So, how do I tell if the bone density of these diseased patients is different than their respective control groups?

Any help would be greatly appreciated. Thanks

- Thread starter STOUCHA
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So, how do I tell if the bone density of these diseased patients is different than their respective control groups?

Any help would be greatly appreciated. Thanks

Patient 1 (male age 25 with disease x) - bone density = 306

Controls (10 males age 25 without disease x) - bone densities = 235, 264, 248, 287, 255, 292,245,226,254,275

Patient 2 (female with disease x, age 60) - bone density = 200

Controls (10 females age 60 without disease x) - bone densities = 150, 135, 165, 186, 134, 155, 165, 143, 176, 123

etc etc for 11 patients.

How do I determine if there is a significant difference in bone density in the diseased patients compared to their controls?

Thanks

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After some thought, here is my solution. Any feedback would be greatly appreciated.

The null is that the bone densities of the diseased patients is no different than age/sex matched controls. This would mean that both the mean and variance are the same as controls.

Thus, if the variance of the diseased patients is different than the variance of controls then I must reject the null.

So, I do a modified Levene's test as follows:

Disease Patient 1: variance^2 = (bone density - mean)^2 where the mean is the mean of the ten age/sex matched controls for patient 1.

Disease Patient 2: variance^2 = (bone density - mean)^2 where the mean is the mean of the ten age/sex matched controls for patient 2, i.e. different than the mean used for the calculation of patient 1

Disease Patient 3: etc etc

This gives me a list of var^2 for diseased patients, i.e. 11 patients in my study.

Next I calculate the variance for all control patients as follows:

Control Pt 1 from control group for disease patient 1: var^2 = (bone density - mean) ^2 where the mean is the mean of all ten control patients for disease patient 1, i.e. this is the same mean used to calculate the var^1 for disease patient 1 above.

repeat this for all controls for disease patient 1 using the mean of the group of controls for disease patient 1.

Perform this same analysis on the 10 control patients for disease patient 2 now using the mean from this group which is the same mean used to calculate the var^2 of patient 2.

Continue calculating the var^2 for all 110 control patients per this method.

Perform a t-test type analysis on these two groups of var^2.

If it is different then I reject the null.

If I reject the null I would say the meaning is that the bone density in the diseased patients is in some way not similar to the bone density in the controls patients.

Any thoughts, and especially any criticisms, are greatly appreciated.

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I know that you've elaborated, but if you could any further about your intentions for this experiment, it would be great.

If the two lines have the same slope, then the vertical distance between the two lines represents the difference in means of the bone densities in the two groups adjusted for any difference in the distribution of the predictors.

This is known as analysis of covariance (ANCOVA).

Good luck with your work.

I know that you've elaborated, but if you could any further about your intentions for this experiment, it would be great.

Sure. Let me explain a little better. First the actual data:

Patient 1 (age 51 bone density 112)

Controls for patient 1

age mean

51 156

50 99.3

51 180

50 159

51 103

50 149

50 149

51 101

50 119

50 128.7

Patient 2 (age 58 bone density 181)

Controls for patient 2

age mean

58 169

59 128

59 153

57 119

58 120

58 147

58 128

59 163

56 132

57 149

Patient 3 (age 59 bone density 153)

controls for patient 3

59 112

58 133

59 71

59 91

57 114

58 117

58 175

59 101

58 166

58 110

Patient 4: age 39, bone density 151

Controls for patient 4

39 168

40 236

38 210

39 181

40 179

39 161

38 173

39 151

39 154

39 219

Patient 5: age 14, bone density 313

Controls for Patient 5

14 243

14 220

14 241

14 271

13 195

14 228

14 273

13 305

14 230

14 254

Patient 6: age 23, mean 272

Controls for patient 6

22 151

22 195

22 227

23 181

22 179

22 213

22 185

23 253

22 217

23 231

Patient 7: age 22, bone density 238

controls for patient 7

21 166

22 195

21 185

21 228

22 169

22 199

21 270

21 169

21 169

21 176

Patient 8: age 40, bone density 124

controls for patient 8

39 216

39 160

40 187

40 144

39 182

40 155

40 172

40 228

40 180

40 236

Patient 9: age 42, bone density 124

Controls for patient 9

41 176

42 185

41 201

42 186

42 201

41 224

41 193

42 183

44 205

40 176

Patient 10: age 43, bone density 200

Controls for patient 10

42 191

42 163

42 170

42 121

42 167

42 109

43 185

42 206

42 129

42 162

Patient 11: age 44, bone density 151

Controls for patient 11

44 139

43 158

43 98

43 167

43 150

44 217

43 140

43 191

43 200

44 170

I tried to put up the graph of the data but i can't seem to. The graph that I have is average bone density of each control group versus age. This shows a general trend towards lower bone density with age...not unsuspected. I have also included the standard deviation of each group as "error bars" at each point. A trend line is added (y = -0.0029x3 + 0.3215x2 - 13.002x + 367.28; R2 = 0.881). Finally, I have plotted the bone density of each cocci patient vs age. What I see is that bone densities of most of the cocci patients are greater than 1 standard deviation from the point estimate of the mean bone density for that age. Some are higher and some are lower than their respective control means. I would expect this from the biology. The question is, is this significant? Do the cocci patients really come from a bone density population that has a variance larger than the variance of the controls (adjusted for age)? Or is it just chance that so many of the cocci patient's bone density fall so far from the control means.

The trick in doing the variance calculation is that there is so much variation with age. I have to figure out how to eliminate that in the calculation. It is sort of a paired Variance test.

It seems that I could normalize the data first and then do a standard F-test or Levene's test but I am not sure exactly how to do that. Or, I could use the standard formula for calculating the Levene's test (or F-test) but use the mean of the control group of for each patient...a sort of Paired Levene's.

Does this make sense.

If someone can tell me how to put my graph up I will do it.

Thanks again!!

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