Productivity loss at work due to declining health- mental, physical or due to other reasons is more common than we think. There have been multiple research studies in the last few decades to understand this problem better and how it is affecting both employees as well as companies qualitatively- wellbeing, happiness of employees and quantitatively- dollar loss for companies. Productivity can be defined and measured differently but there are certain metrics that are commonly used in all studies. Before going further on investigating the problem in hand, here are a few scientific papers/journals I found of value.

3.
Work productivity loss from depression: evidence from an
employer survey.

*Kathryn M Rost1*, Hongdao Meng2 and Stanley Xu3,4*
I
used these (and other) papers to get data samples as well as to educate myself
about the problem and how it has been approached in different studies. I
specifically looked for data/studies for US employees which had large samples
taken from a large enough population- mainly about how productivity loss is defined and can be calculated:

__Productivity Loss (definition):__
I
found a broad agreement on defining Productivity loss, PL as:

PL = Hours Lost in
[Presenteeism] + Hours lost in [Absenteeism] per week

**Presenteeism:**Percent impairment at work (PI) in hours as a 10 point rating of degree of impairment/10. No of hours of productivity impairment (HI) while at work thus was calculated as the hours actually worked (HW) multiplied by the percent impairment while at work.

Productivity
lost due to presenteeism,

**PL**= ((PI/10)*(HW))/(HM+HW) (per week)

_{p}**Absenteeism:**Percent work time missed due to health- hours missed (HM) during previous 7 days divided by hours missed plus hours worked (HW) during this period.

Productivity
lost due to absenteeism,

**PL**= HM/(HM+HW) (per week)

_{a}
This
basic calculation was mostly used. Calculations for other definitions of
productivity loss in terms of actual $ cost etc were also based on above values-

$
productivity loss or cost= Wages/hr * (PL

_{p}+ PL_{a}) (per week) etc.
I
used the above definition of

**Productivity loss**for my calculation-

__Productivity loss, PL = PL___{p}+ PL_{a}

__Data sources/other considerations:__
I
only had access to google search and public/downloadable papers– I am sure with
different search strings or access to online journals I may have found some
other more relevant papers/datasets.

(i)
I
used the papers- 1 and 3 primarily to do two
separate calculations to find a value for productivity loss in terms of hours
per week due to depression (including both presenteeism and absenteeism) and a
confidence interval for the same.

(ii)
Paper
1 (Depression Severity
and productivity loss- 2011- DIAMOND study Minessota), used PHQ-9 questionairre
to ~771 patients to estimate depression severity over a period of 6 months and
the WPAI (Work Productivity and Activity Impairment) Questionaiire to
understand patient productivity loss/work function. The norm for productivity
loss for individuals without depression or other chronic condictions was 8%.

(iii)

__Participant parameters-__**Agegroups**etc:
Also, although significant association was seen
between high PHQ-9 scores and productivity loss (p value<0.05), (similar for
part-time vs full-time employment and health status),

**no correlation was seen for age and productivity loss (p-value~ 0.95)**(Table 4, paper 1). Hence, no attempt was made to find productivity loss as a function of age. I did not find any significant correlation based on age or sex in other papers as well.

**PL in percentage hours**due to Presenteeism and Absenteeism (PLa+ PLp) with n 719 = 37.8 (U=mean) [sd 27.5]

U = 37.8, sd = 27.5, n = 719

Choosing a 95% confidence level and finding z-score from t-distribution table to estimate the population parameter-

PL with 95% confidence level = U +/- zscore*sd/sqrt(n)

Zscore ~ 1.97 for n = 719 and confidence level ~95%

PL with 95% confidence level = 37.8 +/- 1.97 * (27.5)/sqrt(719)

= 37.8 +/- 1.97 * (27.5)/26.8

= 37.80 +/- 2.02 = [35.78, 39.82]

__Conclusion:__**[35.78, 39.82]**__Productivity Loss due to depression at work -95% Confidence level that the mean value lies between the Upper limit and lower limit__

__Calculation II for PL(based on paper 3)-__
Absenteeism loss in days of year for sample size n 325 = 3 (U), 6 (sd)

Presenteeism loss in days of year for sample size n 325 = 16 (U), 34 (sd)

Absenteeism loss in % days of year for sample size n 325 = 3/265 (U), 6 (sd)

Presenteeism loss in % days of year for sample size n 325 = 16/265 (U), 34 (sd)

(Assuming people work 5 days a week, with 52 weekends removed approx)

PL~PLp+PLa= (16+~3)/265 %= 19/265 * 100% (I understand this can at most a logical estimate)

**PL in percentage hours**due to Presenteeism and Absenteeism (PLa+ PLp) with n 325 = U = 19/265 * 100 % = 7.6%

sd = 34, n = 325

Choosing a 95% confidence level and finding z-score from t-distribution table to estimate the population parameter-

PL with 95% confidence level = U +/- zscore*sd/sqrt(n)

Zscore ~ 1.97 for n = 325 and confidence level ~95%

PL (%) with 95% confidence level = 7.6 +/- 1.97 * (34)/sqrt(325)

= 7.6 +/- 1.97 * (34)/18

= 7.6 +/- 3.7 = [3.9, 11.3]

__Conclusion:____Productivity Loss due to depression at work -95% Confidence level that the mean value lies between the Upper limit and lower limit [3.9, 11.3]__

__Assumptions and justifications:__
The
relatively large difference between the two calculations of
productivity loss values and confidence intervals can be understood by
the way the data was gathered in the two studies. In paper 1, (sample
size 1100- participants reduced to 771) patients who went to clinics for
their depressive symptoms were directly investigated at the clinics
itself. The paper has also attributed high values of productivity loss
calculations to the fact that data was gathered in clinics while
patients were reporting/facing mental health issues as opposed to
surveys or census done at home or later about past health issues. Paper 1
mentions that the data is not racially diverse. Data in paper 3 was
gathered from health Analysts of companies over a range of employee data
gathered over a year with a lot of adjustments and
approximations/estimates that may have caused some distortion from real
values. The latter sample was smaller (325) than the earlier sample and
was more racially diverse. There were many other such differences that
could have led to such a diversely different value set.

If
I had to pick one value I would pick the first one, for a better
approximation to real values. I would also adjust the values by a factor
that may be commonly observed when patients are interviewed in clinics
at the time of their health check vs at home, later or in some random
census where they may be both more objective and relaxed about how they
report their productivity loss.

Such a difference of observation has been mentioned in paper 1 results and discussion

*[**The magnitude of productivity loss in this sample of patients (38%) is large compared with normative data for the WPAI that include individuals without health conditions (8%), as well as those with such conditions as diabetes (15%), asthma (15%), back pain (16%), obesity (18%), angina (20%), and chronic pain (22%) (personal communication, Steve Schwartz, Director of Research, Health Media, Inc, Ann Arbor, Michigan; August 25, 2010). The greater productivity loss reported by our patients may be due in part to the fact that the study sample was recruited from outpa- tient clinics during treatment initiation, when depres- sion symptoms were presumably at a peak and recent work function was most affected. In fact, productiv- ity loss for various health conditions is greater when reported in observational studies or clinical trials involving these patients as compared with population- based surveys.17,18 For example, recent studies using the WPAI with clinic-based patient samples show a 28% productivity loss associated with severe asthma, 38% for Crohn disease, and 20% for allergic rhinitis.19**]**(ps: This post is only an effort to bring awareness around this topic based on a preliminary reading of a few papers. There may be incorrect deductions, assumptions, wrong calculations and error in my understanding of statistics- which I will hopefully correct with time. Please do not use/interpret this as an authentic or validated research study.)*

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