Estimating the relative risk in cohort studies and clinical trials of common outcomes

Logistic regression yields an adjusted odds ratio that approximates the adjusted relative risk when disease incidence is rare (<10%), while adjusting for potential confounders. For more common outcomes, the odds ratio always overstates the relative risk, sometimes dramatically. The purpose of this paper is to discuss the incorrect application of a proposed method to estimate an adjusted relative risk from an adjusted odds ratio, which has quickly gained popularity in medical and public health research, and to describe alternative statistical methods for estimating an adjusted relative risk when the outcome is common. Hypothetical data are used to illustrate statistical methods with readily accessible computer software.     

Nesting sub-studies and randomised controlled trials within birth cohort studies

Although birth cohort studies can stand on their own, there are a number of different types of sub-studies that can add value to the overall project. These can be summarised within four main categories: (A) more detailed observations of relatively small subgroups aimed at describing mechanisms and processes; (B) nested case–control studies; (C) use of detailed observations to validate data collection by questionnaire or interview; (D) randomised controlled trials. For each category we give examples of ways in which they have been employed in current pregnancy birth cohort studies.     

Concordance odds ratios and approximate rate ratios in longitudinal twin studies

Odds ratios derived from probandwise concordance rates are usually interpreted as increased risks in twins. Though the odds ratios in case–control studies have been shown to reflect rate ratios, few studies focused on such relationships in twin studies. The authors derived an approximate formula for the ratios of person-time incidence rates after the random assignment of twins into index twins and co-twins, i.e., incidence rate ratios. The resulting rate ratio was estimated as the product of the concordance odds ratio and a term that reflect the follow-up duration and the average time to occurrence of disease. Odds ratios coincide with rate ratios when the average time to occurrence of disease is half the duration of follow-up, although in studies spanning several decades these two measures might be different. The authors illustrated that when the incidence rate is not constant over the follow-up period as in longitudinal twin studies, the conventional odds ratio should not be used as an estimator of rate ratio.     

A note on graphical presentation of estimated odds ratios from several clinical trials

To display a number of estimates of a parameter obtained from different studies it is common practice to plot a sequence of confidence intervals. This can be useful but is often unsatisfactory. An alternative display is suggested which represents intervals as points on a bivariate graph, and which has advantages. When the data are estimates of odds ratios from studies with a binary response, it is argued that for either type of plot, a log scale should be used rather than a linear scale.     

Noninferiority trial designs for odds ratios and risk differences

This study presents constrained maximum likelihood derivations of the design parameters of noninferiority trials for binary outcomes with the margin defined on the odds ratio (ψ) or risk‐difference (δ) scale. The derivations show that, for trials in which the group‐specific response rates are equal under the point‐alternative hypothesis, the common response rate, π^N, is a fixed design parameter whose value lies between the control and experimental rates hypothesized at the point‐null, {π_C, π_E}. We show that setting π^N equal to the value of π_C that holds under H₀ underestimates the overall sample size requirement. Given {π_C, ψ} or {π_C, δ} and the type I and II error rates, or algorithm finds clinically meaningful design values of π^N, and the corresponding minimum asymptotic sample size, N=n_E+n_C, and optimal allocation ratio, γ=n_E/n_C. We find that optimal allocations are increasingly imbalanced as ψ increases, with γ_ψ<1 and γ_δ≈1/γ_ψ, and that ranges of allocation ratios map to the minimum sample size. The latter characteristic allows trialists to consider trade‐offs between optimal allocation at a smaller N and a preferred allocation at a larger N. For designs with relatively large margins (e.g. ψ>2.5), trial results that are presented on both scales will differ in power, with more power lost if the study is designed on the risk‐difference scale and reported on the odds ratio scale than vice versa. Copyright © 2010 John Wiley & Sons, Ltd.     

Unbiased estimation of odds ratios: combining genomewide association scans with replication studies

Odds ratios or other effect sizes estimated from genome scans are upwardly biased, because only the top‐ranking associations are reported, and moreover only if they reach a defined level of significance. No unbiased estimate exists based on data selected in this fashion, but replication studies are routinely performed that allow unbiased estimation of the effect sizes. Estimation based on replication data alone is inefficient in the sense that the initial scan could, in principle, contribute information on the effect size. We propose an unbiased estimator combining information from both the initial scan and the replication study, which is more efficient than that based just on the replication. Specifically, we adjust the standard combined estimate to allow for selection by rank and significance in the initial scan. Our approach explicitly allows for multiple associations arising from a scan, and is robust to mis‐specification of a significance threshold. We require replication data to be available but argue that, in most applications, estimates of effect sizes are only useful when associations have been replicated. We illustrate our approach on some recently completed scans and explore its efficiency by simulation. Genet. Epidemiol. 33:406–418, 2009. © 2009 Wiley‐Liss, Inc.     

Instrumental variable estimation of causal risk ratios and causal odds ratios in Mendelian randomization analyses

In this paper, the authors describe different instrumental variable (IV) estimators of causal risk ratios and odds ratios with particular attention to methods that can handle continuously measured exposures. The authors present this discussion in the context of a Mendelian randomization analysis of the effect of body mass index (BMI; weight (kg)/height (m)(2)) on the risk of asthma at age 7 years (Avon Longitudinal Study of Parents and Children, 1991-1992). The authors show that the multiplicative structural mean model (MSMM) and the multiplicative generalized method of moments (MGMM) estimator produce identical estimates of the causal risk ratio. In the example, MSMM and MGMM estimates suggested an inverse relation between BMI and asthma but other IV estimates suggested a positive relation, although all estimates had wide confidence intervals. An interaction between the associations of BMI and fat mass and obesity-associated (FTO) genotype with asthma explained the different directions of the different estimates, and a simulation study supported the observation that MSMM/MGMM estimators are negatively correlated with the other estimators when such an interaction is present. The authors conclude that point estimates from various IV methods can differ in practical applications. Based on the theoretical properties of the estimators, structural mean models make weaker assumptions than other IV estimators and can therefore be expected to be consistent in a wider range of situations.     

Fluctuations in odds ratios due to variance differences in case-control studies

If small effects of exposure on disease outcome are to be appropriately assessed, it is necessary to consider all potential sources of the fluctuation of relative odds. The authors consider the impact of differential variance in case and control exposure reports on the magnitude of the observed relative odds. With equal dispersion of case and control exposure, a difference in mean exposure generally produces a dose-response increase in relative odds. The combination of equal mean and unequal dispersion of case and control exposure produces a curvilinear pattern of relative odds. Greater mean exposure and dispersion of exposure among cases produce odds ratios lower than those that would be observed if dispersion among cases and controls were equal. Conversely, less dispersion among cases than among controls produces higher relative odds estimates. Differential error as a source of differential dispersion constitutes a potentially important source of bias.     

Estimating crude or common odds ratios in case-control studies with informatively missing exposure data

In case-control studies, the crude odds ratio derived from a 2 x 2 table and the common odds ratio adjusted for stratification variables are staple measures of exposure-disease association. While missing exposure data are encountered in the majority of such studies, formal attempts to deal with them are rare, and a complete-case analysis is the norm. Furthermore, the probability that exposure is missing may depend on true exposure status, so the missing-at-random assumption is often unreasonable. In this paper, the authors present an adjustment to the usual product binomial likelihood to properly account for missing data. Estimation of model parameters without restrictive assumptions requires an additional data collection effort akin to a validation study. Closed-form results are provided to facilitate point and confidence interval estimation of crude and common odds ratios after properly accounting for informatively missing data. Simulations assess performance of the likelihood-based estimates and inferences, and they display the potential for bias in complete-case analyses. An example is presented to illustrate the approach.     

Meta-analyses of chronic disease trials with competing causes of death may yield biased odds ratios

OBJECTIVE: To study the odds ratio (OR) as measure of treatment effect in the context of mutually exclusive causes of death. STUDY DESIGN AND SETTING: As example we consider meta-analyses of randomized trials of implantable cardioverter defibrillator implantation (ICD). We compare the pooled OR to the pooled cause-specific hazard ratio (HR) for each of the mutually exclusive outcomes "sudden cardiac death" (SCD) and "death other than SCD." RESULTS: The pooled OR and cause-specific HR for the reduction of SCD are similar (0.43 and 0.44, respectively) for nine included trials. However, the OR erroneously presumes a potential trend toward an adverse effect of the ICD on "death other than arrhythmia" (OR 1.11 [0.84-1.45]), whereas such an effect is small with the cause-specific HR (HR 1.03 [0.79-1.32]). In general, it is shown that a spurious association of treatment with "other death" may be seen when a substantial number of death from the cause of interest is postponed. CONCLUSION: The OR should be used with caution to study effects of treatment on mutually exclusive causes of death. Practically this concern applies primarily to meta-analysis where the use of the cause-specific HR, whenever available, is recommended.     

Estimating odds ratios adjusting for misclassification in Alzheimer's disease risk factor assessment

Epidemiological studies of Alzheimer's disease and dementia are often two-phase studies including a screening phase and a clinical assessment phase. It is common to interview a relative of the subject at each of these phases to obtain information about the subject's exposure to risk factors. This can result in a misclassification error when assessing risk factors, as the two responses of the relative often differ. This is especially a problem for risk factors involving life-style and family history which cannot be confirmed using the subject's medical records. A naive analysis using data from each phase separately would give two different estimates of the odds ratio; both estimates could be biased. In this paper, we extend the estimation methods adjusting for misclassification developed by Liu and Liang to data collected through two-phase sampling. We first use a latent class analysis and the EM algorithm to estimate the misclassification parameters. We then derive the maximum pseudo-likelihood estimators, conditional on the misclassification parameters, to estimate the odds ratios accounting for the complex sampling study design. We propose to use the jack-knife estimator for estimation of the variances. We apply the above method to data collected in the Indianapolis-Ibadan Dementia Study to estimate the odds ratio for smoking adjusting for misclassification error.     

Sample size requirements for studies estimating odds ratios or relative risks

This paper presents formulae for determining the number of subjects necessary, in either a case-control or a cohort study, to estimate the odds ratio or relative risk, respectively, to within a selected percentage (ε) of the true population value with some specified probability. This approach differs somewhat from previous comparable work that estimated the log odds ratio within a stated fixed distance rather than as a percentage of the actual odds ratio. Comparable development for relative risk has not previously appeared in the literature. These formulae provide guidelines for determination of study size that does not depend on hypothesis testing considerations.     

Impact of missing data due to selective dropouts in cohort studies and clinical trials

BACKGROUND: Many cohort studies and clinical trials use repeated measurements of laboratory markers to track disease progression and to evaluate new therapies. A major problem in the analysis of such studies is that marker data are censored in some patients owing to withdrawal, loss to follow-up, or death. The objective of this paper is to evaluate the impact of selective dropouts attributable to death or disease progression on the estimates of marker change among different groups. METHODS: Data on CD4 cell count in human immunodeficiency virus 1-infected individuals from a clinical trial and a cohort study are used to illustrate this problem and a possible solution. Simulation studies are also presented. RESULTS: When the rate of dropout is greater in subjects whose marker status is declining rapidly, commonly used methods, like random effects models, that ignore informative dropouts lead to overoptimistic statements about the marker trends in all compared groups, because subjects with steeper marker drops tend to have shorter follow-up times and hence are weighted less in the estimation of the group rate of the average marker decline. CONCLUSIONS: The potential biases attributable to incomplete data require greater recognition in longitudinal studies. Sensitivity analyses to assess the effect of dropouts are important.     

鼻咽癌危险因子的危险度计算及其意义

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Optimal multistage designs for randomised clinical trials with continuous outcomes

Multistage designs allow considerable reductions in the expected sample size of a trial. When stopping for futility or efficacy is allowed at each stage, the expected sample size under different possible true treatment effects (δ) is of interest. The δ-minimax design is the one for which the maximum expected sample size is minimised amongst all designs that meet the types I and II error constraints. Previous work has compared a two-stage δ-minimax design with other optimal two-stage designs. Applying the δ-minimax design to designs with more than two stages was not previously considered because of computational issues. In this paper, we identify the δ-minimax designs with more than two stages through use of a novel application of simulated annealing. We compare them with other optimal multistage designs and the triangular design. We show that, as for two-stage designs, the δ-minimax design has good expected sample size properties across a broad range of treatment effects but generally has a higher maximum sample size. To overcome this drawback, we use the concept of admissible designs to find trials which balance the maximum expected sample size and maximum sample size. We show that such designs have good expected sample size properties and a reasonable maximum sample size and, thus, are very appealing for use in clinical trials.     

Effects of garlic intake on cancer: a systematic review of randomized clinical trials and cohort studies

BACKGROUND/OBJECTIVESDue to the rapid increase of global cancer incidence and mortality and a high level of interest in cancer prevention, a systematic review of garlic intake and cancer risk is needed.SUBJECTS/METHODSWe implemented a systematic review to examine the effects of varying levels of garlic intake on cancer. We conducted comprehensive literature searches in three electronic databases (MEDLINE, Embase, and Web of Science) for studies published between database inception and July or September of 2018. Two investigators independently screened abstracts and full-texts, extracted data, and assessed risk of bias (RoB). A total of one medium-quality randomized controlled trial (RCT) and 13 cohort studies graded as high RoB were included.RESULTSThe 1-year follow-up results from a RCT showed that a significant decrease in the number and size of colorectal adenomas among participants with colorectal adenomas who received high-dose aged garlic extract (AGE) compared with those who received low-dose AGE (P < 0.05). The results of prospective observational studies provided inconsistent associations of colorectal cancer risk with garlic supplements and garlic intake as food.CONCLUSIONSIn summary, the AGE was effective in reducing the number and magnitude of colorectal adenomas in one RCT, but there were inconsistent associations between garlic intake and colorectal cancer in cohort studies. Therefore, we could not draw a firm conclusion regarding the effects of garlic on cancer, because the current strength of evidence is inadequate due to a lack of number of high-quality RCTs.     

Total serum cholesterol and ischemic heart disease risk in clinical trials and observational studies

Despite compelling evidence that elevated plasma total and low-density lipoprotein cholesterol plays a causal role in ischemic heart disease (IHD) (evidence derived from molecular biologic, genetic, animal experimental, and human observational studies), the results of individual clinical trials testing the lipid hypothesis have not been regarded as conclusive. Analyzed in aggregate, however, the trials results indicate a dose-response relationship between amount of cholesterol lowering and reduction of ischemic heart disease risk. This summary analysis predicted the quantitative measure of efficacy in the recently completed Lipid Research Clinics Coronary Primary Prevention Trial (LRC-CPPT). There was a quantitatively similar relationship between the amount of IHD risk reduction associated with amount of total plasma cholesterol reduction within the active drug (cholestyramine) treated group. Further, the risk function relating baseline level of total plasma cholesterol to ischemic heart disease incidence in community-based studies such as Framingham was so similar to the risk function of the LRC-CPPT placebo group that it accurately predicted the ischemic heart disease events in the trial. These findings in aggregate provide strong confirmation of the lipid hypothesis, indicate that lowering total plasma cholesterol in middle-aged hypercholesterolemic men will reduce ischemic heart disease risk, and suggest that some extrapolation of the results to lower levels of plasma cholesterol is appropriate. However, aggregate evidence that supports the lipid hypothesis should be distinguished from that required for intervention and treatment programs. Instituting the latter requires the review and evaluation of the evidence relating cholesterol levels and cholesterol reduction not only to ischemic heart disease, but also to other outcomes.(ABSTRACT TRUNCATED AT 250 WORDS)