Statistics in Medicine

In medical research, it is rare that a single variable is sufficient to represent all relevant aspects of epidemiological risk, genomic activity, adverse events, or clinical response. Since biological systems tend to be neither linear, nor hierarchical in nature, the assumptions of traditional multivariate statistical methods based on the linear model can often not be justified on theoretical grounds. Establishing concept validity through empirical validation is not only problematic, but also time consuming. This paper proposes the use of u‐statistics for scoring multivariate ordinal data and a family of simple non‐parametric tests for analysis. The scoring method is demonstrated to be applicable to scoring clinical response profiles in the treatment of psoriasis and then to identifying genomic pathways that best correlate with these profiles. Copyright © 2004 John Wiley & Sons, Ltd.

Propensity score methods are increasingly being used to reduce or minimize the effects of confounding when estimating the effects of treatments, exposures, or interventions when using observational or non‐randomized data. Under the assumption of no unmeasured confounders, previous research has shown that propensity score methods allow for unbiased estimation of linear treatment effects (e.g., differences in means or proportions). However, in biomedical research, time‐to‐event outcomes occur frequently. There is a paucity of research into the performance of different propensity score methods for estimating the effect of treatment on time‐to‐event outcomes. Furthermore, propensity score methods allow for the estimation of marginal or population‐average treatment effects. We conducted an extensive series of Monte Carlo simulations to examine the performance of propensity score matching (1:1 greedy nearest‐neighbor matching within propensity score calipers), stratification on the propensity score, inverse probability of treatment weighting (IPTW) using the propensity score, and covariate adjustment using the propensity score to estimate marginal hazard ratios. We found that both propensity score matching and IPTW using the propensity score allow for the estimation of marginal hazard ratios with minimal bias. Of these two approaches, IPTW using the propensity score resulted in estimates with lower mean squared error when estimating the effect of treatment in the treated. Stratification on the propensity score and covariate adjustment using the propensity score result in biased estimation of both marginal and conditional hazard ratios. Applied researchers are encouraged to use propensity score matching and IPTW using the propensity score when estimating the relative effect of treatment on time‐to‐event outcomes. Copyright © 2012 John Wiley & Sons, Ltd.

Meta‐analyses of a treatment's effect compared with a control frequently calculate the meta‐effect from standardized mean differences (SMDs). SMDs are usually estimated by Cohen's d or Hedges' g. Cohen's d divides the difference between sample means of a continuous response by the pooled standard deviation, but is subject to nonnegligible bias for small sample sizes. Hedges' g removes this bias with a correction factor. The current literature (including meta‐analysis books and software packages) is confusingly inconsistent about methods for synthesizing SMDs, potentially making reproducibility a problem. Using conventional methods, the variance estimate of SMD is associated with the point estimate of SMD, so Hedges' g is not guaranteed to be unbiased in meta‐analyses. This article comprehensively reviews and evaluates available methods for synthesizing SMDs. Their performance is compared using extensive simulation studies and analyses of actual datasets. We find that because of the intrinsic association between point estimates and standard errors, the usual version of Hedges' g can result in more biased meta‐estimation than Cohen's d. We recommend using average‐adjusted variance estimators to obtain an unbiased meta‐estimate, and the Hartung‐Knapp‐Sidik‐Jonkman method for accurate estimation of its confidence interval.

We propose a transmission model to estimate the main characteristics of influenza transmission in households. The model details the risks of infection in the household and in the community at the individual scale. Heterogeneity among subjects is investigated considering both individual susceptibility and infectiousness. The model was applied to a data set consisting of the follow‐up of influenza symptoms in 334 households during 15 days after an index case visited a general practitioner with virologically confirmed influenza.

Estimating the parameters of the transmission model was challenging because a large part of the infectious process was not observed: only the dates when new cases were detected were observed. For each case, the data were augmented with the unobserved dates of the start and the end of the infectious period. The transmission model was included in a 3‐levels hierarchical structure: (i) the observation level ensured that the augmented data were consistent with the observed data, (ii) the transmission level described the underlying epidemic process, (iii) thepriorlevel specified the distribution of the parameters. From a Bayesian perspective, the jointposteriordistribution of model parameters and augmented data was explored by Markov chain Monte Carlo (MCMC) sampling.

The mean duration of influenza infectious period was estimated at 3.8 days (95 per cent credible interval, 95 per cent CI [3.1,4.6]) with a standard deviation of 2.0 days (95 per cent CI [1.1,2.8]). The instantaneous risk of influenza transmission between an infective and a susceptible within a household was found to decrease with the size of the household, and established at 0.32 person day⁻¹(95 per cent CI [0.26,0.39]); the instantaneous risk of infection from the community was 0.0056day⁻¹(95 per cent CI [0.0029,0.0087]). Focusing on the differences in transmission between children (less than 15 years old) and adults, we estimated that the former were more likely to transmit than adults (posteriorprobability larger than 99 per cent), but that the mean duration of the infectious period was similar in children (3.6 days, 95 per cent CI [2.3,5.2]) and adults (3.9 days, 95 per cent CI [3.2,4.9]). Theposteriorprobability that children had a larger community risk was 76 per cent and theposteriorprobability that they were more susceptible than adults was 79 per cent. Copyright © 2004 John Wiley & Sons, Ltd.

This article reviews the basics of Bayesian decision theory, and comments on its use in medical decision making. It emphasizes the subjectivity of the probability and utility inputs, and the desirability, in certain contexts, of representing several decision makers, each with his or her own probabilities and utilities. Applications and ethical considerations are also discussed. A brief bibliography gives pointers to the literature. Copyright © 2005 John Wiley & Sons, Ltd.

An extension of the Wilcoxon rank‐sum test is developed to handle the situation in which a variable is measured for individuals in three or more (ordered) groups and a non‐parametric test for trend across these groups is desired. The uses of the test are illustrated by two examples from cancer research.

The approval process for some medical devices involves a single‐arm trial in which the outcomes associated with the new device are compared to the expected outcomes associated with approved devices, the latter denoted the objective performance criterion (OPC). In this paper, models for multivariate mixed outcomes are applied to derive the OPC for a medical device to be used in clinical evaluations of the same type of device. We illustrate the techniques by determining the OPC for coronary artery stents, metal cages used to widen blocked coronary arteries in patients with coronary artery disease, using data from seven randomized trials of stents approved for use in the U.S.A. involving 5806 patients. The OPC is based on two 9‐month endpoints: target lesion revascularization, a binary outcome, and proportion diameter stenosis, a continuous outcome. To account for the correlation between mixed outcomes we consider factorization of the likelihood into marginal and conditional components, or adoption of a latent variable model. Because the models have different structural forms, standard methods for model comparison (such as the AIC and BIC) cannot be used. We discuss how model identifiability and valid inference are achieved, and then adapt the deviance information criterion (DIC) and the pseudo‐Bayes factor (PSBF) to select the best model. Nine months post‐stenting, we find that the average posterior probability (standard deviation) of target lesion revascularization ranges from 0.086 (0.008) for non‐diabetics with one diseased vessel to 0.163 (0.022) for diabetics with three diseased vessels. When considering proportion diameter stenosis, the corresponding posterior means are 0.375 (0.020) and 0.427 (0.030). The correlation coefficient of the components of the OPC lies in the range 0.042 to 0.116. Copyright © 2003 John Wiley & Sons, Ltd.

This paper is concerned with regression models for correlated mixed discrete and continuous outcomes constructed using copulas. Our approach entails specifying marginal regression models for the outcomes, and combining them via a copula to form a joint model. Specifically, we propose marginal regression models (e.g. generalized linear models) to link the outcomes' marginal means to covariates. To account for associations between outcomes, we adopt the Gaussian copula to indirectly specify their joint distributions. Our approach has two advantages over current methods: one, regression parameters in models for both outcomes are marginally meaningful, and two, the association is ‘margin‐free’, in the sense that it is characterized by the copula alone. By assuming a latent variable framework to describe discrete outcomes, the copula used still uniquely determines the joint distribution. In addition, association measures between outcomes can be interpreted in the usual way. We report results of simulations concerning the bias and efficiency of two likelihood‐based estimation methods for the model. Finally, we illustrate the model using data on burn injuries. Copyright © 2010 John Wiley & Sons, Ltd.

This paper describes the use of the bootstrap,^1,2 a new computer‐based statistical methodology, to help validate a regression model resulting from the fitting of Cox's proportional hazards model³ to a set of censored survival data. As an example, we define a prognostic model for outcome in childhood acute lymphocytic leukemia with the Cox model and use of a training set of 224 patients. To validate the accuracy of the model, we use a bootstrap resampling technique to mimic the population under study in two stages. First, we select the important prognostic factors via a stepwise regression procedure with 100 bootstrap samples. Secondly we estimate the corresponding regression parameters for these important factors with 400 bootstrap samples. The bootstrap result suggests that the model constructed from the training set is reasonable.