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From |
Austin Nichols <austinnichols@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Gene-incidence question/simulation |

Date |
Sun, 22 Mar 2009 12:02:10 -0400 |

moleps islon <moleps2@gmail.com> : Just to be clear: B causes Z and B causes A, but you don't observe B, right? Let's ignore the survival model you are no doubt estimating, and suppose you have gotten an estimate of P(Z|A)=.05 with a SE near zero (a confidence interval of width zero). Now you want to estimate P(Z|B) and P(A|B), and you think P(Z|B) is near .65 and P(Z|~B)=6/100000 (I assume "background incidence" is the probability of Z given not B here; that may reflect my "background ignorance"). You will need much more information to make any progress! Let p=P(B) in the population, y=P(Z|B), x=P(A|B), and w=P(A|~B). Note that ~B means "not B" or B==0. Then P(Z|A)=P(Z|B)P(B|A)+P(Z|~B)P(~B|A)=[ypx+.00006(1-p)w]/[(1-p)w+px] so even if you assume P(Z|A)=.05 and y=.65, you have 3 unknowns and 1 equation; even if you know p, you have two unknowns w and x, so the best you can hope for is to express P(A|B) as a linear function of P(A|~B). For example, if p=.5 and y=.65 and P(Z|A)=.05 then w is 12 times as big as x (i.e. if Z is so rare in a sample of A, when B so likely causes Z, it must be because A is much more likely when not B than when B). If p is 8% then w and x are roughly the same. I suggest you draw out a couple of trees with probabilities and check my math. If you want to estimate y and x, you are out of luck. If you know w and p with certainty, you can express y as a function of x and the estimate of P(Z|A), so if you have estimates of P(Z|A) in memory, you can use -lincom- to get estimates of y conditional on x, but how plausible is it you would know w with certainty when you are trying to estimate x and y? I suppose you could use known p, estimates of P(Z|A) in memory, and -lincom-, to get estimates of y conditional on x and w, then present a table of point estimates and confidence intervals for various values of x and w. Or get estimates of x conditional on y and w, or what have you. But you still have to assume you know p with certainty, or the dimension of that table gets out of control... I have been assuming that P(Z|A) is what you are estimating, but you really have a competing risk model, I am guessing, modeling the hazard of getting Z before death or censoring by some other process. So you need to redefine Z to be not "gets condition Z" but "gets condition Z in my observation period" to use any of the above, which is probably unpalatable. Plus, I don't know if I've translated your description into probabilities correctly--the jargon of genetics is unfamiliar to me (and many other list members--you should translate to the common language of statistics). On Sun, Mar 22, 2009 at 10:37 AM, moleps islon <moleps2@gmail.com> wrote: > Dear statalisters, > I'm studying a tumor A that has a probability (x) of a being linked to > a genetic mutation (B) that also predisposes (penetrance approx 65%(y) > by 70 years) to condition Z. Now I've got 217 cases of A that resulted > in 11 cases of Z over 8534 years of followup years (among the 217 > cases). I need to determine the number of patients with B given that > there is also a background incidence of 6/100000 for Z.We know that > x<<y. Besides running a simulation is there a more analytical way of > estimating x and y given my data??? > > Best wishes, > Moleps * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Gene-incidence question/simulation***From:*moleps islon <moleps2@gmail.com>

**References**:**st: Gene-incidence question/simulation***From:*moleps islon <moleps2@gmail.com>

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