Selection bias is known to affect health surveys and epidemiological studies [1] and can cause results from different studies on the same area of research to disagree or conclude contradictory findings [2] . However even in recent studies, selection bias is still sometimes ignored or dismissed [3] . If selection bias can be reduced across studies and lead to more consistent findings, time and resources could be saved since fewer repeated studies would be required. These savings could be used to develop more focused areas of research, contributing to increased knowledge.

With many selection bias reducing methods to choose from, researchers may find the process daunting and possibly be deterred from implementing a method, for fear of choosing an unsuitable approach. The implementation of a method to reduce selection bias may also be viewed by researchers as an undesirable feature of their study, which could lead to criticisms of their study design and data collection, or potentially reduced chances of publication. There may also be time constraints, whereby study results need to be presented or published within a specific time frame, or a funded piece of research completed. In these instances, research into selection bias and methods to reduce it may not be prioritized. This work aims to provide reassurance to researchers that applying a method to reduce selection bias is a positive aspect of their study which should be encouraged whenever selection bias is suspected. Consideration of selection bias as a possibility should be routine. An appropriate method should be applied and used as either a sensitivity analysis to reassure readers of the study results, or to produce findings with reduced bias. We aim to draw attention to the available methods to reduce selection bias and provide sources for further reading. We intend to give guidance for selecting a method, structured in such a way that it is applicable for any study or survey potentially affected by selection bias.

Various methods, which will be discussed here, have been suggested to reduce selection bias, each with their own requirements and assumptions. Some methods require there to be additional data available external to the study [4] - [7] , some require data regarding the non-participants [8] , and some assume that the variable associated with selection is known and measured [9] - [11] . Each method will be briefly introduced and sources given for further reading. A tool in the form of a straightforward flowchart is also provided to aid the selection of an appropriate method, depending upon the details of a study and any additional information available. Three examples are presented which demonstrate the flowchart. Exploration into the suggested methods can then be conducted, allowing the researcher to select a method to reduce selection bias more easily. We hope this tool encourages the use of such methods and consequently leads to results less affected by selection bias.

Table 1 summarizes the main methods used in the literature to reduce selection bias [3] which will be included in this guidance, and gives suggestions for further reading through original articles, examples or comprehensive summaries. These methods have similar themes, such as using the variable associated with selection in the analysis, weighting responses or predicting the effects of the bias. Additional, less frequently used methods are of course applicable, as are any new methods which are not yet widely used, but this tool is designed to be a starting point which can be developed through time and which should be useful for most types of research affected

by selection bias.

Table 2 includes the data requirements of each method; including whether it requires the variable associated with selection to be known and recorded, whether population data external to the study are required or whether data regarding the non-participants who declined the study are needed. Where more than one category has been ticked, this indicates the method can be adapted for use when an alternative source for the required data is available. For the variable associated with selection to be collected, it is assumed the variable is known and can be recorded during the study. There may be instances where this variable is unknown, cannot be collected, or is impractical to record. This includes data which are expensive to collect, sensitive, or due to an unidentified variable. However there may be instances where a proxy may be used instead. The population data indicates information external to the study, for example from a database or alternative records. Sources may include census data or hospital registries. These data are assumed to be unbiased and represent the entire population of interest. Non-participant data are basic characteristics recorded from those who were unwilling to participate. These are usually data from the subject themselves, but may also be from external sources similar to those used to collect the population data.

Although the three data categories used in Table 2 are sourced from different places (the participants, the population and non-participants respectively), there are relationships between them. For example, if the original potential participants are representative of the population of interest, and relevant information is known for all non-participants, then the non-participant data in conjunction with the participant data could be used to approximate the population data. Therefore under certain circumstances it may be possible to use a different column from Table 2 for the data source, other than the one(s) ticked. Table 2 and the consequent tool can be interpreted as a generalization or guide, which can be adapted by the researcher if these conditions are met.

Although each of the methods in Table 1 is designed to reduce selection bias, they do so using different techniques and assumptions. Therefore, a method which may be optimal for one study may not be suitable for another. Some are also aimed at particular study designs, for example two were developed specifically for case control studies [5] [7] .

Several of the methods in Table 1 have been developed or derived from one another. For example, the bias-breaking method [5] is a form of post-stratification, which is a type of stratification, and the propensity score is derived from stratification. However, their suitability as a method to reduce selection bias differs between studies. There are also similarities amongst some of the methods. For example, predicting the amount of bias present is similar to a sensitivity analysis, and several of the methods also began in survey literature [4] . Figure 1 gives an example of a flowchart based on Table 2 which could be used by researchers to shortlist potential selection bias reducing methods for further investigation. Researchers could extend this flowchart to meet their specific needs for the variables or datasets they encounter, or alternatively disciplines could form a subject-specific chart to which new methods could be added over time.

Three examples of hypothetical studies follow which utilize the flowchart (Figure 1) to determine a suitable method to apply. The flowchart begins in the top-left corner, shown using a bold outline. To answer the first question in the flowchart, the requirements for selection bias to occur must be known. For selection bias to be present, there must be the exposure and outcome of interest, and these must both affect whether or not an individual is selected to participate or self-selects (participates) in the study. This selection variable must then be conditioned on, which it often will be since only those who have participated can be studied [1] .

Once the flowchart has provided a list of possible methods to explore further, it is the responsibility of the researcher to consider each in turn to see which method is most suitable for their particular study. All method assumptions must be considered and the details of the specific study incorporated.

Selection bias can be problematic for surveys and a range of study designs [26] , but particularly those which are retrospective such as case control studies [2] , as seen in Example 3. Biased results can lead to incorrect findings and the unnecessary repetition of studies, wasting valuable time and resources which could instead be used to fund additional research into diseases or their cure.

Any form of bias can be viewed as a negative aspect of a study, but action should be taken to reduce as much bias as possible within the results of a study. This work aims to highlight the importance of bias reduction, specifically selection bias, and provide researchers with a summary of methods currently available to reduce selection bias, along with references for further reading.

A user-friendly flowchart tool has been provided, which can be adapted for particular research areas or depending upon the data resources available, to aid the selection of an appropriate method. The tool is not designed to identify one method to use, but instead guide the researcher to a subset of methods for further consideration. This could be viewed as a limitation, but contemplation of the requirements for each method is necessary. The optimal method depends upon specific details relating to an individual study and would require a complicated flowchart which would be more difficult to use. However, subject-specific flowcharts could be created. This tool is therefore a straightforward flowchart, applicable to a range of study designs, provoking consideration of selection bias while providing references for further reading. We hope demonstration of this versatile tool through examples and raised awareness results in more consideration of selection bias and consequently the implementation of appropriate methods.

Bias reduction is an important part of any study and this work raises awareness of selection bias in particular. A straightforward flowchart, with summaries of the current methods to reduce selection bias, has been provided to guide researchers towards a suitable method, in the hope that more accurate results are generated from studies.

Claire Keeble is funded by an MRC Capacity Building Studentship. Paul D Baxter, Stuart Barber and Graham Richard Law are funded by HEFCE. The funding sources had no involvement in the study design, in the collection, analysis and interpretation of data, in the writing of the report or the decision to submit the article for publication.