Prospects for Combining Survey and Non-Survey Data Sources to 

Improve Estimated Counts of Certain Work-Related Injuries

Brooks Pierce

U.S. Bureau of Labor Statistics, 2 Massachusetts Ave. NE, Washington, DC 20212

Abstract

The Survey of Occupational Injuries and Illnesses (SOII) is the primary survey of nonfatal work-related 

injuries and illnesses in the U.S. Recently the Occupational Safety and Health Administration (OSHA) 

has instituted new rules governing employer report of work-related injuries, raising the possibility that 

OSHA administrative data could be combined with SOII survey data to improve estimates of injury risks 

in the workplace. This work describes the possibilities and practical challenges of some potential 

approaches to such a data combination.

Key words: data combination, administrative data, work-related injuries

1. Introduction

Under the Occupational Safety and Health Act of 1970, many employers are required to record workrelated injuries and illnesses that occur throughout the year. Under the Act, the Occupational Safety and 

Health Administration (OSHA) was created to enforce rules and regulations governing workplace safety,

and provision was made for collection of injury and illness data recorded by employers. To carry out this 

task the BLS conducts the annual Survey of Occupational Injuries and Illnesses (SOII). The microdata the 

SOII collects are essentially OSHA-required forms that log occurring injuries and illnesses.

In 2016, the Occupational Safety and Health Administration (OSHA) issued a new rule mandating certain 

employers to electronically submit injury and illness data directly to OSHA. Employers in non-exempt 

industries had previously only been required to keep a log of their workplace injuries and illnesses on 

forms that the employer maintained. In principle the new OSHA electronic reporting requirements could 

provide complete administrative records – precisely the forms SOII seeks – for a large part of the SOII

scope. 

Although this regulatory change could provide an informational windfall to the SOII, it also would 

present certain challenges. Complete reporting to OSHA is unlikely since employers may be unaware of 

the new reporting rules. Reporting propensities may vary with observable and unobservable factors, and 

would likely change through time. Data obtained through OSHA would presumably be subject to a 

variety of recording errors, some of which would differ from those typically encountered by the SOII.

Finally, in order to elicit complete information, respondents to BLS surveys are assured confidentiality 

under CIPSEA. OSHA is a regulatory agency and plans to post the electronic records publicly. The lack 

of confidentiality may have an impact on OSHA record quality, for example by inducing under-reporting 

of injury risk to OSHA. This and other mode effects could lead to bias in the OSHA-collected records and 

complicate attempts at combining SOII survey data with OSHA-collected records.

Responsible use of OSHA-provided administrative records therefore requires some mechanism to 

combine records from the different sources and to quantify potential biases in the newly acquired 

administrative records. This paper describes some relatively straightforward approaches to data 

combination in this particular context, and some issues that may arise in combining records collected 

through SOII and OSHA.

Section 2 describes relevant details of OSHA reporting rules and forms; and SOII sampling, data 

collection, and estimation. Section 3 describes simulations of various data combination attempts under 
different reporting selection mechanisms. The data combination approaches are simplistic and transparent

adaptations from literatures on dual frame estimation (Lohr and Brick 2012). They are intended to be 

implementable within current production systems, and so do not require record linkage. Section 4 

describes some practical issues that may arise. Section 5 describes record linkage experiments using other 

OSHA reports and BLS data. The experiments attempt to gauge how successful record linkage between 

OSHA electronic records and BLS data might be.

2. Background on OSHA reporting rules and SOII processes

2.1 OSHA reporting requirements

OSHA rules currently require certain private sector employers to maintain records of workplace injuries 

and illnesses, and to post annual summaries for employee viewing. Records are to be retained for a period 

of time, and are subject to request and inspection by OSHA. Separate records are to be maintained for 

separate establishments within a firm. Companies with 10 or fewer employees at all times during a 

calendar year are exempt from record-keeping requirements, as are business establishments within 

specified industries (generally those with lower workplace injury risk). Regulations and subsequent 

interpretative findings specify general recording criteria, employee coverage, determination of workrelatedness, and other factors.1

Employers must maintain three sets of forms. OSHA form 300 is a log listing basic information on each 

recordable case. Information includes the employee’s name and job title, the date of the incident, a brief 

description of the incident, and information on the type of injury or illness (for example, whether the 

injury resulted in time away from work). Form 300A is a summary of the individual case records from 

form 300. This provides annual totals by injury or illness type along with establishment location and 

industry, and the establishment’s average annual employment and total hours worked by all employees. 

Form 301 provides further details on the employee and incident for each recordable case.2,3

The new OSHA rules require employers to electronically submit these forms. The requirement applies to 

business establishments with 250 or more employees in those industries required to maintain forms. For a 

subset of high injury rate industries, business establishments with 20-249 employees must submit the 

Summary form 300A, but not forms relating case level detail. As of this writing, it is unclear if the new 

OSHA rules will take effect as originally constituted; they are under litigation and subject to revision by 

OSHA. However, OSHA has constructed a portal for receiving submitted information and at least by that 

measure the implementation does not hinge on technical considerations.

2.2 SOII 

The SOII is designed to collect occupational injury and illness data directly from employers using a 

random sample of over 250,000 establishments in private industry and state and local governments. The 

SOII sample is stratified by state, establishment size class as determined by establishment employment, 

detailed industry, and ownership group (private, state government, local government). For efficiency 

reasons the SOII disproportionately samples from strata covering larger establishments and higher injury 

rate industries (Selby et al. 2008). As these subpopulations are subject to the new OSHA rules, some form 

 

1 See https://www.osha.gov/recordkeeping/.

2 There are additional OSHA requirements for reporting certain especially severe injuries; the record linkage 

attempts at the end of this paper use data generated from that requirement.

3 Some states administer their own work injury programs, under federal OSHA oversight. Establishments in these 

state-plan states must satisfy equally rigorous recordkeeping rules but would not electronically submit to federal 

OSHA.
of data combination could substantially reduce SOII respondent burden, for example through reduced 

SOII sample size.

Just prior to the start of the year, BLS sends notification and recordkeeping information to establishments 

selected to be in the sample for the upcoming year. Survey response is required by law, even for 

establishments otherwise exempt from OSHA recordkeeping requirements. Over the course of the survey

year, selected employers record injuries and illnesses in their OSHA logs. For certain injuries and 

illnesses, those resulting in days away from work (DAFW), employers also record case-level details such 

as the circumstances surrounding the occurrence and demographic information on the affected employee.4

In the following January, BLS requests that the selected establishments report this information to BLS. 

Data collection continues in the first half of the year and estimates are published in the fall. 

The SOII publishes a very large number of direct estimates on narrowly defined domains. One set of 

estimates reports statistics derived from establishment-level totals for hours worked and injuries and 

illnesses of various types. These statistics are injury and illness totals and mean incidence rates produced 

along establishment-level dimensions such as state, industry, and establishment size class; distributional 

information for incidence rates is also tabulated. A second set of estimates reports statistics derived from 

case-level details about the affected workers, their jobs, and the circumstances surrounding incidents. 

SOII case-level estimates are primarily restricted to cases which result in days away from work.5

2.3 Extent of overlap between SOII and OSHA records

Table 1 gives statistics on the prospective impact in SOII of the electronic reporting rule. Statistics are the 

percentages of establishments, employment, and case totals in the 2015 SOII private sector sample subject 

to the additional OSHA reporting requirements (had they been in force at the time). Establishments are 

subject to either no additional reporting, reporting of summary totals only, or reporting of both summary 

totals as well as case level information. Distributions are given for weighted as well as unweighted 

statistics. Unweighted statistics are useful in gauging the resource impact to SOII; weighted statistics are 

more relevant for gauging the breadth of the rules changes in the economy.

Approximately 40 percent of the establishment records in the SOII would be subject to some form of 

electronic reporting. One could possibly view this as an upper bound estimate for the cost savings realized 

by SOII from fully utilizing an influx of OSHA administrative data. The respondent burden is 

concentrated among larger business establishments in high injury rate sectors, and the weighted statistics 

indicate the burden falls on less than 1 percent of establishments for reporting case level information and 

less than 8 percent of establishments for reporting summary establishment level information. 

In terms of the workforce affected, the weighted statistics indicate that about 42 percent of the private 

sector employees within the SOII scope work in establishments subject to the regulatory changes. These 

42 percent account for 65 percent of all recordable injury and illness cases. That is, nearly two-thirds of 

the primary, top-line private sector statistic produced by SOII is attributable to business units subject to 

the OSHA electronic reporting requirements.

Because the SOII produces a very large number of estimates using reports on cases with days away from 

work, it is useful to separately look at coverage rates at the case level. Here the relevant group is the 

subset of business establishments reporting case records. These are the largest business units (250 or more 

employees) in non-exempt industries. Looking at the weighted statistics, about 25 percent of cases with 

 

4 Sampled establishments generally report the census of DAFW cases, but for establishments with many DAFW 

cases the SOII subsamples at the case level. The SOII also collects information on cases that result in days of job 

transfer and restriction (DJTR), but currently only for a subset of industries.

5 OSHA case level records would include these cases as well as cases that result in job transfer or restriction.
days away from work (DAFW) and about 35 percent of cases with job transfer or restriction (DJTR) 

occur in these establishments.6 This implies, for example, that any mode effects in reporting DAFW case 

characteristics would potentially affect 25 percent of the data underlying SOII case estimates.

The unweighted statistics for DAFW and DJTR cases indicate that, roughly speaking, 60-70 percent of 

case records would potentially come from this subset of establishments. This indicates a substantial 

respondent burden for some establishments. The SOII reduces respondent burden for case-level reporting 

by subsampling cases. Furthermore, the SOII currently collects DJTR cases only for a subset of 

industries. Therefore the 62.7 percent (DAFW) and 69.6 percent (DJTR) statistics in panel A do not 

measure the fraction of current SOII case level records potentially supplanted by OSHA administrative 

records. These unweighted statistics are however relevant to potential SOII costs should SOII process all 

such administrative records. As an example, SOII codes occupational classifications from reported job 

titles for each case record. Part of this coding relies on automated procedures but a substantial part relies 

on human coding. SOII would presumably carry out similar coding for all OSHA-reported case records it 

uses. Therefore any source-specific effects – say, a delayed arrival of OSHA administrative records to 

SOII – would potentially have a large impact on SOII costs.

3. Simulations incorporating OSHA records

We do not yet have OSHA administrative records generated via the new electronic record-keeping rules. 

In lieu of actual data, I show some simulations of outcomes under various scenarios. I focus on strategies 

that seek to utilize all available OSHA data records without having to identify SOII respondents in the 

OSHA source.

The simulations are relatively straightforward. First I constructed a universe frame, which includes both 

establishment level and case level information. Stratified random samples of establishments on the frame 

stand in for SOII samples. A known subset of establishments on the frame is subject to OSHA electronic 

reporting, but only some establishments required to submit do so; the probability an establishment reports 

is assumed to follow various alternative rules. Finally, I combine the SOII and OSHA records to produce 

a given set of estimates, using various different methods. Empirical mean squared error statistics for each 

estimate follow from repeated application of the SOII sampling and OSHA reporting selection 

mechanisms. MSE statistics can then be compared across estimation methods for each postulated OSHA 

reporting selection mechanism.

3.1 Frame generation

I pooled all private sector establishment-level responses from the 2013-2015 SOII samples. For SOII 

strata where the pooled sample sizes exceeded the actual frame unit size, I discarded responses at random 

to achieve frame size.7 Then, within the remaining strata where the pooled sample sizes fell short of 

actual frame size, I duplicated the responses multiple times until achieving a size consistent with the 

actual frame. Because SOII samples at much higher rates for large establishments and high-injury sectors, 

this duplicating of responses is relevant primarily for the non-OSHA portion of the frame. I take the 

resulting set of establishment level information to be my frame for the SOII; this information includes all 

 

6 The greater fraction for DJTR cases suggests that this subset of business establishments more actively pursues 

policies of re-tasking injured workers to other duties. The large percentages for DJTR cases also suggests that the 

SOII might be induced to produce a broader array of estimates for such cases, were the SOII to intake OSHA’s 

electronically reported DJTR case records. This could have further implications, such as an incentive to substitute 

toward additional DJTR collection within the SOII proper.

7 The SOII frame contains many establishments that would be nonviable units were they sampled – for example, 

many units can be expected to be out of business. I take frame size to be the number of viable units within the SOII 

strata as estimated using 2015 SOII data. 
fields from the OSHA summary form 300A. To obtain case-level information consistent with this 

constructed frame I retrieved the SOII DAFW case reports relevant to each establishment-year pairing on 

the frame.

8

3.2 Simulated SOII sampling and post-sampling processing

For the purposes of these simulations, sampling strata are cells determined by state, industry as defined by 

3-digit NAICS codes, and establishment employment size groups. These defined strata are coarser than 

actual SOII strata, particularly along the industry dimension. I used the pooled 2013-2015 SOII samples 

to derive average annual sampling rates for each defined strata. Each simulation applied these sampling 

rates to the constructed frame; on average this results in SOII simulated samples of approximately 

180,000 establishment units and approximately 200,000 DAFW case records. All sampled units are 

assumed to respond fully. Therefore post-sampling processing consists only of setting an establishmentlevel sampling weight equal to the strata’s frame size divided by its sample size. The establishment-level 

weight is carried over to each case record.

9

3.3 Selection mechanisms into administrative reporting

I assume that larger establishments in higher injury rate industries are directed to submit records to an 

administrative authority. I set the reporting size cutoff at 50 employees and further restrict reporting to 

those three-digit industries generally subject to the actual new electronic reporting rules. Establishments 

not required to submit records do not do so. Some establishments required to report also do not do so; 

various models for the probability of reporting are possible. If an establishment reports it does so 

accurately and fully, including all DAFW case record details.

10

There are three different models for the probability of reporting. One sets the probability of report from 

each stratum equal to a randomly drawn constant. That is, the probability of report is determined by frame 

characteristics and is the same for all units in a given stratum. The second sets the probability of reporting 

to be an increasing function of the number of total cases in the establishment. The third sets the 

probability of reporting to be a function of the case profile among DAFW cases in the establishment:

probabilities of reporting are higher for establishments with a worker experiencing an amputation. The 

parameters of these three selection mechanisms do not result in similar amounts or patterns of underreporting to the administrative authority. They are designed only to highlight the challenges faced by 

different estimation approaches in combining the data. I will refer to these selection mechanisms as 

“selection on characteristics”, “selection on total cases”, and “selection on case profiles”, respectively. 

Details on the probabilities are listed in an attachment.

3.4 Simulation and data combination

Each simulation draws a SOII sample from the frame, and also generates a set of establishments reporting 

to the administrative authority, as described above. For domains not subject to administrative reporting, 

estimates rely solely on the SOII sample data. For domains subject to administrative reporting, estimates 

must combine the information from the two sources in some manner. A traditional dual frame approach 

 

8 Due to partial nonresponse and case subsampling, a SOII respondent may have fewer DAFW case records than its 

reported DAFW case total. The SOII constructs a case-level adjustment factor to account for such instances. In my 

pretend frame I maintain that adjustment factor rather than repeat the individual case records to reach the 

establishment’s reported total. Case records in the simulated samples also maintain this adjustment factor.

9 As per the previous footnote, the case level weights equal the establishment level weight times any relevant case 

subsampling adjustment factor.

10 These parameters differ from the actual OSHA electronic reporting rules mainly in that they eliminate the 

distinction between establishment summary-only reporters and case records reporters, while setting the 

establishment size cutoff between that relevant for summary reporting (in some instances 20+ employees) and case 

record reporting (250+ employees). 
takes the estimator to be a convex combination of the source-specific estimators. Letting domain be 

indexed by d, establishments in SOII be indexed by i, and establishments reporting to OSHA be indexed 

by j, one might form

Ŷ

d = θd ∑ I i∈SOII idwiyi + (1 − θd) ∑ I j∈OSHA jdwjyj

(1)

where the Id’s are indicator functions for domain membership, the w’s are appropriate weights, and the y’s 

are outcomes such as the establishment’s number of total cases. The separate indices i and j are meant to 

stress that a given establishment need not be linked across sources to form estimates; the θ and (1-θ) 

weights prevent double-counting. Case-level estimates are formed analogously, but with an additional 

indicator for whether or not the case has the given characteristic (for example, an indicator for an 

amputation case). This approach is exceedingly convenient in that with proper weights modifications one 

can simply append microdata from the different sources and operate on the pooled collection of records. 

In the simulations I calculated estimates for total hours worked, total recordable cases, DAFW cases, 

DJTR cases, and also for two types of particularly severe DAFW cases, those that result in an overnight 

hospitalization and those that result in an amputation. The domains are three-digit NAICS private sector

industry groups, plus an aggregate total, for the US. MSE statistics are calculated based on 500 

simulations.

There are several different approaches to operationalizing (1). One approach is to naively insert the 

OSHA data without weights, analogous to setting the wj = 1.11 Different variants of this naïve approach 

correspond to different values for the θd: ignoring OSHA data; ignoring SOII data; equally weighting the 

two sources; and, taking θd to be the fraction of establishment units in domain d coming from the SOII 

data. These are not reasonable strategies under the assumptions but they usefully document baselines, and 

are potentially useful strategies under a mature regime with more complete reporting. The SOII in fact 

relies on external administrative records for railroad and mining sector data, treating these external 

records as complete censuses for their respective populations, so these strategies have precedence in the 

SOII.

A second approach is to set weights wj via stratifying to cell establishment counts. This stratification will 

eliminate biases associated with under-reporting where the reporting depends entirely on the observable 

characteristics determining the strata cells. For this approach (and the others described below) I take θd to 

be the fraction of establishment units in domain d coming from the SOII data.

A third approach is to make further adjustments based on reported outcome variables. This approach 

starts with stratified OSHA weights as above, and further adjusts them based on reported outcomes in the 

two sources. I look at two variants of this approach. One is a final post-stratification or benchmarking of 

the OSHA weights so that weighted establishment counts within cells defined by injury rates are equal in 

the two sources. This process renders OSHA data less helpful for national level estimates, but (possibly) 

more helpful for smaller domain estimates or estimates of injury subsets. I will refer to this as 

“calibration”. The second variant is to adjust the stratified OSHA weights with a regression coefficient 

from a regression model of domain-level estimates from the two sources. That is, if the regression 

equation is 

Ŷ

d

SOII = α + βŶ

d

OSHA + εd (2)

 

11 In all calculations the w weights reflect case subsampling adjustments described earlier, and for SOII the weights 

also reflect stratification to frame establishment counts.
then the OSHA stratified weights are adjusted by the estimate for β. I refer to this as a Fay-Herriot 

approach (Fay and Herriot 1979, Ybarra and Lohr 2008).

Worthy alternatives which I have not yet investigated include calibration to multiple outcomes (Sarndal 

2007) and a reweighting approach using propensity scores (Elliot and Davis 2005, reminiscent of 

Dinardo, Fortin and Lemieux 1996).

3.5 Simulation results

In general, the naïve approaches without weights adjustments in the OSHA administrative records 

perform poorly. This is unsurprising given their large uncorrected biases. The lowest MSE estimator 

among the naïve approaches involves setting θd in equation (1) to be the fraction of establishment units in 

domain d coming from the SOII data. 

Accordingly, stratifying the OSHA source weights to frame control totals is hugely beneficial. For 

simulations where the probability of reporting to OSHA depends entirely on cell membership, stratifying 

the weights in this way eliminates bias and reduces MSEs below SOII-only levels. For simulations where 

the probability of reporting depends on outcome variables (here, total cases), stratification is still quite 

helpful but does not entirely eliminate bias. In these situations either the calibration or Fay-Herriot 

regression adjustment methods typically further improve MSEs; the data showed a slight preference for 

the calibration method.

Tables 2 and 3 give examples for a few manufacturing industries. Table 2 gives results where the 

selection mechanism is on observable characteristics only; table 3 gives results where the selection 

mechanism is on the outcome variable, total cases. The tables give MSE statistics, specifically, root MSE 

measured as a percentage of the true population value, for several outcome variables. The outcome 

variables include important SOII fields such as DAFW, DJTR, and total case counts; and, full-time 

equivalent employment (an input for SOII incidence rate estimates). I also include statistics for two less 

frequent but very severe outcomes, DAFW cases that result in overnight hospitalization, or in amputation. 

The prevalence in actual data of overnight hospitalizations among private sector DAFW cases is roughly 

1 in 20. The analogous prevalence of amputations is roughly 1 in 200. 

These industries had above-average incidence rates in 2015, based on actual published numbers. Of the 

industries listed, employment is highest in food manufacturing, next highest in beverage and tobacco 

manufacturing, and lower in the two textile-related industries. The relative sizes of the industries are 

reflected in the SOII-only MSE statistics in these tables.

The patterns in table 2 suggest that combining the administrative and survey data is not a good strategy 

without adjusting the administrative source weights to control totals. In these experiments the underreporting is severe enough that discarding the administrative records is generally preferable to using them 

in naïve combination. The exceptions are for the severe but infrequent DAFW incidents in small 

industries, where variance issues dominate. Some of the amputations estimates in table 2 are 

unpublishable according to SOII reliability criteria with SOII data alone, but publishable with the addition 

of the administrative data.

Figure 1 shows MSE statistics for the total cases column for all 49 3-digit industries where there are two 

data sources in the simulations. This is just a visual summary of the first column in table 2, but for all 

industries. 

Table 3 gives MSE statistics under an alternative reporting selection mechanism, where the probability of 

reporting to OSHA increases with the establishment’s total cases. Because establishment characteristics 

such as industry and establishment size correlate with case totals, stratified weights will partially correct 

the resulting bias. However, the bias correction is incomplete and for many estimates the MSEs are larger 

when using the administrative data with stratified weights, than when discarding the administrative data 
altogether. The further weights adjustments either through the Fay-Herriot adjustment or the calibration 

approach generally result in lower MSE estimates. In particular the SOII-only estimates are generally not 

quite competitive with the calibration approach, at least for these example industries. Figure 2 

summarizes the total cases column, showing all industries. There appears to be a negligible benefit to the 

calibration approach, as compared to ignoring the OSHA data entirely. Stratification does not correct the 

OSHA bias sufficiently.

Table 4 gives MSE statistics for the severe DAFW cases, under a third reporting selection mechanism. 

Here the experiments presume that the reporting probability depends on the case profile in the 

establishment. In particular, an establishment experiencing an amputation is assigned a larger than 

average probability of reporting. Therefore any reweighting of the administrative data based on frame 

characteristics or reported total cases will overinflate amputations cases and very slightly underinflate 

other outcomes.12 The bias should generally be at least partly offset by variance considerations. Table 4 

shows the entire private sector aggregate. Figures 3 and 4 give distributions across the 3-digit industries. 

There is some evidence that stratification helps, but more so for high MSE estimates.

A last point is worth stressing. The weights adjustments considered here take place at the establishment 

level and so apply similarly to all fields reported by the establishment. This aspect allows for a single set 

of weights, and guarantees that subcomponents add up correctly to totals. For example, with field-specific 

weights, DAFW case totals plus DJTR case totals would not equal estimated totals for the quantity 

(DAFW cases + DJTR cases). But this aspect could as in table 4 leave us vulnerable to some induced 

bias. 

The simulation results are rather hard-wired. Stratification is generally beneficial relative to simply taking 

the administrative records at face value. However, stratification need not eliminate all biases in the 

administrative records. Benchmarking the administrative records to SOII responses, referred to here as 

“calibration”, may be helpful in estimating domains below the aggregate. Incorporating the external data 

is more helpful for smaller cells where SOII estimates are less precisely estimated.

4. Practical issues

The simulations above suggest there may be sensible and relatively manageable ways to incorporate 

administrative records into SOII estimation processes. The methods do not require record linkage, and do

not appear to require information beyond that normally present in the SOII frame. However, there would 

certainly be practical challenges to overcome, and it is possible that record linkage or other information 

from past surveys or frames could improve estimation, and partially validate any chosen estimation 

method. 

4.1 Issues surrounding post-stratification

The methods above generally require that we perform an analog to post-stratification on the 

administrative records. The control totals are essentially the number of business establishment units 

within strata. The SOII frame contains establishment counts but these counts are subject to updating. 

Some revisions occur directly at the time of SOII survey contact. For example, SOII staff may learn of a 

business closure only through efforts at mailing survey forms. A smaller survey component to the SOII 

would presumably make cell counts less accurate.

Administrative records would surely have errors complicating post-stratification. It is not clear that multiestablishment businesses would accurately separate reports by establishment, as required by the reporting 

 

12 I made the probability of reporting where there is a hospitalization slightly lower than average in some industries, 

so as to exacerbate the underinflation for such cases.
rules. OSHA recognizes this possibility and includes active language designed to prevent aggregated 

reports, but they have limited resources for audits or other data checks. Strictly speaking, the poststratification strategies require disaggregation of a business entity in the same manner as it appears on the 

SOII frame. 

Industry measurement error will occur in the administrative records. SOII processes use industry as it 

appears on the frame at the time of sampling, whereas OSHA records would contain self-reports of 

industry (please note, there are industry-based exemptions to reporting). It may be the case that industry 

measurement error is tolerable at say a 3-digit NAICS level but not at a detailed (6-digit) level, and that 

there are tradeoffs related to industry detail choice for the purposes of post-stratification of the OSHA 

source data.

4.2 Mode effects

The SOII asks respondents to report information as it exists on the forms that OSHA will require be 

submitted electronically. One might expect establishment reports to be similar under the two systems. 

Nevertheless, mode effects are possible. The SOII promises confidentiality whereas OSHA is a regulatory 

agency that intends to broadcast the required information via posting on a publicly accessible web site. It 

may be that different individuals report to the two systems, and at different times, or that SOII system 

processes such as re-contact or data editing result in data differences across systems. (Some SOII 

processes such as de-duplication of reports, handling of inconsistent reports, deletion of out-of-scope 

cases, and so forth would presumably be applied to the administrative data.)

It is also possible that the new rules induce establishments to alter their safety climate or their injury 

record-keeping processes in such a way as to change actual or reported outcomes as they apply to both 

data sources. (Changing actual outcomes is one implicit goal of the rules). This would not necessarily 

pose a problem for analysis or combination of current data but could make use of past information more 

difficult.

4.3 Useful exercises to conduct on OSHA data

The primary piece of information needed to combine the administrative records with SOII data is the 

probability that establishment j reports to the administrative system. The methods described above largely

boil down to getting good measures for that probability, so as to undo reporting biases. Therefore it makes 

sense that a first step with actual data would be to determine how this probability varies with 

establishment characteristics and outcomes. For example, if the establishment DJTR case count is a 

predictor for reporting but DAFW cases are not, then a calibration exercise based on DAFW cases may 

not be the best strategy. Such an analysis would not require linked records.

However, record linkage would be required to settle other issues. Mode effects could be directly

estimated. Linked records might also be used to determine whether multi-establishment firms are 

disaggregating along establishment lines as they exist in the SOII frame. Perhaps most importantly, direct 

comparisons of OSHA and SOII measures of establishment size and industry are needed to produce a 

mapping from OSHA data to the SOII strata. Lohr (2011) discusses a weights adjustment to unwind 

measurement differences for fields defining strata. Such an adjustment requires information on the 

particulars of the misclassification errors, which could in principle come from linked records. Any such 

adjustment could help with bias but inflate variances; realistic simulations might be informative. 

4.4 Implications for sample allocations

Current SOII sample allocation sets sampling rates after accounting for certainty strata according to a 

Neyman allocation rule minimizing the variance of the topline incidence rate (Selby et al. 2008). This rule 

has a side benefit of being very productive for DAFW case records, so that sample sizes support 

comprehensive estimates of case and worker attributes. A substantial influx of administrative records 
would seemingly force SOII to revisit the allocation process. First, SOII sample sizes might be cut. 

Second, allocation rules might target MSE measures and so incorporate bias concerns. One suggestion 

(Raghunathan 2015) is that scientific surveys’ primary purpose may evolve toward providing information 

useful for triangulating to found data, and away from direct estimation. If so, SOII survey information in 

the OSHA overlap portion of the SOII population becomes more important, and this would seem to call 

for different objective functions for the allocation optimization problem. 

5. Linking actual SOII and OSHA records

Although we do not yet have OSHA electronic reports under the new requirements, OSHA does post 

some information it receives under a different reporting requirement: OSHA receives reports on 

especially severe injuries, including amputations and hospitalizations. 

I linked the 2015 OSHA data on severe injuries to 2015 SOII data in two ways. One linkage was an 

attempt to find OSHA-reporting establishments in the SOII frame. This linkage intends to determine 

feasibility of OSHA to SOII frame linkage, and also to quantify differences in industry coding in the two 

sources. A second linkage attempts to determine how often SOII DAFW cases on amputations and 

hospitalizations are reported to OSHA. This second linkage establishes that data are under-reported to 

OSHA for this particular set of reporting requirements. Readers are cautioned that record linkage as 

carried out here is a subjective process involving manual review, and further that under-reporting of 

severe injury cases can be expected to differ from under-reporting processes governing the new electronic 

submission rule.

OSHA requires all private sector employers to promptly report the circumstances surrounding certain 

severe incidents, including fatalities, amputations, and incidents resulting in hospitalization.13 This 

reporting requirement extends to all industries and businesses of any size; the recordkeeping exemptions 

for OSHA forms 300, 300A and 301 described earlier do not apply for these severe incidents. Information 

reported includes company name, street address, city, state, zip code, a NAICS industry code, date of 

injury, and classification of injury circumstances based on narrative text. This information is potentially 

similar to a subset of information that would be required under the new electronic submission rules. 

However, the information does not include complete establishment reports for all cases, and other 

establishment level information (in particular, establishment employment).

5.1 Linkage to the SOII frame

An establishment reporting to OSHA should be in the SOII frame. I took OSHA reports from one state, 

Ohio, and attempted a record linkage to the SOII frame. The algorithm is:

1. Extract OSHA records for hospitalization cases occurring in Ohio during 2015. After removing 

duplicate records and dropping USPS records there are 491 records.

2. Extract private sector Ohio records for the 1st quarter 2015 from the BLS’ Longitudinal Database 

(LDB, approximately equal to the SOII frame). Records include company legal name, trade 

name, and 3 addresses (2*3=6 combinations of name and address). There are approximately 

275K establishment records. 

3. Name/address fields in both sources are pre-processed with standardization software.

4. Probabilistic linkage. Linkage fields are name, street address, city, and 5-digit zip code. Industry 

is not used in linking records. Linkage is carried out 6 times, one for each LDB name/address 

 

13 OSHA receives these reports from employers operating in Federal-OSHA states. Some states operate their own 

job safety and health plans, under Federal OSHA approval. Severe injuries in those states do not appear in the 

Federal OSHA severe injury records.
combination, and possible links collated. A manual review of records was used to gauge how 

numerical match scores relate to probable matches.

Of the 491 establishment records from OSHA, 293 (about 60 percent) were clearly matched, in the sense 

that the OSHA record appeared in the LDB under nearly identical text for the linkage fields. All LDB 

name and address fields were useful in linking records. Among records that were clearly linked, there was 

a fairly substantial disagreement on industry codes in the two sources. The SOII and OSHA industry 

codes agreed approximately 58 percent of the time at the three-digit NAICS level and approximately 72 

percent of the time at the 2-digit NAICS level.

Some qualitative information on linkage error is available. In addition to the 60 percent of records that 

appeared clearly matched, about 17 percent had a linked record that suggested a possible match, but with 

some divergence of representation in the two sources. These possible links might be resolved with access 

to additional data (for example, a federal tax identifier (EIN), or information on the entire case profile of 

the establishment). Some OSHA records were linked to multiple LDB identifiers; distinct LDB identifiers 

were found to have common company name and address information when looking at all name and 

address fields. This phenomenon appeared nonrandom with respect to industry. In addition, some LDB 

identifiers were linked to multiple OSHA records. Multiple linkage generally suggests a weak 

deduplication process. 

Although these results come only from one experiment, they do suggest that record linkage at the 

establishment level would be difficult absent other information. They also suggest real challenges in 

conforming the administrative and SOII records along industry lines.

5.2 Linkage of hospitalization cases

Those SOII DAFW cases from federal-OSHA states that indicate an overnight hospitalization or 

amputation generally should be reported to OSHA. Therefore such a case found in SOII but not OSHA 

records can be presumed to reflect under-reporting to the administrative data, or linkage errors. A case 

found in OSHA records but not SOII may indicate a variety of situations (linkage error, SOII sampling 

rates less than one, a hospitalization that did not result in a day away from work, etc.). I took SOII case 

records for hospitalizations and attempted to find them in the OSHA records. This linkage is less 

informative than the attempt to link establishments, because one would not necessarily expect underreporting for these case types to apply to the new recordkeeping rule to the same extent. Here is the 

algorithm:

1. Extract private sector 2015 SOII DAFW case records indicating overnight hospitalization, in 

federal-OSHA states. This results in 3799 records, with a weighted estimate of approximately 

22,900 cases. 

2. Extract 2015 OSHA hospitalization records, restricting to federal-OSHA states. This gives 7523

cases, about one-third of the SOII weighted total in federal-OSHA states.

3. Name and address fields in both sources are pre-processed with standardization software.

4. Probabilistic linkage. Linkage fields are name, street address, city, 5-digit zip code, state, and date 

of injury. Exact agreement on date of injury and state are required for an accepted link. Industry 

and case characteristics beyond identification as a hospitalization case are not used in linking 

records. Linkage is carried out 6 times, one for each LDB name/address combination, and 

possible links collated. A manual review of records was used to gauge how numerical match 

scores relate to probable matches.

Depending on how stringent one makes the linkage criteria, approximately 20-25% (unweighted) of 

eligible SOII hospitalizations appeared to show up in the OSHA records; weighted numbers are lower.

There are strong patterns in linkage probabilities along dimensions related to SOII cell strata. In 

particular, larger SOII units were much more likely to have their cases appear in the OSHA records.
Therefore we should not expect such substantial under-reporting with the new electronic reporting 

requirements (which apply to larger units). There were also differences across states and industries in 

linkage probabilities. In terms of industries, utilities and manufacturing establishments are much more 

likely to have their cases appear in OSHA records, while service and construction industry units were less 

likely to have their cases appear in OSHA records. Linked case records can show different industry codes 

in the different data sources; agreement at a three-digit NAICS level was comparable or slightly lower in 

these data to that described above for the establishment linkage.

6. Conclusions

This note describes various challenges that may confront BLS should it try to incorporate OSHA 

administrative records into its SOII estimation processes. Two general themes emerge. First, identifying 

the determinants of whether establishments report to OSHA or not is a key task. If the reporting 

determinants sufficiently relate to observables available on the SOII frame, stratification approaches hold 

some promise. Second, merging the two data sources through probabilistic record linkage could yield 

important information, particularly about the appropriate SOII stratum placement of OSHA-reporting 

establishments. Given that record linkage between SOII and actual OSHA data show substantial 

disagreement on industry, further investigation of estimator sensitivity to stratum misclassification 

appears warranted.

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Appendix: Simulation parameters

Selection into reporting to OSHA. Establishments out of scope for the OSHA rules do not report to 

OSHA. Establishments in scope report with a probability assigned under one of three mechanisms. For 

purposes of the simulation, establishments with 50 or more employees that are in industries normally 

subject to (actual) OSHA oversight are assumed to be subject to the electronic reporting rule.

1. Selection on characteristics. Each stratum is assigned a random U[0,1] constant indicating the 

probability an establishment in that stratum reports. 

2. Selection on total cases. Each establishment in the frame reports with probability p(z) = 

exp(z)/(1+exp(z)) where z depends on total cases as follows:

z = 0 if total_cases<=1

z = 0.6*ln(total_cases) if total_cases>1

3. Selection on case profiles. Probabilities of reporting depend on industry sector and whether an 

amputation or a hospitalization case occurs within the establishment. The assigned probabilities 

are largest for establishments in which an amputation case occurs. Reporting probabilities 

assigned are:

Industry Aggregate

Amputation 

present

Hospitalization 

but no 

amputation Any other

Construction 0.8 0.6 0.7

Manufacturing 0.9 0.6 0.8

Natural Resources 0.8 0.7 0.7

Education, Health, Leisure and Hospitality 0.8 0.3 0.3

Financial Activities 1.0 0.5 0.5

Information 1.0 0.8 0.8

Professional, business and other services 0.9 0.7 0.7

Trade, transportation and utilities 0.7 0.5 0.5

Estimators. 

Letting domain be indexed by d, establishments in SOII be indexed by i, and establishments reporting to 

OSHA be indexed by j, estimators are of the form

Ŷ

d = θd ∑ Iidwiyi

i∈SOII

+ (1 − θd) ∑ Ijdwjyj

j∈OSHA

where the Id’s are indicator functions for domain membership, the w’s are weights, and the y’s are case 

counts of various types. For all estimators the SOII weights wi are sampling weights reflecting the inverse 

probability of selection.
1. SOII only, θd=1

2. OSHA only, θd=0 with weights wj = 1.

3. OSHA and SOII equally weighted, θd=0.5 with OSHA weights wj = 1.

4. OSHA and SOII weighted in proportion to domain-specific establishment counts from each 

source, θd=(nd,SOII / (nd,SOII + nd,OSHA)), with OSHA weights wj = 1.

5. θd as in 4, with OSHA weights wj post-stratified to SOII frame establishment totals Nd.

6. As in 5, with OSHA weights wj post-stratified to SOII frame establishment totals Nd and 

additionally multiplied by a coefficient β̂ from a regression 

Ŷ

d

SOII = α + βŶ

d

OSHA + εd

where observations are at the 3-digit industry level and 

Ŷ

d

SOII = ∑ Iidwiyi

i∈SOII

Ŷ

d

OSHA = ∑ Ijdwjyj

j∈OSHA

are estimates for total recordable cases reported in the industry to each source.

7. As in 5, with OSHA weights wj post-stratified to SOII frame establishment totals Nd and then 

additionally multiplied by an adjustment factor from benchmarking to SOII weighted 

establishment counts, for groups determined by the establishment injury rate for total cases.

Estimators 1-4 are naïve incorporation of available OSHA data; results for 2-3 are dominated by 4 and are 

not reported. Estimator 5 is designed to overcome selection on characteristics. Estimators 6-7 are 

designed to reduce bias arising from selection on total cases.
Table 1: Percent of SOII Sample Subject to Electronic Reporting Requirements

Establish

-ments

Reported 

employment

Total 

cases

Cases with 

days away 

from work

Cases with 

days of job 

transfer or 

restriction

A. Unweighted

No reporting 60.4 30.2 13.3 13.3 7.1

Summary records 28.0 16.0 22.0 24.0 23.4

Summary, case records 11.6 53.8 64.7 62.7 69.6

B. Weighted

No reporting 92.3 58.2 35.0 36.6 20.8

Summary records 7.2 23.3 37.5 38.8 43.6

Summary, case records 0.6 18.5 27.6 24.6 35.5

Notes. Statistics sum to 100 percent within column for each panel. Estimates are based 

on 2015 SOII sample data.

Table 2: Root MSE as a Percent of True Values, Select Manufacturing Industries

Industry/Estimator

Total 

cases

FTE 

employment

DAFW

cases

DJTR 

cases

DAFW 

hospitalizations

DAFW 

amputations

Food Manufacturing

SOII only 2.2 1.7 3.1 2.3 8.1 19.4

Naïve combination 15.1 14.5 15.4 15.3 15.9 22.7

Stratified weights 2.2 1.7 2.9 2.3 7.4 18.5

Beverage, Tobacco

SOII only 5.5 3.0 7.6 7.6 36.3 47.4

Naïve combination 15.6 14.2 15.7 18.0 35.9 42.0

Stratified weights 4.7 2.4 5.8 6.0 35.2 41.7

Textile Mills

SOII only 6.3 3.2 10.4 9.1 35.6 27.1

Naïve combination 13.2 12.5 13.0 15.2 35.8 22.1

Stratified weights 4.2 2.2 7.5 6.1 35.2 18.3

Textile Product Mills

SOII only 8.9 3.9 13.5 13.8 43.7 45.6

Naïve combination 12.9 9.9 16.1 16.4 43.4 27.8

Stratified weights 8.1 3.1 12.9 12.3 41.8 23.7

Notes. All reported numbers are based on simulations. The probability an establishment 

reports to OSHA depends on observed establishment characteristics. See appendix for a 

description of data generation and the estimators.
Table 3: Root MSE as a Percent of True Values, Select Manufacturing Industries

Industry/Estimator

Total 

cases

FTE 

employment

DAFW 

cases

DJTR 

cases

DAFW 

hospitalizations

DAFW 

amputations

Food Manufacturing

SOII only 2.2 1.7 3.1 2.3 8.1 19.4

Stratified weights 5.3 2.3 5.5 5.4 8.0 18.8

Fay-Herriot 2.6 2.0 3.1 2.6 7.0 18.5

Calibration 1.9 1.7 2.6 1.9 7.0 18.5

Beverage, Tobacco

SOII only 5.5 3.0 7.6 7.6 36.3 47.4

Stratified weights 7.2 3.1 7.9 8.7 35.2 41.2

Fay-Herriot 5.2 2.2 6.2 6.4 35.1 41.0

Calibration 4.5 2.2 5.6 5.5 35.2 40.9

Textile Mills

SOII only 6.3 3.2 10.4 9.1 35.6 27.1

Stratified weights 7.2 2.6 9.0 8.9 35.3 18.5

Fay-Herriot 4.7 2.3 7.6 6.3 35.1 17.9

Calibration 5.0 3.8 7.6 6.8 35.2 18.3

Textile Product Mills

SOII only 8.9 3.9 13.5 13.8 43.7 45.6

Stratified weights 9.9 3.4 13.5 14.0 42.2 18.1

Fay-Herriot 8.4 2.8 12.9 12.7 42.1 15.4

Calibration 8.3 4.0 12.9 12.5 42.2 18.5

Notes. All reported numbers are based on simulations. The probability an establishment 

reports to OSHA depends on the establishment’s case total. See appendix for a 

description of data generation and the estimators.

Table 4: Root MSE as a Percent of True Values, US Private Sector Aggregate

Estimator DAFW Hospitalizations DAFW Amputations

SOII only 3.53 8.04

Stratified weights 3.80 10.14

Fay-Herriot 3.79 10.20

Calibration 3.84 10.01

Notes. All reported numbers are based on simulations. The probability an establishment 

reports to OSHA depends on whether the establishment experienced an amputation case. 

See appendix for a description of data generation and the estimators.
0 .05 .1 .15 .2 Density

0 10 20 30 Root MSE as percent of true value

SOII only Naive

Stratified

Smoothed densities, 49 industries

OSHA: selection on characteristics

Figure 1. Root MSE, Total Cases

0 .05 .1 .15 .2 Density

0 10 20 30 Root MSE as percent of true value

Calibration

Stratified

SOII only

Smoothed densities, 49 industries

OSHA: selection on total cases

Figure 2. Root MSE, Total Cases
0 .02 .04 .06 Density

0 20 40 60 Root MSE as percent of true value

SOII only Naive

Stratified

Smoothed densities, 49 industries

OSHA: selection on case profiles

Figure 3. Root MSE, Hospitalizations

0 .005 .01 .015 .02 .025 Density

0 50 100 150 Root MSE as percent of true value

SOII only Naive

Stratified

Smoothed densities, 49 industries

OSHA: selection on case profiles

Figure 4. Root MSE, Amputations