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16.02.2015
The width of the confidence interval tells us more about how certain (or uncertain) we are about the true figure in the population. Population size: this does not usually affect the CI but can be a factor if you are working with small and known groups of people. Sample Size: the smaller your sample, the less likely it is you can be confident the results reflect the true population parameter. A 0% confidence level means you have no faith at all that if you repeated the survey that you would get the same results. The confidence coefficient is the confidence level stated as a proportion, rather than as a percentage. In general, the higher the coefficient, the more certain you are that your results are accurate.
In there are many key concepts and terms that are crucial for students to know and understand. Often it can be hard to determine what the most important concepts and terms are, and even once you’ve identified them you still need to understand what they mean. To help you learn and understand key terms and concepts, we’ve identified some of the most important ones and provided detailed definitions for them, written and compiled by Chegg experts.
A 100% confidence level means there is no doubt at all that if you repeated the survey you would get the same results. For example, if you had a confidence level of 99%, the confidence coefficient would be .99. Shouldn’t it be that if the survey were conducted over and over, that the results would fall between 38-3=35% and 38+3=41% in 95% of the survey instances? However, the practice of statistics in medicine is a burgeoning discipline (witness the growth of the respected journal Statistics in Medicine since it was introduced in the early 1980s) and difficult to keep abreast of. What a 95 percent confidence level is saying is that if the poll or survey were repeated over and over again, the results would match the results from the actual population 95 percent of the time.
In reality, you would never publish the results from a survey where you had no confidence at all that your statistics were accurate (you would probably repeat the survey with better techniques). It’s extremely rare to see a coefficient of 1 (meaning that you are positive without a doubt that your results are completely, 100% accurate). The aim of this article will be to summarize some key concepts and techniques in biostatistics with particular reference to clinical trials, not from first principles (this is an interval level variable; that is an ordinal variable), but rather as a guide to analyses and practices commonly employed in ophthalmology journals.
In this case, you would expect the results to be 35 (38-3) to 41 (35+3) percent, 95% of the time. The format of this article is to introduce a variety of these techniques and identify some of the salient features concerning their interpretation. Nevertheless, China’s dramatic gains in recent years do increase the pressure on Asian economies, particularly in ASEAN and South Asia, to seek areas of comparative advantage. This summary is particularly relevant to surgical trials where treatments are compared with respect to incidence rates of treatment failure, rather than, say, medical trials that may compare average differences in intraocular pressure (IOP) lowering.
It makes clear that in the trabeculectomy group the percentage of failures increased steadily from about 1% at four months after surgery to nearly 15% at nine months.
The Baerveldt group failure rate rose to just less than 4%, between about four and six months before leveling off. In a surgical trial this may include re-operation and incidence of postoperative intraocular pressures considered unsafe.The simplest way to compare two treatments is to follow patient groups randomized to those treatments for a fixed period of time, say five years, and then test if proportions of patients failing are different in the two groups. The Kaplan-Meier analysis improves on this by examining whether the time to failure is different between treatment groups. In the latter two situations, when a patient was successful at their last follow-up, but their subsequent state is unknown, we label them censored as of the time of their last visit.As patients fail or become censored they are removed from the calculation.

Because these proportions, calculated at different times from randomization, do not have the same denominator they should be accompanied by their standard errors when included in the article's text.Kaplan-Meier analysis is a method of summarizing time to failure data (in the same sense that an average summarizes a set of measurements), and does not itself generate a p-value.
For example, one concern in the TVT study was whether investigators would be more likely to reoperate on trabeculectomy patients than Baerveldt patients with similar postoperative pressures. In fact examination of pressures prior to reoperation in both groups did not find this to be the case. Kaplan-Meier analysis allows stratification for prognostic factors, but is a univariate technique and is poorly suited to answering these questions.
Cox proportional hazards regression is a flexible and popular statistical method for just this purpose.11 The Cox model is a type of multiple regression analysis appropriate for survival data. This method allows the calculation of the relative risk of failure in a treatment group compared to a control, a group with a given risk (or prognostic) factor compared to one without, or the increase in risk of failure associated with a higher level of a continuous variable, such as an additional decade of age.Rather than explicitly estimating failure risks of different patient groups over time, as in Kaplan-Meier analysis, Cox analysis assumes that even if the risk of failure for two individuals receiving different treatments increases or decreases irregularly with time, their relative risk remains constant. In other words, their hazard rates are proportional.Specifically, the analysis gives the investigator coefficients, standard errors, and p-values assessing the importance of each variable included in the Cox model. Of course the evaluation of the treatment effect was also the reason for this prospective study, while the heart disease effect was only one of many risk factors evaluated after the fact and became non-significant in multivariate analysis. When estimating risks with Cox (and logistic) regression risk ratios for continuous variables, such as IOP, it becomes important to understand that the risk ratio is expressed for a particular increment of that variable.
It is a misconception to think that if a person has an IOP 2 or 3 mm Hg higher than another, their risk has doubled or tripled.
Because Cox regression is an exponential model, the change in risk ratio is calculated by use of exponents.
In fact, the second ratio is close to the actual five year OHTS incidence rates.(2)The Cox proportional hazards assumption may not fit a particular set of data.
Problems of this sort can be addressed with a stratified model.(3)With data sets having small sample sizes, especially when including few failures, a Cox model may not converge-that is, the computer program may be unable to correctly calculate model parameters. The choice of beta, together with an estimate of likely treatment efficacy, allows calculation of the necessary sample size, which increases as beta decreases. In any case, sample size calculations are almost always approximate because details of treatment efficacy are necessarily estimates (or there would be no reason to do the study) in a study's planning stages.Once a study has been completed, however, the power with which it was designed is immaterial to the analysis.
Conversely a study conducted with lower power may be "lucky" and uncover an actual clinically meaningful treatment effect with a small sample size.
The statement in the methods section of a clinical trial report specifying a high power is not a guarantee to the reader that the study's conclusions are correct, but rather an affirmation that the study was well designed. Second, negative studies (those with a nonsignificant result) designed with low power are unlikely to be published. In other words, to be considered statistically significant, a p-value must be less than 0.05. The p-value quantifies the probability that a treatment effect of the size observed could be due to chance. Similarly, a significant p-value could mean that there is a clinically important treatment effect or that the study had a large enough sample size to make significant a small or modest treatment effect.
Table 1 displays the results of analyses comparing failure rates of three imaginary treatments to an imaginary standard treatment as well as the OHTS comparison of medication to observation groups. The comparison of experimental treatment 1 to the standard treatment provides little useful information. The ability to generalize the results of a clinical trial rests on the inclusion of all eligible patients; that is, selection bias in who enters the trial must be minimized. An investigator, recognizing that a patient's two eyes are likely to respond similarly to treatment, may well be reluctant to randomize the second eye if the first eye has already failed a study surgery.
Follow-up; Honest Accounting of Missing Data in Research Reports One analytical method known to be invalid is comparison of proportions at "last follow-up".

This method is prone to important selection bias related errors.19 Last observation carried forward analyses can, in some settings, provide insight when participants are withdrawing from a study for systematic reasons.
For example, a one-year follow-up visit might in practice include follow-up times ranging from 9 to 15 months postsurgery.
The reason is that all participants are likely to contribute preoperative measurements but, almost certainly, not all of them will be measured at each follow-up visit. Those patients contributing follow-up data may well have different initial measurements from those missing follow-up. Therefore, the reader of a report will be misled by themselves subtracting preoperative and postoperative means. Authors have to balance the desirability of full disclosure within the constraints of clarity and available journal space. Bonferroni and the Multiple Comparison Problem: Reasons not to Adjust There are two data analysis situations referred to as "multiple comparison" problems. In the first, a test such as an analysis of variance (ANOVA) reveals a difference with respect to some measurement (e.g. In this situation, a multiple comparison method, such as the least significant difference test or multiple pairwise Bonferroni adjusted tests must be employed to determine which groups are different from each other.20 Approaches to dealing with this problem are not controversial. Similarly, when many statistical significance tests are made within a single study it may be feared that 5% of them will be statistically significant by chance. A common prescription for this problem is to "adjust" the p-value required for significance to less than 0.05 to an extent determined by the number of significance tests performed. Two popular methods are the Bonferroni and the slightly less conservative Sidak procedures. For example, a number of GDX parameters may all be sensitive to the same underlying glaucomatous structural defects and would be incorrectly characterized as independent.To what family of statistical tests should the adjustment be applied? Probably some true differences are being ignored (beta error).Science does not proceed as a string of unconfirmed answers to questions. Results are either explicitly replicated by other researchers or tested by inference to other related studies.
A better strategy is for researchers to indicate clearly thoseprospective hypotheses a study was designed to evaluate as opposed to ancillary ones considered after the data were collected, and that readers (and reviewers) become "informed consumers" of p-values. A reader should place more weight on the results of the main hypotheses the study was designed to evaluate, and informally take into account the number of tests conducted when evaluating discussions and conclusions. They should view with suspicion a single significant counter-intuitive result among many tested. Still, unplanned ancillary tests - sometimes called "hypothesis generating" - are an important mechanism for identifying future research directions and should be encouraged as long as they are presented with suitable caveats. Comparison of glaucomatous progression between untreated patients with normal-tension glaucoma and patients with therapeutically reduced intraocular pressures.
Reduction of intraocular pressure and glaucoma progression: results from the Early Manifest Glaucoma Trial.
Cataract extraction in the collaborative initial glaucoma treatment study: incidence, risk factors, and the effect of cataract progression and extraction on clinical and qualityof-life outcomes.
The Ocular Hypertension Treatment Study: A randomized trial determines that topical ocular hypotensive medication delays or prevents the onset of primary open-angle glaucoma.
Design and analysis of randomized trials requiring prolonged observation of each patient: II.

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