratively at the end of the trial. Various authors have presented methods for estimation of sample size or power under these assumptions, some of which allow for an R-year accrual period with T total years of study, T greater than R. The method of Lachin (1981, Controlled Clinical Trials 2, 93-113) is extended to allow for cases where patients enter the trial in a nonuniform manner over time, patients may exit from the trial due to loss to follow-up (other than administrative), other patients may continue follow-up although failing to comply with the treatment regimen, and a stratified analysis may be planned according to one or more prognostic covariates.
Analysis of Variance↗
Mass spectrometry identification of biliary bile acids in bile from patients with gallstones before and during treatment with chenodeoxycholic acid. An ancillary study of the National Cooperative Gallstone Study.
The chemical structure of individual bile acids in 255 duodenal bile samples obtained from patients with radiolucent gallstones before and during treatment with chenodeoxycholic acid (375 or 750 mg/day) was determined by coupled gas chromatography/mass spectrometry. The two primary bile acids, cholic acid and chenodeoxycholic acid, and their metabolic products, deoxycholic acid, lithocholic acid, and ursodeoxycholic acid, were present in all bile samples and constituted greater than 97% of all bile acids. In pretreatment samples, the 12-oxo derivative of deoxycholic acid (3 alpha-hydroxy-12-oxo-cholanoic acid) was the next most abundant bile acid, being present in 62% of the samples; the average concentration was 1%, but three individuals had 6% to 8% of this bile acid. The 7-oxo derivative of chenodeoxycholic acid was also present in the majority of samples, but at a lower proportion (0.3%); five individuals had 2% to 3%. The 7-oxo derivative of cholic acid was present in a minority of samples (37%) in trace concentrations; isodeoxycholic acid and the 3-oxo derivatives of chenodeoxycholic acid and deoxycholic acid were also present in trace amounts. Four patients had 1% to 11% ursocholic acid in bile. During treatment with chenodeoxycholic acid, bile became enriched in it in direct relation to dosage; the concentration of its bacterial metabolites increased, and the proportion of cholic acid and its bacterial metabolites showed a reciprocal decrease. No unusual bile acids appeared, indicating that treatment with these doses of chenodeoxycholic acid does not result in the occurrence of additional uncommon bile acids in bile. It is suggested that the paucity of uncommon bile acids in bile, which contrasts strikingly with the great variety of uncommon bile acids known to be present in urine and feces, is the result of two factors: (1) the conversion of uncommon bile acids to common bile acids by reduction, hydroxylation, or epimerization during hepatic passage; and (2) efficient hepatic transport of common but not uncommon bile acids into bile.
Bile↗
Major issues in the organization and implementation of the National Cooperative Gallstone Study (NCGS).
The National Cooperative Gallstone Study (NCGS) was a cooperative, randomized, controlled trial of a drug, chenodiol, for the medical dissolution of gallstones. The design and procedures of the NCGS were complex, having developed as a result of extensive involvement of many experts in the field of gallstone disease and biliary lipids. During the design and implementation of the protocol, many important issues required consideration and resolution. The aim of this article is to review these issues and the deliberations surrounding their resolution and provide personal conclusions and recommendations that may be helpful to other investigators involved in cooperative, controlled trials.
Chenodeoxycholic Acid↗
Low-dose chenodiol to prevent gallstone recurrence after dissolution therapy.
Chenodiol is a safe and effective agent for the medical dissolution of gallstones in selected patients; however, after dissolution and cessation of treatment, gallstones recur. This study was done to determine the recurrence rate after successful medical treatment and cessation of chenodiol therapy; compare the efficacy and safety of low-dose chenodiol, as compared to placebo, for prophylaxis against recurrence; and identify factors predictive of recurrence. In a randomized, double-blind fashion, 53 patients with gallstone dissolution received either chenodiol, 375 mg/d, or placebo, for at least 2 years. Standardized oral cholecystograms were done at 6 months, 1 year, and then yearly thereafter. Routine laboratory testing was done every 6 months. The cumulative rate of recurrence (life-table) was 27% in patients followed for up to 3.5 years. Chenodiol, 375 mg/d, was ineffective in preventing the recurrence of gallstones. No demographic, clinical, roentgenographic, or biochemical characteristics were predictive of recurrence.
Aged↗
The natural history of cholelithiasis: the National Cooperative Gallstone Study.
The National Cooperative Gallstone Study, a double-masked, placebo-controlled, therapeutic trial of chenodiol (chenodeoxycholic acid), provided an opportunity to study the natural history of cholelithiasis in patients who choose nonsurgical management. The major component of the study comprised 916 patients, 305 of whom were randomly assigned to receive a placebo for 24 months. Among these 305 patients, the probability of having biliary tract pain during the 24 months of prospective evaluation was significantly increased if the patient had had a history of biliary tract pain in the 12 months before entry into the study (69% versus 31%). Thirty-eight percent of patients had stone growth (greater than 0.5 cm3), and 18% had a spontaneous decrease in stone volume. Despite the high incidence of biliary tract pain, nonelective cholecystectomy was required in only 4% of patients during the 24 months.
Actuarial Analysis↗
Effects of dose relative to body weight in the National Cooperative Gallstone Study: a fixed-dose trial.
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Body Weight↗
The National Cooperative Gallstone Study viewed by its investigators.
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Chenodeoxycholic Acid↗
National Cooperative Gallstone Study: the effect of chenodeoxycholic acid on lipoproteins and apolipoproteins.
Subjects in the National Cooperative Gallstone Study undergoing 12 mo of therapy with chenodeoxycholic acid for the dissolution of gallstones (low-dose, 375 mg/day, n =252; high-dose, 750 mg/day, n = 253) had a mean increase in serum cholesterol of 20 mg/dl as compared with a 5 mg/dl increase in the placebo group (n = 258). The effect of chenodeoxycholic acid on lipoproteins was determined in a random subset of the high-dose (n = 136) and placebo (n = 143) groups. For men, the mean baseline adjusted estimated low-density lipoprotein cholesterol level at 12 mo was significantly higher in the high-dose group than in the placebo group (159 vs. 148 mg/dl, p less than 0.01), whereas among women this difference was not demonstrated. Change in low-density lipoprotein cholesterol level was inversely related to baseline cholesterol to an equivalent degree in each group among men and women. Women in the high-dose group had significantly lower very-low-density lipoprotein cholesterol levels than did the corresponding placebo group (27 vs. 32 mg/dl, p less than 0.003). Very-low-density lipoprotein cholesterol levels did not differ significantly between the high-dose and placebo group in men. Treatment did not significantly affect the levels of high-density lipoprotein cholesterol or apoproteins A-I, A-II, or B. Chenodeoxycholic acid therapy produces an increase in total cholesterol and low-density lipoprotein cholesterol but does not alter high-density lipoprotein cholesterol levels.
Apolipoprotein A-I↗
Pretreatment biliary lipid composition in white patients with radiolucent gallstones in the National Cooperative Gallstone Study.
Biliary lipid classes (bile acids, phospholipids, cholesterol) as well as individual biliary bile acids were measured in duodenal bile samples obtained before treatment from 284 white men and 264 white women participating in the National Cooperative Gallstone Study. The patients had radiolucent gallstones present in visualizing gallbladders. Calculated biliary cholesterol saturation was significantly higher in women (143 +/- 43, mean +/- SD, vs. 132 +/- 39 for men). Chenodeoxycholic acid was the major biliary bile acid in both sexes (40.0 +/- 9.9 in men; 38.8 +/- 9.3 in women, NS). Cholic acid was the second most common bile acid, constituting 32.9 +/- 8.8 in men and 31.8 +/- 8.9 in women (NS). When other demographic and clinical characteristics, including serum lipids, were related with biliary lipid composition, only percent ideal body weight correlated significantly. The partial correlation coefficient adjusted for percent ideal body weight indicated that the proportion of chenodeoxycholic acid correlated negatively with the mole fraction of cholesterol in bile in men, but not in women. Multiple regression analyses showed that bile saturation could not be predicted reliably from any clinical, chemical, or radiologic measurement in either sex. Published data for biliary lipid composition in individuals with biliary disease showed considerable overlap with the National Cooperative Gallstone Study data reported here, suggesting that cholesterol gallstone disease is not caused solely by increased biliary cholesterol saturation.
Adult↗
Introduction to sample size determination and power analysis for clinical trials.
The importance of sample size evaluation in clinical trials is reviewed and a general method is presented from which specific equations are derived for sample size determination or the analysis of power for a wide variety os statistical procedures. The method is discussed and illustrated in relation to the t test, tests for proportions, tests of survival time, and tests for correlations as they commonly occur in clinical trials. Most of the specific equations reduce to a simple general form for which tables are presented.
Clinical Trials as Topic↗