BIOSTATISTICS — DU B.Sc (hons) Statistics Previous Year Question Papers

(b) Show that Pi and Qis are unbiased estimators of pi , Qis respectively. Also, find var (Tis.) and cov (Fis, Qie). 3(a) Survival time T follows the Weibull distribution with parameters y and 2. Derive the mean survival time, variance, and coefficient of variation. Also, find these expressions when the shape parameter =l. (b) Define net probability type-A and estimate this probability of death using the maximum likelihood method. 4 (a) Define the segregation matrix and construct a segregation matrix for gamate Ab. Compute g1,82,83 and gafor the sixth and seventh generation for given g, = 0.38, gz = 0.2, g3 = (b) Suppose there are two linked loci A and B, each with two alleles. Let 2 be the recombination traction. Suppose the gametic probabilities of the initial population are y: gı = P(AB) = P(y1), g2 = P(Ab) = P(y2), g3 = P(aB) = P(y3), g4 = P(ab) = P(y+). Obtain the appropriate segregation matrix for the gamete y1. Hence, derive the distribution of the gametic output for y, = AB in the 5(a) A team of researchers started their study on 22 patients to test the efficacy of a drug for the remission of stomach infection. Researchers terminated the study after the recovery of the 12th patient. The remission times (in days) are: Assuming times of remission follow an exponential distribution. Explain the type of censoring to obtain the mean survival time and the variance of the estimated mean survival time. (b) Explain Type-1 censoring. Also. obtain the estimate of the mean survival time (u ) and its variance Var(ù) assuming the sample is taken from an exponential population. 6(a) Explain the life table method for estimating the survival function. Using this method, estimate the survival function and compute the variance of the estimated survival function at each time interval. (b) Consider a clinical trial in which 13 patients are observed to have the following survival pattern (in months): Estimate the survival function and standard error of its estimated survival function at each uncensored survival times. 7(a) Define partially crude probability of death. Given below the survival history of 600 patients and deaths due to cancer (R), CVD (R), and road accident (R). Compute the probability of death due to road accidents when the risk of CVD was eliminated from the population: Age Number of Number Number of Number of Number of Interval atients alive at dying in deaths due deaths due deaths due the beginning of the to cancer to CVD to road the Interval accidents (b) A team of doctors carried out their study on 18 patients at Apollo Hospital to test the efficacy of a drug for the remission of blood infection. The hospital terminated the study after one month (1 month=30 days). The remission times (in days) are: Assuming times of remission follow an exponential distribution. Explain the type of censoring to obtain the mean survival time and the variance of the estimated mean survival time.