Iztok Hozo

Estimating the mean and variance from the median, range, and the size of a sample

BackgroundUsually the researchers performing meta-analysis of continuous outcomes from clinical trials need their mean value and the variance (or standard deviation) in order to pool data. However, sometimes the published reports of clinical trials only report the median, range and the size of the trial.MethodsIn this article we use simple and elementary inequalities and approximations in order to estimate the mean and the variance for such trials. Our estimation is distribution-free, i.e., it makes no assumption on the distribution of the underlying data.ResultsWe found two simple formulas that estimate the mean using the values of the median (m), low and high end of the range (a and b, respectively), and n (the sample size). Using simulations, we show that median can be used to estimate mean when the sample size is larger than 25. For smaller samples our new formula, devised in this paper, should be used. We also estimated the variance of an unknown sample using the median, low and high end of the range, and the sample size. Our estimate is performing as the best estimate in our simulations for very small samples (n ≤ 15). For moderately sized samples (15 70), the formula range/6 gives the best estimator for the standard deviation (variance).We also include an illustrative example of the potential value of our method using reports from the Cochrane review on the role of erythropoietin in anemia due to malignancy.ConclusionUsing these formulas, we hope to help meta-analysts use clinical trials in their analysis even when not all of the information is available and/or reported.

When Should Potentially False Research Findings Be Considered Acceptable

Summary Ioannidis estimated that most published research findings are false [1], but he did not indicate when, if at all, potentially false research results may be considered as acceptable to society. We combined our two previously published models [2,3] to calculate the probability above which research findings may become acceptable. A new model indicates that the probability above which research results should be accepted depends on the expected payback from the research (the benefits) and the inadvertent consequences (the harms). This probability may dramatically change depending on our willingness to tolerate error in accepting false research findings. Our acceptance of research findings changes as a function of what we call “acceptable regret,” i.e., our tolerance of making a wrong decision in accepting the research hypothesis. We illustrate our findings by providing a new framework for early stopping rules in clinical research (i.e., when should we accept early findings from a clinical trial indicating the benefits as true?). Obtaining absolute “truth” in research is impossible, and so society has to decide when less-than-perfect results may become acceptable.

Dual processing model of medical decision-making.

BackgroundDual processing theory of human cognition postulates that reasoning and decision-making can be described as a function of both an intuitive, experiential, affective system (system I) and/or an analytical, deliberative (system II) processing system. To date no formal descriptive model of medical decision-making based on dual processing theory has been developed. Here we postulate such a model and apply it to a common clinical situation: whether treatment should be administered to the patient who may or may not have a disease.MethodsWe developed a mathematical model in which we linked a recently proposed descriptive psychological model of cognition with the threshold model of medical decision-making and show how this approach can be used to better understand decision-making at the bedside and explain the widespread variation in treatments observed in clinical practice.ResultsWe show that physician’s beliefs about whether to treat at higher (lower) probability levels compared to the prescriptive therapeutic thresholds obtained via system II processing is moderated by system I and the ratio of benefit and harms as evaluated by both system I and II. Under some conditions, the system I decision maker’s threshold may dramatically drop below the expected utility threshold derived by system II. This can explain the overtreatment often seen in the contemporary practice. The opposite can also occur as in the situations where empirical evidence is considered unreliable, or when cognitive processes of decision-makers are biased through recent experience: the threshold will increase relative to the normative threshold value derived via system II using expected utility threshold. This inclination for the higher diagnostic certainty may, in turn, explain undertreatment that is also documented in the current medical practice.ConclusionsWe have developed the first dual processing model of medical decision-making that has potential to enrich the current medical decision-making field, which is still to the large extent dominated by expected utility theory. The model also provides a platform for reconciling two groups of competing dual processing theories (parallel competitive with default-interventionalist theories).

Peptidoglycan Recognition Proteins Kill Bacteria by Inducing Oxidative, Thiol, and Metal Stress

Mammalian Peptidoglycan Recognition Proteins (PGRPs) are a family of evolutionary conserved bactericidal innate immunity proteins, but the mechanism through which they kill bacteria is unclear. We previously proposed that PGRPs are bactericidal due to induction of reactive oxygen species (ROS), a mechanism of killing that was also postulated, and later refuted, for several bactericidal antibiotics. Here, using whole genome expression arrays, qRT-PCR, and biochemical tests we show that in both Escherichia coli and Bacillus subtilis PGRPs induce a transcriptomic signature characteristic of oxidative stress, as well as correlated biochemical changes. However, induction of ROS was required, but not sufficient for PGRP killing. PGRPs also induced depletion of intracellular thiols and increased cytosolic concentrations of zinc and copper, as evidenced by transcriptome changes and supported by direct measurements. Depletion of thiols and elevated concentrations of metals were also required, but by themselves not sufficient, for bacterial killing. Chemical treatment studies demonstrated that efficient bacterial killing can be recapitulated only by the simultaneous addition of agents leading to production of ROS, depletion of thiols, and elevation of intracellular metal concentrations. These results identify a novel mechanism of bacterial killing by innate immunity proteins, which depends on synergistic effect of oxidative, thiol, and metal stress and differs from bacterial killing by antibiotics. These results offer potential targets for developing new antibacterial agents that would kill antibiotic-resistant bacteria.

Thalidomide versus bortezomib based regimens as first-line therapy for patients with multiple myeloma: a systematic review

Thalidomide (T) or bortezomib (B) in combination with melphalan plus prednisone (MP) is superior to MP as first line therapy for previously untreated myeloma. However, direct head‐to‐head comparison of Melphalan, Prednisone plus Bortezomib (MPB) versus Melphalan, Prednisone plus Thalidomide (MPT) is lacking. We performed an indirect meta‐analysis to assess the treatment effects of MPB versus MPT via common comparator MP using the systematic review and meta‐analytical techniques. A comprehensive literature search (MEDLINE and gray literature) was undertaken. Systematic review was performed as per the Cochrane Collaboration recommendations. Initial search yielded 1,013 citations, of which six randomized controlled trials (RCTs) enrolling 2,798 patients met the inclusion criteria. Comparison of MPT versus MP (five RCTs) showed no survival difference [hazard ratio (HR) 0.82, 95% confidence interval (CI) 0.64–1.05] but a statistically significant difference in event‐free survival favoring MPT (HR 0.66, 95% CI 0.56–0.77) without excessive treatment‐related mortality [risk ratio (RR) 1.11, 95% CI 0.64–1.92]. Comparison of MPB vs. MP (one RCT) showed a statistically significant benefit for survival (HR 0.65, 95% CI 0.51–0.84) and event‐free survival (HR 0.48, 95% CI 0.37–0.63) without difference in treatment‐related mortality (RR 0.42, 95% CI 0.11–1.63) with MPB. The indirect comparison of MPB versus MPT showed no difference between MPB versus MPT for all outcomes but a significant benefit for complete response (RR 2.34, 95% CI 1.12–4.90), and grade III/IV adverse events (RR 0.53, 95% CI 0.38–0.73) favoring MPB. There is an uncertainty about definitive superiority of one type of regimen over the other. Therefore, direct head‐to‐head comparison between these competing regimens is warranted. Am. J. Hematol., 2011.

Treatment Success in Cancer: Industry Compared to Publicly Sponsored Randomized Controlled Trials

Objective To assess if commercially sponsored trials are associated with higher success rates than publicly-sponsored trials. Study Design and Settings We undertook a systematic review of all consecutive, published and unpublished phase III cancer randomized controlled trials (RCTs) conducted by GlaxoSmithKline (GSK) and the NCIC Clinical Trials Group (CTG). We included all phase III cancer RCTs assessing treatment superiority from 1980 to 2010. Three metrics were assessed to determine treatment successes: (1) the proportion of statistically significant trials favouring the experimental treatment, (2) the proportion of the trials in which new treatments were considered superior according to the investigators, and (3) quantitative synthesis of data for primary outcomes as defined in each trial. Results GSK conducted 40 cancer RCTs accruing 19,889 patients and CTG conducted 77 trials enrolling 33,260 patients. 42% (99%CI 24 to 60) of the results were statistically significant favouring experimental treatments in GSK compared to 25% (99%CI 13 to 37) in the CTG cohort (RR = 1.68; p = 0.04). Investigators concluded that new treatments were superior to standard treatments in 80% of GSK compared to 44% of CTG trials (RR = 1.81; p<0.001). Meta-analysis of the primary outcome indicated larger effects in GSK trials (odds ratio = 0.61 [99%CI 0.47–0.78] compared to 0.86 [0.74–1.00]; p = 0.003). However, testing for the effect of treatment over time indicated that treatment success has become comparable in the last decade. Conclusions While overall industry sponsorship is associated with higher success rates than publicly-sponsored trials, the difference seems to have disappeared over time.

Improving the Drug Development Process: More Not Less Randomized Trials

Drug development is often a lengthy and expensive process. Extensive preclinical testing via in vitro and animal experimentation aims to select drugs most likely to work in humans. Under the current system, only about half of the drugs succeed in moving from phase 1 (dose-finding) to phase 2 (safety and efficacy).1 For drugs that enter phase 2, less than 1 in 3 succeed; for those entering phase 3 (pivotal efficacy), that number decreases to less than 1 in 2.1,2 Less than 20% of drugs entering phase 1 testing successfully reach the end of the 3-phase evaluation. The percentage can vary from one specialty area to another, and it can be less than 5% to 10% for oncologic and neurologic diseases.3

Decitabine versus 5-azacitidine for the treatment of myelodysplastic syndrome: adjusted indirect meta-analysis

We read with great interest the systematic review and meta-analysis by Gurion et al . assessing the efficacy of hypomethylating agents (HMA) versus supportive care for the treatment of patients with myelodysplastic syndromes (MDS).[1][1] The meta-analysis included 4 randomized controlled trials (RCT

Uncertainty in Clinical Medicine

Publisher Summary This chapter review and classify uncertainties in clinical medicine. Epistemic uncertainty is intimately linked to the relationship between theory, evidence, and knowledge. The relationships among observed, observable, and unobservable realities express uncertainties that can be characterized as a lack of knowledge about what is known (unknown knowns), what is known to be unknown (known unknowns), and not knowing what is unknown (unknown unknowns). Intimately linked with this classification of uncertainty is the psychological taxonomy that categorizes uncertainty based on knowledge of the external world and on our own state of knowledge. It is suggested that any attempt to develop a comprehensive treatise of uncertainty in clinical medicine must take into account the insights obtained from psychological research on uncertainty. Uncertainty can be effectively managed by explicitly recognizing its many sources, improving the quality of medical evidence, using better information technology tools, searching for sources of bias, and applying probability and decision theory to decisions under uncertainty.

Extensions to Regret-based Decision Curve Analysis: An application to hospice referral for terminal patients

BackgroundDespite the well documented advantages of hospice care, most terminally ill patients do not reap the maximum benefit from hospice services, with the majority of them receiving hospice care either prematurely or delayed. Decision systems to improve the hospice referral process are sorely needed.MethodsWe present a novel theoretical framework that is based on well-established methodologies of prognostication and decision analysis to assist with the hospice referral process for terminally ill patients. We linked the SUPPORT statistical model, widely regarded as one of the most accurate models for prognostication of terminally ill patients, with the recently developed regret based decision curve analysis (regret DCA). We extend the regret DCA methodology to consider harms associated with the prognostication test as well as harms and effects of the management strategies. In order to enable patients and physicians in making these complex decisions in real-time, we developed an easily accessible web-based decision support system available at the point of care.ResultsThe web-based decision support system facilitates the hospice referral process in three steps. First, the patient or surrogate is interviewed to elicit his/her personal preferences regarding the continuation of life-sustaining treatment vs. palliative care. Then, regretDCA is employed to identify the best strategy for the particular patient in terms of threshold probability at which he/she is indifferent between continuation of treatment and of hospice referral. Finally, if necessary, the probabilities of survival and death for the particular patient are computed based on the SUPPORT prognostication model and contrasted with the patients threshold probability. The web-based design of the CDSS enables patients, physicians, and family members to participate in the decision process from anywhere internet access is available.ConclusionsWe present a theoretical framework to facilitate the hospice referral process. Further rigorous clinical evaluation including testing in a prospective randomized controlled trial is required and planned.