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Statistics in Medicine and Disability

Statistics in Medicine and Disability

Disability Statistics

The average approval rate of initial Social Security Disability (SSDI) claims is approximately 36%. Of course, that means across the country that approximately 64% all initial disability claims are denied.

About 4.7% of the population between 18 and 64 years of age are disabled and receiving long-term Social Security Disability income. In January 2019, the average amount of disability benefits is $1,234 per month. (The maximum is up to $2,861 per month.)

There are >38 million adults (15.5%) with significant hearing problems. Nearly 27 million (10.9%) have vision problems.

About 38.2 million adults (15.5%) have significant physical and functional impairments. Of those, 17.6 million (7.1%) are unable to walk a quarter mile.

The three states with the highest rates of SSDI approvals are Hawaii (67%), Utah (63%), and New Mexico (56%). The three lowest approval states are Alaska (17%), Kansas (33%), and Delaware (35%). California is the 21st highest approval state (47%).


Survival Statistics: The “Kaplan–Meier” Curve

Statistics are used to evaluate whether a treatment is successful in prolonging life (“survival statistics”). The “Kaplan–Meier” plot is a regression analysis model that is often used to measure the rate of patient survival after a therapy is given, in horizontal steps over time. Simply put, a Kaplan-Meier graph illustrates what percentage of patients are alive after 1, 5, or 10 years after diagnosis or treatment of a disease.

Survival statistics can be used to show “relative” survival, “cause specific” survival, or “disease specific” survival. Survival rates can be used to compare the effectiveness of treatments and to predict the prognosis of patients.

Mean, Median, and Mode

When doctors refer to survival statistics, the “mean” or average survival is calculated by taking the sum of the survival data and dividing by the number of data points or observations. This is typically the most useful statistical calculation, but it can be skewed by a few extreme outliers.

The median is the mid-point of the data, meaning there is an equal number of survivors above and below the median survival. The median is not as useful for statistical analysis, but it is less affected by extreme outliers that could skew the data.

The mode is simply the most common data point in the dataset. It's not too useful in statistical analysis, but its strength is that sometimes it can give clues as to the cause or etiology of diseases.

In reporting data, the mean, median, and mode all have their strengths and weaknesses.

Dispersion or Variability

The “range” is calculated by subtracting the lowest observed value from the highest. It represents a simple measure of the variability of the data. If treatment data show, for example, that the average or mean survival of a certain type of leukemia is 5 years, then knowing the range would be of considerable importance. Is the range 1 year or 4 years? A narrow range would mean that almost all the patients survived about 5 years, whereas a wide range meant that some patients survived much longer (or died much sooner).

More sophisticated measurements of dispersion around the mean are the “variance” and the “standard deviation.” There are statistical formulas for performing those calculations. For example, the variance is calculated as the sum of the squared deviations divided by the total number of observations minus one (Ʃ (x-ẋ)²/n-1). The standard deviation is the square root of the variance.

It is generally considered that if a person is within one standard deviation (SD) of the mean (average), then that's in the “normal” or “average” range. In terms of percentile ranking, 1 SD is equivalent to being between the 16th and the 84th percentile rank. A 1.5 SD is equivalent to being between the 7th and 93rd percentile rank. A deviation of 2 SD's from the mean falls between the 2nd and 98th percentile rank.

When psychologists, for example, diagnose Attention Deficit Disorder, they typically consider a SD of 1.5 to 2.0, for traits such as hyperactivity, impulsivity, or inattention, as being diagnostic.

Correlation Studies

Correlation studies are descriptive studies, such as epidemiologic studies. An example of a correlation study is the mean consumption of wine in different cultures compared to the incidence of coronary artery disease performed by St Leger and colleagues that showed there was a strong inverse relationship between the amount of wine consumed and the likelihood of having heart disease. [Reference:]

A strong inverse correlation means that countries with higher wine consumption had lower rates of heart disease and countries with lower wine consumption had higher rates of heart disease.

A correlation coefficient (“Pearson's r”) describes how strongly positive or negative the correlation is between two variables, in this example, wine consumption and heart disease. A +1 indicates a perfect correlation, and -1 indicates a perfect inverse correlation.

A weakness of the St Leger study, and of all correlation studies, is that a correlation, even a very strong positive or negative one (+1 or -1), does not prove cause-and-effect. In other words, we cannot say that drinking more wine will decrease your chance of developing heart disease. If we wish, we can infer that from the data, but we cannot prove it.

Experimental Studies

In order to “prove” this, you would need to do an experimental study. In the St Leger example, that could be done by assigning patients to a high-wine consumption group (“treatment group”) and to a non-consumption group (“control group”), and then after a suitable period of time, evaluating both groups to see if the high wine-consumption group had significantly less heart disease than the control group.

Sensitivity and Specificity

The terms sensitivity and specificity are often used to describe how “useful” a diagnostic test is when doctors use it to test (or exclude) a certain disease.

When a test has high “sensitivity,” it means that there is a high probability that a person will test positive on that test if they have the disease you are looking for. “Specificity” is the probability that a person will test negative if they do not have the disease.

It's great if a test is highly sensitive and highly specific. However, that's not always the case. For example, the anti-nuclear antibody (ANA) test is often used to diagnose systemic lupus erythematosus, which is an autoimmune disorder. In clinical practice, the ANA is highly sensitive, but unfortunately it is not very specific. What that means is that most patients who have lupus will test positive on the ANA, but a lot of patients that don't have lupus will also have positive ANA's.

The anti-dsDNA antibody test is just the opposite in lupus patients. The dsDNA is very specific for lupus, but not very sensitive. Therefore, many patients with lupus will test negative for the dsDNA, but when patients test positive, they almost always have lupus and not something else.

Predictive Value

The “positive predictive value” (PPV) is the probability that a disease is truly present if a test for that disease is positive. The negative predictive value (NPV) is the probability that a disease is truly absent when the test for that disease is negative.

It gets tricky, because in clinical use the PPV increases with prevalence of the disease you are testing for and the NPV decreases with prevalence of the disease in the population.

Odds Ratio, Relative Risk, and Confidence Intervals

When talking about clinical data, doctors frequently use terms like the odds ratio (OR), relative risk (RR), and the confidence intervals (CI).

The odds ratio is the probability of an event occurring divided by the probability of the event not occurring. For example, the odds of rolling four on a dice are 1/5 or 20%. Odds Ratio (OR) is a measure of association between exposure and an outcome.

The relative risk or risk ratio is calculated from exposed and non-exposed individual who are followed over time and the incidence of events for the exposed and unexposed groups is measured. If the risk ratio is 1 (or almost 1), there is little or no difference in risk. But if a risk ratio > 1, this suggests an increased risk, and a risk ratio < 1 suggests a reduced risk in the exposed group.

Both the OR and RR have confidence intervals (CI) as a measure of uncertainty. A Confidence Interval is a range of values that we are very confident will contain our value.

For example, if we measured the heights of 60 men and found that their mean height was 69 inches and let us assume that we calculated the standard deviation of their heights and found it to be 7.9 inches, then the 95% confidence interval would be 69 plus/minus 7.9 inches.

That means if we measured all men (not just a sample of 60 men), their mean height 95% of time would be 69 plus/minus 7.9 inches. But there is a 1 in 20 chance that it wouldn't be.

Therefore, there is a 1-in-20 chance (5%) that our Confidence Interval does not include the true mean. Confidence intervals are calculated from the same equations that calculate p-values (calculated probability). In statistical language, if a 95% CI excludes the value 1.0, then the ratio is significant at the level of p<0.05.

Bell-Shaped Curve

A bell-shaped curve (also known as a “normal” or Gaussian distribution) is a symmetrical distribution of values from the average or “mean” value in the middle of the “bell.”

The “standard deviation” is a calculation that is used with a bell-shaped curve to indicate how spread out the values are on both sides (above and below) from the average (mean) value. A low standard deviation indicates that all the other numbers are closer to the average, while a higher standard deviation indicates the numbers are more spread out.

One standard deviation represents about 68% of the set of numbers; two standard deviations represents approximately 95%; and three standard deviations represent about 99.7%.

Standard Scores (SS)

Standard scores are typically used to measure intelligence (IQ) and achievement. They care be used to diagnose a Learning Disability if there is a strong discrepancy between intelligence (IQ) and achievement. Standard Scores have a mean of 100, and a Standard Deviation of 15.

A standard score of 100 is average, or a 50th percentile rank. But an SS of 85 is a 16th percentile rank, meaning 84 out of 100 children are at or above this score, while 16 out of 100 children are at or below this score.

Psychologists would consider a high IQ score and a low standard achievement score as reflecting a learning disability or related to lack of motivation, socioeconomic, and/or other factors.


T-Scores have a mean of 50, and a Standard Deviation of 10. The measurement of bone density (DEXA scan) for the diagnosis and treatment of osteoporosis relies on T-scores. A normal bone density is when the T score is between +1.0 and -1.0, Osteoporosis is defined as a bone density score (T score) that is less than minus 2.5 (-2.5). T scores in between “normal” and “osteoporosis” are called “osteopenia.”

A difference of 10 from the mean (up or down) is equivalent to one standard deviation. A score of 70 is 2 SD's above the mean, while a score of 0 is 1 SD below the mean.

Body Mass Index

To calculate your Body Mass Index (BMI), take your weight in pounds, multiple by 704.7, and divide by the square of your height in inches. Or, just use an on-line calculator. [Reference:]

Conclusion: Mark Twain, in his autobiography, famously said “'there are three kinds of lies: lies, damned lies, and statistics.” While there may be considerable truth in that statement, statistics are the language of medicine and of scientific studies. Some familiarity with the most common statistical measures and descriptions used by doctors can be helpful in interpreting medical data, disability, and understanding recommendations based on clinical trials.

Your disablity lawyer must work closely with your treating physician to get the proper documentation of your specific findings and impairments into the medical records. At Law Med that's what we