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The two-stage model of carcinogenesis is based on the premise that for a cancer to develop, a normal cell must first undergo a “first hit” and mutate to become a susceptible or intermediate cell. An intermediate cell then must undergo a “second hit” and mutate to become a malignant cell. A cancer develops if at least one cell becomes a malignant cell. This model has been applied to the development of breast cancer in females (Moolgavkar et al. [15]).
Suppose there are 108 normal breast cells and 0 intermediate or malignant breast cells among 20-year-old females. The probability that a normal breast cell will mutate to become an intermediate cell is 10−7 per year.
What is the expected number of intermediate cells by age 45?
The probability that an intermediate cell will mutate to become a malignant cell is 5 × 10−7 per year.
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EBK FUNDAMENTALS OF BIOSTATISTICS
- Researchers suspect that drinking tea might enhance the production of interferon gamma, a molecule that helps the immune system fight bacteria, viruses, and tumors. A recent study involved 20 healthy people who did not normally drink tea or coffee. Ten of the participants were randomly assigned to drink five cups of tea a day, while 10 were asked to drink the same amount of coffee. After two weeks, blood samples were exposed to an antigen and production of interferon gamma were measured. The results are shown in the following table: Теа: 55 17 54 49 10 46 21 14 53 Coffee: 16 12 20 52 37 15 22 30 3 Let X ~ N(ux,o3) be the interferon gamma production for participants who drink tea and observations for the ten participants who drink tea are a random sample from X. Let Y ~ N(uy,o) be the interferon gamma production for participants who drink coffee and observations for the ten participants who drink coffee are a random sample from Y. Some R output that may help. > p1 qnorm(p1) [1] -2.326…arrow_forwardCardiovascular disease is a major cause of death and illness worldwide, with high blood pressure and high LDL cholesterol both being established risk factors. Because most cardiovascular events occur in persons with average risk and no previous cardiovascular disease history, the present research examined the simultaneous use of both blood pressure‑reducing drugs and cholesterol‑reducing drugs on this population rather than focus on only those at high risk. Subjects included men at least 55 years old and women at least 65 years old without cardiovascular disease who had at least one additional risk factor besides age, such as recent or current smoking, hypertension, or family history of premature coronary heart disease. Those with current cardiovascular disease were excluded from the study. Subjects were randomly assigned to the treatment (cholesterol‑ and blood pressure‑reducing drugs) or a placebo, and the number suffering the primary outcome of a fatal cardiovascular event or a…arrow_forwardA number of studies have examined how alcohol consumption affects neuroticism using an animal model. Two kittens are randomly selected from each of 7 litters (two cats from each litter). One cat from each pair is assigned to the experimental group which is subjected to a procedure that induces temporary neurosis. The other cat from each pair is part of the control group (no neurosis induction). All the cats are then offered milk spiked with 5% alcohol. The amount of milk consumed in three minutes is measured (in milliliters). Do the kittens in the experimental group drink more alcohol than the kittens in the control group? What test should you use and why?arrow_forward
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- luyckx et al. 2012 discovered that resistances to the bacterial parasite Pasteuria ramosa is genetically variable in the common freshwater crustacean Daphnia magna. to investigate the genetic basis of this cariation, they crossed a completely resistant lineage to a completely susceptible lineage. All the F1 offspring were resistant. these offspring, when mature, were then crossed to each other to produce an F2 generation. if resistance is the result of only a single gene with 2 forms (alleles), then resistant and suspectible F2 offspring should occur in a 3:1 ratio. of 71 F2's tested,57 were resistant and 14 were susceptible. Answer these Q's: a) calculate the range of most-plausible values for the proportion of resistant offspring. Does the plausible range include the proportion predicted if resistence is determined by a single gene? b.) give two other values for the proportion that are also consistent with the data. c.) test the genetic hypothesis. Are the results compatible with…arrow_forwardA physiologist believes he has discovered a new steroid hormone that can affect the blood glucose in reptiles. In an experiment he injects turtles with a small amount of this steroid hormone and, after a suitable waiting period measures the blood glucose level of the turtles. In his sixteen experimental turtles he obtains the following levels of blood glucose {2, 1, 3, 5, 2, 1, 1, 5, 3, 2, 1, 1, 2, 1, 1, 5}. From previous studies of thousandsof normal, un-manipulated turtles he knows that the mean (μ) blood glucose level in this species of turtle (his laboratory population) is 3. Evaluate the hypothesis that this new steroid hormone affects blood glucose levels. Use an α-level of 0.01 for this analysis. D) Find the critical value: E) Calculate the obtained statistic: F) Make a decision: G) What does your decision mean? Please show step-by-step how you solved each problem. In addition, please explain in words how you calculated the obtained statistic.arrow_forwardA physiologist believes he has discovered a new steroid hormone that can affect the blood glucose in reptiles. In an experiment he injects turtles with a small amount of this steroid hormone and, after a suitable waiting period measures the blood glucose level of the turtles. In his sixteen experimental turtles he obtains the following levels of blood glucose {2, 1, 3, 5, 2, 1, 1, 5, 3, 2, 1, 1, 2, 1, 1, 5}. From previous studies of thousandsof normal, un-manipulated turtles he knows that the mean (μ) blood glucose level in this species of turtle (his laboratory population) is 3. Evaluate the hypothesis that this new steroid hormone affects blood glucose levels. Use an α-level of 0.01 for this analysis. A) What is the appropriate test? B) State the null hypothesis: C) State the alternative hypothesis: D) Find the critical value: E) Calculate the obtained statistic: F) Make a decision: G) What does your decision mean? Please explain how you got the answers Thank youarrow_forward
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