Indicators of disease

Question

I have this dataset with size (rows) and shape (columns) and in each cell #disease/#in cell . How would I answer the following questions?

Is size an indicator of disease?
Is shape an indicator of disease?
Is there a size*shape effect?

Size          shapea    shapeb     shapec    %a    %b    %c
<4 mm       5 / 5771    0 / 26    1 / 522  0.1%  0.0%  0.2%
4-6 mm      9 /  739    1 / 11    2 / 149  1.2%  9.1%  1.3%
6-8 mm      3 /  496    0 /  7    1 / 126  0.6%  0.0%  0.8%
>=8 mm     33 /  276   18 / 26    8 / 146 12.0% 69.2%  5.5%

Total      50 / 7282   19 / 70   12 / 943  0.7% 27.1%  1.3%

Thanks, Luther88

Edits

@suncoolsu in detail these are nodule data. size is the size of the nodule (the cutoffs are what have been published and accepted as standards). shape is the shape of the nodule. the numerator is the number of malignant nodules and the denominator is the number of nodules of given size and shape combinations.

@onestop i do not have the raw data to do logistic regression. just this table.

any further suggestions?

Answer 1

You can use logistic regression to answer these questions. Disease is the outcome. Fitting a model with size and shape as covariates will allow you to test for a size effect and a shape effect, and adding an interaction between size and shape will allow you to test for a size*shape interaction. You can get p-value for each from likelihood ratio tests.

It probably makes sense to treat shape as categorical, i.e. use indicator variables, but fit a linear effect of size, at least to start off with. To do that you could represent size by the midpoint of the two inner bounded intervals, i.e. 5 and 7, and for the outer two intervals either use the mean sizes if you know them or pick some reasonable values (you know more than me how small and large the smallest and largest values are so what are reasonable values).