A study was conducted on $185$ patients aged more than $45$ years which are followed until

the time of death or up to $10$ years, whichever comes first. The patients have different

covariates: age, gender $($male$/$female$),$ systolic blood pressure, smoking $($yes$/$no$),$ total

serum cholesterol and diabetes $($yes$/$no$).$ The objective of this study is to determine which

covariate influences the survival time. An analysis is conducted to investigate differences

in all$-$cause mortality between men and women participating in the study. Suppose we

obtain the following results after applying the Cox regression hazard model analyses:

Risk Factor Parameter Estimate SE

Age $0\mathrm{.}1500\mathrm{.}010$

Gender $0\mathrm{.}4500\mathrm{.}150$

Systolic Blood Pressure $0\mathrm{.}0150\mathrm{.}008$

Smoking $0\mathrm{.}6500\mathrm{.}170$

Total Serum Cholesterol $0\mathrm{.}0020\mathrm{.}004$

Diabetes $-0\mathrm{.}3500\mathrm{.}250$

$($i$)$ Obtain hazard ratio and interpret the results.

$($ii$)$ Find the $99\%$ confidence interval for the hazard ratio.

$($iii$)$ Test whether the covariates are significant or not at $1\%$ level of

significance.