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.     

The relative gonadal index: an alternative index for quantification of reproductive condition

Gonadal indices (i.e. GSI = gonadal wt/body wt X 100) commonly are used to quantify reproductive condition in fishes. These indices may be inappropriate with specimens of different sizes, however, for gonadal growth often is allometric. A new gonadal index (relative gonadal index, RGI) was developed to quantify the reproductive condition of animals independent of body size. The RGI is based on the underlying model W = alpha i X S beta i, where W is gonadal weight, S is body size (less gonadal weight if body weight is used), and alpha i and beta i are parameters to be estimated for gonadal developmental stage i. Assuming that a multiplicative lognormal error is appropriate, parameter estimates for alpha i and beta i were obtained by linear least squares regression for the log-transformed model ln(W) = beta i X ln(S) + ln(alpha i), where, in this form, beta i is the slope and ln(alpha i) is the intercept. Only if estimates of beta i do not differ significantly among ovarian developmental stages, as in our case, can a pooled estimate of beta be used to obtain the relative gonadal index, RGI = alpha i = W/S beta. Applicability of the RGI was tested using ovaries of three ecologically distinct fish species. The RGI was found to be more appropriate than the gonosomatic index for all three species.     

A kinetic study of cyclic adenosine 3':5'-monophosphate binding and mode of activation of protein kinase from Drosophila melanogaster embryos.

Cyclic AMP-dependent protein kinase and its regulatory subunit were isolated from Drosophila melanogaster embryos. The profiles of cyclic AMP binding by these proteins were significantly different. In order to explain such a difference and to find the mode of enzyme activation by cyclic AMP, a kinetic study of cyclic AMP binding was carried out. First, the association rate constant k1 and dissociation rate constant k-1 in the cyclic AMP-regulatory subunit interaction at 0 degrees C were estimated to be 2.3 X 10(6)M-1s-1 and 1.1 X 10(-3)s-1, respectively. Secondly, the three possible modes of enzyme activation by cyclic AMP were mathematically considered and could be described by a unique formula: r=APt + BQt (A + B=1) in which the parameters A, B, P, and Q are equivalent to rate constants in the sense that the rate constants are simply expressed by these parameters. Thirdly, the values of the parameters and subsequently the values of rate constants involved in the possible mechanisms were evaluated using a curve-fitting technique and compared with experimental observation. It was then found that the following mechanism was the only one which fitted the experimental observations. Namely, RC + L k3 equilibrium k-3 LRC k4 equilibrium k-4 RL + C where R, C, and L represent the regulatory and catalytic subunits and cyclic AMP as a ligand. Thus, our results indicate that in the presence of cyclic AMP the active enzyme (C) is released from a ternary intermediate which is the primary product of the cyclic AMP-holoenzyme interaction. The estimated values of the rate constants are: k3=3.5 X 10(6)M-1s-1;k-3=7.3 X 10(-1)s-1;and k4=3.8 X 10(-2)s. These estimates indicate that the reaction LRC leads to RL + C is relatively slow and limits the rate of the overall reaction. By comparing k-3 and k4, it is apparent that a large part of newly formed ternary intermediate reverts to the holoenzyme.     

On genetic information uncertainty and the mutator phenotype in cancer

Recent evidence supports the existence of a mutator phenotype in cancer cells, although the mechanistic basis remains unknown. In this paper, it is shown that this enhanced genetic instability is generated by an amplified measurement uncertainty on genetic information during DNA replication. At baseline, an inherent measurement uncertainty implies an imprecision of the recognition, replication and transfer genetic information, and forms the basis for an intrinsic genetic instability in all biological cells. Genetic information is contained in the sequence of DNA bases, each existing due to proton tunnelling, as a coherent superposition of quantum states composed of both the canonical and rare tautomeric forms until decoherence by interaction with DNA polymerase. The result of such a quantum measurement process may be interpreted classically as akin to a Bernoulli trial, whose outcome X is random and can be either of two possibilities, depending on whether the proton is tunnelled (X=1) or not (X=0). This inherent quantum uncertainty is represented by a binary entropy function and quantified in terms of Shannon information entropy H(X)=-P(X=1)log(2)P(X=1)-P(X=0)log(2)P(X=0). Enhanced genetic instability may either be directly derived from amplified uncertainty induced by increases in quantum and thermodynamic fluctuation, or indirectly arise from the loss of natural uncertainty reduction mechanisms.     

Time-dependent ROC curves for censored survival data and a diagnostic marker

ROC curves are a popular method for displaying sensitivity and specificity of a continuous diagnostic marker, X, for a binary disease variable, D. However, many disease outcomes are time dependent, D(t), and ROC curves that vary as a function of time may be more appropriate. A common example of a time-dependent variable is vital status, where D(t) = 1 if a patient has died prior to time t and zero otherwise. We propose summarizing the discrimination potential of a marker X, measured at baseline (t = 0), by calculating ROC curves for cumulative disease or death incidence by time t, which we denote as ROC(t). A typical complexity with survival data is that observations may be censored. Two ROC curve estimators are proposed that can accommodate censored data. A simple estimator is based on using the Kaplan-Meier estimator for each possible subset X > c. However, this estimator does not guarantee the necessary condition that sensitivity and specificity are monotone in X. An alternative estimator that does guarantee monotonicity is based on a nearest neighbor estimator for the bivariate distribution function of (X, T), where T represents survival time (Akritas, M. J., 1994, Annals of Statistics 22, 1299-1327). We present an example where ROC(t) is used to compare a standard and a modified flow cytometry measurement for predicting survival after detection of breast cancer and an example where the ROC(t) curve displays the impact of modifying eligibility criteria for sample size and power in HIV prevention trials.     

Limits of diffusion in the hydrolysis of substrates by the phosphotriesterase from Pseudomonas diminuta.

The catalytic mechanism for the enzymatic hydrolysis of a series of paraoxon analogues by the phosphotriesterase from Pseudomonas diminuta has been determined. The Br?nsted plots relating the pKa of the leaving group to the observed kinetic parameters, Vmax and V/Km, are both nonlinear. This observation is consistent with a change in the rate-limiting step from chemical to physical events as the pKa of the leaving group is decreased. This conclusion is confirmed by the effects of solvent viscosity on Vmax and V/Km for the same series of analogues. The data were fitted to the scheme E k1A in equilibrium k2 EA k3----EP k7----E'P k9----E + products where EA is the enzyme-substrate complex, EP is the enzyme-product complex, E'P is the enzyme-product complex after a viscosity-independent unimolecular reaction, and the values for k1, k2, k7, and k9 are 4.1 X 10(7) M-1 s-1, 2550 s-1, 3370 s-1, and 5940 s-1, respectively. The magnitude of the chemical step, represented by k3, is dependent on the pKa of the leaving group phenol as predicted by the Br?nsted equation (log k3 = beta pKa + C) where beta = -1.8 and the constant (C) = 17.7. The magnitude of beta indicates that the transition state for substrate hydrolysis is very product-like.     

Kinetic studies on the interaction of eglin c with human leukocyte elastase and cathepsin G

We have investigated the inhibition of human leukocyte elastase and cathepsin G by recombinant Eglin c under near physiological conditions. The association rate constants k on of Eglin c for elastase and cathepsin G were 1.3 X 10(7) M-1 s-1 and 2 X 10(6) M-1 s-1, respectively. Under identical conditions, the k on for the association of human plasma alpha 1-proteinase inhibitor with the two leukocproteinases were 2.4 X 10(7) M-1 s-1 and 10(6) M-1 s-1, respectively. The consistency of these data could be verified using a set of competition experiments. The elastase-Eglin c interaction was studied in greater detail. The dissociation rate constant k off was determined by trapping of free elastase from an equilibrium mixture of elastase and Eglin c with alpha 1-proteinase inhibitor or alpha 2-macroglobulin. The rate of dissociation was very low (k off = 3.5 X 10(-5) s-1). The calculated equilibrium dissociation constant of the complex, Ki(calc) = k off/k on, was found to be 2.7 X 10(-12) M. Ki was also measured by adding elastase to mixtures of Eglin c and substrate and determining the steady-state rates of substrate hydrolysis. The Ki determined from these experiments (7.5 X 10(-11) M) was significantly higher than Ki(calc). This discrepancy might be explained by assuming that the interaction of Eglin c with elastase involves two steps: a fast binding reaction followed by a slow isomerization step. From the above kinetic constants it may be inferred that at a therapeutic concentration of 5 X 10(-7) M, Eglin c will inhibit leukocyte elastase in one second and will bind this enzyme in a "pseudo-irreversible" manner.     

Electrostatic attraction governs the dimer assembly of human hemoglobin

We have investigated the effect of surface charge on the rate of assembly of alpha beta dimers of human hemoglobin A: alpha + beta k a----alpha beta. Heme intact beta A subunits were compared with four mutant subunits which differ by integral units of charge: beta N(Lys-95----Glu) (2-); beta J(Gly-16----Asp) (1-); beta S(Glu-6----Val) (1+); beta C(Glu-6----Lys) (2+). Subunit competition experiments were performed as follows. Varying amounts of 3H-labeled alpha A subunits were added to a mixture containing equal amounts of beta A and beta X subunits so that alpha/(beta A + beta X) ranged from 0.05-1.0. The reconstituted 3H-labeled Hbs A and X were analyzed by ion-exchange high pressure liquid chromatography as well as by gel electrofocusing and fluorography. Under the solvent conditions employed (10 mM PO4(Na), pH 7.0, 0 degrees C) a predominant proportion of the beta subunits was monomeric. Therefore, the ratio of Hb X to Hb A formed from subunit reconstitution when alpha/(beta X + beta A) approached zero provides a direct measure of the relative rates of monomer combination: kXa/kAa. The experimental values of this ratio decreased monotonically with the overall charge of the variant beta subunit: beta N = 2.6; beta J = 1.5; beta S = 0.41; beta C = 0.13. In contrast surface charge had no significant effect on the rate of dissociation of the alpha beta dimer: alpha beta kd----alpha + beta. At pH 8.0, where the alpha chains lack a net surface charge, they combined equally well to beta A and beta C chains. These experiments are consistent with a two-step mechanism, alpha + beta in equilibrium (alpha...beta) in equilibrium alpha beta, where the oppositely charged monomers diffuse together under the influence of their mutual electrostatic interaction to form a nonspecifically bound encounter complex [alpha...beta] that undergoes a surface charge-independent rearrangement to form the stable dimer.     

A stochastic-covariate failure model with an application to case-control analysis

A stochastic process X(t) is periodically stationary (and ergodic) if, for every k> or =1 and every (t(1),ellipsis,t(k)) in R(k), the sequence of random vectors (X(t(1)+n),ellipsis,X(t(k)+n))n=0,+1, ellipsis, is stationary (and ergodic). For such an ergodic process, let T be a positive random variable defined on the sample space of the process, representing a time of failure. The local failure-rate function is assumed to be of the form up(x),-infinity0 is a small number, tending to 0; and, for each u,T=T(u) is the corresponding failure-time. It is shown that X(T(u)) and uT(u) have, for u-->0, a limiting joint distribution and are, in fact, asymptotically independent. The marginal distributions are explicitly given. Let Y be a random variable whose distribution is the limit of that of X(T(u)). Under the hypothesis that p(x) is unknown or of known functional form but with unknown parameters, it is shown how p(x) can be estimated on the basis of independent copies of the random variable Y. The results are applied to the analysis of a case-control study featuring a 'marker' process X(t) and an 'event-time' T. The event in the study is considered to be particularly rare, and this is reflected in the assumption u-->0. The control-distribution is identified with the average marginal distribution of the (periodically stationary) marker process X(t), and the case-distribution is identified with that of Y. The particular application is a biomedical trial to determine the risk of stroke in terms of the level of an anticoagulant in the blood of the patient.     

Studies on the effect of serine protease inhibitors on activated contact factors. Application in amidolytic assays for factor XIIa, plasma kallikrein and factor XIa

Amidolytic assays have been developed to determine factor XIIa, factor XIa and plasma kallikrein in mixtures containing variable amounts of each enzyme. The commercially available chromogenic p-nitroanilide substrates Pro-Phe-Arg-NH-Np (S2302 or chromozym PK), Glp-Pro-Arg-NH-Np (S2366), Ile-Glu-(piperidyl)-Gly-Arg-NH-Np (S2337), and Ile-Glu-Gly-Arg-NH-Np (S2222) were tested for their suitability as substrates in these assays. The kinetic parameters for the conversion of S2302, S2222, S2337 and S2366 by beta factor XIIa, factor XIa and plasma kallikrein indicate that each active enzyme exhibits considerable activity towards a number of these substrates. This precludes direct quantification of the individual enzymes when large amounts of other activated contact factors are present. Several serine protease inhibitors have been tested for their ability to inhibit those contact factors selectively that may interfere with the factor tested for. Soybean trypsin inhibitor very efficiently inhibited kallikrein, inhibited factor XIa at moderate concentrations, but did not affect the amidolytic activity of factor XIIa. Therefore, this inhibitor can be used to abolish a kallikrein and factor XIa contribution in a factor XIIa assay. We also report the rate constants of inhibition of contact activation factors by three different chloromethyl ketones. D-Phe-Pro-Arg-CH2Cl was moderately active against contact factors (k = 2.2 X 10(3) M-1 s-1 at pH 8.3) but showed no differences in specifity. D-Phe-Phe-Arg-CH2Cl was a very efficient inhibitor of plasma kallikrein (k = 1.2 X 10(5) M-1 s-1 at pH 8.3) whereas it slowly inhibited factor XIIa (k = 1.4 X 10(3) M-1 s-1) and factor XIa (k = 0.11 X 10(3) M-1 s-1). Also Dns-Glu-Gly-Arg-CH2Cl was more reactive towards kallikrein (k = 1.6 X 10(4) M-1 s-1) than towards factor XIIa (k = 4.6 X 10(2) M-1 s-1) and factor XIa (k = 0.6 X 10(2) M-1 s-1). Since Phe-Phe-Arg-CH2Cl is highly specific for plasma kallikrein it can be used in a factor XIa assay selectively to inhibit kallikrein. Based on the catalytic efficiencies of chromogenic substrate conversion and the inhibition characteristics of serine protease inhibitors and chloromethyl ketones we were able to develop quantitative assays for factor XIIa, factor XIa and kallikrein in mixtures of contact activation factors.     

Reactions of nitrogen dioxide in aqueous model systems: oxidation of tyrosine units in peptides and proteins

By application of pulse radiolysis it was demonstrated that nitrogen dioxide (NO2.) oxidizes Gly-Tyr in aqueous solution with a strongly pH-dependent rate constant (k6 = 3.2 X 10(5) M-1 S-1 at pH 7.5 and k6 = 2.0 X 10(7) M-1 S-1 at pH 11.3), primarily generating phenoxyl radicals. The phenoxyl can react further with NO2. (k7 approximately 3 X 10(9) M-1 S-1) to form nitrotyrosine, which is the predominant final product in neutral solution and at low tyrosyl concentrations under gamma-radiolysis conditions. Tyrosine nitration is less efficient in acidic solution, due to the natural disproportionation of NO2., and in alkaline solutions and at high tyrosyl concentrations due to enhanced tyrosyl dimerization. Selective tyrosine nitration by interaction of NO2. with proteins (at pH 7 to 9) was demonstrated in the case of histone, lysozyme, ribonuclease A, and subtilisin Carlsberg. Nitrotyrosine developed slowly also under incubation of Gly-Tyr with nitrite at pH 4 to 5, where NO2. is formed by acid decomposition of HONO. It is recalled in this context that NO2.-induced oxidations, by regenerating NO2-, can propagate NO2./NO2- redox cycling under acidic conditions. Even faster than with tyrosine is the NO2.-induced oxidation of cysteine-thiolate (k9 = 2.4 X 10(8) M-1 S-1 at pH 9.2), involving the transient formation of cystinyl radical anions. The interaction of NO2. with Gly-Trp was comparably slow (k approximately 10(6) M-1 S-1), and no reaction was detectable by pulse radiolysis with Met-Gly and (Cys-Gly)2, or with DNA. Slow reactions of NO2. were observed with arachidonic acid (k approximately 10(6) M-1 S-1 at pH 9.0) and with linoleate (k approximately 2 X 10(5) M-1 S-1 at pH 9.4), indicating that NO2. is capable of initiating lipid peroxidation even in an aqueous environment. NO2.-Induced tyrosine nitration, using 50 microM Gly-Tyr at pH 8.2, was hardly inhibited, however, in the presence of 1 mM linoleate, and was not affected at all in the presence of 5 mM dimethylamine (a nitrosamine precursor). It is concluded that protein modifications, and particularly phenol and thiol oxidation, may be an important mechanism, as well as initiation of lipid peroxidation, of action of NO2. in biological systems.     

Improving efficiency of inferences in randomized clinical trials using auxiliary covariates

Summary .   The primary goal of a randomized clinical trial is to make comparisons among two or more treatments. For example, in a two-arm trial with continuous response, the focus may be on the difference in treatment means; with more than two treatments, the comparison may be based on pairwise differences. With binary outcomes, pairwise odds ratios or log odds ratios may be used. In general, comparisons may be based on meaningful parameters in a relevant statistical model. Standard analyses for estimation and testing in this context typically are based on the data collected on response and treatment assignment only. In many trials, auxiliary baseline covariate information may also be available, and it is of interest to exploit these data to improve the efficiency of inferences. Taking a semiparametric theory perspective, we propose a broadly applicable approach to adjustment for auxiliary covariates to achieve more efficient estimators and tests for treatment parameters in the analysis of randomized clinical trials. Simulations and applications demonstrate the performance of the methods.     

Estrogen receptor in chicken oviduct: receptor dissociation kinetics and transformation

Cytosolic and nuclear estrogen receptor forms of chicken oviduct have been studied by (1) measuring hormone dissociation kinetics and by (2) sucrose density gradient analysis on high salt gradients. Estradiol dissociates from the receptor in chicken oviduct cytosol at 22 degrees C following a two-phase exponential process. The fraction of receptor with a fast dissociation rate (k = 120 X 10(-3) min-1) decreases as a function of the pre-incubation at 22 degrees C; after prolonged pre-incubation only the slowly dissociating (k = 12.3 X 10(-3) min-1) form remains. Dissociation of moxestrol, a synthetic estrogen with a higher affinity, from the cytosol receptor at 30 degrees C is similar, showing a transition of a fast dissociating form (k = 120 X 10(-3) min-1) to a slowly dissociating form (k = 7.6 X 10(-3) min-1) as a result of pre-incubation at 30 degrees C. A concomitant temperature-dependent shift of the estrogen receptor from a 4.8 S to a 6.1 S form was observed with moxestrol but not with estradiol as a ligand. Sodium molybdate (20 mM) and NaSCN (400 mM) inhibit the temperature-dependent increase in sedimentation coefficient, but molybdate allows the formation of a receptor form which shows intermediary dissociation kinetics. Estrogen receptor, precipitated with ammonium sulfate (0-35%) shows monophasic dissociation kinetics of estradiol (k = 39.5 X 10(-3) min-1) and for moxestrol (k = 10.8 X 10(-3) min-1), suggesting full receptor activation only with moxestrol as a ligand. Moxestrol-receptor complexes obtained by ammonium sulfate precipitation sediment at 0 degree C at 4.8 S. Only after subsequent incubation at 30 degrees C a shift from 4.8 S to 5.9 S is observed, suggesting that the formation of the slowly dissociating form of the receptor may precede the formation of a stable transformed receptor complex. The nuclear estrogen receptor with estradiol as a ligand shows biphasic dissociation kinetics at 22 degrees C (k = 70 X 10(-3) min-1; k = 14.0 X 10(-3) min-1). The ratio of both components (1:1) does not change after preincubation of the nuclear receptor extract at 22 degrees C. Moxestrol dissociates from the nuclear receptor at 30 degrees C monophasically with a slow rate (k = 6.1 X 10(-3) min-1), suggesting that it is extracted as an activated hormone-receptor complex.(ABSTRACT TRUNCATED AT 400 WORDS)     

Computer analysis of sub-parameters of depurination and depolymerization rate constants in Feulgen DNA hydrolysis

Feulgen DNA hydrolysis curves derived from cytofluorometry at various temperatures and HCl concentrations were computer analyzed with least squares fit to Bateman function. By comparing the depurination (k1) and depolymerization (k2) rate constants at different hydrolysis conditions, it was found that the two parameters of temperature and HCl concentration can be expressed as k = AN2 X exp (-B/T), where A and B are constants, N is the HCl concentrations, and T is the absolute temperature. From the analysis of Feulgen hydrolysis curves with 2N HCl at various temperatures, it was calculated that A = 5.3590 X 10(14) and B = 12133.543, for k1, and A = 6.2401 X 10(14) and B = 12181.660, for k2 for mouse 4C hepatocytes fixed with absolute methanol. Computer generated theoretical hydrolysis curves using the above k1 and k2 values were compared with experimental curves at various temperatures and HCl-concentrations. The two types of hydrolysis curves coincided with each other when 1-3 N HCl was used at temperatures between 30-40 degrees C. The peak times of hydrolysis curves at different conditions determined by experimental analysis and theoretical estimations also coincided reasonably well with each other. The physico-chemical phenomena underlying the equation designating k1 and k2 values are discussed.     

Bayesian Estimation in a Generalized Negative Binomial Distribution

A generalized negative binomial (GNB) distribution was introduced by JAIN and CONSUL (1971) and was modified by NELSON (1975). The probability function of the distribution is defined by the function p(x; m, β, θ)= θ^x (1 - θ)^m+βx—x for x=0, 1, …, and zero otherwise, where m>0, 0<θ<1 and β=0 or 1≦β<θ^?1. The Bayes estimators for a number of parametric functions of θ when m and β are known are derived. The prior information on θ may be given by a beta distribution, B(a, b), to which no subjective significance is attached. It has been illustrated that the parameters in the prior distribution can be assigned by a computer. Comparisons are made of the Bayes estimate of P(X=k) to the corresponding ML estimate and the MVU estimate for any given sample to the order n^?1 for different values of k..     

Unbalanced regression analysis with residuals having a covariance structure of intra-class form.

Let Yi be an ni X 1 vector of observations, Xi an ni X p matrix of known values, and beta an unknown p X 1 with the structure Yi = Xi beta + epsilon i, where the covariance matrix of epsilon i is of intra-class form, that is Cov (epsilon i) = sigma2[(1 - rho) Ii + rho e i e i'] where Ii is the ni X ni identity matrix and e i is the ni X 1 vector each element of which is unity. This article develops the maximum likelihood estimators of beta, sigma2, and rho when one observes N pairs (Xi, Yi). This situation arises typically in biological problems where one samples clusters of related organisms. The estimation procedure is illustrated in a commonly occurring genetics situation.     

Characteristics of thermal inactivation of lysozyme in solution

In the buffer solution (pH 6,2) at 20-80 degrees, the lysozyme thermoinactivation was studied by monitoring of its activity decrease in the lysis of M. lysodeicticus cells. Protein inactivation was characterized by effective pseudofirst order rate constants which depend on enzyme concentration and are described by equation k = k0 . exp [-alpha 0 (1-gamma/T) [E]0], where k0 is inactivation rate constant at "infinite" enzyme dilution, [E0] is an initial lysozyme concentration, alpha 0 and gamma are the coefficients independent on [E0]. By extrapolation of the "k" dependencies on [E]0 the constants k0 were determined. In the range 40-70 degrees C, the rate constant k0 is equal 4,0 X 10(11) . exp (-24 200/RT) sec-1.     

Influence of trial duration on the bias of the estimated treatment effect in clinical trials when individual heterogeneity is ignored

In randomized clinical trials where the times to event of two treatment groups are compared under a proportional hazards assumption, it has been established that omitting prognostic factors from the model entails an underestimation of the hazards ratio. Heterogeneity due to unobserved covariates in cancer patient populations is a concern since genomic investigations have revealed molecular and clinical heterogeneity in these populations. In HIV prevention trials, heterogeneity is unavoidable and has been shown to decrease the treatment effect over time. This article assesses the influence of trial duration on the bias of the estimated hazards ratio resulting from omitting covariates from the Cox analysis. The true model is defined by including an unobserved random frailty term in the individual hazard that reflects the omitted covariate. Three frailty distributions are investigated: gamma, log‐normal, and binary, and the asymptotic bias of the hazards ratio estimator is calculated. We show that the attenuation of the treatment effect resulting from unobserved heterogeneity strongly increases with trial duration, especially for continuous frailties that are likely to reflect omitted covariates, as they are often encountered in practice. The possibility of interpreting the long‐term decrease in treatment effects as a bias induced by heterogeneity and trial duration is illustrated by a trial in oncology where adjuvant chemotherapy in stage 1B NSCLC was investigated.     

On the covariate-adjusted estimation for an overall treatment difference with data from a randomized comparative clinical trial

To estimate an overall treatment difference with data from a randomized comparative clinical study, baseline covariates are often utilized to increase the estimation precision. Using the standard analysis of covariance technique for making inferences about such an average treatment difference may not be appropriate, especially when the fitted model is nonlinear. On the other hand, the novel augmentation procedure recently studied, for example, by Zhang and others (2008. Improving efficiency of inferences in randomized clinical trials using auxiliary covariates. Biometrics 64, 707-715) is quite flexible. However, in general, it is not clear how to select covariates for augmentation effectively. An overly adjusted estimator may inflate the variance and in some cases be biased. Furthermore, the results from the standard inference procedure by ignoring the sampling variation from the variable selection process may not be valid. In this paper, we first propose an estimation procedure, which augments the simple treatment contrast estimator directly with covariates. The new proposal is asymptotically equivalent to the aforementioned augmentation method. To select covariates, we utilize the standard lasso procedure. Furthermore, to make valid inference from the resulting lasso-type estimator, a cross validation method is used. The validity of the new proposal is justified theoretically and empirically. We illustrate the procedure extensively with a well-known primary biliary cirrhosis clinical trial data set.     

Inactivation of cysteine proteases by (acyloxy)methyl ketones using S'-P' interactions

We have synthesized (acyloxy)methyl ketone inactivators of papain, cathepsin B, and interleukin-1beta conversion enzyme (ICE) that interact with both the S and S' subsites. The value of k(inact)/K(i) for these inactivators is strongly dependent on the leaving group. For example, Z-Phe-Gly-CH(2)-X is a poor inactivator of papain when X is OCOCH(3) (k(inact)/K(i) = 2.5 M(-)(1) s(-)(1)) but becomes a potent inactivator when X is OCO-L-Leu-Z (k(inact)/K(i) = 11 000 M(-)(1) s(-)(1)). Since these leaving groups have similar chemical reactivities, the difference in potency must be attributed to interactions with the S' sites. The potency of the leaving group correlates with the P' specificity of papain. Similar results are also observed for the inactivation of cathepsin B by these compounds. A series of inactivators with the general structure Fmoc-L-Asp-CH(2)-X were designed to inactivate ICE. No inhibition was observed when X was OCOCH(3). In contrast, ICE is inactivated when X is OCO-D-Pro-Z (k(inact)/K(i) = 131 M(-)(1) s(-)(1)). These results demonstrate that S'-P' interactions can be utilized to increase the efficacy and selectivity of (acyloxy)methyl ketone inactivators.