Background In meta-analysis, researchers often pool the results from a set of similar studies. A number of studies, however, often tend to report only the minimum and maximum values, median, and/or the first and third quartiles. Recently, many methods have been discussed for estimating the mean and standard deviation from those sample summaries. However, these methods may provide a substantially biased estimate of the inverse variance that is needed for the meta-analysis. Research Design We use Basu’s theorem to derive unbiased estimators for σ−2 from the most commonly used sample summaries from the normal distribution. While there are no closed formulas for these estimators, we use simulations to obtain simple approximations for the estimators. Results The proposed approximate estimators still show a little to no bias for normally distributed data and generally show smaller bias than the usual methods even for some non-normal distributions. The proposed estimators have lower mean squared error. Conclusions The proposed estimators are recommended for the purpose of obtaining inverse-variance weights, particularly in the context of meta-analyses.

OBJECTIVES:Our goal was to evaluate the bias in the usual method of estimating study weights in a meta-analysis and to develop a suitable bias correction. STUDY DESIGN AND SETTING:In meta-analyses, it is standard practice to weight studies by the inverse variance of their treatment effects. Weights are usually calculated by taking reciprocals of the estimated variances, but we show that this approach is biased. We established an exact expression for the bias with continuous data, yielding a correction factor for the study weights that yields improved estimation of the treatment effect. RESULTS:With the usual method, the weight for each study is always overestimated, particularly with small samples; also, the variance of the summary treatment effect is underestimated. Our correction yields an unbiased estimate of the summary treatment effect with minimum variance. We illustrate the bias numerically for various scenarios and show how it can substantially affect actual meta-analyses in practice. CONCLUSION:We recommend that the standard method of obtaining study weights should be modified by our bias correction factor. Our method is simple and straightforward to apply. Elimination of this bias will enhance the validity of conclusions from a meta-analysis, compared with the situation when the standard weights are used.

We show that the expected value of the largest order statistic in Gaussian samples can be accurately approximated as (0.2069 ln (ln (n)) + 0.942)(4), where n is an element of [2,10(8)] is the sample size, while the standard deviation of the largest order statistic can be approximated as -0.4205arctan(0.5556[ln (ln (n)) - 0.9148 vertical bar) + 0.5675. We also provide an approximation of the probability density function of the largest order statistic which in turn can be used to approximate its higher order moments. The proposed approximations are computationally efficient, and improve previous approximations of the mean and standard deviation given by Chen and Tyler (1999).

BACKGROUND:Patients with a tibial shaft fracture experiencing their first postoperative complication following treatment with intramedullary nails may be at greater risk of subsequent complications than the whole population. We aimed to determine whether the initial method of nail insertion influences outcome in patients with a tibial shaft fracture requiring multiple reoperations.METHODS:Using the Study to Prospectively Evaluate Reamed Intramedullary Nails in Tibial Shaft Fractures trial data, we categorized patients as those not requiring reoperation, those requiring a single reoperation and those requiring multiple reoperations, and we compared them by nail insertion technique (reamed v. unreamed) and fracture type (open v. closed). We then determined the number of patients whose first reoperation was in response to infection, and we compared other clinical outcomes between the reamed and unreamed groups.RESULTS:Among 1226 patients included in this analysis, 175 (14.27%) experienced a single reoperation and 44 patients (3.59%) underwent multiple reoperations. Nail insertion techniques (reamed v. unreamed) did not play a role in the need to perform multiple reoperations. Seventy-five percent of patients requiring multiple reoperations had open tibial shaft fractures. An equal number of these were reamed and unreamed insertions. The majority of patients had their course complicated by infection and almost 50% of patients whose first reoperation was for infection required more than 2 reoperations for management. The rest required multiple procedures for nonunion or bone loss.CONCLUSION:Our findings corroborate those of other studies, in which open fracture type rather than nail insertion technique was found to be the cause of morbidity following intramedullary nailing of tibial fractures.CLINICAL TRIAL REGISTRATION:www.CLINICALTRIALS:gov, no. NCT00038129.

Purpose We assessed the risk of death from prostate cancer (PCa) in relation to men’s screening histories, i.e., screening attendance among men who were offered screening. Methods Men in the Finnish Randomized Study of Screening for Prostate Cancer (FinRSPC) screening arm were invited to up to three screening rounds with the serum prostate-specific antigen (PSA) test at 4-year intervals during 1996–2007. Case subjects ( n = 330) were men who died from PCa. Each case was matched to five controls ( n = 1544) among the men who were free of PCa. Screening history was defined as (1) never/ever attended screening prior to the case diagnosis; (2) attended at the first screening round; and (3) recency of screening, calculated as the time from last screening attendance to the date of case diagnosis. The association between screening history and the risk of death from PCa was estimated by odds ratios (OR) with 95% confidence intervals (CI) using conditional logistic regression. Results Having ever attended screening versus never attended was associated with a reduced risk of PCa death (OR 0.60, 95% CI 0.45–0.81) and a similar association was found for those attended (versus not attended) the first screening round (OR 0.67, 95% CI 0.51–0.87). The effect by time since last screen for the risk of PCa death was significantly lower 2–7 years since last screen. Conclusion Among men invited to screening, subjects who attended any PSA screening during the previous 19 years had a 40% reduction in PCa mortality compared to non-screened men.

Factorial allow for the simultaneous evaluation of more than one treatment, by randomizing patients to their possible combinations, including control. However, the statistical power of one treatment can be influenced by the effectiveness of the other, a matter that has not been widely recognized. In this paper, we evaluate the relationship between the observed effectiveness of one treatment and the implied power for a second treatment in the same trial, under a range of conditions. We provide analytic and numerical solutions for a binary outcome, under the additive, multiplicative, and odds ratio scales for treatment interaction. We demonstrate how the minimum required sample size for a trial depends on the two treatment effects. Relevant factors include the event rate in the control group, sample size, treatment effect sizes, and Type-I error rate thresholds. We show that that power for one treatment decreases as a function of the observed effectiveness of the other treatment if there is no multiplicative interaction. A similar pattern is observed with the odds ratio scale at low control rates, but at high control rates, power may increase if the first treatment is moderately more effective than its planned value. When treatments do not interact additively, power may either increase or decrease, depending on the control event rate. We also determine where the maximum power occurs for the second treatment. We illustrate these ideas with data from two actual factorial trials. These results can benefit investigators in planning the analysis of factorial clinical trials, in particular, to alert them to the potential for losses in power when one observed treatment effect differs from its originally postulated value. Updating the power calculation and modifying the associated required sample size can then ensure sufficient power for both treatments.

Researchers should ideally conduct clinical trials under a presumption of clinical equipoise, but in fact trial patients will often prefer one or other of the treatments being compared. Receiving an unblinded preferred treatment may affect the study outcome, possibly beneficially, but receiving a non-preferred treatment may induce 'reluctant acquiescence', and poorer outcomes. Even in blinded trials, patients' primary motivation to enrol may be the chance of potentially receiving a desirable experimental treatment, which is otherwise unavailable. Study designs with a higher probability of receiving a preferred treatment (denoted as 'concordance') will be attractive to potential participants, and investigators, because they may improve recruitment and hence enhance study efficiency. Therefore, it is useful to consider the concordance rates associated with various study designs. We consider this question with a focus on comparing the standard, randomised, two-arm, parallel group design with the two-stage randomised patient preference design and Zelen designs; we also mention the fully randomised and partially randomised patient preference designs. For each of these designs, we evaluate the concordance rate as a function of the proportions randomised to the alternative treatments, the distribution of preferences over treatments, and (for the Zelen designs) the proportion of patients who consent to receive their assigned treatment. We also examine the equity of each design, which we define as the similarity between the concordance rates for participants with different treatment preferences. Finally, we contrast each of the alternative designs with the standard design in terms of gain in concordance and change in equity.

IMPORTANCE Infections are largely modifiable causes of cancer. However, there remains untapped potential for preventing and treating carcinogenic infections in the US. OBJECTIVE To estimate the percentage and number of incident cancers attributable to infections in the US among adults and children for the most recent year cancer incidence data were available (2017). DATA SOURCES A literature search from 1946 onward was performed in MEDLINE on January 6, 2023, to obtain the data required to calculate population attributable fractions for 31 infection-cancer pairs. National Health and Nutrition Examination Survey data were used to estimate the population prevalence of hepatitis B and C viruses and Helicobacter pylori. STUDY SELECTION Studies conducted in the US or otherWestern countries were selected according to specific infection-cancer criteria. DATA EXTRACTION AND SYNTHESIS Data from 128 studieswere meta-analyzed to obtain the magnitude of an infection-cancer association or prevalence of the infection within cancer cells. MAIN OUTCOMES AND MEASURES The proportion of cancer incidence attributable to 8 infections. RESULTS Of the 1 666 102 cancers diagnosed in 2017 among individuals aged 20 years or older in the US, 71 485 (4.3%; 95% CI, 3.1%-5.3%) were attributable to infections. Human papillomavirus (n = 38 230) was responsible for the most cancers, followed by H pylori (n = 10 624), hepatitis C virus (n = 9006), Epstein-Barr virus (n = 7581), hepatitis B virus (n = 2310), Merkel cell polyomavirus (n = 2000), Kaposi sarcoma-associated herpesvirus (n = 1075), and human T-cell lymphotropic virus type 1 (n = 659). Cancers with the most infection-attributable cases were cervical (human papillomavirus; n = 12 829), gastric (H pylori and Epstein-Barr virus; n = 12 565), oropharynx (human papillomavirus; n = 12 430), and hepatocellular carcinoma (hepatitis B and C viruses; n = 10 017). The burden of infection-attributable cancers as a proportion of total cancer incidence ranged from 9.6% (95% CI, 9.2%-10.0%) for women aged 20 to 34 years to 3.2%(95% CI, 2.4%-3.8%) for women aged 65 years or older and from 6.1% (95% CI, 5.2%-7.0%) for men aged 20 to 34 years to 3.3%(95% CI, 1.9%-4.4%) for men aged 65 years or older. Among those aged 19 years or younger, 2.2%(95% CI, 1.3%-3.0%) of cancers diagnosed in 2017 were attributable to Epstein-Barr virus. CONCLUSIONS AND RELEVANCE Infections were estimated to be responsible for 4.3% of cancers diagnosed among adults in the US in 2017 and, therefore, represent an important target for cancer prevention efforts.

Objective In meta-analyses, it is standard practice to weight studies by the inverse variance of their estimated treatment effects. The usual method to obtain study weights is to simply take reciprocals of the estimated variances. It is apparent that this naïve approach is biased. Our goal was to examine the degree of bias in the usual method, and to develop a suitable bias correction.Methods We established an exact expression for the bias, leading to a correction factor for the study weights that yields improved estimation of the treatment effect. Results With the usual method, the weight for each study is always overestimated, particularly with small samples; also, the variance of the summary treatment effect is under-estimated. Our bias correction yields an unbiased estimate of the summary treatment effect with minimum variance. We illustrate the bias for typical scenarios, and show how it can substantially affect actual meta-analyses in practice.Conclusions We recommend that the standard method of obtaining study weights should be modified by our correction factor. Our method is simple and straightforward to apply. Elimination of this bias will avoid the over-confidence in the results of meta-analyses that occurs if the standard weights are used.

The group testing procedure divides sampled units into several groups, and then obtains an overall test result for each group. It is used to identify specific individuals who have a given attribute, or to estimate the overall prevalence of the attribute in the population. We here investigate how group retesting can improve precision of estimation and its cost-efficiency, which are important considerations for investigators. Retesting uses two or more group stages, with repeat testing of the original samples at each stage. Previous authors have proposed a procedure with two stages having equal group sizes, and where the number of groups tested at the second stage is based on the number of positive groups in the first stage. In this paper, our main focus is on estimating the prevalence p of affected individuals in a population, and identifying cost-efficient experimental designs, when using two-stage testing with unequal group sizes at each stage. We use analytical solutions for the precision of estimation, together with simulations to evaluate various experimental designs. We consider the value of retesting at the second stage, and determine when using only one stage of testing might be sufficiently precise.

Recently, various methods have been developed to estimate the sample mean and standard deviation when only the sample size, and other selected sample summaries are reported. In this paper, we provide a unified approach to optimal estimation that can be easily adopted when only some summary statistics are reported. We show that the proposed estimators have the lowest variance among linear unbiased estimators. We also show that in the most commonly reported cases, that is, when only a three-number or five-number summary is reported, the newly proposed estimators match the previously developed estimators. Finally, we demonstrate the performance of the estimators numerically.

Background: Risk stratification of individual patients who are prone to infection would allow surgeons to monitor high-risk patients more closely and intervene early when needed. This could reduce infection-related consequences such as increased health-care costs. The purpose of this study was to develop a machine learning (ML)-derived risk-stratification tool using the SPRINT (Study to Prospectively Evaluate Reamed Intramedullary Nails in Patients with Tibial Fractures) and FLOW (Fluid Lavage of Open Wounds) trial databases to estimate the probability of infection in patients with operatively treated tibial shaft fractures (TSFs). Methods: Patients with unilateral TSFs from the SPRINT and FLOW trials were randomly split into derivation (80%) and validation (20%) cohorts. Random forest algorithms were used to select features that are relevant to predicting infection. These features were included for algorithm training. Five ML algorithms were trained in recognizing patterns associated with infection. The performance of each ML algorithm was evaluated and compared based on (1) the area under the ROC (receiver operating characteristic) curve (AUC), (2) the calibration slope and the intercept, and (3) the Brier score. Results: There were 1,822 patients included in this study: 170 patients (9%) developed an infection that required treatment, 62 patients (3%) received nonoperative treatment with oral or intravenous antibiotics, and 108 patients (6%) underwent subsequent surgery in addition to antibiotic therapy. Random forest algorithms identified 7 variables that were relevant for predicting infection: (1) Gustilo-Anderson or Tscherne classification, (2) bone loss, (3) mechanism of injury, (4) multitrauma, (5) AO/OTA fracture classification, (6) age, and (7) fracture location. Training of the penalized logistic regression algorithm resulted in the best-performing prediction model, with AUC, calibration slope, calibration intercept, and Brier scores of 0.75, 0.94, 0.00, and 0.076, respectively, in the derivation cohort and 0.81, 1.07, 0.09, and 0.079, respectively, in the validation cohort. Conclusions: We developed an ML prediction model that can estimate the probability of infection for individual patients with TSFs based on patient and fracture characteristics that are readily available at hospital admission.

An estimated 33–37% of incident cancers in Canada are attributable to modifiable risk factors. Interventions targeting these risk factors would minimize the substantial health and economic burdens Canadians face due to cancer. We estimate the future health and economic burden of cancer in Canada by incorporating data from the Canadian Population Attributable Risk of Cancer (ComPARe) study into OncoSim, a web-based microsimulation tool. Using the integrated OncoSim population attributable risk and population impact measures, we evaluated risk factor-targeted intervention scenarios implemented in 2020, assuming the targeted risk factor prevalence reduction would be achieved by 2032 with a 12-year latency period. We estimate that smoking will be the largest contributor to cancer-related costs, with a cost of CAD $44.4 billion between 2032 and 2044. An estimated CAD $3.3 billion of the cost could be avoided with a 30% reduction in smoking prevalence by 2022. Following smoking, the next highest cancer management costs are associated with inadequate physical activity and excess body weight, accounting for CAD $10.7 billion ($2.7 billion avoidable) and CAD $9.8 billion ($3.2 billion avoidable), respectively. Avoidable costs for other risk factors range from CAD $90 million to CAD $2.5 billion. Interventions targeting modifiable cancer risk factors could prevent a substantial number of incident cancer cases and billions of dollars in cancer management costs. With limited budgets and rising costs in cancer care in Canada, these simulation models and results are valuable for researchers and policymakers to inform decisions and prioritize and evaluate intervention programs.

A variety of methods have been proposed to estimate a standard deviation, when only a sample range has been observed or reported. This problem occurs in the interpretation of individual clinical studies that are incompletely reported, and also in their incorporation into meta-analyses. The methods differ with respect to their focus being either on the standard deviation in the underlying population or on the particular sample in hand, a distinction that has not been widely recognized. In this article, we contrast and compare various estimators of these two quantities with respect to bias and mean squared error, for normally distributed data. We show that unbiased estimators are available for either quantity, and recommend our preferred methods. We also propose a Taylor series method to obtain inverse-variance weights, for samples where only the sample range is available; this method yields very little bias, even for quite small samples. In contrast, the naïve approach of simply taking the inverse of an estimated variance is shown to be substantially biased, and can place unduly large weight on small samples, such as small clinical trials in a meta-analysis. Accordingly, this naïve (but commonly used) method is not recommended.

Modifiable lifestyle, environmental, and infectious risk factors associated with cancer impact both cancer incidence and mortality at the population level. Most studies estimating this burden focus on cancer incidence. However, because these risk factors are associated with cancers of disparate mortality rates, the burden associated with cancer incidence could differ from cancer mortality. Therefore, estimating the cancer mortality attributable to these risk factors provides additional insight into cancer prevention. Here, we estimated future cancer deaths and the number of avoidable deaths in Canada due to modifiable risk factors. The projected cancer mortality data came from OncoSim, a web-based microsimulation tool. These data were applied to the methodological framework that we previously used to estimate the population attributable risks and the potential impact fractions of modifiable risk factors on Canadian cancer incidence. We estimated that most cancer deaths will be attributed to tobacco smoking with an average of 27,900 deaths annually from 2024 to 2047. If Canada’s current trends in excess body weight continue, cancer deaths attributable to excess body weight would double from 2786 deaths in 2024 to 5604 deaths in 2047, becoming the second leading modifiable cause of cancer death. Applying targets to reduce these risk factors, up to 34,600 cancer deaths could be prevented from 2024 to 2047. Our simulated results complement our previous findings on the cancer incidence burden since decreasing the overall burden of cancer will be accelerated through a combination of decreasing cancer incidence and improving survival outcomes through improved treatments.

This article considers how to estimate the accuracy of a diagnostic test when there are repeated observations, but without the availability of a gold standard or reference test. We identify conditions under which the structure of the observed data is rich enough to provide sufficient degrees of freedom, such that a suitable latent class model can be fitted with identifiable accuracy parameters. We show that a Rule of Three applies, specifying that accuracy can be evaluated as long as there are at least three observations per individual with the given test. This rule also applies if the three observations arise from combinations of different test methods, or from a sequential design in which individuals are tested for a maximum number of times with the same test but stopping if a positive (or negative) result occurs. The rule pertains to tests having an arbitrary number of response categories. Accuracy is evaluated by parameters reflecting rates of misclassification among the response categories, and the model also provides estimates of the underlying distribution of the true disease state. These ideas are illustrated by data from two medical studies. Issues discussed include the advantages and disadvantages of analyzing the response variable as binary or multinomial, as well as the feasibility of testing goodness of fit when the model incorporates a large number of parameters. Comparisons are possible between models that do or do not assume equal accuracy rates for the observations, and between models where certain misclassification parameters are or are not assumed to be zero.

There has been a long-standing controversy among scientists regarding the appropriate use of P-values and statistical significance in clinical research. This debate has resurfaced through recent calls to modify the threshold of P-value required to declare significance, or to retire statistical significance entirely. In this article, we revisit the issue by discussing: i) the connection between statistical thinking and evidence-based practice; ii) some history of statistical significance and P-values; iii) some practical challenges with statistical significance or P-value thresholds in clinical research; iv) the on-going debate on what to do with statistical significance; v) suggestions to shift the focus away from binary thinking of statistical significance and towards education for key stakeholders on research essentials including statistical thinking, critical thinking, good reporting, basic clinical research concepts and methods, and more. We then conclude with remarks and illustrations of the potential deleterious public health consequences of poor methods including selective choice of analysis approach and misguided reliance on binary use of P-values to report and interpret scientific findings.

Background:Tibial shaft fractures are the most common long-bone injury, with a reported annual incidence of more than 75 000 in the United States. This study aimed to determine whether patients with tibial fractures managed with intramedullary nails experience a lower rate of reoperation if treated at higher-volume hospitals, or by higher-volume or more experienced surgeons.Methods:The Study to Prospectively Evaluate Reamed Intramedullary Nails in Patients with Tibial Fractures (SPRINT) was a multicentre randomized clinical trial comparing reamed and nonreamed intramedullary nailing on rates of reoperation to promote fracture union, treat infection or preserve the limb in patients with open and closed fractures of the tibial shaft. Using data from SPRINT, we quantified centre and surgeon volumes into quintiles. We performed analyses adjusted for type of fracture (open v. closed), type of injury (isolated v. multitrauma), gender and age for the primary outcome of reoperation using multivariable logistic regression.Results:There were no significant differences in the odds of reoperation between high- and low-volume centres (p = 0.9). Overall, surgeon volume significantly affected the odds of reoperation (p = 0.03). The odds of reoperation among patients treated by moderate-volume surgeons were 50% less than those among patients treated by verylow-volume surgeons (odds ratio [OR] 0.50, 95% confidence interval [CI] 0.28–0.88), and the odds of reoperation among patients treated by high-volume surgeons were 47% less than those among patients treated by very-low-volume surgeons (OR 0.53, 95% CI 0.30–0.93).Conclusion:There appears to be no significant additional patient benefit in treatment by a higher-volume centre for intramedullary fixation of tibial shaft fractures. Additional research on the effects of surgical and clinical site volume in tibial shaft fracture management is needed to confirm this finding. The odds of reoperation were higher in patients treated by very-low-volume surgeons; this finding may be used to optimize the results of tibial shaft fracture management. Clinical trial registration: ClinicalTrials.gov, NCT00038129

Cost-effectiveness analysis is widely adopted as a means to inform policy and decision makers in setting priorities for healthcare resource allocation. In resource-constrained settings, decision makers are confronted with healthcare resource reallocation decisions, e.g., moving funds from one or more existing healthcare programs to fund new healthcare programs. The decision-making plane (DMP) has been developed as a means to graphically present the results of reallocating available healthcare resources when healthcare program costs and effects are uncertain. Mapping a value function over the DMP allows the analyst to value all possible combinations of net costs and net effects that may result from reallocating available healthcare resources under conditions of uncertainty. In this paper, we extend this approach to include a change in portfolio risk, stemming from a change in the portfolios of funded healthcare programs, as an additional source of uncertainty, and demonstrate how this can be incorporated into the value function over net costs and net effects for a risk-averse decision maker. The methodology presented in this paper is of particular interest to decision makers who are risk averse, as it will help to better incorporate their preferences in the process of deciding how to best allocate scarce healthcare resources.