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Statistical analysis

statistical analysis

Statistics is a science derived from mathematics which can be stratified into two different branches: descriptive and inferential. Descriptive statistics are commonly used as the first step in data analysis. It refers to measures that summarize and characterize a set of data allowing inferences regarding to its distribution – it answers questions like: How many people have the disease? How often did the event occur? Descriptive statistics can identify similarities and differences between groups, but on their own are rarely enough to confirm or refute a hypothesis. Inferential statistics allows hypothesis testing based on the probability theory. It answers the key question: How likely is it that this difference (that we observed between two groups) is due to chance alone?

An important step before applying any statistical test is to identify the dependent and independent variables. In clinical trials, the dependent variable is the outcome(s) of the study (e.g. mortality rate; decrease in renal function) and the independent variables are the factors under investigation that could possibly be modifying the outcome, the most important of which is the randomized treatment allocation (i.e. intervention vs. control). Other independent variables (e.g. proteinuria, blood pressure) may be used in multivariable analysis, however this is almost always a secondary analysis in a clinical trial because randomization has been used to balance all other factors between groups.

Statistical analysis plan

Before analyzing you data you should have a Statistical Analysis Plan (see below for links to templates, guidelines and examples). This document describes what statistical tests you will perform and assigns them to a hierarchy of primary, secondary and, sometimes, exploratory. Many researchers will publish the statistical analysis plan, either summarized as part of a design paper or study protocol, or by making it available online. This ensures transparency and encourages rigorous scientific method.

Primary, secondary and exploratory analyses

Your primary analysis relates to your primary study outcome. It is essential to spell this out from the start. Remember that a P-value of 0.05 just means a likelihood of one in twenty, meaning that if you do twenty statistical tests, the chances are that one of them will be ‘positive’ with a P-value < 0.05. So it is important to specify your primary outcome before doing the analysis so that readers know that you have not simply performed many statistical tests and chosen the one with the significant P-value. Analyses that you plan to do in advance, alongside the primary analysis are called secondary analyses. Any analysis that you decide to do only after looking at the data is always considered exploratory meaning that it can only ever provide a suggestion for further research and should never be used as proof.

Types of data

Even before planning data analysis researchers should have in mind that the type of data to be analyzed will result in strengths and limitations in terms of the possible mathematical tests and the interpretation of the obtained results. For instance, different statistical tests will apply whether the variables under study are continuous or categorical. Similarly, the calculation of some important study parameters as sample size, power and statistical significance will be directly impacted by the type of the sample distribution (e.g normal versus skewed data). Researchers must consider this when designing their study. For example, if CKD stage is collected then one must use a categorical data analysis, however if eGFR is collected then one can use a continuous data analysis or convert them to CKD categories to use a categorical analysis. Therefore, a careful plan to adjust the study design according to the research question and the characteristics of the study variables is always desirable. Finally, it is important to note if your data (if continuous) is normal or non-normal in distribution, as this dramatically affects the way it can be analysed.

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Funding

funding

In order to be successful in obtaining funding for your clinical research, you need to be creative, establish what are your goals, and look for different sources of funding.

Writing a detailed written plan of the study (a study protocol) is essential for funding since the protocol is the scientific component of any proposal, this proposal also contains administrative and supporting information required by any funding agency.


Obtain funding

Any investigator who is working on a research protocol for a trial should begging by getting advice from senior colleagues about the choice of a funding agency. Then the investigator should carefully review agency’s written guidelines. Be aware that the process of writing a proposal usually takes much longer than expected, and this process should include the following aspects:  organizing a team with the necessary expertise, finding a model proposal, outlining the proposal along the agency guidelines, and having regular meetings with the whole team for reviewing the progress.  Senior colleagues should review the proposal; this will give the investigator the opportunity to polish his/her proposal with especial attention on details.

For being successful on getting your trial funded; your proposal not only requires a good research question, study plan, and research team, but also a good presentation. Bellow is a check list to achieved a good proposal presentation:

    The proposal must communicate clearly and concisely
    The proposal must follow a logical outline
    The proposal should indicate the advantages and disadvantages of trade-offs in the study plan.
    The merits of the proposal should stand out so that a busy reviewer will not miss them.

As an investigator you could find four main sources for supporting your trial:

    Government sources (e.g. NIH) that usually the largest providers of support, but for example in the case of the NIH government sources use a complex system of peer and administrative review process that moves slowly but encourages good science.
    Foundations and societies like the ISN Clinical Research Program who are often interested in promising research questions, and have review procedures that are quicker but also encouraging good science.
    Manufactures of drugs and devices are a very large source of support that is usually channeled to company-run studies of new drugs or medical devices, however corporations value partnerships with leading scientists and support some investigator initiated research.
    Intramural funds tend to have more favorable funding rates for getting small amounts of money quickly, and are suitable for pilot studies and beginning investigators.

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Randomization

randomization

Randomization aims to avoid systematic error (bias) due to the imbalance in confounding factors between intervention and comparator groups in a clinical trial. While it would be possible to record multiple patient characteristics (such as age, sex, diabetes status, etc) and then divide patients into approximately equal groups, this method could only be applied once all participants have been recruited and, more importantly, it does not take into account unmeasured or unknown factors which might still affect the outcome of the trial. Moreover, if the treating physician or researcher is able to decide allocation, selection bias might compromise the results of a study. Randomization solves these problems and has become the cornerstone of modern clinical research.

Proper randomization relies on computer-generated random numbers. The use of naturally occurring patterns – such as allocating patients dialyzing on the morning shift to intervention and those dialyzing on the afternoon shift to comparator – is not randomization. Although it may appear that patients fall into these natural groups ‘at random’, it cannot be guaranteed that confounding factors will be evenly spread between such groups.

Randomization methods can be divided into two categories: fixed allocation randomization and adaptive randomization. Most trials use fixed randomization, in which participants are allocated to intervention or comparator with a ‘fixed’ probability that does not change through the study. Fixed randomization can be further divided into simple, blocked and stratified randomization. Adaptive randomization is more complex and permits the allocation probability to change as the study progresses. Below you will find a brief description of these methods.


Fixed allocation randomization

A) Simple Randomization

Simple randomization uses a random digit table (generated by a computer) or can even be done by flipping a coin. Because the allocation of each participant is completely independent, it is impossible to guess which group a participant will be allocated to before performing the randomization – the essential feature of allocation concealment. However, for trials with a small sample size this method can often result in imbalanced groups – simply by chance.
B) Blocked Randomization

In this method, the principal investigator defines block sizes so that randomization will occur in blocks of a fixed number. This method has the potential advantage of decreasing the likelihood that at the end of the study there will be differences in the number of subjects across groups of treatment (imbalances). However, a potential disadvantage to this method is that investigators might guess the treatment allocation at the end of the block. This could result in selection bias since a researcher might consider not randomizing the next patient if certain the next patient will be allocated to a specific arm of the study.
C) Stratified Randomization

In this method, patients are randomized in strata of covariates considered to play a role in the outcome of study (e.g age, CKD stage). This method provides more control to the possibility of imbalances for important covariates since only after a given patient is assigned to each stratum, they will be randomized into the active or the placebo groups. This is a more complex method which can lead to bias if associated with the simple randomization technique. Since patients will be further divided into strata, the issue of imbalances for small sample sizes can be hard to overcome. On the other hand, if block randomization is used, the potential problem of unblinding subjects at the end of blocks should be considered.

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Implementation research

Implementation research

Implementation research is the study of the impact of new programs in health. This may be changes in a referral process, the provision of routine patient education, a new community health service or an entire vaccination program. It is important that such projects are evaluated to ensure that they meet their stated goals, fix weaknesses in their initial design and to learn lessons to inform future projects.

A detailed overview of implementation research is provided by the WHO Special Programme for Research and Training in Tropical Diseases. Although the subject matter is not nephrology, the information is appropriate to medical services in general.

TDR Implementation Research Toolkit

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



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Sample size calculation

sample size calculation

One of the pivotal aspects of planning a clinical trial is the calculation of the sample size. It is logically that would be not feasible or practical to study the whole population in any trial. Therefore, a set of participants/subjects is selected from the entire population, which is less in number (size) but adequately represents the population (sample) from which it is drawn so that true inferences about the population can be made from the results obtained. This set of individuals is known as the sample.

The population in a trial is defined as the complete set of people; for example in the ISN 0by25 pilot study that aimed to achieved 0 preventable deaths due to community acquired AKI by 2025 the population will be the entire population of the participating centers in Malawi, Nepal and Bolivia, the “target population” is a subset of individuals with specific clinical and demographic characteristics in whom you want to study your intervention (e.g., patients with risk factors for community acquired AKI like CKD, HIV infection, cardiac failure, diarrhea, hypotension, etc.), and “sample” is a further subset of the target population which we would like to include in the study. Thus a “sample” is a portion, piece, or segment that is representative of a whole.

The calculation of an adequate sample size thus becomes crucial in any clinical study and is the process by which we calculate the optimum number of participants required to be able to arrive at ethically and scientifically valid results.

When estimating sample size for your trial, the following steps need to be taken:

First state the null and alternative hypotheses and specified the number of sides.
Second select a statistical test that could be used to analyze the data, based on the types of predictor and outcome variables (table 1).
Third estimate the effect size.
Fourth specify appropriate values for alpha (a) and beta (b) based on the importance of avoiding Type I and Type II errors.

Even if the exact value for one or more of the components is uncertain, it is important to estimate the sample size early in the design phase.

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