1. ## Negative Trend

I am hypothesizing a decrease in a type of injury over the past decade. I have the number of admissions to my hospitals and the number of patients with the condition.

I had originally performed a Cochran-Armitage Trend test, grouping patients based on whether they had the condition, so using proportions. I was wondering if there may be a better approach, since there are very few cases per year, say 1 out of 1500 patients or ~ 0.06%.

I did not know if I should treat it as count data or if there may be a better way to look at it to examine a negative trend in data with a very very low prevalence of the condition.

Thanks!

2. ## Re: Negative Trend

Could you look at the time between admissions for this condition then analyze like a survival analysis? If your hypothesis were true, you should see a decreasing hazard function.

3. ## The Following User Says Thank You to Miner For This Useful Post:

hlsmith (10-09-2014)

4. ## Re: Negative Trend

Hmm, interesting I have not seen anything like that before. Did you just come up with that or have you seen an approach similarly used before.

Just for a little more clarification, this is a very trauma condition that is rare, so an individual patient would not have a readmission for it. Also, I have data for 12 years, so if I played around with the PHREG approach. I do think that approach would work, but I wouldn't rule it out.

So hypothetically say I have.

2000: 0 / 1500
2001: 1 / 1500
2002: 2 / 1500
2003: 3 / 1500
2004: 6 / 1500
2005: 3 / 1500
2006: 1 / 1500
2007: 2 / 1500
2008: 0 / 1500
2009: 2 / 1500

So, I don't necessarily have incidence, just counts. Miner, you do run charts and quality engineering right? Is there some thing you all do that may work?

5. ## Re: Negative Trend

There are several approaches used in quality. For binomial responses, a P-chart is used. However, there are several known issues with P-charts that occur for large sample sizes or low pBar (mean p). Your data does not have too large a sample size, but the pBar is quite low for a p-chart. When p becomes this low, a T-chart for time between rare events is more appropriate. Another consideration is that control chart limits are economically based, not statistically. Three standard deviation limits (alpha = 0.003, not 0.05) were established to balance the economic cost of chasing false alarms versus missing a process signal.

Since you do not have the times, what about a binomial ANOM?

I use reliability/survival analysis to analyze any events in time data. It is not limited to product failures or disease progression.

6. ## The Following User Says Thank You to Miner For This Useful Post:

hlsmith (10-09-2014)

7. ## Re: Negative Trend

Miner did you make me graphs using my hypothetical data - thank you! I not sure if these get at trend and I just got some more years of data and even given my hypothesis, I am pretty sure a trend does not exist in my data. I will look up the ANOM figure, when I get a chance.

8. ## Re: Negative Trend

Originally Posted by Miner
There are several approaches used in quality. For binomial responses, a P-chart is used. However, there are several known issues with P-charts that occur for large sample sizes or low pBar (mean p). Your data does not have too large a sample size, but the pBar is quite low for a p-chart. When p becomes this low, a T-chart for time between rare events is more appropriate. Another consideration is that control chart limits are economically based, not statistically. Three standard deviation limits (alpha = 0.003, not 0.05) were established to balance the economic cost of chasing false alarms versus missing a process signal.

Since you do not have the times, what about a binomial ANOM?

I use reliability/survival analysis to analyze any events in time data. It is not limited to product failures or disease progression.
wait... were those graphs done in MINITAB?!

9. ## Re: Negative Trend

Originally Posted by hlsmith
Miner did you make me graphs using my hypothetical data - thank you!
Yes. This was just to illustrate using the hypothetical data.

10. ## Re: Negative Trend

Originally Posted by spunky
wait... were those graphs done in MINITAB?!
Yes, they were done in Minitab.

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