Applying statistical disclosure control

The assessment of the risk of re-identification attached to a data item or statistical outputs, and the use of appropriate methods to reduce the disclosure risk, is known as statistical disclosure control (SDC). In OpenSAFELY, researchers must apply SDC at the stage where their aggregated results are ready to be released from the results server (the Level 4 environment) for sharing with collaborators for feedback, or for publication as papers, reports, blogs, etc. Examples of SDC techniques to manage the disclosure risk include redacting (suppressing) low values, rounding values, or redesigning outputs so that sparse table cells, for example, are combined. In general, good SDC is consistent with good statistics: many observations, no influential outliers, well-behaved distributions etc both prevent disclosure and increase confidence in the statistics. The one area to be wary of is where you can say something for certain about entire groups (‘all patients presenting with X also needed treatment for Y’). Be cautious about statements like this.

To understand what checks have to be made to outputs it is important to understand the attribute types that exist in data and how these could lead to primary or secondary disclosure. Importantly, OpenSAFELY requires that researchers redact any outputs based on counts <= 7 before they can be released.

Note

Individual researchers who have Level 4 access have responsibility for redacting sensitive information, or choosing not to publish it at all. The study author should do everything they can to make this easy; for example, carrying out low number suppression automatically, documenting code clearly, and only selecting essential items for publication when deciding what to label as moderately_sensitive.

Attribute types🔗

Datasets made available for analysis may contain the following types of attributes:

Direct identifiers - attributes that definitively identify an individual. This includes information such as name, NHS number or hospital appointment reference. By design these attributes are not made available to OpenSAFELY as data shared into the OpenSAFELY platform is pseudonymised at source and then de-identified before being made available for analysis.
Quasi-identifiers - attributes that in themselves are not direct identifiers, but in combination may allow an individual to be identified; for example, age plus gender plus home address plus the date of a recent hospital visit (see L. Sweeney, Simple Demographics Often Identify People Uniquely. Carnegie Mellon University, Data Privacy Working Paper 3. Pittsburgh 2000 for more detail and examples). It is not possible to say what variables are quasi-identifiers outside of a specific context; ethnicity, number of children, GP surgery or other characteristics could be disclosive in some circumstances and not in others. Medical data provides a lot of variables that could be identifying, such as medical diagnoses and prescriptions. Hence, deciding the riskiness of an output requires judgement and an understanding of context.

Primary vs secondary disclosure🔗

Primary disclosure describes the situation where confidential data can be obtained directly from the data. An example of primary disclosure can be seen in the table below, where you can learn that only 1 member of the population who is aged 21-30 has heart disease.

	Age band	Heart disease	Population
	21-30	1	1
	31-40	10	100
	41-50	15	90
	51+	25	85
Total		51	276

To prevent primary disclosure, you could choose to redact the value for this individual as done below.

Secondary disclosure is where an individual's attributes can be indirectly learned using other available information. An example of this is shown below, where the column totals can be used to deduce that there is only one individual in the 20-30 age band with heart disease, despite the fact this value was protected from primary disclosure by redacting the value.

	Age band	Heart disease	Population
	21-30	[REDACTED]	[REDACTED]
	31-40	10	100
	41-50	15	90
	51+	25	85
Total		51	276

Secondary disclosure can also occur across different tables involving the same population. In the below tables, showing a breakdown of heart disease by age band in the total population and in males alone, there are no disclosive small numbers. However, by differencing the values in the two tables, it can be inferred that there is only one female aged 20-30 who has heart disease.

Total Population	Age Band	Heart Disease	Population
	21-30	8	20
	31-40	10	25
	41-50	15	30
	51+	25	40
Total		58	115

Male Population	Age Band	Heart Disease	Population
	21-30	7	19
	31-40	5	15
	41-50	8	18
	51+	13	25
Total		33	64

When applying disclosure controls to your outputs, you should consider the potential for both primary and secondary disclosure.

Redacting counts less than or equal to 7🔗

Before requesting files to be released, work through the moderately sensitive files in the workspace folder systematically to identify any tables, figures, and other released text and objects that may be a disclosure risk.

The general principle is that any statistic describing 7 or fewer patients, either directly or indirectly, should be redacted or combined into other statistics. This includes:

Redacting counts <=7 in frequency tables. Row and column totals should be recalculated after you have redacted the cell values, to ensure that the redacted values can not be inferred from the totals.
Redacting summaries of numeric variables (eg mean values) describing 7 or fewer patients.
Redacting maximum or minimum values. These often relate to one or two individuals (eg ‘the oldest patient is 103’) and so should be avoided. In some cases the maximum and minima are informative about individuals (‘the target population was schoolchildren from 11 to 16’); these broad sample characteristics are okay.
Redacting graphical figures whose underlying values describe 7 or fewer patients. Figures which include print-outs of patient counts (such as Kaplan-Meier plots) should be checked and redacted. Underlying data for plots should be checked - do not rely upon ‘it’s too small to read’ as a justification for having low numbers. These underlying counts should be provided when requesting the release of any figures.

Note

Our previous requirement was to redact counts <=5. When combined with rounding counts to the nearest 5, this led to occassions where counts of 5 could be inferred to be either 6 or 7. Redacting counts <=7 followed by rounding provides the same protection for all counts.

Below are some other principles to consider:

Counts of zero can be retained in general, but be aware that zero or 100% counts can be disclosive (‘none of the males aged 45-49 used condoms’; ‘THC was detected in all premature births in the 17-18 age group’) and should be removed. This can be difficult, as these results are often the most valuable from a policy perspective, so be particularly cautious when reporting on these.
Analytical results, such as model coefficients, test statistics, or goodness-of-fit measures generally do not generally present any disclosure risk, as long as these are genuine analyses (eg standard deviation does not present a confidentiality risk, unless it is a standard deviation calculated from just two observations)
Other outputs, such as log files that reveal information about the underlying data, should also be checked and redacted if necessary. It is very unlikely that outputs such as log files should be required for publication outside the secure environment (see below for more detail).
We recommend rounding of results that could be at risk of secondary disclosure. This is an alternative to redaction, or can be used in combination. However, be careful to round all your results to the same base number - see below.

Where possible it should be clear what has been redacted, so for example do not redact table titles and category names. By convention redactions take the form [REDACTED] to make redacted elements easier to search for.

If you find yourself redacting a lot of results, consider re-thinking the categories you are using. For example, suppose the category ‘age 95+’ is often needing to be redacted. Is there sufficient distinction between those age 90-94 and those aged 95+ to warrant the extra category? If not, then combine the category. You should always consider this option before deciding to redact individual cells. Focusing on the statistical value of the results can give better results (consistency across tables) compared to treating SDC as a table-by-table problem.

This current approach to disclosure control is conservative and deliberately reduces the need for judgement calls, as these simple rules can be applied by all and provide a good degree of protection. As noted above, good disclosure protection is generally consistent with good statistics. Exceptions can be made if they can be justified as being both materially important for the study conclusions (i.e. providing significant public benefit) and having a very low risk of disclosure. This must be discussed with the OpenSAFELY team. Moreover, these must be rare exceptions: ignoring these guidelines, or continually asking for ‘exceptions’ will not be tolerated.

If you are unsure about anything, please email us: [email protected].

Note

Remember to also always check the permitted study results policy as it describes any additional rules regarding the release of data describing organisations and regions.

Rounding counts🔗

The redaction of any counts <=7 reduces the risk of primary disclosure, but it does not remove the risk of secondary disclosure. As there are many active projects using the OpenSAFELY platform and datasets, there is a risk that your results might be combined with other results to reveal information about individuals or groups. To reduce this risk, we ask that you round any counts to the nearest 5. This includes rounding counts underlying any figures requested for release. In most cases this is unlikely to have a significant impact on your results. If it does, please highlight why it is important to release non-rounded counts when making an output review request.

Note

Rounding does not remove the need to redact counts <=7. You should first redact counts <=7 and then round to the nearest 5.

Below is an example of a table before (top) and after (bottom) rounding has been applied. Note that column and row totals are the sum of the rounded counts.

Total Population	Age Band	Heart Disease	Population
	21-30	3	18
	31-40	8	23
	41-50	16	31
	51+	23	44
Total		50	116

Total Population	Age Band	Heart Disease	Population
	21-30	[REDACTED]	20
	31-40	10	25
	41-50	15	30
	51+	25	45
Total		50	120

Rounding rates🔗

A rate consists of a numerator and denominator, which are generally both counts. In OpenSAFELY, any rate calculated from counts <=7 should also be redacted (see the note above for why a threshold of 7 is used). In addition, we recommend rounding because redaction alone is vulnerable to differencing. When future calculations rely on rates not being mapped to a non-numerical like [REDACTED] and/or a distinction between a rate of zero and a non-zero rate is desirable, we recommend rounding the numerator and denominator to 'midpoint 6'. In short, rounding to 'midpoint 6' allows differentiating between zero and non-zero rates, by not breaking our suppression rules and without introducing bias.

Midpoint 6 rounding🔗

By rounding to midpoint 6, we make sure that the numerator and denominator of our rate do not break our suppression rules. The method has desirable properties such as:

It's unbiasedness
- Rounding to r is unbiased. For non-negative values (like counts), the binwidth is r everywhere except for the lowest bin, where the binwidth is ceiling(r/2) (e.g. rounding to 6, the lowest bin is [1, 2, 3] → 0). Rounding to 6 is not sufficient to comply with our suppression rule of redacting counts of five or lower. We could instead round to the nearest 10, which means that [1, 2, 3, 4, 5] → 0 (not breaking our suppression rule) but reducing precision and not preserving non-zero counts. Another alternative is to round to the nearest 6 and combine the two lowest bins such that [1, 2, 3, 4, 5, 6, 7, 8] → 6 (not breaking our suppression rule and preserving zero-is-zero) but introducing bias. Alternatively, we could round up using a ceiling function such that [1, 2, 3, 4, 5, 6] → 6 and [7, 8, 9, 10, 11, 12] → 12 etc. (not breaking our suppression rule and preserving zero-is-zero) but introducing bias since the mean of the rounded numbers is higher than the mean of the true numbers by 3 (in general, by r/2 for rounding up to ceiling r). Rounding to midpoint 6 fixes the bias in the last option by deducting to r/2, preserving zero-is-zero and the rounded numbers are unbiased.
Zero-are-zero’s
For non-zero rounded values of x, we know true values range between x-2 and x+3

Note

Our recommendation of rounding to midpoint 6 is restricted to situations where these properties (zero-is-zero, unbiasedness and redaction to numericals) are important, for example for Kaplan-Meier estimates from life-tables or similar rates.

The following R function gives an example of how midpoint 6 rounding can be applied:

roundmid_any <- function(x, to=6){
  # like round_any, but centers on (integer) midpoint of the rounding points
  ceiling(x/to)*to - (floor(to/2)*(x!=0))
}

Which results in the following mapping:

Range of true value	Value rounded to midpoint 6
0	0
1-6	3
7-12	9
13-18	15
...	...

Naming convention for midpoint 6 rounding🔗

Please note that the numbers between 1-6 are mapped to ‘3’, which is lower than 5 (our redaction threshold). This ‘3’ is not a true 3 and is only a label for all numbers ranging between 1 and 6. A ‘3’ as a result from using midpoint 6 rounding therefore follows our suppression rules. However, without appropriate context, this may not be obvious to anyone viewing the output (including output checkers). For any outputs that use midpoint rounding, we therefore suggest adding the suffix _midpoint6 to your column name. Similarly, we suggest adding the suffix _midpoint6_derived to values that are derived from the midpoint 6 rounded values and take values of 6, 12, 18,... (for example in life-tables). Alongside this naming convention, we ask people to explicitly point to sections of the code where midpoint rounding was applied.

Extended principles🔗

Below are a couple of examples of common secondary disclosure issues encountered when using OpenSAFELY.

Repeated analyses When producing repeated reports at different time points, it is possible that there can be a small change in the number of people in your analysis. E.g. “number of people with condition X receiving treatment Y” increases from N to N+1). Although this is not typically likely to be disclosive, it may carry a small risk on some occasions (e.g. an individual/GP may be able to identify themselves/their patient or believe that that can do so) and therefore should be routinely avoided to minimise burden on output checking.

The solution for this is to use rounding across the entire report (to the nearest 5, 7, or 10). Rounding eliminates the need for output checkers to compare different versions of the report outputs, as no small increases can occur. It is not likely that rounding will significantly affect the report in any meaningful way. Statistical analyses can be carried out prior to rounding and the results displayed as normal provided they are classed as low risk. If only charts are shown, rounding is not always necessary, but charts should have sufficiently low resolution that any small number changes cannot be precisely determined. However, numbers could be rounded nonetheless, as this would not noticeably affect the figures.

Running similar studies There may be cases where you have run an analysis and results have been released following approval from the output checking team, but at a later date you decide you want to make changes to the analysis such as adding an extra code to a codelist. This may result in small changes in the outputs that can be disclosive, ie, <=7 individuals have the new code recorded. In these cases, you may need to wait until there has been enough change in the underlying study population (due to the movement of patients between practices) before rerunning the study.

If you are likely to release data multiple times, e.g. for initial discussion with collaborators, use rounding of outputs initially and/or a threshold substantially higher than 5 for suppressing low numbers.

Applying statistical disclosure control

Attribute types🔗

Primary vs secondary disclosure🔗

Redacting counts less than or equal to 7🔗

Rounding counts🔗

Rounding rates🔗

Midpoint 6 rounding🔗

Naming convention for midpoint 6 rounding🔗

Extended principles🔗

Further reading🔗